## 2.1 Global temperature (and related empirical context)

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### Model specification for global temperature
- Observed global temperature: T_Gt = μ_Gt + w_Gt.
  - μ_Gt: smooth climate trend component.
  - w_Gt: short-run weather component.
- Climate trend dynamics:
  - μ_Gt = μ_Gt−1 + β_Gt.
  - β_Gt = c_G + ψ_G β_Gt−1 + e_Gt,   e_Gt ∼ N(0, σ^2_e,G), |ψ_G| < 1.
  - Long-run warming rate: β*_G = c_G /(1 − ψ_G).
  - Innovations e_Gt have permanent effects on μ_Gt.
- Weather dynamics:
  - w_Gt = φ_G w_Gt−1 + ε_Gt,   ε_Gt ∼ N(0, σ^2_ε,G).

### Empirical findings for global temperature
- Data:
  - Global temperature (land and ocean surface) from NOAA; sample 1960 - 2022.
- Key empirical patterns:
  - Observed global temperature and μ_Gt trended upward by about 1 ◦C over the sample.
  - Estimated β_Gt trended up from 1970s–1990s, then stabilized at roughly 0.02 to 0.03 ◦C per year in the 2000s–2010s.
  - ψ_G = 0.716298, implying gradual shifts rather than one-time level jumps.
  - e_Gt (warming shocks) fluctuate around zero, consistent with white-noise innovations to the warming rate.
- Weather behavior:
  - w_Gt and ε_Gt move closely consistent with an AR(1): shocks generate contemporaneous jumps that decay according to φ_G.

---

### Box 1 — Interpretation and dynamics of the estimated coefficient −0.2542

### Interpretation of −0.2542
- Long-run level association:
  - A one-degree Celsius increase in the permanent climate component associates with approximately a 22 percent lower level of trend GDP in the long run (exp(−0.254) = 0.776).
- "Permanent" denotes the persistent temperature trend, not a one-time change.
- The estimate describes the long-run level after full adjustment over many decades, not an immediate annual impact.
- Effect visible across the distribution after removing country and year fixed effects.

### Time profile and channels
- Adjustment speed:
  - Roughly half of the long-run loss materializes after about 30 years.
  - Close to a century to close 90 percent of the gap.
- Slow-moving channels: capital depreciation, infrastructure durability, labor productivity, health, sectoral reallocation.
- Levels specification preferred because annual changes in μT are very small and first-difference estimation is underpowered.

### Error-correction evidence (selected estimates from Table 2)
- ̂ECTc,t−1: −0.0232 ∗∗∗ (0.0028)
- ∆μTc,t: −0.0036 (0.0120)
- ∆μyc,t−1: 0.4423 ∗∗∗ (0.0291)
- ∆μyc,t−2: 0.0598 ∗∗∗ (0.0169)
- ∆wc,t: −0.0006 (0.0013)
- ∆wc,t−1: −0.0012 (0.0009)
- Country fixed effects: Yes; Year fixed effects: Yes; Observations: 9,367; Countries: 192; Within R2: 0.294.
- Interpretation:
  - ̂φ ≈ −0.0232 implies roughly 2.3 percent of the remaining deviation is eliminated each year.
  - Initial annual drag on trend growth ≈ 0.6 percentage points in first few years (0.0232×0.254≈0.006).
  - 95 percent confidence intervals: half-life 24-39 years; time to close 90 percent: 79-129 years.

### Robustness
- First-difference regressions imprecise and statistically insignificant at annual frequency.
- Long-difference regressions (1970–2022) yield large, negative, highly significant estimates consistent with cointegration results.
- HP-filtered GDP and alternative trend measures: coefficients −0.254 ∗∗∗, −0.252 ∗∗∗, −0.251 ∗∗∗.
- HP-filtered temperature trends: −0.207 ∗∗∗ and −0.151 ∗∗∗.
- 30-year moving average temperature: −0.2901 ∗∗∗.
- Controlling for initial GDP per capita paths and for SO2 emissions does not eliminate the long-run effect in robustness checks noted.

---

### 4.5 Comparison with conventional raw temperature regressions; Global vs Local climate

### Limits of conventional raw temperature regressions
- Conventional regressions relate output to raw observed temperature and mix persistent climate change with transitory weather.
- Findings (Appendix Table A10):
  - Dependent variables: trend output and log real GDP.
  - Observed temperature coefficients: negative and statistically significant but much smaller than decomposition-based estimates.
  - Output growth regressions: smaller and less significant effects, reflecting short-run weather responses.
- Conclusion: conventional regressions are limited for assessing long-run macroeconomic impacts; decomposition isolating μ_T is preferred.

### Global versus local climate decomposition
- Country-level climate decomposed as μ_Tc,t = λ_c μ_Gt + μ_locc,t.
  - λ_c: country-specific loading (exposure).
  - μ_locc,t: local deviations orthogonal to global factor.
- Variance decomposition (within-country variance of μ_Tc,t):
  - Global-exposure term λ_c μ_Gt: about 117% of within-country variance.
  - Local component μ_locc,t: about 10%.
  - Negative covariance term 2 Cov(λ_c μ_Gt, μ_locc,t): about −27% (local deviations partially offset global movements).

### Empirical estimates (Table 3) — global vs local effects on μ_Yc,t
- Dependent variable: μ_Yc,t (trend/permanent output).
- Coefficient on λ_c μ_Gt:
  - Column (1): −0.3236 ∗∗∗ (0.0786)
  - Column (2): −0.1927 ∗∗ (0.0912)
- Coefficient on μ_locc,t:
  - Column (1): −0.0114 (0.1274); Column (2): excluded.
- Observations: 9,943; Countries: 192.
- Within R^2: Column (1): 0.7120; Column (2): 0.725.
- Interpretation:
  - Exposure to the global climate factor drives long-run negative effects on trend output.
  - Local climate deviations are small and statistically indistinguishable from zero.
  - Effects persist with climate-zone-by-year fixed effects, indicating differential exposure to global factor matters.

---

### 6 Structural decomposition of long-run climate damages (population and per capita)

### Accounting identity and empirical object
- log Y_c,t = log (Y_c,t / N_c,t) + log N_c,t.
- Permanent components: μ_Yc,t = μ_Y/Nc,t + μ_Nc,t.
- Empirical goal: relate μ_Tc,t to (i) μ_Y/Nc,t and (ii) μ_Nc,t using fixed-effects cointegration.

