## wpiea2019145

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### Research context and literature
- Recent research links GDP growth, greenhouse gas (GHG) emission, global warming, and climate-related disasters; low income countries and regions are particularly vulnerable and have only little economic and financial capacity to adapt.
- Financial-economics literature on rare large crashes studies destruction of capital stocks and jumps in risk premia after rare large economic and financial crises; cited approaches include:
  - Rietz (1988); Barro (2006); Barro and Ursua (2008); Gabaix (2011); Gourio (2012); Fernandez-Villaverde and Levintal (2016).
- Macroeconomic climate-disaster literature cited includes Burke et al. (2015), Cantelmo et al. (2017), Adam and Bevan (2014), Bevan and Adam (2016), Hochrainer-Stigler et al. (2014), Kovacevic and Pflug (2011), Thomas et al. (2013), Thomas and Lopez (2015).
- Distinction emphasized: causes of climate disaster risk differ from financial crises, but effects (capital destruction, reduced potential capacity, hysteresis) can be similar.

### Empirical approach and data
- Objective: explore link between rising carbon dioxide levels in the atmosphere and the frequency of climate disasters in seven regions:
  - East Asia and Pacific (EAS); Europe and Central Asia (ECS); Latin America and the Caribbean (LCN); Middle East and North Africa (MEA); North America (NAC); South Asia (SAS); Sub-Saharan Africa (SSF).
- Data source: EMDAT database (CRED). EMDAT reports events causing at least 10 deaths, affecting at least 100 people, or prompting state of emergency or international assistance.
- Dependent variable: disaster frequency = sum of climate-related disasters per year and region (floods, droughts, landslides, wildfires, storms, extreme temperature).
- Data choices:
  - Use data starting in 1976 to mitigate early under-reporting.
  - Focus on number of disasters (frequency) rather than monetary cost due to severe data issues.
  - Regional classification follows World Bank Atlas method.
- CO2 data:
  - Annual increase in carbon dioxide expressed as a mole fraction in dry air from Mauna Loa Observatory, 1976–2017 first differences.
  - Mauna Loa annual increase is used as proxy for global annual increase.

### Stylized empirical findings (1976–2017)
- Droughts:
  - No strong trending behavior overall.
  - MEA, NAC, SAS: limited occurrence; EMDAT reports no droughts for MEA since 2010.
  - ECS: spike in 2000 with 10 droughts; 2004 and 2017 each with 4.
  - SSF: highly volatile.
- Floods:
  - Upward trend in almost every region except NAC and MEA.
  - Strong increases for EAS and SSF; recent downward pattern in SSF, EAS, SAS, and ECS.
  - Regional maxima: ECS in 2005; SSF in 2007; EAS in 2006; SAS in 2005.
- Landslides:
  - Flat in NAC and MEA (never surpasses 1).
  - EAS upward trend with 13 in 2013.
  - ECS and LCN volatile with no trend; SAS small upward trend; SSF increasing since late 1990s.
- Storms:
  - Upward trend in EAS since 1970s; weaker patterns in LCN, NAC, SSF.
  - No upward trend in ECS, MEA, SAS.
  - ECS spike in 1990 with 66 storms; 26 in 2005.
- Wildfires:
  - Limited for most regions.
  - NAC maximum 9 in 2002.
  - SAS maximum 4 in 1999.
  - ECS maximum 16.
- Extreme temperature:
  - Limited except ECS: 43 events in 2012; second highest 22 in 2005.
- Aggregate climate-related disasters (sum of six categories):
  - ECS: upward trend until 2005, then some decrease.
  - EAS and LCN: increasing trend over sample.
  - SSF: increasing with decrease from all-time high 74 in 2007 to 39 in 2017.
  - MEA and NAC: less pronounced trends; NAC shows positive trend.
  - SAS: upward trend observed.

### Empirical strategy and estimation
- Dependent variable: Disaster Frequency (number of disaster events per year).
- Key regressors:
  - Disaster Frequency t-1 (lagged dependent variable).
  - Sum of the current increase in CO2 and 17 lags (Sum of CO2 increases) in ppm (Mauna Loa first differences).
- Models estimated:
  - Poisson regressions by region with robust standard errors (Table 1).
  - Linear fixed effects panel regressions with individual (regional) effects, robust to heteroskedasticity and cross-sectional serial correlation (Table 2); two panel specifications:
    - Complete Data-set (all EMDAT disasters).
    - Large Disasters Data-set (disasters affecting at least 1,000 people or causing 100 deaths).
  - Fixed effects panel on first differences to mimic an error-correction model (Table 3).

### Main empirical findings (coefficients and statistics preserved)
- Poisson regressions by region — Disaster Frequency t-1 coefficients (standard errors):
  - EAS: 0.008 ∗∗∗ (0.002)
  - ECS: 0.007 ∗ (0.003)
  - LCN: 0.010 ∗∗ (0.003)
  - NAC: 0.027 ∗∗∗ (0.005)
  - SAS: 0.009 (0.007)
  - SSF: 0.022 ∗∗∗ (0.003)
  - MEA: 0.023 (0.018)
- Poisson regressions by region — Sum of CO2 increases coefficients (standard errors):
  - EAS: 0.023 ∗ (0.009)
  - ECS: 0.045 ∗∗ (0.015)
  - LCN: 0.038 ∗∗∗ (0.010)
  - NAC: 0.023 ∗∗ (0.009)
  - SAS: 0.037 ∗∗∗ (0.011)
  - SSF: 0.021 (0.014)
  - MEA: 0.044 ∗ (0.022)
- Poisson sample sizes:
  - Observations: 41 for EAS, ECS, LCN, NAC, SAS, SSF; 40 for MEA.
  - Example region fit statistics: EAS Log Likelihood −166.262; Akaike Inf. Crit. 338.524 (region-specific Log Likelihood and Akaike Inf. Crit. reported).
- Interpretation: Sum of CO2 increases coefficient is positive and statistically significant for 6 of 7 regions; SSF is exception.

