## 3.1 Households (wpiea2019217-print-pdf)

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---

### Introduction and scope
- Focus: the long-term effects of more frequent weather-related natural disasters (cyclones, tornadoes, floods) on macroeconomic outcomes and welfare of disaster-prone countries (typically small states or low-income countries, LICs).
- Modeling approach: small-open economy dynamic stochastic general equilibrium (DSGE) model embedding disaster shocks as in Gourio (2012), solved with Taylor projection (Levintal, 2018; Fernandez-Villaverde and Levintal, 2018).
- Key modeling features: stochastic disaster shocks, Epstein-Zin preferences, public investment, external debt, sovereign risk premium, resilient public infrastructure, and international aid.
- Rationale: natural disasters can be very large (shocks can be as big as 50% of GDP), invalidating linear approximations and changing the stochastic steady state.

### Main findings (macro and welfare)
- Growth and long-run outcomes:
  - Disaster-prone countries grow on average by 1 percent less a year than their non-disaster-prone peers due solely to more frequent and powerful natural disasters.
  - Climate change, assuming shifts in the disaster distributions similar to those observed in the past decade, may amplify the growth gap to 3 percent a year.
- Welfare:
  - Permanent loss in consumption of 1.6 percent relative to non-disaster-prone ones.
  - Climate change scenario: welfare losses about seven times larger than baseline disaster-prone outcomes.
- Public debt and fiscal outcomes:
  - On average, disaster-prone countries have a public debt 1.54 percentage points of GDP higher than non-disaster-prone countries.
  - Under a climate change scenario this difference increases to 11 percent of GDP.
- Transmission channels:
  - Destruction of private and public capital (modeled as a permanent one-off depreciation of existing capital).
  - Temporary decline in productivity following disasters.
  - Lower output leads to lower government revenues and higher public debt.

### Disaster-prone country statistics and stylized facts (EM-DAT; sample 1998-2017)
- Sample: 129 low- and middle-income economies (per capita GNI below $12,055 in 2017); dataset covers 1998-2017 and uses EM-DAT for droughts, extreme temperatures, floods, fog, landslides, storms and wildfires.
- Definition: disaster-prone countries = top 25% of the distribution of annual probability of experiencing a natural disaster per 1000 squared kilometers; non-disaster-prone = remaining 75%.
- Event counts: sample includes 2516 events (393 in disaster-prone countries, 2123 in non-disaster-prone countries).
- Probability distributions (textual highlights):
  - In 97% of non-disaster-prone countries the annual probability of a natural disaster is below 1 percent; remaining 3% between 1% and 2% (highest non-disaster-prone = 1.29%).
  - In disaster-prone countries: none have annual probability below 1%; 29% face 1%-2%; 26% face 2%-5%; 36% face 5%-60%; 9% have annual probability between 80% and 100%.
- Damages (% of GDP):
  - In non-disaster-prone countries: 88% of natural disasters destroy less than 1% of GDP and all events in that group cause damages not exceeding 15% of GDP.
  - In disaster-prone countries: 23% of events have losses between 1% and 5% of GDP; 12% of events have losses above 5% of GDP.
- Table 1 (Average Annual Probabilities of Natural Disasters per 1000 Squared Kilometers (%).) — preserved exactly:
  - Full sampleSubsamples
    1998-20171998-2007  2008-2017
    Disaster-prone countries16.213.818.7
    Non-disaster-prone countries0.280.290.27
- Table 2 (Damages to GDP from Natural Disasters (%).) — preserved exactly:
  - Full sampleSubsamples
    1998-20171998-20072008-2017
    Average MaxAverage MaxAverage Max
    Disaster-prone countries6.65    2604.70    1488.58    260
    Non-disaster-prone countries   0.52   72.90.63   72.90.41   12.6

### Distributional findings on disaster damages (Appendix A highlights)
- Damages in percent of GDP computed by dividing EM-DAT damages (US dollars) by GDP of the year of the event; distributions computed for each country group over 1998-2017 and subsamples.
- The most damaging events in disaster-prone countries:
  - Hurricane Ivan destroyed 148% of Grenada’s GDP in 2004.
  - Hurricane Maria caused damages of the order of 260% of GDP in Dominica in 2017.
- The most damaging events in non-disaster-prone countries:
  - Hurricane Mitch caused damages of the order of 73% of GDP in Honduras in 1998.
  - Cyclone Nargis destroyed 12.6% of GDP in Myanmar in 2008.
- Over time:
  - Average damages to GDP in disaster-prone countries became larger in 2008-2017 relative to 1998-2007, while in non-disaster-prone countries the average damages to GDP slightly fell.
  - A noted trend: 19% in the more recent past ten years, increasing the divergence between the two country groups. (text presence preserved exactly as in source)

### Country-group composition and small economies
- Definitions (preserved from source):
  - Small states: population below 1.5 million that are not advanced economies or high-income oil exporting countries (IMF).
  - Low-income-countries: GNI per capita below $995 in 2017 (World Bank).
- Shares:
  - 74% of disaster-prone countries are small economies.
  - 66% of non-disaster-prone countries fall in the non-small economies definition.
- Mechanism: Small surface area, small population, or low-income status implies that large and/or frequent disasters affect a large share of GDP in many disaster-prone countries.

### Damage by disaster type
- Focused on three most frequent and powerful disasters: droughts, floods and storms.
- For storms:
  - In disaster-prone countries, storms destroy 12 percent of GDP on average.
  - In non-disaster-prone countries, storms destroy 1 percent of GDP on average.
- Stylized facts:
  - Disaster-prone developing countries incur overwhelmingly larger losses per disaster as a fraction of GDP than non-disaster-prone peers.
  - The lion’s share of damages are caused by storms; many disaster-prone countries are located in tropical areas.

### Research question and motivation
- Core question: whether differences in the disaster distributions alone have significant weight on the growth path and welfare of disaster-prone countries relative to peers.
- Explanation: the stark difference in damages to GDP is largely explained by the size of the economy: smaller economies (by geography or development) suffer larger GDP shares lost.

### Model overview (single-good small-open-economy RBC with disasters)
- Baseline model: single-good small-open-economy real-business-cycle (RBC) model augmented with:
  - investment adjustment costs,
  - stochastic trend growth,
  - disaster shocks as in Gourio (2012) and Fernandez-Villaverde and Levintal (2018).
- Four key augmentations:
  1. Detailed public sector: government invests in public infrastructure, finances expenditures via a consumption tax, and accumulates debt; reconstruction of public capital after disasters entails fiscal cost borne by households through higher consumption taxes.
  2. Small-open-economy dimension: allows accumulation of external government debt and captures higher sovereign risk premium faced by countries hit by natural disasters.
  3. Government can invest in resilient public infrastructure to dampen effects of natural disasters.
  4. Grants from abroad can be injected to alleviate fiscal burden post-disaster or to finance resilient public investment.
- Limitation: model has only one sector and does not explicitly include agriculture; it does not capture damages to crops due to droughts or storms.

### Households — key structure and equations (preserved)
- Epstein-Zin preferences:
  - V_{t}^{1−ψ} = U_{t}^{1−ψ} + β E_{t}(V_{t+1}^{1−γ})^{(1−ψ)/(1−γ)}, with U_{t} = c_{t} (1−l_{t})^{ν}.
- Budget constraint:
  - (1 + τ_{t}) c_{t} + x_{t} + b_{t+1} = w_{t} l_{t} + r_{t} k_{t} + R_{t−1} b_{t} + F_{t} + T_{t}.
- Investment adjustment cost:
  - S[x_{t}/x_{t−1}] = κ/2 (x_{t}/x_{t−1} ˆz_{t} − ˆz)^{2}.
- Law of motion of private capital:
  - k^{*}_{t} = (1−δ) k_{t} + (1 − S[ x_{t}/x_{t−1} ]) x_{t}.
  - log k_{t} = log k^{*}_{t−1} − d_{t} θ_{t}.
- Disaster process:
  - d_{t} is i.i.d. binary: d_{t} = 1 with probability p_{d}, 0 otherwise.
  - log θ_{t} = (1−ρ_{θ}) log ̄θ + ρ_{θ} log θ_{t−1} + σ_{θ} ϵ_{θ,t}; ϵ_{θ,t} ∼ N(0,1).
- First-order conditions (preserved forms):
  - 1 = E_{t} M_{t+1} R_{t}.
  - w_{t} = ν c_{t} (1−l_{t}).
  - q_{t} = E_{t}( M_{t+1} exp(−d_{t+1} θ_{t+1}) [ r_{t+1} + q_{t+1} (1−δ) ] ).
  - Investment condition: 1 = q_{t} [ 1 − S[ x_{t}/x_{t−1} ] − S′[ x_{t}/x_{t−1} ] x_{t}/x_{t−1} ] + E_{t} M_{t+1} q_{t+1} S′[ x_{t+1}/x_{t} ] ( x_{t+1}/x_{t} )^{2}.