### Decomposition results (Table 4)
- Dependent variables:
  - Column (1): μ_Nc,t (trend log population).
  - Column (2): μ_Y/Nc,t (trend log real GDP per capita).
- Coefficients on μ_Tc,t (°C):
  - Column (1): −0.2052 ∗∗∗ (0.0575)
  - Column (2): −0.0490 (0.0704)
- Observations: 9,943; Countries: 192.
- Within R^2: Column (1): 0.6680; Column (2): 0.363.
- Findings:
  - Persistent warming is negatively and statistically significantly associated with trend log population.
  - Relationship between μ_Tc,t and μ_Y/Nc,t is small and statistically insignificant in the full sample.
  - Implication: a substantial portion of aggregate output losses operates through demographic adjustment at the global level.
- Caveat: long-run demographic trends may reflect non-climate structural forces; interpret as decomposition rather than definitive causal evidence.

### Heterogeneity by country groups (6.2)
- Advanced economies (Table 5):
  - μ_Tc,t coefficients:
    - Population (Column (1)): −0.2287 ∗∗∗ (0.0786)
    - GDP per capita (Column (2)): −0.2811 ∗ (0.1532)
  - Observations: 1,923; Countries: 37; Within R^2: Column (1): 0.627; Column (2): 0.775.
  - Interpretation: both demographic and per-capita channels contribute to AE aggregate output losses; per-capita decline consistent with capital-adjustment mechanisms.
- EMDEs (Table 6):
  - μ_Tc,t coefficients:
    - Population (Column (1)): −0.0751 (0.0770)
    - GDP per capita (Column (2)): −0.1154 (0.0898)
  - Observations: 8,020; Countries: 155; Within R^2: Column (1): 0.713; Column (2): 0.306.
  - Findings: within EMDEs, neither channel is statistically significant; coefficients smaller and imprecisely estimated relative to AEs.

---

### 7 Capital structure and long-run climate vulnerability

### Conceptual motivation
- Persistent warming interacts with capital stock structure because capital adjusts slowly.
- High capital intensity and more durable capital imply slower turnover and larger adjustment costs.
- Hypothesis: countries with higher capital intensity or greater capital durability exhibit stronger long-run output responses to μ_Tc,t.

### 7.1 Capital accumulation channel — findings
- Purpose: relate μ_Tc,t to permanent components of capital stock (μK), capital per worker (μK/L), and TFP (μA) using PWT and fixed effects.
- Advanced economies:
  - Persistent warming associated with statistically significant declines in capital stock and capital per worker.
  - No significant relationship with μA.
  - Interpretation: climate depresses effective productivity of capital; adjustment operates primarily via capital accumulation.
- EMDEs:
  - No statistically significant associations between μ_Tc,t and μK, μK/L, or μA.
  - Interpretation: lower capital intensity and faster turnover reduce adjustment costs captured by these regressions.

### Reported regression coefficients (Table 7 — selected)
- Advanced Economies μT c,t coefficients: −0.662 ∗∗∗, −0.330 ∗∗, −0.009 (for μK, μK/L, μA respectively).
- EMDEs μT c,t coefficients: −0.141, −0.003, −0.080.
- Notes:
  - Country fixed effects: Yes; Year fixed effects: Yes.
  - Robust SEs clustered by country; significance: ∗∗∗, ∗∗, ∗ denote 1, 5, 10 percent.

### 7.2 Continuous evidence — interactions with capital structure (Table 8)
- Measures:
  - Capital intensity: log(K/E), averaged 1970–1990.
  - Capital durability: log(1/δ), averaged 1970–1990.
- Advanced economies (selected coefficients):
  - Baseline μT c,t: 4.459 ∗∗∗ (column (1)); 0.637 (column (2)); 5.175 ∗∗∗ (column (3)).
  - μT c,t × log(K/E): −0.369 ∗∗∗ (col (1)); −0.359 ∗∗∗ (col (3)).
  - μT c,t × log(Durability): −0.300 (col (2)); −0.246 ∗ (col (3)).
  - Interpretation: greater capital intensity and durability amplify long-run declines in trend GDP per capita.
- EMDEs (selected coefficients):
  - Baseline μT c,t: 1.200 ∗∗∗; 1.407 ∗∗∗; 2.288 ∗∗∗ across columns.
  - μT c,t × log(K/E): −0.117 ∗∗∗; −0.104 ∗∗∗.
  - μT c,t × log(Durability): −0.492 ∗∗∗; −0.388 ∗∗.
  - Interpretation: within EMDEs, higher capital intensity and greater durability also amplify adverse long-run effects; durability strengthens in EMDEs.

### 7.3 Bucket evidence (Table 9)
- Approach: discrete buckets combining capital intensity (low/high) and durability (low/high) within AEs and EMDEs.
- Findings:
  - Relative to baseline (low intensity, low durability), interaction coefficients become more negative with higher intensity or durability; most negative where both are high.
- Advanced economies (selected reported coefficients):
  - μT c,t (Low intensity – Low durability): 0.1128 0.0837 (reported as two numbers).
  - μT c,t × (Low intensity – High durability): −0.2974.
  - μT c,t × (High intensity – Low durability): −0.3457 ∗.
  - μT c,t × (High intensity – High durability): −0.3508 ∗.
- EMDEs (selected reported coefficients):
  - μT c,t (Low intensity – Low durability): (0.2725)(0.1035).
  - μT c,t × (Low intensity – High durability): −0.3090 ∗.
  - μT c,t × (High intensity – Low durability): −0.3694 ∗∗∗.
  - μT c,t × (High intensity – High durability): −0.4220 ∗∗∗.
- Interpretation: evidence consistent with capital-adjustment mechanism—higher capital intensity and slower turnover increase long-run vulnerability.

---

### 8 Short-run dynamics of global and local weather shocks (Sections 8.1–8.3)

### Conceptual distinctions
- Climate: slow-moving shifts with long-run level effects.
- Weather: transitory deviations; short-run fluctuations.
- Global weather shocks: synchronized phenomena (e.g., El Niño) that generate correlated short-to-medium-run macroeconomic effects.
- Local weather shocks: idiosyncratic, primarily affect domestic short-run outcomes.

### Econometric specification for short-run weather dynamics
- Weather shocks constructed from state-space decomposition:
  - Global weather shock: εG t (innovation to wG t = TG t − μG t).
  - Local weather shock: ε` c,t (innovation to wc,t = Tc,t − (αc + λc μG t + μloc c,t)).
  - Both orthogonal to persistent climate dynamics.
- Local projections (Jordà 2005 style):
  - For horizons h = 0,1,...,H: ∆y c,t+h = α(h) c + θG h εG t + θ` h ε` c,t + Σ_{j=1}^2 ρ(h) j ∆y c,t−j + u(h) c,t+h.
  - ∆y c,t is year-on-year change in log real GDP (not trend GDP).
- Identification:
  - Year fixed effects excluded because εG t is common across countries.
  - Global identification from common time-series variation; local identification from cross-country heterogeneity.