- Fixed effects panel regressions (Table 2)
  - Complete Data-set:
    - Disaster Frequency t-1: 0.517 ∗∗∗ (0.071)
    - Sum of CO2 increases: 0.947 ∗∗∗ (0.168)
    - Observations: 280
    - R2: 0.526; Adjusted R2: 0.512
    - F Statistic: 150.216 ∗∗∗ (df = 2; 271)
  - Large Disasters Data-set:
    - Disaster Frequency t-1: 0.618 ∗∗∗ (0.071)
    - Sum of CO2 increases: 0.626 ∗∗∗ (0.168)
    - Observations: 277
    - R2: 0.624; Adjusted R2: 0.612
    - F Statistic: 222.036 ∗∗∗ (df = 2; 268)
  - Interpretation: Increases in CO2 positively influence disaster frequency in both samples; magnitude is smaller for Large Disasters but remains positive and significant.

- First-difference fixed effects panel (Table 3)
  - Dependent variable: Diff Disaster Frequency
  - Complete Data-set:
    - Disaster Frequency t-1: −0.483 ∗∗∗ (0.1047)
    - Sum of CO2 increases: 0.947 ∗∗∗ (0.2732)
    - Observations: 280
    - R2: 0.242; Adjusted R2: 0.219
    - F Statistic: 43.215 ∗∗∗ (df = 2; 271)
  - Large Disasters Data-set:
    - Disaster Frequency t-1: −0.382 ∗∗∗ (0.0713)
    - Sum of CO2 increases: 0.627 ∗∗∗ (0.1677)
    - Observations: 277
    - R2: 0.190; Adjusted R2: 0.166
    - F Statistic: 31.395 ∗∗∗ (df = 2; 268)
  - Interpretation: Positive relationship between increases in CO2 concentration and change in disaster frequency; lagged disaster frequency enters negatively in differenced specification.

### Modeling approach and policy instrumentation
- Model lineage: builds on Bonen et al. (2016), Maurer et al. (2018), Semmler et al. (2018); solution method for multi-phase model from Maurer et al. (2018).
- Model features:
  - Multi-phase dynamic macro model with phase-specific climate disasters and explicit fiscal and financial resource allocation.
  - Policies operationalized as time-varying shares of public capital supporting carbon-neutral productivity-enhancing infrastructure, mitigation and adaptation capital.
  - Endogenized carbon intensity via extraction of a non-renewable resource; renewable energy can be phased in via public investment.
  - Integrates SCC-style approaches with Hotelling (1931) and Pindyck (1978) resource extraction frameworks.
  - Allows agents to combine mitigation and adaptation; mitigation may reduce vulnerability.
- Three-phase policy sequencing:
  - Phase 1: taxation and fiscal tools (BAU).
  - Phase 2: disaster phase with scaling up investments via bond financing and jumps in depreciation and risk premia.
  - Phase 3: bond repayment and debt reduction through an income tax.
  - Single-stage model contrasted in Appendix A.3.

### Three-phase model structure (state and control variables preserved)
- State vector X = (K,R,M,b,g) where:
  - K: private (green) capital
  - R: stock of non-renewable resource
  - M: atmospheric concentration of CO2
  - b: government debt
  - g: public capital
- Control vector U = (C,eP,u) where:
  - C: consumption
  - eP: tax revenue
  - u: quantity of resource R extracted per period
- Representative dynamics (selected equations preserved):
  - Phase 1 (example):
    - ̇K = Y·(ν_1 g)^β − C − e_P − (δ^{dis}_K + n)K − uψR − ζ.
    - ̇R = −u.
    - ̇M = γ u − μ(M − κ ̃M) − θ(ν_3 · g)^φ.
    - ̇b = (r r − n) b − (1 − α_1 − α_2 − α_3)· e_P + ς_k g.
    - ̇g = α_1 e_P + i_F − (δ^{dis}_g + n) g + ς_k g.
  - Phase 3 (post-disaster example):
    - ̇K = Y·(ν_1 g)^β (1 − τ_k) − C − e_P − (δ_K + n)K − uψR − ζ.
    - ̇R = −u.
    - ̇M = γ u − μ(M − κ ̃M) − θ(ν_3 · g)^φ.
    - ̇b = (r r r − n) b − (1 − α_1 − α_2 − α_3)· e_P − Y·(ν_1 g)^β τ_k.
    - ̇g = α_1 e_P + i_F − (δ_g + n) g.
- Timing example:
  - First period t_0 = 0 to t_1 = 13.
  - Second period t_1 = 13 to t_2 = 23.
  - Last period until T = 40.
- Shock parameterization (Table 4 summary preserved):
  - Weak shock risk rate across periods: r = 0.04; rr = 0.08; rrr = 0.05.
  - Strong shock risk rate across periods: r = 0.04; rr = 0.12; rrr = 0.10.
  - Example depreciation jumps in strong shock: δ^{dis}_g = δ^{dis}_K jumps from 0.1 to 0.17; r jumps from 0.04 to 0.12.