### Firms and production (preserved)
- Firms maximize profits: max_{k_{i,t}, l_{i,t}} [ y_{i,t} − w_{i,t} l_{i,t} − r_{i,t} k_{i,t} ].
- Production function:
  - y_{i,t} = A_{t} ( k_{i,t}^{1−α_{g}} ̄k_{g,t}^{α_{g}} )^{α} l_{i,t}^{1−α}.
- Aggregate technology process:
  - log A_{t} = log A_{t−1} + Λ_{A} + z_{A,t} − (1−α) d_{t} θ_{t}.
  - z_{A,t} follows AR(1): log(z_{A,t}/z_{A}) = ρ_{za} log(z_{A,t−1}/z_{A}) + σ_{za} ϵ_{a,t}.
- Factor prices:
  - r_{t} = α (1−α_{g}) y_{t} / k_{t}.
  - w_{t} = (1−α) y_{t} / l_{t}.

### Government: fiscal policy, resilient capital, grants, and debt
- Public expenditure: interest on debt R_{t} b_{g,t−1}, government consumption g (constant), and investment in public capital.
- Public capital composition:
  - ̄k_{g,t} = k_{g,t} + k_{ga,t−1} (standard + resilient; perfect substitutes).
- Standard public capital law of motion:
  - k^{*}_{g,t} = (1−δ_{g}) k_{g,t} + x_{g,t}; log k_{g,t} = log k^{*}_{g,t−1} − d_{t} θ_{t}.
- Resilient public capital law of motion:
  - k_{ga,t} = (1−δ_{g}) k_{ga,t−1} + x_{ga,t}; resilient capital is not damaged by natural disasters.
- Resilient investment cost premium and donor financing:
  - Investment in resilient capital is more expensive by a factor (1 + ι).
  - Donors can finance a fraction θ ∈ [0,1] of the extra cost ι in some simulations.
- Government budget constraint:
  - b_{g,t} = R_{t−1} b_{g,t−1} + g + x_{g,t} + [1 + (1−θ) ι] x_{ga,t} − τ_{c,t} c_{t} − φ_{t}.
- Tax rule:
  - log( τ_{c,t} / τ_{c} ) = ρ_{τ} log( τ_{c,t−1} / τ_{c} ) + ρ_{τb} log( b_{t} / b ).
- Grants rule (post-disaster donors):
  - log( φ_{t} / φ ) = ρ_{φ} log( φ_{t−1} / φ ) + (1−ρ_{φ}) ρ_{φd} ( d_{t} θ_{t} / ̄d ̄θ ).
- Sovereign risk premium:
  - R_{t} = R^{e} η ( b_{g,t} / b_{g} − 1 ), with baseline η = 0.

### Market clearing and balance of payments (model closure)
- Resource constraint (equation (25)):
  - y_t = c_t + x_t + g + x_{g,t} + [1 + (1−θ)ι] x_{ga,t} + n_{x,t}.
- Balance of payments (equation (26)):
  - −(b_{g,t} − b_{g,t−1}) = n_{x,t} + φ_t − R_{t−1} b_{g,t−1}.
- These identities close the model and enforce market clearing across goods and the external sector.

### Calibration and solution method
- Calibration frequency: quarterly; calibrated to an average EMDE.
- Disaster and non-disaster-prone countries symmetric except for disaster shocks.
- Selected calibrated targets and parameters (preserved exactly):
  - Government investment to GDP: x̄_g / y = 0.0700
  - Share of standard public capital α_g = 0.2200
  - Government consumption to GDP g / y = 0.1600
  - Public debt to annual GDP b / 4y = 0.5800
  - Steady-state consumption tax rate τ_c = 0.2100
  - Net exports to GDP n_x / y = -0.1200
  - Leisure preference parameter ν = 1.6500
  - Discount factor β = 0.9830
  - Capital share α = 0.3200
  - Λ_A = 0.0035
  - κ = 12.0000
  - δ = 0.0250
  - δ_g = 0.0125
  - Ψ̂ = 0.5000
  - γ = 3.8000
  - ρ_A = 0.5000
  - σ_A = 0.0250
  - ρ_τ = 0.9000
  - ρ_θ = 0.9000
- Uncertain fiscal parameters (baseline choices):
  - ρ_{τb} = 0.2250
  - ρ_{xg} = 0.8000
- Disaster shocks calibration:
  - Disaster-prone countries:
    - p_d = 0.1620 (annual)
    - θ̄ = 0.0665 (6.65% of GDP)
    - σ_θ = 0.1270
  - Non-disaster-prone countries:
    - p_d = 0.0028 (annual)
    - θ̄ = 0.0052 (0.52% of GDP)
    - σ_θ = 0.0170
- Baseline sets η, ψ_g, ρ_{xga}, ι, φ_y, ρ_φ, ρ_{φd,θ} = 0 to shut down those channels initially.
- Solution method:
  - Taylor projection up to third order used for simulation and solution.

### Simulation protocol and welfare metric
- Simulation protocol:
  - Simulate model calibrated to a disaster-prone country for 1000 periods (250 years).
  - Discard first 100 quarters; compute averages of selected macroeconomic variables.
  - Repeat for non-disaster-prone country; compute percentage differences of disaster-prone relative to non-disaster-prone averages.
- Welfare metric (consumption equivalent loss ω):
  - V̄_NDP{ (1−ω) c_{NDP,t}, l_{NDP,t} } = V̄_DP{ c_{DP,t}, l_{DP,t} }  (equation (27)).
  - ω × 100 represents the percent permanent loss in consumption for non-disaster-prone countries to be as well off as disaster-prone ones.

### The effects of a one-off natural disaster (selected impulse responses)
- Average disaster shock: destroys 6.65% of GDP on impact (θ̄ = 0.0665).
- Responses (summary):
  - Consumption and public investment fall by about 6% on impact.
  - Private investment falls only marginally on impact and subsequently overshoots to replace lost capital.
  - Public debt to GDP increases by 3.5 percentage points on impact then gradually decreases as the tax rate increases.
  - Recovery: economy takes about three years to fully recover from an average disaster.
- Extreme disaster example (Hurricane Matthew, Haiti, 2016):
  - Shock ≈ 25% of GDP.
  - Shock is almost four times larger than the average event in disaster-prone countries.
  - Effects are much more persistent; five years after the shock GDP, consumption, public and private investment remain far from pre-disaster levels.
  - Private investment may take 15 years to return to stochastic steady state for such an extreme shock.

### Long-run effects of natural disasters (Section 5.2 simulation averages relative to non-disaster-prone countries)
- Long-run macroeconomic impacts (simulation averages relative to non-disaster-prone countries):
  - GDP growth (annual): -0.96
  - Public debt (% of annual GDP): 1.54
- Cyclical component effects (percent differences):
  - GDP: -0.29
  - Consumption: -0.89
  - Private Investment: -1.28
- Level divergence over 30 years (percent differences):
  - GDP: -37.9
  - Consumption: -39.4
  - Private Investment: -37.3
- Welfare effects (consumption-equivalent, ω×100):
  - Welfare loss: 1.59
- Interpretation:
  - Average annual GDP growth is almost 1% lower in disaster-prone countries absent policy interventions.
  - Disaster-prone countries exhibit public debt on average 1.54 percentage points of annual GDP higher.
  - After 30 years, GDP, private consumption and private investment are almost 40% lower in disaster-prone countries relative to peers.
  - Households in disaster-prone countries suffer welfare loss equivalent to a permanent reduction in consumption of 1.59%.