### Impulse-response evidence (Section 8.3)
- Global weather shocks (one degree Celsius):
  - Output growth declines on impact.
  - Output growth turns positive in the first two years after the shock.
  - Output growth then reverses sharply several years later before gradually converging to zero.
  - Non-monotonic profile consistent with delayed propagation (e.g., disasters and reconstruction).
- Local weather shocks (one degree Celsius):
  - Small, statistically weak, short lived; wide confidence bands indicating heterogeneity.
  - Local shocks absorbed through short-run adaptation, spatial reallocation, sectoral adjustment.
- Synthesis:
  - Global weather shocks generate larger, systematic macroeconomic effects; local shocks generate limited short-run effects and do not alter long-run growth trajectories.
  - Persistent global climate change anchors long-run output levels: estimated long-run decline in real GDP ≈ 22 percent following a one-degree Celsius increase in the permanent component.

---

### Supporting numerical and sample facts (exact values reported)
- Sample and coverage:
  - Countries: 192.
  - Temperature observations: 9,943.
  - GDP observations: 9,943.
  - Mean observations per country: 51.79.
  - Minimum observations per country: 15.
  - Median observations per country: 53.
- Selected summary statistics:
  - Observed temperature (C): N = 9,943; Mean = 23.62; Min = 2.74; p1 = 6.40; p10 = 12.38; p25 = 18.01; p50 = 26.27; p75 = 28.62; p90 = 31.14; p99 = 35.02; Max = 36.33.
  - Log real GDP: N = 9,943; Mean = 12.68; Min = 1.16; p1 = 3.71; p10 = 7.81; p25 = 10.20; p50 = 12.95; p75 = 15.20; p90 = 17.15; p99 = 22.00; Max = 23.43.
  - GDP growth (%): N = 9,943; Mean = 3.54; Min = −15.98; p1 = −15.98; p10 = −2.65; p25 = 0.00; p50 = 3.76; p75 = 6.52; p90 = 9.52; p99 = 22.85; Max = 22.85.
- Representative estimated coefficients and robustness entries:
  - Partial regression fitted coefficient (Appendix Figure A1): coef = −.25422017, (robust) se = .07201591, t = −3.53.
  - Baseline long-run coefficient: β = −0.252 (Table 1 reference).
  - First-difference: ∆μT coefficient: −0.290 (label).
  - Long-difference regressions: −0.222 ∗∗∗ and −0.222 ∗∗∗ (Table A5).
  - HP-filtered GDP: −0.254 ∗∗∗, −0.252 ∗∗∗, −0.251 ∗∗∗ (Table A6).
  - HP-filtered temperature: −0.207 ∗∗∗ and −0.151 ∗∗∗ (Table A7).
  - 30-year moving average temperature: −0.2901 ∗∗∗ (Table A8).
  - Raw temperature benchmark regressions: −0.052 ∗∗∗, −0.051 ∗∗∗, and −0.163 (Table A10).

---

### Research and policy implications (drawn from the analysis)
- Research directions:
  - Historical estimates reflect past adaptation, technology, and structure; future damages may differ as economies adapt.
  - Further work should investigate mechanisms (capital vintage, infrastructure design, sectoral specialization) using micro and structural approaches.
- Policy-relevant inferences:
  - Long-run damages concentrate in capital-intensive countries and those with slower capital turnover.
  - Policy focus: capital adaptation, infrastructure resilience, investment vintage management.
  - Short-run volatility from global weather shocks highlights the importance of disaster preparedness and synchronized international resilience measures because global climatic forces can strain adjustment capacity across countries.

*Source: wpiea2026115-source-pdf - excerpted content unit (sections 2.1, Box 1, 4.5, 6, 7, 8).*

### 2.1    Global temperature

### 2.1    Global temperature

### Model specification for global temperature
- Observed global temperature at time t, denoted T_Gt, is decomposed as:
  - T_Gt = μ_Gt + w_Gt
  - μ_Gt is the smooth climate trend component.
  - w_Gt is the short-run weather component.
- Global climate trend dynamics:
  - μ_Gt = μ_Gt−1 + β_Gt
  - β_Gt = c_G + ψ_G β_Gt−1 + e_Gt,   e_Gt ∼ N(0, σ^2_e,G), |ψ_G| < 1.
  - β_Gt is the global warming rate; c_G is the slope drift.
  - Long-run warming rate β*_G = c_G /(1 − ψ_G).
  - Innovations e_Gt are innovations to the global warming rate and have permanent effects on μ_Gt.
- Global weather dynamics:
  - w_Gt = φ_G w_Gt−1 + ε_Gt,   ε_Gt ∼ N(0, σ^2_ε,G).

### Empirical findings for global temperature
- Data and sample:
  - Global temperature data (land and ocean surface) are obtained from NOAA and span the period 1960 - 2022.
- Key patterns and estimated parameters:
  - Observed global temperature and the estimated climate component trended upward by about 1 ◦C over the sample period.
  - The estimated warming rate β_Gt exhibited variability: generally trended upward from the 1970s through the 1990s, then stabilized at roughly 0.02 to 0.03 ◦C per year in the 2000s and 2010s.
  - ψ_G is estimated equal 0.716298, implying gradual shifts in the trajectory of temperature rather than one-time level jumps.
  - Estimated warming shocks e_Gt fluctuate around zero with no apparent persistence, consistent with white-noise innovations to the warming rate.
- Weather component behavior:
  - The estimated global weather component w_Gt and its shocks ε_t move closely together consistent with an AR(1) process: shocks generate contemporaneous jumps in the weather series that then decay according to the autoregressive parameter.

### Figures described (qualitative)
- Figure 1 panels:
  - (a) Observed global temperature (T_Gt) and estimated climate component μ_Gt: upward trend ~1 ◦C since 1960s.
  - (b) Estimated warming rate β_Gt: variability and stabilization at ~0.02 to 0.03 ◦C per year in 2000s–2010s.
  - (c) Estimated warming shocks e_Gt: mean-zero, no persistent pattern.
- Figure 2:
  - Global weather w_Gt (blue) and weather shocks ε_Gt (red): contemporaneous movements and gradual decay.

### Implications from the global model
- Shocks to the warming rate (e_Gt) have lasting effects on the global climate trend μ_Gt because β_Gt innovations permanently affect μ_Gt.
- The estimated ψ_G = 0.716298 indicates persistence in deviations from the long-run warming rate and supports modeling global climate change as evolving through gradual shifts rather than abrupt level changes.