### Results of the three-phase model (summary of outcomes)
- Results overview:
  - Red lines denote weak shocks; blue lines denote strong shocks.
  - Continuous growth more successfully achieved without strong shocks: weak shocks (red) generally dominate strong shocks (blue) except for fossil fuel resource and stock of CO2.
- Dynamics by shock strength:
  - Weak shock (red):
    - Consumption, private capital K, and public capital g rise.
    - Higher debt due to financing mitigation and adaptation via ςk g, but lower debt-to-capital ratios and higher welfare.
    - Stronger fossil fuel extraction and build up of CO2 stock (partly counteracted by policy).
    - Welfare value function: V = 26.46.
  - Strong shock (blue):
    - Longer disaster period; consumption, private and public capital stay low; debt stays low in absolute terms though b/K ratio can rise.
    - Declining extraction of fossil fuel and declining stock of CO2 emissions during disaster period.
    - Public and private capital damaged and shrink after 13 periods; later recovery via bond financing.
    - Welfare value function: V = −36.26.
- Key statistics and debt sustainability:
  - Welfare:
    - Weak shock: V = 26.46
    - Strong shock: V = −36.26
  - Debt-to-capital-stock ratio b/K:
    - Strong shocks: b/K = 0.33
    - Weak shocks: b/K = 0.25
  - Note: Absolute debt increases more in weak shock scenario, but b/K is higher for strong shocks.

### Policy implications and instruments
- Bond financing:
  - Can scale up mitigation, adaptation, and recovery; bonds repaid later via income taxes τk.
  - Benefits: decelerates GHG emissions via mitigation and energy-efficiency investments; funds energy mix changes, renewable energy, grids, and infrastructure; supports adaptation, early warning systems, and rebuilding public infrastructure.
  - Limitations: may be less efficient for immediate recovery; low and middle income countries face financing bottlenecks and limited access to issuing climate bonds.
- Complementary tools and practical considerations:
  - Monetary policy can support by accepting green bonds as collateral, easing credit flows after disasters, and preventing bottlenecks; central banks could provide low-interest loans and sufficient credit flows for reconstruction.
  - Alternatives for low income countries: grants, donor support, sovereign insurance, risk pooling, reserve funds, increased taxation, budget reallocation.
  - Types of bonds: government-backed, municipal, corporate green bonds, asset-backed securities, covered bonds, bundled soft/hard and low/high risk bonds; issuers include private businesses, governments, municipalities, and multilateral agencies.
  - Context: recent increase in number/value of green bonds and proportion of global GHG emissions covered by carbon tax policy since roughly 2011–2013; large global pools of funds of $80 to $100 trillion or more could potentially include climate bonds.

### Modeling features relevant to interpretation
- Emissions directly damage welfare; mitigation and adaptation appear via public funds and credit flows.
- The model studies rare disasters and long-run effects on productive capacity (physical, infrastructural, human capital).
- Vulnerability of disasters is reduced with greater public capital; high stock of emitted M reduces household welfare.

*Source: wpiea2019145 - IMF Working Paper (Introduction; empirical analysis; three-phase model and results).*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Research context and literature
- Recent research links GDP growth, greenhouse gas (GHG) emission, global warming, and climate-related disasters; low income countries and regions are particularly vulnerable and have only little economic and financial capacity to adapt.
- Financial-economics literature on rare large crashes studies destruction of capital stocks and jumps in risk premia after rare large economic and financial crises; examples and approaches cited:
  - Rietz (1988): rare market crashes and equity risk premia.
  - Barro (2006): disaster measure as decline of GDP growth.
  - Barro and Ursua (2008), Gabaix (2011): declines of consumption spending due to large disaster.
  - Gourio (2012): measure disasters in terms of loss in total factor productivity (TFP) and capital stock via sudden increase in capital depreciation rate.
  - Fernandez-Villaverde and Levintal (2016): numerical solution methods for DSGE models with disasters modeled as highly persistent shocks with mean reversion.
- Macroeconomic climate-disaster literature:
  - Burke et al. (2015): non-linear effects of climate change (Gumbel extreme value theory).
  - Cantelmo et al. (2017): climate disaster losses introduced as capital losses, implying persistent effects; fiscal policy suggested for disaster management.
  - Adam and Bevan (2014), Bevan and Adam (2016): role of public capital for disaster management.
  - Hochrainer-Stigler et al. (2014), Kovacevic and Pflug (2011): disaster insurance and trapping probabilities.
  - Thomas et al. (2013), Thomas and Lopez (2015): panel models for count data finding positive relationship between disaster frequency and disaster risk factors caused by man-made GHG emission.
- Distinction emphasized: while causes of disaster risk from climate differ from those of large financial crises, effects can be similar (short-run output recovery but reduced potential capacity, destruction of physical/public/human capital, hysteresis).

### Empirical approach and data
- Objective: explore link between rising carbon dioxide levels in the atmosphere and the frequency of climate disasters in seven regions:
  - East Asia and Pacific (EAS)
  - Europe and Central Asia (ECS)
  - Latin America and the Caribbean (LCN)
  - Middle East and North Africa (MEA)
  - North America (NAC)
  - South Asia (SAS)
  - Sub-Saharan Africa (SSF)
- Data source: EMDAT database provided by the Centre for Research on the Epidemiology of Disasters (CRED).
  - EMDAT reports events which cause at least 10 deaths, affect at least 100 people, or prompt a declaration of a state of emergency or a call for international assistance as a disaster.
- Dependent variable: disaster frequency constructed by summing the number of climate-related disasters in six categories for a given year and region:
  - floods, droughts, landslides, wildfires, storms, extreme temperature.
- Data preparation choices:
  - Use data starting in 1976 to mitigate severe data distortions and under-reporting in earlier years.
  - Focus on the number of disasters (disaster frequency) rather than reported real climate disaster cost due to severe data issues in cost measures.
  - Regional classification follows the World Bank Atlas method.