### Policy responses and effectiveness (ex-post grants vs ex-ante resilient investment)
- Ex-post international aid (grants) findings:
  - Simulation reaction parameter ρφd varied in [0,35] to obtain grant amounts as a % of GDP.
  - Baseline yearly grant: 0.58% of GDP (ρφd = 17.5); equals about 47 millions of US dollars every year for the average disaster-prone country (using average GDP in constant 2010 USD).
  - Welfare gains are monotonically decreasing in the persistence of grants (ρφ ∈ [0,0.50]); immediate disbursement is optimal given discounting.
  - The magnitude of the grant matters far more than timing.
  - Typical donor commitments cited (examples preserved): 41.6 millions of US dollars under their Rapid Credit Facility (RCF); 105 millions of US dollars from US government as of October 2017; IFAD announced 11 millions of US dollars in August 2018 — these are far less than what simulations indicate is needed to eliminate welfare losses.
  - Conclusion: post-disaster grants mitigate welfare losses but typical international donor commitments fall short of substantially reducing welfare losses.
- Ex-ante public investment in resilient capital:
  - Assumptions: resilient investment is 25% more expensive (ι = 0.25); ρxga = 0.80; donor financing share θ ∈ {0, 0.5, 1}.
  - Self-financing (θ = 0): welfare gains are tiny; above a resilient-capital share of 35% welfare gains decrease and eventually turn negative due to fiscal costs and required tax increases.
  - Donor-financed resilience (θ = 0.5 or θ = 1): welfare gains increase with a larger share of resilient public capital.
  - If donors finance the entire extra cost (θ = 1), disaster-prone countries may completely eliminate the welfare loss from natural disasters by reaching a share of resilient capital of about 70%.
  - Eliminating the welfare loss ex-ante under full donor financing requires a yearly grant of 1.06% of GDP, or about 87 millions of US dollars (average disaster-prone country, constant 2010 USD).
  - Comparative efficiency: to reduce welfare loss by one-fifth via ex-ante grants, reaching a 15% share of resilient capital requires about 5 millions of US dollars every year—compared to 47 millions of US dollars needed post-natural-disaster for the same welfare improvement.
  - Policy implication: donors have to disburse less than a half the resources ex-ante (to finance resilient infrastructure extra cost) than would be needed ex-post to achieve the same welfare outcome.
  - Ex-ante donor support tied to resilience investment may reduce moral hazard associated with expectations of ex-post aid.
- Overarching policy finding:
  - International aid can improve welfare in disaster-prone countries but is substantially more effective when used to finance ex-ante resilient public infrastructure than when used only for ex-post interventions.

### Appendix highlights (A–C)
- Appendix A: country distribution by annual probability of natural disaster per 1000 sq. km over 1998-2017; Table A.1 lists Fourth Quartile disaster-prone countries with Annual Probability and Damages (% of GDP) Average and Max; notation for Small states ∗ and Low-income-countries ∗∗ preserved.
- Appendix B: Table B.1 lists the 20 most damaging natural disasters (1998-2017) with Damages (% of GDP) (largest: Dominica 2017 — 260; Grenada 2004 — 148; Dominica 2015 — 90.2; Honduras 1998 — 72.9).
- Appendix C: full detrended stationary DSGE model equations (C.1–C.33) presented and used for solution and analysis (equations preserved exactly).

*Italic: Source — wpiea2019217-print-pdf (Chapter excerpts and tables from the IMF working paper PDF).*

### 3.1  Households  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   14

### 3.1  Households

### Introduction and scope
- Focus: the long-term effects of more frequent weather-related natural disasters (cyclones, tornadoes, floods) on macroeconomic outcomes and welfare of disaster-prone countries (typically small states or low-income countries, LICs).
- Modeling approach: small-open economy dynamic stochastic general equilibrium (DSGE) model embedding disaster shocks as in Gourio (2012), solved with Taylor projection (Levintal, 2018; Fernandez-Villaverde and Levintal, 2018).
- Key modeling features: stochastic disaster shocks, Epstein-Zin preferences, public investment, external debt, sovereign risk premium, resilient public infrastructure, and international aid.
- Rationale: natural disasters can be very large (shocks can be as big as 50% of GDP), invalidating linear approximations and changing the stochastic steady state.

### Main findings (macro and welfare)
- Growth and long-run outcomes:
  - Disaster-prone countries grow on average by 1 percent less a year than their non-disaster-prone peers due solely to more frequent and powerful natural disasters.
  - Climate change, assuming shifts in the disaster distributions similar to those observed in the past decade, may amplify the growth gap to 3 percent a year.
- Welfare:
  - Sizable welfare losses in disaster-prone countries: permanent loss in consumption of 1.6 percent relative to non-disaster-prone ones.
  - Climate change scenario: welfare losses about seven times larger than baseline disaster-prone outcomes.
- Public debt and fiscal outcomes:
  - On average, disaster-prone countries have a public debt 1.54 percentage points of GDP higher than non-disaster-prone countries.
  - Under a climate change scenario this difference increases to 11 percent of GDP.
- Transmission channels:
  - Destruction of private and public capital (modeled as a permanent one-off depreciation of existing capital).
  - Temporary decline in productivity following disasters.
  - Lower output leads to lower government revenues and higher public debt.

### Disaster-prone country statistics and stylized facts (EM-DAT; sample 1998-2017)
- Sample: 129 low- and middle-income economies (per capita GNI below $12,055 in 2017); dataset covers 1998-2017 and uses EM-DAT for droughts, extreme temperatures, floods, fog, landslides, storms and wildfires.
- Definition: disaster-prone countries = top 25% of the distribution of annual probability of experiencing a natural disaster per 1000 squared kilometers; non-disaster-prone = remaining 75%.
- Event counts: sample includes 2516 events (393 in disaster-prone countries, 2123 in non-disaster-prone countries).
- Distributions (textual highlights):
  - In 97% of non-disaster-prone countries the annual probability of a natural disaster is below 1 percent; remaining 3% between 1% and 2% (highest non-disaster-prone = 1.29%).
  - In disaster-prone countries: none have annual probability below 1%; 29% face 1%-2%; 26% face 2%-5%; 36% face 5%-60%; 9% have annual probability between 80% and 100%.
  - Damages (% of GDP): 88% of natural disasters in non-disaster-prone countries destroy less than 1% of GDP and all events in that group cause damages not exceeding 15% of GDP. In disaster-prone countries: 23% of events have losses between 1% and 5% of GDP; 12% of events have losses above 5% of GDP.
- Table 1 (Average Annual Probabilities of Natural Disasters per 1000 Squared Kilometers (%).) — preserved exactly as presented:
  - Full sampleSubsamples
    1998-20171998-2007  2008-2017
    Disaster-prone countries16.213.818.7
    Non-disaster-prone countries0.280.290.27
- Table 2 (Damages to GDP from Natural Disasters (%).) — preserved exactly as presented:
  - Full sampleSubsamples
    1998-20171998-20072008-2017
    Average MaxAverage MaxAverage Max
    Disaster-prone countries6.65    2604.70    1488.58    260
    Non-disaster-prone countries   0.52   72.90.63   72.90.41   12.6

### Policy responses and effectiveness
- Two policy channels studied:
  - Ex-post international aid: grants disbursed in the aftermath of natural disasters.
  - Ex-ante public investment in resilient capital: a fraction of public infrastructure is assumed not to be damaged by natural disasters but entails an additional fiscal cost that can be financed in part or in full by donors.
- Key policy conclusions:
  - Disaster-prone countries can only mildly improve welfare by self-financing investment in resilient capital.
  - International aid is crucial to improve welfare outcomes but needs to exceed historically observed amounts to be effective.
  - Aid is more effective when it finances ex-ante investment in resilient public infrastructure rather than only ex-post disaster relief: to eliminate welfare losses via grants that finance the extra cost of resilient infrastructure, donors would have to disburse less than half the amount required to finance post-disaster intervention.