---

*Source: wpiea2026115-source-pdf - 2.1    Global temperature*

### Box 1:  How to Read the Estimated Coefficient -0.2542 in Table 1

### Box 1: How to Read the Estimated Coefficient -0.2542 in Table 1

### Interpretation of the estimated coefficient (−0.2542)
- The point estimate implies that a one-degree Celsius increase in the permanent climate component is associated with approximately a 22 percent lower level of trend GDP in the long run, within country (exp(−0.254) = 0.776).
- “Permanent” refers to the underlying persistent temperature trend in the model, not to a one-time or irreversible increase in temperature.
- The estimate describes a long-run level association after full adjustment over many decades, not an immediate impact or a short-run forecast.
- The estimate reflects the cumulative impact of persistent climate change and anchors the level around which the economy operates in the long run, rather than implying a one-year or near-term collapse in GDP.
- The negative relationship is visible across the distribution of the data after removing country and year fixed effects, indicating the effect is unlikely driven by outliers.

### Time profile and economic channels
- Adjustment is exceptionally slow:
  - Roughly half of the long-run loss materializes only after about 30 years.
  - It takes close to a century to close 90 percent of the gap.
- Slow-moving channels driving the level effect include capital depreciation, infrastructure durability, labor productivity, health, and sectoral reallocation; these operate through long-lived stocks and unfold over decades.
- The estimated long-run level effect can be economically large even when short-run growth responses are modest or difficult to detect at annual frequency.
- The 22 percent figure is based on historical patterns across 192 countries from 1970 to 2022 and should not be extrapolated mechanically to particular future scenarios; different adaptation, technology, or policy could lead to different outcomes.

### Equivalent growth interpretation
- The levels relationship has an equivalent representation in terms of growth:
  - ∆μYc,t = (τt − τt−1) + β∆μTc,t + ∆uc,t
- The same coefficient β links changes in permanent output to changes in permanent temperature, but annual changes in the permanent temperature component are very small, so estimation in annual first differences is statistically underpowered.
- The levels specification therefore provides a more informative estimate of the long-run semi-elasticity of permanent output with respect to permanent temperature.

### Error-correction dynamics (evidence and magnitudes)
- The error-correction term is constructed as ̂ECTc,t ≡ μyc,t − ̂αc − ̂τt − ̂β μTc,t.
- Table 2 (error-correction model for trend GDP growth) — selected estimates:
  - ̂ECTc,t−1 (error-correction term): −0.0232 ∗∗∗ (0.0028)
  - ∆μTc,t (permanent climate change): −0.0036 (0.0120)
  - ∆μyc,t−1: 0.4423 ∗∗∗ (0.0291)
  - ∆μyc,t−2: 0.0598 ∗∗∗ (0.0169)
  - ∆wc,t (local weather): −0.0006 (0.0013)
  - ∆wc,t−1 (local weather): −0.0012 (0.0009)
  - Country fixed effects: Yes
  - Year fixed effects: Yes
  - Observations: 9,367
  - Countries: 192
  - Within R2: 0.294
- Interpretation of the error-correction coefficient:
  - ̂φ ≈ −0.0232 implies roughly 2.3 percent of the remaining deviation is eliminated each year.
  - Following a one-degree permanent increase in temperature, it takes approximately 30 years to close half of the resulting output gap and close to a century (around 95–100 years) to eliminate 90 percent of the gap toward the lower climate-consistent path.
  - The initial annual drag on trend growth is about 0.6 percentage points in the first few years (given by 0.0232×0.254≈0.006), then declines as the gap narrows.
  - The estimated standard error implies approximate 95 percent confidence intervals of 24-39 years for the half-life and 79-129 years for the time required to close 90 percent of the gap.

### Short-run associations and weather
- Contemporaneous changes in the permanent climate component ∆μTc,t have a limited short-run association with trend growth at annual frequency.
- Local weather shocks have no statistically significant effect on trend GDP growth once long-run climate conditions and error-correction dynamics are controlled for, indicating idiosyncratic weather fluctuations mainly influence short-run volatility rather than the long-run path.

### Panel cointegration diagnostics
- Westerlund (2007) error-correction-based panel tests are used to assess whether deviations from the candidate long-run relationship are corrected over time, allowing for heterogeneous adjustment and cross-sectional dependence via bootstrap inference.
- Full sample (192 countries): panel statistic (Pt) rejects the null hypothesis of no cointegration at the 10% level using dependence-robust bootstrap p-values; group-mean statistics provide weaker evidence.
- Restricted sample (179 countries, excluding prolonged exceptional growth episodes): the panel statistic rejects no cointegration at the 5% level; the estimated long-run coefficient on permanent temperature is −0.265 in this restricted sample.
- These diagnostics are interpreted as suggestive evidence of long-run adjustment between permanent temperature and output components.

### Robustness checks (specifications and results)
- First differences:
  - Panel regression of annual real GDP growth on annual changes in the permanent climate component yields an imprecise and statistically insignificant coefficient at annual frequency (Appendix Table A5). This is expected due to small annual changes in the climate trend and dominance of short-run cyclical variation.
- Long differences:
  - Long-difference regressions relating changes in output between 1970 and 2022 to corresponding changes in the permanent climate component produce large, negative, and highly statistically significant estimates, similar in magnitude to the cointegration specification.
- HP-filtered GDP and alternative trend measures:
  - Baseline trend output is from a state-space decomposition; robustness uses HP-filtered log real GDP with annual smoothing parameters of λ = 100 and λ = 6.25, and also log GDP levels without filtering (Appendix Table A6).
  - The estimated coefficient on the permanent climate component remains negative, highly statistically significant, and quantitatively close to baseline across these alternatives.
- HP-filtered country temperature:
  - Replacing the state-space permanent climate component with HP-filtered country temperature trends (λ = 100 and λ = 6.25) yields negative and statistically significant coefficients (Appendix Table A7), modestly attenuated relative to baseline.
- 30-year moving average temperature:
  - Using a backward-looking 30-year moving average of annual temperature (climatological standard) produces a negative and statistically significant coefficient of −0.29 (Appendix Table A8), close to baseline estimates.
- Controlling for differential growth paths:
  - Specification augmented by interacting year fixed effects with initial GDP per capita (Penn World Table) to allow flexible time paths by initial development level (equation (18) and differenced form (19)).
  - Using initial GDP per capita measured in 1990 and 1970, the estimated coefficient on the permanent climate component remains negative and statistically significant and broadly comparable to baseline.
- Potential reverse causation:
  - Climate science indicates local surface temperature changes are driven by accumulation of global emissions rather than contemporaneous national emissions; national output fluctuations are unlikely to meaningfully affect local temperature trends.
  - Aerosol reductions (cooling effect) could coincidentally correlate with economic transitions, but the identification is from within-country variation over time and remains strong when restricted to advanced economies.
  - Controlling for SO2 emissions does not eliminate the estimated long-run impact for advanced economies (results not shown).