### Stylized empirical findings (1976–2017)
- Droughts:
  - No strong trending behavior overall.
  - Middle East and North Africa, North America, and South Asia: limited occurrence of droughts; EMDAT reports no droughts for Middle East and North Africa since 2010.
  - Europe and Central Asia: large spike in 2000 with 10 droughts; second largest values in 2004 and 2017 with 4 occurrences each.
  - Sub-Saharan Africa: highly volatile number of droughts over the sample.
- Floods:
  - Upward trending behavior for floods in almost every region except North America and Middle East and North Africa.
  - Strong increases pronounced for East Asia and Sub-Saharan Africa.
  - Recent years show downward pattern in Sub-Saharan Africa, East Asia, South Asia, and Europe and Central Asia.
  - Regional maxima timing:
    - Europe and Central Asia: maximum in 2005.
    - Sub-Saharan Africa: maximum in 2007.
    - East Asia: highest value in 2006.
    - South Asia: highest value in 2005.
- Landslides:
  - Flat number per year in North America and Middle East and North Africa (never surpasses a value of one).
  - East Asia: upward trend with highest reported value 13 landslides in 2013.
  - Europe and Central Asia, Latin America and the Caribbean: volatile with no discernible trend.
  - South Asia: small upward trend with large year-on-year changes.
  - Sub-Saharan Africa: increasing number of landslides since the late 1990s.
- Storms:
  - Upward trend in East Asia since the 1970s.
  - Similar, but weaker, patterns in Latin America and the Caribbean, North America, and Sub-Saharan Africa.
  - No upward trend in Europe and Central Asia, Middle East and North Africa, and South Asia.
  - Europe and Central Asia: large spike in 1990 when 66 storms were recorded; second largest value in 2005 with 26 reported incidents.
- Wildfires:
  - Very limited for most regions.
  - South Asia: maximum value 4 wildfires in 1999.
  - Middle East and North Africa: very small numbers.
  - Sub-Saharan Africa: very small numbers.
  - Europe and Central Asia: higher numbers with a maximum reported value of 16 wildfires.
- General note: Figures 1–7 present number of climate-related disasters by region for 1976–2017; Figure 8 shows annual CO2 mole fraction increase (in parts per million) from 1976 until 2017.

### Modeling approach and policy instrumentation
- Model lineage:
  - Builds on macro models by Bonen et al. (2016), Maurer et al. (2018), and Semmler et al. (2018).
  - Solution method for the multi-phase model presented in Maurer et al. (2018).
- Model features:
  - Multi-phase dynamic macro model that allows phase-specific climate disasters and explicit fiscal and financial resource allocation.
  - Policies operationalized as time-varying shares of public capital in support of carbon-neutral productivity-enhancing infrastructure, mitigation and adaptation capital.
  - Carbon intensity is endogenized by linking emissions to extraction of a non-renewable resource (e.g., fossil fuels).
  - Renewable energy can be phased in through public-sector investment, thereby phasing out fossil energy.
  - Integrates ‘social cost of carbon’ (SCC) style approaches from Integrated Assessment Models with Hotelling (1931) and Pindyck (1978) resource extraction frameworks.
  - Allows agents to respond to climate change by combining mitigation and adaptation actions; mitigation may reduce vulnerability.
- Three-phase climate-finance model (policy sequencing emphasized):
  - Phase 1: taxation and fiscal tools.
  - Phase 2: scaling up investments via bond financing.
  - Phase 3: bond repayment and debt reduction through an income tax.
  - A single-stage model is described in appendix A.3 and contrasted with the multi-phase model.
- Policy instruments analyzed:
  - Fiscal, monetary, and financial policy interventions to manage disasters.
  - Focus on scaling up climate investment through bond issuance and combining fiscal, financial, and monetary policies for tackling climate change.
  - Study of effects of large disasters on risk premia, credit cost, credit spread, and credit constraints within the model.
- Hypothesized mechanisms and concerns:
  - Large temporary shocks and capital losses can steeply raise risk premia and borrowing costs, increasing credit constraints and potentially creating trapping probabilities and slow recoveries.
  - Trade-offs between mitigation (expensive with long-run benefits) and adaptation (more effective short-term but costlier if mitigation is underfunded); short-run substitutes can become long-run complements.

*Source: wpiea2019145 - 1. Introduction (IMF Working Paper chapter).*

### 2000. In North America the largest value is observed in 2002 with 9 wildfires. F or East

### wpiea2019145 - 2000. In North America the largest value is observed in 2002 with 9 wildfires. F or East

### Regional patterns in climate-related hazards (1976–2017)
- Wildfires
  - In North America the largest value is observed in 2002 with 9 wildfires.
  - East Asia: number of wildfires is limited but higher than for the Middle East and North Africa, Latin America and the Caribbean and Sub-Saharan Africa.
  - Latin America and the Caribbean: number of wildfires is very limited.
- Extreme temperature events
  - Number of observations is very limited for all regions except Europe and Central Asia.
  - For all regions but Europe and Central Asia, the number of observations for this disaster category is below 10 for each year.
  - Europe and Central Asia: 43 extreme temperature events reported in 2012; second highest value was 22 in 2005.
- Aggregate climate-related disasters (sum of six disaster categories)
  - Europe and Central Asia: clear upward trend until 2005, followed by some decrease.
  - East Asia and Latin America and the Caribbean: increasing trend over the entire sample period.
  - Sub-Saharan Africa: similar increasing pattern with a small decrease in the most recent years; number of disasters decreases from an all-time high of 74 observations in 2007 to 39 climate related disaster in 2017.
  - Middle East and North Africa and North America: trends less pronounced, but North America shows a positive trend.
  - South Asia: upward trend observed.