_Italic: Source — wpiea2019217-print-pdf (Chapter excerpts and tables from the IMF working paper PDF)._

### Appendix A for the complete distribution. EM-DAT provides damages in US dollars. Damages in percent of

### wpiea2019217-print-pdf - Appendix A for the complete distribution. EM-DAT provides damages in US dollars. Damages in percent of

### Distributional findings on disaster damages
- Damages in percent of GDP are obtained dividing damages by GDP of the year of the event; distributions of damages (% of GDP) are computed for each country group using data for each single event over the sample 1998-2017 and over the two subsamples.
- Average and maximum damages (% of GDP) are computed for each country group by using data for each single event over the sample 1998-2017 and over the two subsamples.
- The most damaging events in disaster-prone countries:
  - Hurricane Ivan destroyed 148% of Grenada’s GDP in 2004.
  - Hurricane Maria caused damages of the order of 260% of GDP in Dominica in 2017.
- The most damaging events in non-disaster-prone countries:
  - Hurricane Mitch caused damages of the order of 73% of GDP in Honduras in 1998.
  - Cyclone Nargis destroyed 12.6% of GDP in Myanmar in 2008.
- Over time: average damages to GDP in disaster-prone countries became larger in the last decade (2008-2017) relative to the first decade of the sample (1998-2007), while in non-disaster-prone countries the average damages to GDP slightly fell.
- A noted trend: 19% in the more recent past ten years, increasing the divergence between the two country groups. (text presence preserved exactly as in source)

### Country-group composition and small economies
- Definition and classification (preserved from source):
  - Disaster-prone countries are those with an annual probability of a natural disaster in the top 25% of the distribution (annual probability per 1000 squared kilometers over 1998-2017).
  - Non-disaster-prone countries comprise the remaining 75% of countries.
  - Small economies comprise small states and low-income countries.
  - Small states are countries with a population below 1.5 million that are not advanced economies or high-income oil exporting countries (IMF).
  - Low-income-countries are those with a GNI per capita below $995 in 2017 (World Bank).
- Shares:
  - 74% of disaster-prone countries are small economies.
  - 66% of non-disaster-prone countries fall in the non-small economies definition.
- Mechanism: Small surface area, small population, or low-income status implies that large and/or frequent disasters affect a large share of GDP in many disaster-prone countries.

### Damage by disaster type
- Focused on three most frequent and powerful disasters: droughts, floods and storms.
- For storms:
  - In disaster-prone countries, storms destroy 12 percent of GDP on average.
  - In non-disaster-prone countries, storms destroy 1 percent of GDP on average.
- Stylized facts highlighted:
  - Disaster-prone developing countries are more exposed and incur overwhelmingly larger losses per disaster as a fraction of GDP than non-disaster-prone peers.
  - Effects of climate change have likely been more pronounced in disaster-prone countries, which have recently experienced higher frequencies and magnitudes of climate-related events.
  - The lion’s share of damages are caused by storms; many disaster-prone countries are located in tropical areas.

### Research question and motivation
- The evidence motivates the research question on whether differences in the disaster distributions alone have (and will likely have) a significant weight on the growth path and welfare of disaster-prone countries relative to the rest of their peers.
- The stark difference in damages to GDP is largely explained by the size of the economy: smaller economies (by geography or development) suffer larger GDP shares lost.

### Model overview (single-good small-open-economy RBC with disasters)
- Baseline model: single-good small-open-economy real-business-cycle (RBC) model augmented with:
  - investment adjustment costs,
  - stochastic trend growth,
  - disaster shocks as in Gourio (2012) and Fernandez-Villaverde and Levintal (2018).
- Key augmentations (four dimensions) to capture transmission channels and policies important for disaster-prone countries:
  1. Detailed public sector: government invests in public infrastructure, finances expenditures via a consumption tax, and accumulates debt; reconstruction of public capital after disasters entails fiscal cost borne by households through higher consumption taxes.
  2. Small-open-economy dimension: allows accumulation of external government debt and captures higher sovereign risk premium faced by countries hit by natural disasters.
  3. Government can invest in resilient public infrastructure to dampen effects of natural disasters.
  4. Grants from abroad can be injected to alleviate fiscal burden post-disaster or to finance resilient public investment.
- Limitation noted: model has only one sector and does not explicitly include agriculture; it does not capture damages to crops due to droughts or storms.

### Households (key structure and equations preserved)
- Preferences: recursive (Epstein-Zin) preferences:
  - V_{t}^{1−ψ} = U_{t}^{1−ψ} + β E_{t}(V_{t+1}^{1−γ})^{(1−ψ)/(1−γ)}, with U_{t} = c_{t} (1−l_{t})^{ν}.
- Budget constraint (real terms):
  - (1 + τ_{t}) c_{t} + x_{t} + b_{t+1} = w_{t} l_{t} + r_{t} k_{t} + R_{t−1} b_{t} + F_{t} + T_{t}.
- Investment adjustment cost:
  - S[x_{t}/x_{t−1}] = κ/2 (x_{t}/x_{t−1} ˆz_{t} − ˆz)^{2}.
- Law of motion of private capital:
  - k^{*}_{t} = (1−δ) k_{t} + (1 − S[ x_{t}/x_{t−1} ]) x_{t}.
  - log k_{t} = log k^{*}_{t−1} − d_{t} θ_{t}.
- Disaster process:
  - d_{t} is i.i.d. binary: d_{t} = 1 with probability p_{d} (disaster), 0 otherwise.
  - log θ_{t} = (1−ρ_{θ}) log ̄θ + ρ_{θ} log θ_{t−1} + σ_{θ} ϵ_{θ,t}; ϵ_{θ,t} ∼ N(0,1).
- First-order conditions (preserved forms):
  - 1 = E_{t} M_{t+1} R_{t}.
  - w_{t} = ν c_{t} (1−l_{t}).
  - q_{t} = E_{t}( M_{t+1} exp(−d_{t+1} θ_{t+1}) [ r_{t+1} + q_{t+1} (1−δ) ] ).
  - Investment condition: 1 = q_{t} [ 1 − S[ x_{t}/x_{t−1} ] − S′[ x_{t}/x_{t−1} ] x_{t}/x_{t−1} ] + E_{t} M_{t+1} q_{t+1} S′[ x_{t+1}/x_{t} ] ( x_{t+1}/x_{t} )^{2}.

### Firms (production and disaster effects)
- Continuum of firms i ∈ (0,1) maximize profits: max_{k_{i,t}, l_{i,t}} [ y_{i,t} − w_{i,t} l_{i,t} − r_{i,t} k_{i,t} ].
- Production function (Cobb-Douglas) with public capital:
  - y_{i,t} = A_{t} ( k_{i,t}^{1−α_{g}} ̄k_{g,t}^{α_{g}} )^{α} l_{i,t}^{1−α}.
- Aggregate technology process:
  - log A_{t} = log A_{t−1} + Λ_{A} + z_{A,t} − (1−α) d_{t} θ_{t}.
  - z_{A,t} follows AR(1): log(z_{A,t}/z_{A}) = ρ_{za} log(z_{A,t−1}/z_{A}) + σ_{za} ϵ_{a,t}.
- Factor prices equal marginal products:
  - r_{t} = α (1−α_{g}) y_{t} / k_{t}.
  - w_{t} = (1−α) y_{t} / l_{t}.

### Government (fiscal policy, resilient capital, grants, and debt)
- Public expenditure allocation: interest on debt R_{t} b_{g,t−1}, government consumption g (assumed constant), and investment in public capital.
- Public capital composition:
  - Total public capital ̄k_{g,t} = k_{g,t} + k_{ga,t−1} (standard + resilient; perfect substitutes).
- Standard public capital law of motion:
  - k^{*}_{g,t} = (1−δ_{g}) k_{g,t} + x_{g,t}; log k_{g,t} = log k^{*}_{g,t−1} − d_{t} θ_{t}.
- Resilient public capital law of motion:
  - k_{ga,t} = (1−δ_{g}) k_{ga,t−1} + x_{ga,t}; resilient capital is not damaged by natural disasters.
- Public investment rules:
  - log( x_{j,t} / x_{j} ) = −ρ_{xj} log( k_{j,t} / k_{j} ), for j = g, ga.
- Resilient investment cost premium and donor financing:
  - Investment in resilient capital is more expensive by a factor (1 + ι).
  - Donors can finance a fraction θ ∈ [0,1] of the extra cost ι in some simulations.
- Government budget constraint:
  - b_{g,t} = R_{t−1} b_{g,t−1} + g + x_{g,t} + [1 + (1−θ) ι] x_{ga,t} − τ_{c,t} c_{t} − φ_{t}.
- Tax rule (consumption tax):
  - log( τ_{c,t} / τ_{c} ) = ρ_{τ} log( τ_{c,t−1} / τ_{c} ) + ρ_{τb} log( b_{t} / b ).
- Grants rule (post-disaster donors):
  - log( φ_{t} / φ ) = ρ_{φ} log( φ_{t−1} / φ ) + (1−ρ_{φ}) ρ_{φd} ( d_{t} θ_{t} / ̄d ̄θ ).
- Sovereign risk premium and interest rate on public debt:
  - R_{t} = R^{e} η ( b_{g,t} / b_{g} − 1 ), where η governs elasticity of interest rate on public debt; baseline assumes η = 0 (constant interest rate).
- Discussed mechanism: higher interest rates (if η > 0) following disasters worsen fiscal position, potentially creating a vicious cycle for disaster-prone countries.