*Source: Box 1, wpiea2026115-source-pdf.*

### 4.5    Comparison with conventional raw temperature regressions

### 4.5    Comparison with conventional raw temperature regressions

### Comparison with conventional raw temperature regressions
- Conventional panel regressions relate output directly to raw observed temperature and do not distinguish persistent climate change from transitory weather fluctuations.
- Purpose of the exercise: illustrate behavior of standard temperature regressions when applied to output levels and growth, not to provide alternative long-run damage estimates.
- Appendix Table A10 (fixed-effects, country and year fixed effects, cluster SEs at country level):
  - Columns (1) and (2): dependent variables are trend output and log real GDP, respectively.
    - Estimated temperature coefficient: negative, statistically significant, and much smaller in magnitude compared to the baseline decomposition-based result.
    - Interpretation is unclear because raw temperature mixes persistent climate change with high-frequency weather variation.
  - Column (3): regression of output growth (winsorized at p1 and p99) on observed temperature — the common specification in the literature.
    - Estimated effect: smaller and less significant, reflecting short-run weather responses rather than persistent climate change.
- Conclusion: Conventional temperature regressions are limited for assessing long-run macroeconomic impacts and motivate the decomposition-based approach that isolates the persistent climate component and links it to trend output in a panel cointegration framework.
- Note on SO2 emissions: included solely as a robustness check and should not be interpreted as a preferred control because SO2 emissions are closely correlated with economic activity and industrial structure and conditioning on them may absorb part of endogenous output responses.

*Source: wpiea2026115-source-pdf - 4.5    Comparison with conventional raw temperature regressions*

### Global or Local Climate as a Main Driver?
- Literature perspective:
  - A new literature emphasizes climate change as a global phenomenon rather than independent local shocks.
  - Bilal and Känzig (2026) find global temperature fluctuations have substantially larger and more persistent macroeconomic effects than country-level variation.
  - Reason: global temperature captures climate system evolution and is closely linked to extreme climatic events; local temperature variation is weakly correlated with these extremes and understates macroeconomic costs.
- This section’s approach:
  - Decompose country-level climate into exposure to a common global climate factor and a residual local climate component to isolate macroeconomic effects of globally-driven climate change from country-specific deviations.
  - Estimated specification (equation (20)):
    μ_Tc,t = α_c + τ_t + β_1(λ_c μ_Gt) + β_2 μ_locc,t + u_c,t
    - μ_Tc,t: climate-driven component of temperature for country c at time t.
    - μ_Gt: common global climate factor.
    - λ_c: country-specific loading (exposure) estimated from temperature dynamics.
    - μ_locc,t: local climate deviations orthogonal to the global factor.
    - Identification via country fixed effects α_c and year fixed effects τ_t.
- Variance decomposition of μ_Tc,t = λ_c μ_Gt + μ_locc,t:
  - Global-exposure term λ_c μ_Gt accounts for essentially most (about 117%) of the within-country variance of μ_Tc,t.
  - Local component μ_locc,t accounts for about 10%.
  - Negative covariance term 2 Cov(λ_c μ_Gt, μ_locc,t) contributes about −27%.
  - Interpretation: negative covariance indicates local climate deviations tend to partially offset globally-driven climate movements.

### Empirical estimates: Table 3 (Global versus Local Climate Components)
- Dependent variable: μ_Yc,t (trend/permanent output)
- Key estimates (fixed-effects):
  - Coefficient on λ_c μ_Gt:
    - Column (1): −0.3236 ∗∗∗ (standard error (0.0786))
    - Column (2): −0.1927 ∗∗ (standard error (0.0912))
  - Coefficient on μ_locc,t:
    - Column (1): −0.0114 (standard error (0.1274))
    - Column (2): excluded
- Specification details:
  - Column (1): country and year fixed effects; Climate-zone×year FE: No.
  - Column (2): country fixed effects and Climate-zone×year FE: Yes; year fixed effects replaced with climate-zone-by-year fixed effects; local climate component excluded to isolate within-zone heterogeneity in exposure.
  - Observations: 9,943
  - Countries: 192
  - Within R^2:
    - Column (1): 0.7120
    - Column (2): 0.725
- Findings:
  - Exposure to the global climate factor λ_c μ_Gt has a large, negative, and statistically significant effect on trend output.
  - Local climate component μ_locc,t is small and statistically indistinguishable from zero.
  - Result persists when using climate-zone-by-year fixed effects (Column (2)), indicating effects are driven by differential exposure to the global climate factor rather than generic cold-region trends.
- Interpretation:
  - Long-run climate damage to trend output is driven primarily by exposure to the global warming trend rather than by persistent country-specific local climate drift.
  - Local deviations are comparatively small and more likely to be offset through adaptation, migration, or changes in production patterns.

*Source: wpiea2026115-source-pdf - 4.5    Comparison with conventional raw temperature regressions*

### 6    Structural Decomposition of Long-Run Climate Damages

### Accounting identity and empirical objects
- Definitions and identity:
  - Y_c,t: real GDP for country c at time t.
  - N_c,t: population for country c at time t.
  - Log identity: log Y_c,t = log (Y_c,t / N_c,t) + log N_c,t
  - Apply trend–cycle methodology to obtain permanent components:
    - μ_Yc,t: permanent (trend) component of log real GDP.
    - μ_Nc,t: permanent component of log population.
    - μ_Y/Nc,t: permanent component of log real GDP per capita.
  - Permanent components satisfy μ_Yc,t = μ_Y/Nc,t + μ_Nc,t, where μ_Y/Nc,t ≡ μ_Yc,t − μ_Nc,t.
- Empirical objective:
  - Estimate long-run relationships between the permanent climate component μ_Tc,t and:
    - (i) permanent GDP per capita μ_Y/Nc,t, and
    - (ii) permanent population μ_Nc,t,
  - Using the same fixed-effects cointegration specification as in Section 4.
  - Examine heterogeneity across country groups and, for advanced economies, relate permanent GDP per capita losses to baseline capital intensity and capital durability.