### CO2 growth data and rationale for focusing on CO2
- Data
  - Annual increase in carbon dioxide expressed as a mole fraction in dry air from Mauna Loa Observatory, representing 1976–2017 growth (first differences).
  - Mauna Loa annual increase is very similar to the global annual increase and is used for both hemispheres in this study.
- Rationale
  - Increased GHG emissions alter climate variables (temperature and precipitation) and thereby increase frequency of climate-related hazards.
  - CO2 concentration represents an indirect effect on climate-related disasters but has empirical merits:
    - Long-lived GHG like CO2 show only small geographic variations and can be measured at few sites with low uncertainty.
    - Changes in surface temperature show high geographic variation and are affected by factors like the El-Niño Southern Oscillation, solar variability, and volcanic activity.

### Empirical strategy
- Dependent variable: number of disaster events for a given year (Disaster Frequency).
- Key regressors:
  - Lagged dependent variable (Disaster Frequency t-1).
  - Sum of the current increase in CO2 and 17 lags (Sum of CO2 increases) measured in ppm (Mauna Loa first differences). Sum of CO2 increases represents the sum of all CO2 added and removed from the atmosphere for a given year by human activities and natural processes.
- Models estimated:
  - Poisson regressions by region with robust standard errors (Table 1).
  - Linear fixed effects panel regressions with individual (regional) effects, robust to heteroskedasticity and cross-sectional serial correlation (Table 2).
    - Two panel specifications: Complete Data-set (all EMDAT disasters) and Large Disasters Data-set (disasters affecting at least 1,000 people or causing 100 deaths).
  - Fixed effects panel on first differences (change in disaster frequency) to mimic an error-correction model (Table 3).

### Main empirical findings (preserve reported coefficients and significance)
- Poisson regressions by region (Table 1)
  - Disaster Frequency t-1 coefficients (with standard errors):
    - EAS: 0.008 ∗∗∗ (0.002)
    - ECS: 0.007 ∗ (0.003)
    - LCN: 0.010 ∗∗ (0.003)
    - NAC: 0.027 ∗∗∗ (0.005)
    - SAS: 0.009 (0.007)
    - SSF: 0.022 ∗∗∗ (0.003)
    - MEA: 0.023 (0.018)
  - Sum of CO2 increases coefficients (with standard errors):
    - EAS: 0.023 ∗ (0.009)
    - ECS: 0.045 ∗∗ (0.015)
    - LCN: 0.038 ∗∗∗ (0.010)
    - NAC: 0.023 ∗∗ (0.009)
    - SAS: 0.037 ∗∗∗ (0.011)
    - SSF: 0.021 (0.014)
    - MEA: 0.044 ∗ (0.022)
  - Observations: 41 for EAS, ECS, LCN, NAC, SAS, SSF; 40 for MEA.
  - Log Likelihood and Akaike Inf. Crit. reported per region (e.g., EAS Log Likelihood −166.262; Akaike Inf. Crit. 338.524).
  - Interpretation: Sum of CO2 increases coefficient is positive and statistically significant for 6 out of 7 regions, with Sub-Saharan Africa (SSF) being the exception.
- Fixed effects panel regressions (Table 2)
  - Complete Data-set:
    - Disaster Frequency t-1: 0.517 ∗∗∗ (0.071)
    - Sum of CO2 increases: 0.947 ∗∗∗ (0.168)
    - Observations: 280
    - R2: 0.526; Adjusted R2: 0.512
    - F Statistic: 150.216 ∗∗∗ (df = 2; 271)
  - Large Disasters Data-set:
    - Disaster Frequency t-1: 0.618 ∗∗∗ (0.071)
    - Sum of CO2 increases: 0.626 ∗∗∗ (0.168)
    - Observations: 277
    - R2: 0.624; Adjusted R2: 0.612
    - F Statistic: 222.036 ∗∗∗ (df = 2; 268)
  - Interpretation: Positive influence of increases in CO2 on frequency of natural disasters in both complete and large-disaster samples; coefficient magnitude decreases for Large Disasters Data-set but remains positive and statistically significant.
- First-difference fixed effects panel (Table 3)
  - Dependent variable: Diff Disaster Frequency
  - Complete Data-set:
    - Disaster Frequency t-1: −0.483 ∗∗∗ (0.1047)
    - Sum of CO2 increases: 0.947 ∗∗∗ (0.2732)
    - Observations: 280
    - R2: 0.242; Adjusted R2: 0.219
    - F Statistic: 43.215 ∗∗∗ (df = 2; 271)
  - Large Disasters Data-set:
    - Disaster Frequency t-1: −0.382 ∗∗∗ (0.0713)
    - Sum of CO2 increases: 0.627 ∗∗∗ (0.1677)
    - Observations: 277
    - R2: 0.190; Adjusted R2: 0.166
    - F Statistic: 31.395 ∗∗∗ (df = 2; 268)
  - Interpretation: Positive relationship between increases in CO2 concentration and (change in) frequency of disasters; lagged disaster frequency enters negatively in difference specification.