*Italic source attribution preserved from the provided content.*

### 3.4  Market Clearing and the Balance of Payments

### 3.4  Market Clearing and the Balance of Payments

### Market clearing and model closure
- In equilibrium all markets clear and the model is closed by the following identities:
  - y_t = c_t + x_t + g + x_{g,t} + [1 + (1−θ)ι] x_{ga,t} + n_{x,t}  (equation (25)) — resource constraint including net exports, n_{x,t}.
  - −(b_{g,t} − b_{g,t−1}) = n_{x,t} + φ_t − R_{t−1} b_{g,t−1}  (equation (26)) — balance of payments linking external public debt and net exports.

### Interpretation
- Equation (25) is the resource constraint; it explicitly features net exports, n_{x,t}.
- Equation (26) is the balance of payments and defines the link between external public debt and the country’s net exports.

### Note
- These identities close the model and enforce market clearing across goods and the external sector.

---

### Calibration and Solution Method

### Calibration overview
- Model calibrated to an average country in the group of EMDEs at a quarterly frequency.
- Disaster and non-disaster-prone countries assumed perfectly symmetric except for calibration of natural disaster shocks.
- Table 3 reports baseline parameter values.

### Parameters matched to data (1998-2017 averages across EMDEs)
- Government investment to GDP: x̄_g / y = 0.0700
- Share of standard public capital α_g = 0.2200
- Government consumption to GDP g / y = 0.1600
- Public debt to annual GDP b / 4y = 0.5800
- Steady-state consumption tax rate τ_c = 0.2100
- Net exports to GDP n_x / y = -0.1200
- Calibration targets:
  - Public investment to GDP calibrated at 7%.
  - Steady-state ratio of private investment to GDP targeted at 16%.
  - Government consumption and stock of public debt calibrated to observed ratios to GDP of 16% and 58% respectively.
  - Tax rate set so tax revenue equals observed 15% of GDP.
  - Net exports set to achieve −12% of GDP (trade deficit on average).

### Parameters taken from the literature (baseline values)
- Leisure preference parameter ν = 1.6500 (agents work 1/3 of time)
- Discount factor β = 0.9830 (steady-state annual (net) interest rate of 8.52% or 2.13% quarterly)
- Capital share of income α = 0.3200
- Total factor productivity trend growth rate Λ_A = 0.0035
- Investment adjustment costs κ = 12.0000
- Private capital depreciation rate δ = 0.0250
- Public capital depreciation rate δ_g = 0.0125
- Inverse intertemporal elasticity of substitution Ψ̂ = 0.5000
- Risk aversion γ = 3.8000
- Persistence of total factor productivity ρ_A = 0.5000
- Standard deviation of total factor productivity shocks σ_A = 0.0250
- Persistence of tax rate ρ_τ = 0.9000
- Persistence of disaster risk shocks ρ_θ = 0.9000

### Uncertain fiscal parameters (baseline choices and rationale)
- Tax rate responsiveness to public debt ρ_{τb} = 0.2250
  - Chosen as approximately the minimum value guaranteeing stability across exercises.
  - Robustness checks performed in Section 5.5 (not reproduced here).
- Standard public investment responsiveness ρ_{xg} = 0.8000
  - Set assuming less than one-to-one reconstruction within the quarter; robustness checked later.

### Disaster shocks calibration
- Disaster-prone countries:
  - Annual disaster probability p_d = 0.1620
  - Mean disaster size θ̄ = 0.0665 (6.65% of GDP)
  - Standard deviation of disaster risk shocks σ_θ = 0.1270 (matches quarterly dispersion of damages to GDP of 28%)
- Non-disaster-prone countries:
  - Annual disaster probability p_d = 0.0028
  - Mean disaster size θ̄ = 0.0052 (0.52% of GDP)
  - Standard deviation of disaster risk shocks σ_θ = 0.0170 (quarterly dispersion of damages to GDP of 3.5%)

### Parameters related to additional channels and policies (baseline)
- Sovereign risk premium, resilient capital, and international aid parameters (η, ψ_g, ρ_{xga}, ι, φ_y, ρ_φ, ρ_{φd,θ}) are set to zero in the baseline, effectively shutting down these channels; they are introduced one at a time in later exercises.

### Solution method
- Model simulated using Taylor projection (Levintal, 2018; Fernandez-Villaverde and Levintal, 2018).
  - Taylor projection up to third order used.
  - Shown to be more accurate and faster than perturbation up to fifth order and projection (Smolyak collocation) up to third order for DSGE models with rare disasters.
  - Combines projection methods with Taylor expansions, allowing accurate approximation at many points of the state-space and handling large nonlinearities.
  - Particularly suitable for studying natural disasters within a DSGE model.

---

### The Macroeconomic Effects of Natural Disasters and Climate Change: Methodology and Welfare Metric

### Simulation protocol for long-run stochastic outcomes
- Simulate the model calibrated to a disaster-prone country for 1000 periods (250 years).
- Discard first 100 quarters; compute averages of selected macroeconomic variables.
- Repeat for a non-disaster-prone country; compute percentage differences of disaster-prone relative to non-disaster-prone averages.

### Welfare metric: consumption equivalent loss
- Let V̄_NDP and V̄_DP be average welfare in non-disaster-prone and disaster-prone countries respectively.
- Welfare loss ω is defined implicitly by:
  - V̄_NDP{ (1−ω) c_{NDP,t}, l_{NDP,t} } = V̄_DP{ c_{DP,t}, l_{DP,t} }  (equation (27))
  - ω × 100 represents the percent permanent loss in consumption that should occur in non-disaster-prone countries for their households to be as well off as in disaster-prone countries.
- This metric is standard in optimal monetary and fiscal policy literature and comparable to other disaster-related welfare metrics.

---

### The Effects of a One-Off Natural Disaster (Selected Findings)

### Impulse response overview (one-off average disaster in a disaster-prone country)
- Shock: natural disaster that destroys 6.65% of GDP on impact (θ̄ = 0.0665).
- Responses reported in percent deviations from stochastic steady state (trend included), except tax rate and public debt to annual GDP which are absolute percentage changes.
- Key responses:
  - Consumption and public investment fall by about 6% on impact.
  - Private investment falls only marginally on impact and subsequently overshoots to replace lost capital, driving recovery.
  - Public debt to GDP increases by 3.5 percentage points on impact and then gradually decreases as the tax rate increases.
- Recovery dynamics:
  - Persistent effects: economy takes about three years to fully recover from an average disaster.
  - Note: this exercise considers a one-off event of average intensity; frequent shocks can prevent full recovery and cause cumulative long-run damage (see Subsection 5.2 for stochastic sequences).

### Large (extreme) disaster scenario: Hurricane Matthew intensity (Haiti, 2016)
- Hurricane Matthew example: damages of 25% of GDP in Haiti (shock ≈ 25% of GDP).
- Comparative impulse responses:
  - Shock of Hurricane Matthew intensity is almost four times larger than the average event in disaster-prone countries.
  - Effects are remarkably larger and much more persistent than average disaster.
  - Five years after the shock, GDP, consumption, public and private investment remain far from pre-disaster levels.
  - Simulations (not shown) imply private investment takes 15 years to return to the stochastic steady state for such an extreme shock.
- Implication:
  - Non-linear solution method (Taylor projection) captures how shock intensity increases persistence of macroeconomic effects — an aspect linearized models would miss.

### Fiscal reaction and debt sustainability
- Increase in the tax rate following disasters is necessary in the model to prevent public debt from exploding and to ensure model stability.
- Absent tax increases, expenditure cuts, or international aid, sovereign debt sustainability challenges may arise.

---

*Source: wpiea2019217-print-pdf - 3.4  Market Clearing and the Balance of Payments*

### 5.2  The Long-Run Effects of Natural Disasters

### 5.2 The Long-Run Effects of Natural Disasters

### Long-run macroeconomic impacts (simulation averages relative to non-disaster-prone countries)
- GDP growth (annual): -0.96
- Public debt (% of annual GDP): 1.54

### Cyclical component effects (percent differences)
- GDP: -0.29
- Consumption: -0.89
- Private Investment: -1.28

### Level divergence over 30 years (percent differences)
- GDP: -37.9
- Consumption: -39.4
- Private Investment: -37.3

### Welfare effects (consumption-equivalent, ω×100)
- Welfare loss: 1.59

### Key interpretative points from the simulation
- Results indicate large and permanent effects: average annual GDP growth is almost 1% lower in disaster-prone countries absent policy interventions or other compensatory mechanisms.
- Disaster-prone countries exhibit a public debt level on average 1.54 percentage points of annual GDP higher than non-disaster-prone countries.
- Cyclical losses average 0.29% for GDP, 0.89% for private consumption, and 1.28% for private investment.
- After 30 years, GDP, private consumption and private investment are almost 40% lower in disaster-prone countries relative to non-disaster-prone peers.
- Households in disaster-prone countries suffer a welfare loss equivalent to a permanent reduction in consumption of 1.59%. This is smaller than some rare-disaster calibrations (e.g., Barro (2009) 8-9%) because the baseline here assumes more frequent but smaller average damages (16.2% disaster probability with 6.65% average damage vs Barro’s 1.7% probability with 26% damage).