### Decomposition results: Table 4 (Population and GDP per Capita)
- Dependent variables:
  - Column (1): μ_Nc,t (trend log population)
  - Column (2): μ_Y/Nc,t (trend log real GDP per capita)
- Key estimates:
  - Coefficient on μ_Tc,t (°C):
    - Column (1): −0.2052 ∗∗∗ (standard error (0.0575))
    - Column (2): −0.0490 (standard error (0.0704))
- Specification details:
  - Country fixed effects: Yes
  - Year fixed effects: Yes
  - Observations: 9,943
  - Countries: 192
  - Within R^2:
    - Column (1): 0.6680
    - Column (2): 0.363
- Findings:
  - Persistent warming is negatively and statistically significantly associated with trend log population.
  - Relationship between permanent temperature and permanent GDP per capita is small and statistically insignificant in the full sample.
  - Implication: substantial portion of long-run aggregate output losses operates through demographic adjustment rather than declines in output per person at the global level.
- Caveat:
  - Long-run demographic trends could reflect structural forces unrelated to climate (e.g., aging, declining fertility); correlations with gradual warming could confound causal interpretation.
  - Therefore, these results should be viewed as a decomposition of the aggregate climate-output relationship rather than definitive causal evidence of demographic responses.

*Source: wpiea2026115-source-pdf - 4.5    Comparison with conventional raw temperature regressions*

### 6.2    Decomposition by country groups

- Advanced economies (Table 5):
  - Dependent variables: μ_Nc,t (trend log population) and μ_Y/Nc,t (trend log real GDP per capita).
  - Coefficient on μ_Tc,t (°C):
    - Column (1): −0.2287 ∗∗∗ (population) (standard error (0.0786))
    - Column (2): −0.2811 ∗ (GDP per capita) (standard error (0.1532))
  - Specification details:
    - Country fixed effects: Yes
    - Year fixed effects: Yes
    - Observations: 1,923
    - Countries: 37
    - Within R^2:
      - Column (1): 0.627
      - Column (2): 0.775
  - Findings:
    - In advanced economies, persistent climate change is associated with sizeable long-run demographic adjustment and meaningful declines in output per person.
    - Both demographic and per capita channels contribute to long-run aggregate output losses in AEs.
    - Per-capita decline is consistent with capital-adjustment mechanisms.
    - Caution: population changes may also reflect broader demographic forces not directly related to climate.

- Emerging market and developing economies (EMDEs) (Table 6):
  - Dependent variables: μ_Nc,t (trend log population) and μ_y/nc,t (trend log real GDP per capita).
  - Coefficient on μ_Tc,t (°C):
    - Column (1): −0.0751 (population) (standard error (0.0770))
    - Column (2): −0.1154 (GDP per capita) (standard error (0.0898))
  - Specification details:
    - Country fixed effects: Yes
    - Year fixed effects: Yes
    - Observations: 8,020
    - Countries: 155
    - Within R^2:
      - Column (1): 0.713
      - Column (2): 0.306
  - Findings:
    - Within EMDEs, neither demographic nor per-capita channels is statistically significant.
    - Estimated coefficients are negative but smaller and imprecisely estimated compared with advanced economies.
    - On average within EMDEs, persistent climate change does not show a clear long-run association with either permanent population or permanent GDP per capita.

*Source: wpiea2026115-source-pdf - 4.5    Comparison with conventional raw temperature regressions*

### 7    Capital Structure and Long-Run Climate Vulnerability

### Conceptual motivation
- Observation: In advanced economies, per-capita declines suggest climate affects per-capita productive capacity.
- Hypothesized mechanism: interaction between persistent climate change and capital stock structure.
  - Climate evolves slowly; capital adjusts gradually.
  - High capital intensity or durable (long-lived) capital implies slower capital turnover and slower adaptation to new climatic conditions.
  - Consequence: persistent warming may generate larger efficiency losses when production relies heavily on installed, long-lived capital.
  - Conversely, economies with lower capital intensity or faster capital turnover may adjust more rapidly as older capital depreciates and is replaced.

### Structural features of interest
- Two capital-stock characteristics likely relevant for climate vulnerability:
  - Capital intensity: economies with higher capital intensity rely more on installed capital.
  - Capital durability: economies with more durable capital have slower capital turnover due to lower depreciation rates.
- Empirical implication: countries with higher capital intensity or more durable capital stocks may exhibit stronger long-run output responses to climate change.

*Source: wpiea2026115-source-pdf - 4.5    Comparison with conventional raw temperature regressions*

### 7.1    Capital Accumulation Channel

### 7.1    Capital Accumulation Channel

### Key findings on capital accumulation
- Purpose: investigate whether persistent climate change affects capital accumulation directly by relating the permanent climate component to the permanent components of the capital stock (μK), capital per worker (μK/L), and total factor productivity (μA) using Penn World Table data and fixed-effects regressions.
- Advanced economies:
  - Persistent warming is associated with a statistically significant decline in the capital stock and in capital per worker.
  - Estimated coefficients indicate that higher permanent temperatures are linked to lower levels of installed capital and reduced capital deepening over the long run.
  - No statistically significant relationship is found between persistent temperature and total factor productivity (μA).
  - Interpretation offered: climate change may depress the effective productivity of capital, while technological progress and adaptation partly offset these effects in measured TFP, so adjustment operates primarily through capital accumulation; adaptation is embedded in the observed equilibrium adjustment.
- EMDEs:
  - No statistically significant association between persistent warming and changes in the capital stock (μK), capital per worker (μK/L), or total factor productivity (μA).
  - Interpretation offered: economies with lower capital intensity and faster capital turnover face smaller adjustment costs when climatic conditions shift persistently.
  - Emphasis that weaker estimated capital-channel effects in EMDEs do not imply lower overall climate vulnerability, but reflect differences in which channels are captured by this framework.

### Reported regression coefficients and model details (Table 7)
- Table 7: Persistent Climate Change and Capital Accumulation
  - Advanced Economies (columns (1)-(3)): μT c,t coefficients: −0.662 ∗∗∗, −0.330 ∗∗, −0.009
  - EMDEs (columns (4)-(6)): μT c,t coefficients: −0.141, −0.003, −0.080
  - Robust standard errors (country-clustered) reported in parentheses in the source.
  - Country fixed effects: Yes (all regressions)
  - Year fixed effects: Yes (all regressions)
  - Observations row as reported in the source: 1,7351,7351,7116,8486,4214,027
  - Countries row as reported in the source: 35353513613683
  - Within R2 row as reported in the source: 0.8460.7600.3620.7790.3940.126
- Notes from source:
  - Regressions relate μT c,t to μK, μK/L, and μA.
  - Robust standard errors clustered at the country level are reported in parentheses.
  - ∗∗∗, ∗∗, and ∗ denote statistical significance at the 1, 5, and 10 percent levels, respectively.
  - Sample of countries is smaller than in the baseline due to PWT data availability.