### Modeling disaster shocks and financing contractions: three-phase macro model
- Purpose and features
  - Dynamic multi-phase macro model including a disaster phase, allowing for tax and credit finance of climate policies, and feedback effects by credit flow dynamics affecting climate variables and the real sector.
  - Model permits shifts into a persistent disaster regime (a prolonged disaster phase that may lead to slow recovery and self-reinforcing feedback effects).
  - Incorporates mitigation and adaptation policy instruments activated by the public sector and monetary authority.
  - Focus on rare large disasters and different shock sizes (weak and strong).
- Model structure (three phases)
  - Phase 1 (mitigation and adaptation financed through taxation; BAU period)
    - Objective function W(T,X,U) = ∫_0^T e^{−(ρ−n)t} ( C(α_2 e_P)^η (M−  ̃M) − (ν_2 g)^ω )^{1−σ} −1 /(1−σ) dt. (equation (1))
    - State dynamics (representative equations):
      - ̇K = Y·(ν_1 g)^β − C − e_P − (δ^{dis}_K + n)K − uψR − ζ. (2)
      - ̇R = −u. (3)
      - ̇M = γ u − μ(M − κ  ̃M) − θ(ν_3 · g)^φ. (4)
      - ̇b = (r r − n) b − (1 − α_1 − α_2 − α_3)· e_P + ς_k g. (5)
      - ̇g = α_1 e_P + i_F − (δ^{dis}_g + n) g + ς_k g. (6)
    - Variables: K private (green) capital; R stock of non-renewable resource; M atmospheric CO2; b government debt; g public capital.
  - Phase 2 (disaster phase with capital losses and increased risk premia)
    - Modeled by jumps in depreciation and risk premium, e.g., δ^{dis}_g = δ^{dis}_K jumping from 0.1 to 0.17 and r jumping from r = 0.04 to r = 0.12 for strong shock example.
    - Additional credit (bond) financing added in this phase: ς_k g affecting debt and public capital dynamics.
  - Phase 3 (post-disaster period with no additional bond issuing; bonds repaid by tax rate τ)
    - State dynamics (representative equations):
      - ̇K = Y·(ν_1 g)^β (1 − τ_k) − C − e_P − (δ_K + n)K − uψR − ζ. (7)
      - ̇R = −u. (8)
      - ̇M = γ u − μ(M − κ  ̃M) − θ(ν_3 · g)^φ. (9)
      - ̇b = (r r r − n) b − (1 − α_1 − α_2 − α_3)· e_P − Y·(ν_1 g)^β τ_k. (10)
      - ̇g = α_1 e_P + i_F − (δ_g + n) g. (11)
    - Capital losses cease but elevated risk premia may persist (example r r r = 0.10 in strong shock).
  - Timing example (pre-fixed)
    - First period from t_0 = 0 to t_1 = 13.
    - Second period from t_1 = 13 to t_2 = 23.
    - Last period until T = 40.
- Shock parameterization and scenarios (Table 4 summary)
  - Weak shock parameter values across periods:
    - Time period t_1–t_2, t_2–t_3, t_3–T
    - risk rate, weak shock: r = 0.04; rr = 0.08; rrr = 0.05
    - weak shock: σ_K,(σ_G) 0.1, (0.075)   0.12, (0.12)   0.1, (0.075)
  - Strong shock parameter values across periods:
    - risk rate, strong shock: r = 0.04; rr = 0.12; rrr = 0.10
    - strong shock: σ_K,(σ_G)   0.1, (0.075)   0.17, (0.17)   0.1, (0.075)
  - Modeling choices
    - Strong shock example: δ^{dis}_g = δ^{dis}_K jumps from 0.1 to 0.17; risk premium r jumps from 0.04 to 0.12.
    - Weak shock has smaller depreciation shocks and smaller risk premia in phase two and three.
- Model interpretation and policy relevance
  - The three-phase model allows study of:
    - How disaster-induced capital losses and higher risk premia affect growth, debt sustainability, and recovery.
    - Effects of financing choices (tax-financed mitigation/adaptation vs. bond-financed public responses) on post-disaster dynamics.
    - Role of monetary policy in influencing risk premia, with caveats that post-disaster premia may remain elevated.

*Source: Authors’ estimates and model description from wpiea2019145 (EMDAT data; Mauna Loa Observatory CO2 data).*

### 3.2 Results of the three-phase model

### 3.2 Results of the three-phase model

### Results overview
- Parameter shifts of table 4 are used; effects are drawn with red lines for weak shocks and blue lines for strong shocks.
- Overall continuous growth is more successfully achieved without strong shocks: red lines (weak shocks) are above blue lines (strong shocks) for most variables except fossil fuel resource and stock of CO2.
- For weak shocks the economy can continuously grow with high borrowing, financing climate-related infrastructure investments, and appropriate mitigation and adaptation policies; this involves strong evolution of debt co-financing mitigation and adaptation.

### Dynamics by shock strength (consumption, capital, emissions, extraction)
- Weak shock (red):
  - Consumption, private capital, and public capital stock rise (red above blue in figures 9–13).
  - Higher debt due to financing of mitigation and adaptation via financial sources, ςk g, but lower debt-to-capital ratios and higher welfare.
  - Strong extraction of fossil fuel and build up of stock of CO2 emissions (counteracted by climate policy measures).
  - Private (green) capital K and public capital g build up during the second and third period; consumption rises.
  - After first phase some plots remain constant while stock of emitted M becomes high, in particular for weak shocks, producing a negative externality on welfare.
  - Welfare value function: V = 26.46.