*Source: wpiea2019217-print-pdf - 5.2  The Long-Run Effects of Natural Disasters*

### 41.6 millions of US dollars under their Rapid Credit Facility (RCF, link here) to sustain the

### wpiea2019217-print-pdf - 41.6 millions of US dollars under their Rapid Credit Facility (RCF, link here) to sustain the

### Welfare effects of post-disaster grants in disaster-prone countries
- Simulation setup compares ex-ante versus ex-post interventions; reaction parameter ρφd varied in [0,35] to obtain grant amounts as a % of GDP.
- A yearly grant of 0.58% of GDP (ρφd = 17.5) is used as a baseline case to study disbursement dynamics; this equals about 47 millions of US dollars every year for the average disaster-prone country (using average GDP in constant 2010 USD).
- Welfare metric: consumption-equivalent welfare losses and welfare gains computed as percentage differences relative to baseline simulation losses.
- Key findings from Figure 6 dynamics:
  - Welfare gains are monotonically decreasing in the persistence of grants (persistence parameter ρφ ∈ [0,0.50]).
  - Given discounting, immediately disbursing the entire grant is optimal versus spreading it over time.
  - The magnitude of the grant is far more important than the timing: reductions in welfare losses from increasing grant amounts are at least an order of magnitude larger than gains from changing disbursement dynamics.
- Empirical comparison:
  - Typical donor commitments (examples cited: 41.6 millions of US dollars under RCF; 105 millions of US dollars from US government as of October 2017; IFAD announced 11 millions of US dollars in August 2018) are far less than what simulations indicate is needed to eliminate welfare losses.
- Conclusion for ex-post grants:
  - Post-disaster grants mitigate welfare losses but typical international donor commitments fall short of substantially reducing welfare losses.

### Ex-ante public investment in resilient capital
- Assumptions:
  - Investment in resilient capital is 25% more expensive than investment in standard public capital (ι = 0.25).
  - Government reaction to deviations in resilient capital stock set equal to that for standard public capital: ρxga = 0.80.
  - Donor financing of the extra cost of resilience parameterized by θ ∈ {0, 0.5, 1}.
- Self-financing (θ = 0):
  - Welfare gains from investing in resilience are tiny when disaster-prone countries fully bear the extra cost.
  - Above a share of resilient capital in total public capital stock of 35%, welfare gains start decreasing and eventually turn negative due to higher government expenditure and required tax increases to stabilize public debt.
- Donor-financed resilience (θ = 0.5 or θ = 1):
  - If donors finance half or all of the extra cost, welfare gains increase with a larger share of resilient public capital.
  - If donors finance the entire extra cost (θ = 1), disaster-prone countries may completely eliminate the welfare loss from natural disasters by reaching a share of resilient capital of about 70%.
  - Eliminating the welfare loss ex-ante under full donor financing requires a yearly grant of 1.06% of GDP, or about 87 millions of US dollars (average disaster-prone country, constant 2010 USD).
- Comparison ex-ante vs ex-post effectiveness:
  - To reduce welfare loss by one-fifth via ex-ante grants, reaching a 15% share of resilient capital requires about 5 millions of US dollars every year—compared to 47 millions of US dollars needed post-natural-disaster for the same welfare improvement.
  - Relative efficiency: donors have to disburse less than a half the resources ex-ante (to finance resilient infrastructure extra cost) compared to resources required for post-disaster intervention to achieve the same welfare outcome.
- Policy implications:
  - Disaster-prone countries alone cannot significantly improve welfare by self-financing resilient capital; international aid is crucial.
  - International aid is more effective when financing ex-ante investment in resilient public infrastructure rather than only ex-post disaster relief.
  - Ex-ante donor support tied to resilience investment may reduce moral hazard associated with expectations of ex-post aid.

### Aggregate macroeconomic and welfare conclusions
- Model and method: DSGE model augmented with natural disaster shocks, solved using Taylor projection.
- Long-run growth and fiscal impacts:
  - Disaster-prone countries grow on average by 1 percent less a year than their non-disaster-prone peers due to more frequent and powerful natural disasters.
  - On average, disaster-prone countries have public debt 1.54 percentage points of GDP higher than non-disaster-prone countries.
  - Disaster-prone countries suffer a permanent reduction in consumption of 1.6 percent relative to non-disaster-prone ones.
- Climate change amplification:
  - Climate change may make the gap in GDP growth three times larger.
  - Public debt and welfare losses may be increased by a factor of nine and seven, respectively, under continued increases in magnitude and frequency of natural disasters.
- Overarching policy finding:
  - International aid can improve welfare in disaster-prone countries but is substantially more effective when used to finance ex-ante resilient public infrastructure than when used only for ex-post interventions. Donors need to disburse less than half the resources ex-ante (targeted to resilience) than would be needed ex-post to achieve equivalent welfare reductions.

*Source: wpiea2019217-print-pdf - 41.6 millions of US dollars under their Rapid Credit Facility (RCF, link here) to sustain the (IMF working paper content provided).*

### Appendix A shows the distribution of EMDEs according to the annual probability of

### wpiea2019217-print-pdf - Appendix A shows the distribution of EMDEs according to the annual probability of

### Appendix A — Country Distribution and Statistics on Natural Disasters
- Appendix A shows the distribution of EMDEs according to the annual probability of experiencing a natural disaster.
- Countries are ordered by the annual probability of a natural disaster per 1000 squared kilometers over the sample 1998-2017.
- EM-DAT provides damages in US dollars. Damages in percent of GDP are obtained dividing damages by GDP of the year of the event. Damages (% of GDP) are computed for each country by using data for each single event over the sample 1998-2017.
- Small economies comprise small states and low-income countries.
- Notation in tables:
  - "Small states" denoted by ∗: countries with a population below 1.5 million that are not advanced economies or high-income oil exporting countries (IMF).
  - "Low-income-countries" denoted by ∗∗: countries with a GNI per capita below $995 in 2017 (World Bank).

- Table A.1: Disaster-Prone Countries: Fourth Quartile (75%-100%) of the Annual Probability Distribution of Natural Disasters. (Countries ordered by annual probability per 1000 sq. km; Damages (% of GDP) reported as Average and Max; "Small economy" indicated)
  - Marshall Islands — Annual Probability per 1000 sq. km: 100.00; Damages (% of GDP) Average: 2.72; Max: 2.72; Small economy: Yes ∗
  - St. Vincent and the Grenadines — 100.00; Average: 4.57; Max: 15.0; Yes ∗
  - Tuvalu — 100.00; Average: N.A.; Max: N.A.; Yes ∗
  - Micronesia, Fed. Sts. — 50.00; Average: 1.85; Max: 3.49; Yes ∗
  - St. Lucia — 48.39; Average: 1.07; Max: 3.13; Yes ∗
  - Tonga — 46.67; Average: 12.22; Max: 29.0; Yes ∗
  - Grenada — 44.12; Average: 74.8; Max: 148; Yes ∗
  - Dominica — 33.33; Average: 1182; Max: 260; Yes ∗
  - Kiribati — 24.69; Average: N.A.; Max: N.A.; Yes ∗
  - Maldives — 16.67; Average: N.A.; Max: N.A.; Yes ∗
  - Comoros — 10.75; Average: 0.84; Max: 0.84; Yes ∗
  - Mauritius — 9.80; Average: 1.69; Max: 4.03; Yes ∗
  - Samoa — 8.80; Average: 8.58; Max: 16.6; Yes ∗
  - Jamaica — 5.91; Average: 1.41; Max: 8.82; No
  - Gambia — 5.31; Average: N.A.; Max: N.A.; Yes ∗∗
  - Cabo Verde — 4.96; Average: 0.07; Max: 0.07; Yes ∗
  - Fiji — 4.11; Average: 1.70; Max: 12.9; Yes ∗
  - Vanuatu — 4.10; Average: 30.26; Max: 0.1; Yes ∗
  - Haiti — 3.60; Average: 3.69; Max: 25.1; Yes ∗∗
  - El Salvador — 3.33; Average: 1.87; Max: 5.33; No
  - Macedonia, FYR — 2.72; Average: 0.44; Max: 0.86; No
  - Burundi — 2.69; Average: 0.24; Max: 0.42; Yes ∗∗
  - Rwanda — 2.47; Average: 0.00; Max: 0.00; Yes ∗∗
  - Swaziland — 2.30; Average: 0.00; Max: 0.00; Yes ∗
  - Belize — 1.96; Average: 12.83; Max: 3.4; Yes ∗
  - Lebanon — 1.91; Average: N.A.; Max: N.A.; No
  - Montenegro — 1.81; Average: N.A.; Max: N.A.; Yes ∗
  - Dominican Republic — 1.75; Average: 1.03; Max: 9.14; No
  - Albania — 1.74; Average: 0.16; Max: 0.39; No
  - Solomon Islands — 1.73; Average: 0.80; Max: 2.04; Yes ∗
  - Timor-Leste — 1.68; Average: N.A.; Max: N.A.; Yes ∗
  - Costa Rica — 1.57; Average: 0.21; Max: 0.67; No
  - Sri Lanka — 1.52; Average: 0.24; Max: 1.47; No
  - Moldova — 1.33; Average: 2.47; Max: 9.22; No