---

### 7.2    Continuous Evidence

### Purpose and variables
- Goal: relate the long-run response of GDP per capita to persistent climate change to cross-country variation in capital intensity and capital durability.
- Measures (from PWT):
  - Capital intensity: capital stock to employment ratio (log(K/E)), averaged over 1970–1990.
  - Capital durability: inverse depreciation rate (1/δ), measured as log(1/δ) and averaged over 1970–1990 (proxy for capital durability).
- Identification strategy: interact pre-determined (1970–1990) country averages of capital intensity and durability with the permanent climate component μT c,t in a fixed-effects specification to mitigate reverse causality concerns.

### Main empirical findings (Table 8)
- Advanced economies (columns (1)-(3)):
  - Baseline μT c,t coefficient: 4.459 ∗∗∗ (column (1)); 0.637 (column (2)); 5.175 ∗∗∗ (column (3))
  - Interaction μT c,t × log(K/E): −0.369 ∗∗∗ (column (1)); −0.359 ∗∗∗ (column (3))
  - Interaction μT c,t × log(Durability): −0.300 (column (2)); −0.246 ∗ (column (3))
  - Interpretation: economies with more capital-intensive production structures and more durable capital stocks experience larger long-run declines in trend GDP per capita in response to persistent warming; both capital intensity and durability amplify the long-run impact.
- EMDEs (columns (4)-(6)):
  - Baseline μT c,t coefficients: 1.200 ∗∗∗ (column (4)); 1.407 ∗∗∗ (column (5)); 2.288 ∗∗∗ (column (6))
  - Interaction μT c,t × log(K/E): −0.117 ∗∗∗ (column (4)); −0.104 ∗∗∗ (column (6))
  - Interaction μT c,t × log(Durability): −0.492 ∗∗∗ (column (5)); −0.388 ∗∗ (column (6))
  - Interpretation: within EMDEs, economies with higher capital intensity and greater capital durability also experience larger adverse long-run effects from persistent warming.
- Model details and reported rows as in source:
  - Country fixed effects: Yes
  - Year fixed effects: Yes
  - Observations row as reported: 1,8171,8171,8176,9327,0916,932
  - Countries row as reported: 353535133136133
  - Within R2 row as reported: 0.8400.7950.8460.3840.3760.398
- Notes from source:
  - Robust standard errors clustered by country are reported in parentheses.
  - ∗∗∗, ∗∗, and ∗ denote significance at the 1, 5, and 10 percent levels, respectively.
  - Robustness: augmenting with interaction of μT c,t and initial GDP per capita (1990) yields that initial GDP per capita interaction is small and statistically insignificant, while capital structure interactions retain sign and significance—durability strengthens in EMDEs—supporting capital structure as a distinct channel.

---

### 7.3    Bucket Evidence

### Purpose and approach
- Alternative specification: group countries into discrete buckets based on combinations of capital intensity and capital durability, constructed separately within advanced economies and EMDEs so thresholds reflect within-group distributions.
- Baseline group: low capital intensity and low capital durability.

### Main findings (Table 9)
- Pattern: relative to the baseline (low intensity, low durability), interaction coefficients become increasingly negative as either capital intensity or capital durability increases; the most negative effects occur where high capital intensity and high capital durability coincide.
- Advanced economies (reported coefficients):
  - μT c,t (Low capital intensity – Low durability): 0.1128 0.0837 (reported as two numbers in the source row)
  - μT c,t × (Low capital intensity – High durability): −0.2974 (column as reported)
  - μT c,t × (High capital intensity – Low durability): −0.3457 ∗ (column as reported)
  - μT c,t × (High capital intensity – High durability): −0.3508 ∗ (column as reported)
- EMDEs (reported coefficients):
  - μT c,t (Low capital intensity – Low durability): (0.2725)(0.1035) (numbers reported in source row)
  - μT c,t × (Low capital intensity – High durability): −0.3090 ∗ (reported)
  - μT c,t × (High capital intensity – Low durability): −0.3694 ∗∗∗ (reported)
  - μT c,t × (High capital intensity – High durability): −0.4220 ∗∗∗ (reported)
- Model details as in source:
  - Country fixed effects: Yes
  - Year fixed effects: Yes
  - Observations row as reported: 1,8176,932
  - Countries row as reported: 35133
  - Within R2 row as reported: 0.8130.3897
- Interpretation: economies with more capital-intensive production structures and slower capital turnover face larger long-run economic losses from persistent climate change; economies with lower capital intensity and faster depreciation exhibit smaller responses—consistent with a capital-adjustment mechanism where persistent climate change interacts with existing capital vintages.

---

### 8    Short-Run Dynamics of Global and Local Weather Shocks

### Conceptual distinction (Section 8.1)
- Climate vs. weather:
  - Climate: slow-moving shifts in the underlying state of the climate system; associated with long-run level effects on output.
  - Weather: transitory deviations around that state; associated with short-run fluctuations and adjustment dynamics.
  - Complementarity: short-run weather shocks occur around a climate-dependent baseline; their effects may depend on prevailing climate conditions.
- Global vs. local weather:
  - Global weather phenomena (e.g., El Nino, synchronized heat anomalies) generate correlated shocks across countries and can affect global economic activity in the short to medium run.
  - Local weather shocks are idiosyncratic and primarily influence domestic outcomes.
  - Neither global nor local weather necessarily determines long-run output levels once persistent global climate exposure is accounted for.

### Econometric specification for short-run weather dynamics (Section 8.2)
- Weather shocks construction (from state-space decomposition):
  - Global weather shocks: wG t = TG t − μG t ; εG t denotes innovation to the AR(1) process governing wG t.
  - Local weather shocks: wc,t = Tc,t − (αc + λc μG t + μloc c,t) ; ε` c,t denotes innovation to local weather.
  - By construction, both εG t and ε` c,t are orthogonal to persistent climate dynamics and capture unpredictable, transitory temperature fluctuations.
- Local projections specification (Jordà 2005 style):
  - For each horizon h = 0,1,...,H, estimate:
    ∆y c,t+h = α(h) c + θG h εG t + θ` h ε` c,t + Σ_{j=1}^2 ρ(h) j ∆y c,t−j + u(h) c,t+h
  - Where ∆y c,t is year-on-year change in log real GDP (not trend GDP); θG h and θ` h trace impulse responses of output growth to global and local weather shocks.
- Identification choices:
  - Year fixed effects are not included because εG t is identical across countries by construction and would be mechanically absorbed by time fixed effects.
  - Identification of global weather shocks relies on common time-series variation; identification of local weather effects relies on cross-country heterogeneity in ε` c,t.