- Strong shock (blue):
  - Stronger and longer disaster period; consumption stays low, private and public capital stock stay low, and debt stays low.
  - Lower growth and smaller increase of capital stocks lead to declining extraction of fossil fuel and declining stock of CO2 emissions (consistent with empirical findings that emissions decline in times of a negative output gap).
  - Debt rises steadily in some descriptions because risk premia are increasing.
  - Public and private capital are damaged during the disaster phase and shrink after 13 periods.
  - Capital stocks fall in the period after t1; later recovery of public and private capital occurs due to additional bond financing accelerating mitigation and adaptation.
  - CO2 emission rises only slightly and total remaining fossil fuel stock is only falling slightly; much fossil energy remains unexploited.
  - Welfare value function: V = −36.26.

### Key statistics and debt sustainability
- Computed welfare:
  - Weak shock: V = 26.46
  - Strong shock: V = −36.26
- Debt-to-capital-stock ratio, b/K:
  - Strong shocks: b/K = 0.33
  - Weak shocks: b/K = 0.25
- Although absolute debt levels increase more strongly in the weak shock scenario, the b/K ratio is higher for strong shocks.

### Modeling features relevant to interpretation
- Emissions are modeled as having direct (damaging) effects on welfare (Appendix A.3); the model incorporates adaptive responses via public funds and credit flows.
- The three-phase model allows study of rare disasters and long-run gradual effects on productive capacity (physical, infrastructural, human capital).
- Vulnerability of disasters is reduced with greater public capital (see equation (1)); high stock of emitted M reduces household welfare (see equation (1)).

### Policy implications: bond financing, monetary and other policies
- Bond issuance (including long maturity and green bonds) can scale up mitigation, adaptation, and recovery policies; bonds must be repaid later via income taxes τk.
- Benefits of bond financing:
  - Stimulates deceleration of greenhouse gas emissions via timely mitigation and energy-efficiency investments.
  - Funds energy mix changes, development of renewable energy, grids, and infrastructure.
  - Provides funds for adaptation to reduce frequency/severity of disasters and to reverse slow long-run impacts (water cycles, air quality, oceanic warming, sea level rise, etc.).
  - Supports early warning systems and disaster-reducing infrastructure, and is very effective in rebuilding public infrastructure.
- Limitations:
  - Bond financing may be less efficient for immediate recovery policies; other monetary and credit policies may be more suitable for recovery.
  - Low and middle income countries face financing bottlenecks and limited access to issuing climate bonds; alternative mechanisms (grants, donor support, sovereign insurance, risk pooling, reserve funds) are needed for those countries.
- Practical considerations:
  - Types of bonds: government-backed, municipal, corporate green bonds, asset-backed securities, covered bonds, bundled soft/hard and low/high risk bonds.
  - Issuers include private businesses, governments and municipalities, and multilateral agencies (e.g., World Bank).
  - Recent increase in both number/value of green bonds and proportion of global GHG emissions covered by carbon tax policy since roughly 2011–2013 (figure 14).
  - Current macro and monetary environment (low interest rates, low risk premia, low expected inflation) makes long-term bonds attractive; many bonds are inflation adjusted (e.g., US TIPS).
  - Large global pools of funds of $80 to $100 trillion or more could potentially include climate bonds in their portfolios.

### Complementary policy tools and considerations
- Monetary policy can support climate policy by accepting green bonds as collateral, easing credit flows after disasters, and preventing bottlenecks in supply of goods and services.
- Fiscal/financial policy trade-offs exist between mitigation investments and adaptation/disaster prevention; borrowing and bond issuing relax constraints but may be impractical for low income countries.
- For low income countries, alternatives discussed in the literature include sovereign disaster risk insurance, increased taxation, budget reallocation, risk pooling, grants, reserve accumulation, and donor support; debt sustainability remains a central concern.
- Broader risk-pooling mechanisms suggested: private/public insurance schemes, multilateral safety nets, regional catastrophic insurance schemes.
- Monetary policy could provide low-interest loans and sufficient credit flows for reconstruction to avoid hysteresis effects on productive capacity.

### Summary of modeled outcome patterns
- Weak shocks: higher consumption, rising private and public capital, higher debt but lower debt-to-capital ratio, higher welfare (V = 26.46), stronger fossil fuel extraction and higher CO2 stock (partially counteracted by policy).
- Strong shocks: lower consumption, lower capital stocks, lower absolute debt (though higher b/K = 0.33), lower welfare (V = −36.26), reduced fossil fuel extraction and lower increases in CO2 stock.

*wpiea2019145 - 3.2 Results of the three-phase model*

### References

### wpiea2019145 - References

### Fixed effects coefficients for panel model (Appendix A.1)
- Table context: Fixed effects coefficients for the panel model in Table 2. Dependent variable: number of disaster events for a given year (Disaster Frequency). Independent variables include the lagged dependent variable (Disaster Frequency t-1) and the sum of the current and 17 most recent increases in CO2 concentration (ppm). Standard errors in parenthesis. ModelComplete Data-set considers all disasters in the EMDAT database. ModelLarge Disasters Data-set only includes disasters with at least 1,000 affected or 100 people killed.
- Reported coefficients and standard errors (as in source):
  - EAS7.69494.7931
    - (4.5543)(3.3237)
  - ECS-6.9858-11.4663
    - (4.6638)(3.8024)
  - LCN-5.8552-5.1752
    - (4.6501)(3.4959)
  - MEA-22.6248-15.7693
    - (5.2799)(4.0410)
  - NAC-15.9695-10.4356
    - (4.9672)(3.7610)
  - SAS-12.6648-7.8858
    - (4.8411)(3.5922)
  - SSF-10.4200-6.8432
    - (4.7600)(3.5461)