- Table A.2: Non-Disaster-Prone Countries: Third Quartile (50%-75%)
  - Djibouti — 1.29; N.A.; N.A.; Yes ∗
  - Bosnia and Herzegovina — 1.17; Average: 1.85; Max: 2.87; No
  - Lesotho — 1.15; N.A.; N.A.; No
  - Guinea-Bissau — 0.97; N.A.; N.A.; Yes ∗∗
  - Armenia — 0.84; Average: 1.93; Max: 5.23; No
  - Guatemala — 0.83; Average: 0.97; Max: 3.86; No
  - Honduras — 0.80; Average: 7.64; Max: 72.9; No
  - Cuba — 0.73; Average: 2.64; Max: 7.77; No
  - Malawi — 0.72; Average: 1.64; Max: 6.12; Yes ∗∗
  - Georgia — 0.72; Average: 1.47; Max: 6.54; No
  - Togo — 0.70; N.A.; N.A.; Yes ∗∗
  - Tajikistan — 0.70; Average: 2.44; Max: 16.3; Yes ∗∗
  - Sierra Leone — 0.69; Average: 0.79; Max: 0.79; Yes ∗∗
  - Nicaragua — 0.69; Average: 3.56; Max: 21.3; No
  - Nepal — 0.68; Average: 0.34; Max: 2.43; Yes ∗∗
  - Bangladesh — 0.67; Average: 1.30; Max: 8.60; No
  - Korea, Dem. People’s Rep. — 0.66; N.A.; N.A.; Yes ∗∗
  - Bulgaria — 0.59; Average: 0.37; Max: 1.54; No
  - Bhutan — 0.52; Average: 0.87; Max: 0.87; Yes ∗
  - Serbia — 0.45; Average: 2.45; Max: 4.63; No
  - Cambodia — 0.44; Average: 1.36; Max: 4.35; No
  - Senegal — 0.41; Average: 0.46; Max: 0.84; Yes ∗∗
  - Romania — 0.40; Average: 0.45; Max: 1.34; No
  - Benin — 0.39; Average: 0.01; Max: 0.01; Yes ∗∗
  - Uganda — 0.35; Average: 0.01; Max: 0.02; Yes ∗∗
  - Philippines — 0.33; Average: 0.21; Max: 3.73; No
  - Vietnam — 0.30; Average: 0.44; Max: 3.49; No
  - Burkina Faso — 0.29; Average: 0.70; Max: 1.79; Yes ∗∗
  - Azerbaijan — 0.29; Average: 1.33; Max: 0.90; No
  - Malaysia — 0.27; Average: 0.08; Max: 0.50; No

- Table A.3: Non-Disaster-Prone Countries: Second Quartile (25%-50%)
  - Liberia — 0.27; N.A.; N.A.; Yes ∗∗
  - Guinea — 0.26; N.A.; N.A.; Yes ∗∗
  - Ecuador — 0.25; Average: 0.34; Max: 1.62; No
  - Lao PDR — 0.25; Average: 0.57; Max: 1.71; No
  - Ghana — 0.25; Average: 0.15; Max: 0.27; No
  - Congo, Dem. Rep. — 0.23; Average: 0.04; Max: 0.04; Yes ∗∗
  - Paraguay — 0.20; Average: 0.06; Max: 0.22; No
  - Belarus — 0.19; Average: 0.10; Max: 0.24; No
  - Syrian Arab Republic — 0.19; N.A.; N.A.; Yes ∗∗
  - Thailand — 0.19; Average: 0.56; Max: 10.9; No
  - Kenya — 0.17; Average: 0.07; Max: 0.20; No
  - Eritrea — 0.17; N.A.; N.A.; Yes ∗∗
  - Jordan — 0.17; N.A.; N.A.; No
  - Morocco — 0.16; Average: 0.42; Max: 2.16; No
  - Zimbabwe — 0.15; Average: 1.30; Max: 3.49; Yes ∗∗
  - Madagascar — 0.15; Average: 1.32; Max: 5.73; Yes ∗∗
  - Afghanistan — 0.15; Average: 0.18; Max: 0.79; Yes ∗∗
  - Papua New Guinea — 0.15; Average: 0.55; Max: 1.24; No
  - Guyana — 0.14; Average: 15.93; Max: 35.5; Yes ∗
  - Cameroon — 0.14; Average: 0.01; Max: 0.01; No
  - Somalia — 0.13; Average: 0.03; Max: 0.03; Yes ∗∗
  - Central African Republic — 0.13; N.A.; N.A.; Yes ∗∗
  - Myanmar — 0.13; Average: 1.84; Max: 12.6; No
  - Pakistan — 0.13; Average: 0.60; Max: 5.35; No
  - Cote d’Ivoire — 0.12; N.A.; N.A.; No
  - Tunisia — 0.12; N.A.; N.A.; No
  - Ukraine — 0.12; Average: 0.23; Max: 0.96; No
  - Mozambique — 0.11; Average: 1.30; Max: 8.38; Yes ∗∗
  - Turkey — 0.11; Average: 0.09; Max: 0.36; No
  - Nigeria — 0.10; Average: 0.02; Max: 0.11; No
  - Iraq — 0.10; Average: 0.00; Max: 0.00; No

- Table A.4: Non-Disaster-Prone Countries: First Quartile (0%-25%)
  - Namibia — 0.10; Average: 0.25; Max: 0.51; No
  - Colombia — 0.09; Average: 0.11; Max: 0.69; No
  - Bolivia — 0.09; Average: 1.01; Max: 4.50; No
  - Zambia — 0.09; Average: 0.59; Max: 0.59; No
  - Tanzania — 0.08; Average: 0.00; Max: 0.00; Yes ∗∗
  - South Africa — 0.08; Average: 0.06; Max: 0.17; No
  - Ethiopia — 0.08; Average: 0.41; Max: 2.17; Yes ∗∗
  - Venezuela, RB — 0.08; Average: 0.66; Max: 3.22; No
  - Niger — 0.07; Average: 0.91; Max: 2.65; Yes ∗∗
  - Peru — 0.07; Average: 0.52; Max: 1.51; No
  - Angola — 0.07; Average: 0.06; Max: 0.11; No
  - Mali — 0.06; N.A.; N.A.; Yes ∗∗
  - Suriname — 0.06; N.A.; N.A.; Yes ∗
  - Botswana — 0.06; Average: 0.20; Max: 0.30; No
  - Mauritania — 0.06; Average: 0.03; Max: 0.03; No
  - Gabon — 0.06; N.A.; N.A.; No
  - Indonesia — 0.05; Average: 0.09; Max: 1.36; No
  - Mexico — 0.05; Average: 0.11; Max: 0.90; No
  - Iran, Islamic Rep. — 0.05; Average: 0.27; Max: 2.90; No
  - Chad — 0.04; Average: 0.07; Max: 0.08; Yes ∗∗
  - Sudan — 0.04; Average: 0.42; Max: 1.04; Yes ∗∗
  - Uzbekistan — 0.03; Average: 0.36; Max: 0.36; No
  - Algeria — 0.03; Average: 0.17; Max: 0.55; No
  - India — 0.03; Average: 0.15; Max: 0.81; No
  - Egypt, Arab Rep. — 0.03; Average: 0.02; Max: 0.03; No
  - Mongolia — 0.03; Average: 2.10; Max: 7.04; No
  - Kazakhstan — 0.02; Average: 0.03; Max: 0.10; No
  - Congo, Rep. — 0.01; Average: 0.00; Max: 0.00; No
  - Brazil — 0.01; Average: 0.03; Max: 0.25; No
  - China — 0.01; Average: 0.16; Max: 3.08; No
  - Russian Federation — 0.01; Average: 0.04; Max: 0.29; No
  - Libya — 0.00; N.A.; N.A.; No

### Appendix B — The Most Damaging Natural Disasters
- Appendix B reports information about the 20 most damaging natural disasters in the dataset, ordered from the largest to the smallest (1998-2017). Damages reported as percent of GDP for the event year.