*Italic source: Excerpt from the supplied PDF content unit "wpiea2026115-source-pdf - 7.1    Capital Accumulation Channel" (sections 7.1–8.2) as provided.*

### 8.3    Short-run responses to global and local weather shocks

### 8.3    Short-run responses to global and local weather shocks

### Impulse-response evidence: global weather shocks
- The analysis reports the impulse response of output growth to a one degree Celsius global weather shock (innovation to the transitory global weather component orthogonal to the global climate trend).
- Key dynamics:
  - Output growth declines on impact.
  - Output growth turns positive in the first two years following the shock.
  - Output growth then reverses sharply several years later before gradually converging back toward zero.
  - The profile is non monotonic, indicating delayed propagation (such as natural disasters or reconstruction).
- Interpretation and mechanism:
  - These dynamics relate closely to the mechanism emphasized by Bilal and K̈anzig (2026): global temperature shocks generate large macroeconomic effects because they are associated with extreme climate events such as natural disasters.
  - Although disasters materialize as discrete local events, their economic impact reflects exposure to common global climatic forces that simultaneously strain adjustment capacity across countries.
  - Innovations to global weather around the climate path induce substantial short-run macroeconomic fluctuations.

### Impulse-response evidence: local weather shocks
- The impulse response of output growth to a one degree Celsius local weather shock is:
  - Small, statistically weak, and short lived.
  - Accompanied by wide confidence bands, indicating substantial heterogeneity across countries.
- Interpretation:
  - Local weather shocks are absorbed through short-run adaptation, spatial reallocation, and sectoral adjustment.
  - Local weather variation contributes to transitory volatility but does not give rise to sustained aggregate responses once global climate exposure is accounted for.

### Synthesis: global vs local weather shocks
- Contrasting global and local responses reinforces Bilal and K̈anzig (2026):
  - Shocks driven by global climatic forces (observed through disaster realizations or synchronized weather anomalies) generate larger and more systematic macroeconomic effects.
  - Purely local shocks generate limited short-run effects and do not alter long-run growth trajectories.
- Analytical approach distinction:
  - This paper decomposes temperature into a persistent climate component and a transitory weather component using a state-space framework.
  - The shocks analyzed in this Section are explicitly weather shocks, defined as innovations orthogonal to the underlying climate path, allowing study of short-run dynamics around a climate-dependent baseline while keeping long-run climate anchoring analytically separate.

### Link to long-run climate findings (summary from the paper)
- Persistent global climate change anchors long-run output levels (Section 6).
- Global weather shocks, larger in magnitude, generate sizable short-run dynamics around that path.
- Local weather shocks primarily affect transitory volatility without shaping aggregate growth trajectories.
- Long-run result highlighted in the paper:
  - An increase in the permanent component of temperature leads economies to converge gradually to a lower output path, with an estimated decline in the long-run level of real GDP of roughly 22 percent following a one-degree Celsius increase in this component.
- Additional long-run insights:
  - Long-run climate damages operate through multiple structural margins; in the full sample a substantial portion of aggregate output loss reflects demographic adjustment.
  - In advanced economies persistent warming is associated with declines in both population and GDP per capita.
  - The per-capita channel operates primarily through capital accumulation rather than through total factor productivity, highlighting the role of capital deepening and capital adjustment.
  - Economies with higher capital intensity and more durable capital stocks experience significantly larger long-run output losses.

### Supporting numerical and sample facts (exact values from the source)
- Sample and data coverage:
  - The sample includes 192 countries.
  - Number of temperature observations: 9,943.
  - Number of GDP observations: 9,943.
  - Mean number of observations per country: 51.79.
  - Minimum number of observations per country: 15.
  - Median number of observations per country: 53.
- Summary statistics (exact entries):
  - Observed temperature (C): N = 9,943; Mean = 23.62; Min = 2.74; p1 = 6.40; p10 = 12.38; p25 = 18.01; p50 = 26.27; p75 = 28.62; p90 = 31.14; p99 = 35.02; Max = 36.33.
  - Log real GDP: N = 9,943; Mean = 12.68; Min = 1.16; p1 = 3.71; p10 = 7.81; p25 = 10.20; p50 = 12.95; p75 = 15.20; p90 = 17.15; p99 = 22.00; Max = 23.43.
  - GDP growth (%): N = 9,943; Mean = 3.54; Min = −15.98; p1 = −15.98; p10 = −2.65; p25 = 0.00; p50 = 3.76; p75 = 6.52; p90 = 9.52; p99 = 22.85; Max = 22.85.
- Representative estimated coefficients and robustness checks (exact values as reported):
  - Partial regression fitted coefficient in Appendix Figure A1: coef = −.25422017, (robust) se = .07201591, t = −3.53.
  - Baseline long-run coefficient reported in text/tables: β = −0.252 (Table 1 reference).
  - Robustness table entries:
    - First-difference regression: Change in permanent climate (∆μT): −0.290 (column label).
    - Long-difference regressions: Trend GDP and GDP level coefficients reported as −0.222 ∗∗∗ and −0.222 ∗∗∗ in Table A5.
    - HP-filtered GDP specifications: Permanent climate component (μT) coefficients −0.254 ∗∗∗, −0.252 ∗∗∗, −0.251 ∗∗∗ (Table A6).
    - HP-filtered temperature trend specifications: coefficients −0.207 ∗∗∗ and −0.151 ∗∗∗ (Table A7).
    - 30-year moving average temperature regression: coefficient −0.2901 ∗∗∗ (Table A8).
    - Benchmark regressions using raw temperature: Observed temperature coefficients −0.052 ∗∗∗, −0.051 ∗∗∗, and −0.163 (Table A10).

### Implications for research and policy (drawn from the analysis)
- Research directions:
  - Estimates are based on historical data and reflect past patterns of adaptation, technology, and economic structure; future damages may differ as economies adjust or implement new policies.
  - Future research should aim to uncover mechanisms and vulnerabilities underlying long-run climate damages, with emphasis on capital vintage, infrastructure design, and sectoral specialization using micro-level data and structural approaches.
- Policy-relevant inference:
  - Long-run damages concentrate in capital-intensive countries and those with slower capital turnover, suggesting policy attention to capital adaptation, infrastructure resilience, and investment vintage.
  - Short-run macroeconomic volatility from global weather shocks underscores the importance of disaster preparedness and synchronized international resilience measures because global climatic forces can strain adjustment capacity across countries.

*Persistent Temperature, Capital Structure, and the Long-Run Level of Output — Working Paper No. WP/2026/115*

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026115-source-pdf.pdf_