### Empirics of climate disaster cost (Appendix A.2)
- Data coverage and limitation:
  - Time span: 1976 and 2017.
  - Data is worldwide aggregated only due to lack of regionally complete data.
  - Many missing values in real (GDP-deflated) estimated damages; some disaster categories have missing real damages for certain years.
- Empirical observations:
  - Figure 15 (not reproduced here) shows the logarithm of estimated real damages by disaster category between 1976 and 2017.
  - Storm-related real damage costs increased in recent years and dominate aggregated damage fluctuations (Figure 16).
- Methodological decision:
  - Given severe data issues and the influence of societal changes (population and wealth increases) and exceptionally big disasters (e.g., Hurricane Sandy), the empirical analysis focuses on the number of disasters per year instead of disaster cost.
  - Cited view: Mohleji and Pielke (2014) argue societal changes suffice to explain increasing disaster damages (see also Bouwer, 2011).

### Baseline macro dynamic model (Appendix A.3)
- Purpose and linkages:
  - Model traces: economic growth → extraction/use of fossil fuel → CO2 emissions → increased atmospheric CO2 concentration and reduced economic growth/welfare.
  - Mitigation and adaptation pursued via fiscal and/or financial instruments, activated by the public sector and public capital; debt-financed public capital creates sustainability concerns.
- State variables and control variables:
  - State vector: X= (K,R,M,b,g)∈R5,(12)
    - K: private (green) capital
    - R: stock of the non-renewable resource
    - M: atmospheric concentration of CO2
    - b: government’s debt
    - g: public capital
  - Control vector: U= (C,eP,u)∈R3,(18)
    - C: consumption
    - eP: tax revenue
    - u: quantity of resource R extracted per period
- Core dynamic equations (numbering preserved):
  - ̇K = Y·(ν1 g)β − C − eP − (δK + n)K − uψR − ζ,(13)
  - ̇R = −u,(14)
  - ̇M = γ u − μ(M − κ ̃M) − θ(ν3 · g)φ,(15)
  - ̇b = (r − n)b − (1 − α1 − α2 − α3)·eP .(16)
  - ̇g = α1 eP + iF − (δg + n)g,(17)
- Production function and parameters:
  - CES production function: Y(K,u) := A(AK K + Au u)α (19)
  - A: multifactor productivity; AK and Au: efficiency indices of K and u.
  - Public infrastructure enhances productivity via ν1 g, 0 ≤ ν1 ≤ 1; output becomes Y(ν1 g)β with β the output elasticity of public infrastructure.
  - Marginal cost of extracting u tied to remaining resource stock via scale and shape parameters ψ and ζ (Hotelling (1931) style).
- Emissions dynamics:
  - Non-renewable resource emits CO2 at rate γ (equation (15)).
  - Stable CO2 level is κ > 1 of the pre-industrial level M ̃, natural reabsorption at rate μ.
  - Emissions reduction from infrastructure mitigation allocation ν3 (0 ≤ ν3 ≤ 1) appears via −θ(ν3 · g)φ.
- Debt and public capital dynamics:
  - Public debt grows at fixed interest rate r and is serviced with share of tax revenue eP not allocated to capital accumulation α1, social transfers α2, or administrative overhead α3 > 0; define α4 ≡ 1 − α1 − α2 − α3.
  - Public capital evolves via α1 eP and inflows iF (positive for some developing countries; iF = 0 may be assumed for developed countries); g depreciates at δg and adjusted for population growth n.
- Infrastructure allocation constraint:
  - νk ≥ 0 (k = 1,2,3), ν1 + ν2 + ν3 = 1.(20)
  - ν1, ν2, ν3 are either fixed or treated as additional optimization variables in later analysis.
- System form and constraints:
  - Compact dynamics: ̇X(t) = f(X(t),U(t)), X(0) = X0 .(21)
  - Terminal constraint: K(T) = KT ≥ 0,(22)
  - Control constraint: 0 ≤ u(t) ≤ umax,(23)
  - State constraint: M(t) ≤ Mmax ∀ t ∈ [0,T].(24)
- Objective functional (social welfare) and utility specification:
  - Maximize W(T,X,U) = ∫T0 e−(ρ−n)t ( C(α2 eP)η (M − ̃M)− (ν2 g)ω )1−σ − 1 1−σ dt.(25)
  - Felicity function: isoelastic with four per-capita inputs:
    - consumption C
    - share 0 ≤ α2 ≤ 1 of tax revenue eP used for direct welfare enhancement
    - atmospheric concentration M above pre-industrial level M ̃
    - share 0 ≤ ν2 ≤ 1 of infrastructure g allocated to adaptation
  - Exponents η, , ω > 0 ensure social expenditures and adaptation are utility enhancing; carbon emissions directly reduce utility.
  - Discount factor adjusts for population growth n from pure discount rate ρ.
- Problem statement:
  - The model defines an optimal control problem OC(p): maximize (25) subject to dynamics (21) and constraints (22)–(24).
  - Multi-phase extension: phases with different objective functions, state variables and specifications (see Maurer et al. (2018) referenced in source).

*Source: wpiea2019145 - References (Appendix A: A.1–A.3)*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019145.pdf_