- Table B.1: The 20 Most Damaging Natural Disasters (1998-2017)
  - Dominica — 2017 — Storm — Hurricane Maria — Damages (% of GDP): 260 — Disaster-prone country: Yes — Small economy: Yes ∗
  - Grenada — 2004 — Storm — Hurricane Ivan — 148 — Yes — Yes ∗
  - Dominica — 2015 — Storm — Tropical Storm Erika — 90.2 — Yes — Yes ∗
  - Honduras — 1998 — Storm — Hurricane Mitch — 72.9 — Yes — No
  - Vanuatu — 2015 — Storm — Cyclone Pam — 60.1 — Yes — Yes ∗
  - Guyana — 2005 — Flood — N.A. — 35.5 — No — Yes ∗
  - Belize — 2000 — Storm — Hurricane Keith — 33.4 — Yes — Yes ∗
  - Tonga — 2001 — Storm — Tropical Cyclone Waka — 29.0 — Yes — Yes ∗
  - Belize — 2001 — Storm — Hurricane Iris — 28.7 — Yes — Yes ∗
  - Haiti — 2016 — Storm — Hurricane Matthew — 25.1 — Yes — Yes ∗∗
  - Nicaragua — 1998 — Storm — Hurricane Mitch — 21.3 — No — No
  - Samoa — 2012 — Storm — Cyclone Evan — 16.6 — Yes — Yes ∗
  - Tajikistan — 2008 — Ex. Temp. — N.A. — 16.3 — Yes — Yes ∗∗
  - St. Vin.Gr. — 2013 — Flood — N.A. — 15.0 — Yes — Yes ∗
  - Fiji — 2016 — Storm — Tropical Storm Winston — 12.9 — Yes — Yes ∗
  - Myanmar — 2008 — Storm — Cyclone Nargis — 12.6 — No — No
  - Guyana — 2006 — Flood — N.A. — 11.6 — No — Yes ∗
  - Thailand — 2011 — Flood — N.A. — 10.9 — No — No
  - Moldova — 2007 — Drought — N.A. — 9.22 — Yes — No
  - Dominican R. — 1998 — Storm — Hurricane Georges — 9.14 — Yes — No

### Appendix C — The Stationary DSGE Model (Detrended System)
- The model exhibits a stochastic trend growth rate; variables are detrended by z_t = A_t^(1/(1−α)) unless otherwise stated.
- Detrended variable notation: ̃x_t = x_t / z_t. Growth rates notation: ˆx_t = x_t / x_{t−1}.

- Key equations of the full detrended system (equation labels preserved):
  - (C.1) d_{t+1} = μ_d + (ε_{d,t+1} − μ_d)
  - (C.2) log θ_{t+1} = (1−ρ_θ) log θ̄ + ρ_θ log θ_t + σ_θ ε_{θ,t+1}
  - (C.3) z_{A,t+1} = σ_A ε_{A,t+1}
  - (C.4) log ˆA_t = Λ_A + z_{A,t} − (1−α) d_t θ_t
  - (C.5) ˆA_t = A_t / A_{t−1}
  - (C.6) log ˆz_t = 1/(1−α) log ˆA_t
  - (C.7) ˆz_t = z_t / z_{t−1}
  - (C.8) ̃U_t = ̃c_t (1−l_t)^ν e^{ξ_t}
  - (C.9) U_{c,t} = (1−l_t)^ν e^{ξ_t}
  - (C.10) ̃U_{l,t} = −ν ̃c_t (1−l_t)^{ν−1} e^{ξ_t}
  - (C.11) ̃λ_t = (1−ψ) ̃U_t^{−ψ} U_{c,t} (1 + τ_{c,t})
  - (C.12) −̃λ_t ̃w_t = (1−ψ) ̃U_t^{−ψ} ̃U_{l,t}
  - (C.13) M_t+1 = β (̃λ_{t+1} / ̃λ_t) ˆz_{t+1}^{−ψ}
  - (C.14) ̃q_t = E_t [ M_{t+1} exp (−d_{t+1} θ_{t+1}) [ ̃r_{t+1} + ̃q_{t+1} (1−δ) ] ˆμ_{t+1} ]
  - (C.15–C.16) 1 = ̃q_t [ 1 − S[ ̃x_t ̃x_{t−1} ˆz_t ] − S′[ ̃x_t ̃x_{t−1} ˆz_t ] ̃x_t ̃x_{t−1} ˆz_t ] + E_t [ M_{t+1} ̃q_{t+1} S′[ ̃x_{t+1} ̃x_t ˆz_{t+1} ] ( ̃x_{t+1} ̃x_t ˆz_{t+1} )^2 ]
  - (C.17) S[ ̃x_t ̃x_{t−1} ˆz_t ] = κ/2 ( ̃x_t ̃x_{t−1} ˆz_t − ˆz )^2
  - (C.18) S′[ ̃x_t ̃x_{t−1} ˆz_t ] = κ ( ̃x_t ̃x_{t−1} ˆz_t − ˆz )
  - (C.19) ̃y_t = ̃c_t + ̃x_t + ̃g_t + ̃x_{g,t} + [1 + (1−θ) ι] ̃x_{ga,t} + ̃n_{x,t}
  - (C.20) ̃b_{g,t} = R_{t−1} ̃b_{g,t−1} ˆz_t + ̃g + ̃x_{g,t} + [1 + (1−θ) ι] ̃x_{ga,t} − τ_{c,t} ̃c_t − ̃φ_t
  - (C.21) −( ̃b_{g,t} − ̃b_{g,t−1} ˆz_t ) = ̃n_{x,t} + ̃φ_t − R_{t−1} ̃b_{g,t−1} ˆz_t
  - (C.22) R_t = R e^{η( ̃b_{g,t} / ̃b_g − 1 )}
  - (C.23) log ( ̃φ_t / ̃φ ) = ρ_φ log ( ̃φ_{t−1} / ̃φ ˆz / ˆz_t ) + (1−ρ_φ) ρ_φ^d ( d_t θ_t / ̄d ̄θ )
  - (C.24) ̃k^*_t = (1−δ) ̃k_t + (1−S[ ̃x_t ̃x_{t−1} ˆz_t ]) ̃x_t
  - (C.25) ̃k_t = ̃k^*_{t−1} ˆz_t exp (−d_t θ_t)
  - (C.26) ̃k^*_{g,t} = (1−δ_g) ̃k_{g,t} + ̃x_{g,t}
  - (C.27) ̃k_{g,t} = k^*_{g,t−1} ˆz_t exp (−d_t θ_t)
  - (C.28) log ( ̃x_{g,t} / ̃x_g ) = −ρ_{xg} log ( ̃k_{g,t} / ̃k_g ); ̃̄k_{g,t} = ̃k_{g,t} + ̃k_{ga,t−1}
  - (C.29) ̃k_{ga,t} = (1−δ_g) ̃k_{ga,t−1} ˆz_t + ̃x_{ga,t}
  - (C.30) log ( ̃x_{ga,t} / ̃x_{ga} ) = −ρ_{xga} log ( ̃k_{ga,t} / ̃k_{ga} )
  - (C.31) ̃r_t = α (1−α_g) ̃y_t / ̃k_t
  - (C.32) ̃w_t = (1−α) ̃y_t / l_t
  - (C.33) ̃y_t = ˆA_t ˆz_t [ ̃̄k_{g,t}^{α_g} ( ̃k^*_{t−1} exp (−d_t θ_t) )^{1−α_g} ]^{α} l_t^{1−α}

- The appendix presents the detrended stationary model equations used for solution and analysis.

*Sources: EM-DAT and authors’ calculations.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019217-print-pdf.pdf_