## wpiea2019054

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### I. Introduction — context and main result
- Small developing states (SDS) face average annual disaster costs of 2 percent of GDP, more than four times that for larger countries (International Monetary Fund, 2016).
- Climate change disproportionally affects SDS through intensified natural disasters and gradual effects (rising sea levels, droughts).
- Two-pronged resilience strategy:
  - Financial protection: self-insurance, risk-transfer instruments, and financial tools providing immediate liquidity for relief and prompt reconstruction; reduces contingent liabilities and can improve debt sustainability.
  - Structural protection: investment in resilient infrastructure (roadways, water supply systems, land use planning, agriculture) that raises marginal product of private capital and stimulates private investment.
- Trade-offs:
  - Self-insurance carries an opportunity cost versus reducing government debt.
  - Risk-transfer instruments may be expensive in shallow markets.
  - Resilient capital (“building back better”) is significantly more expensive than standard capital.
- This paper uses a dynamic general equilibrium model calibrated to St. Lucia to assess macroeconomic impact of financial versus structural protection, accounting for high public debt and an ECCU regional debt target of 60 percent of GDP by 2030.
- Main headline result:
  - Both financial protection and structural protection significantly reduce output loss from natural disasters. Choice hinges on liquidity constraints and efficiency of public investment.

### II. Model — structure and key mechanisms
- Base model: DIGNAD, an extension of DIG (Buffie and others, 2012) with traded and non-traded goods, public capital as input alongside private capital and labor, and natural disasters.
- Policy instruments modeled:
  - Standard public capital and adaptation (resilient) public capital as separate inputs.
  - Savings fund provides immediate liquidity for reconstruction.
- Five key extensions:
  1. Natural disasters as continuous annual shocks with permanent effects on GDP.
  2. Endogenous replenishment of the savings fund:
     - Fund law of motion: 픰_௧ = (1+푟_௙)픰_௧ିଵ + 픰_௧_௜௡ − 픰_௧_௢௨௧.
     - Money injection rule: 픰_௧_௜௡ = 휙픰 (픰_௧ିଵ − 픰_଴), with 휙픰 >1 governing injection speed.
     - Momentum calibrated so that the savings fund is restored to initial level after use.
  3. Endogenous reconstruction of public capital constrained by capacity and liquidity:
     - Standard public investment: 푖_௭௜,௧ = 휙_௭ [푧_଴௜ − (1− 훿_௭௜) 푧_௧ିଵ௜].
     - Adaptation public investment: 푖_௭௔,௧ = 휙_௭ [푧_଴௔ − (1− 훿_௭௔) 푧_௧ିଵ௔].
     - 휙_௭ ∈ [0,1] measures reconstruction speed; 휙_௭ =1 implies full reconstruction within the year.
  4. Fiscal reaction function:
     - Government adjusts consumption tax to attain ECCU public debt target of 60 percent of GDP by 2030.
     - Condensed government budget constraint shown in the model (uses domestic, concessional, and commercial debt stocks and interest terms).
  5. Resilient capital is more damage-resistant but more expensive:
     - 푃_௭௔,௧ = (1+휀) 푃_௭௜,௧ with ε ∊ [0,1].

### III. Calibration — St. Lucia baseline values and parameters
- Selected initial values and parameters:
  - Public standard investment to GDP 푖_௭௜,௢ = 3.9
  - Public adaptation investment to GDP 푖_௭௔,௢ = 0.0
  - Public domestic debt to GDP 푏_௢ = 35.3
  - Public concessional debt to GDP 푑_௢ = 20.4
  - Public external (commercial) debt to GDP 푑_௖,௢ = 12.0
  - Real interest rate on public domestic debt 푟_௢ = 5.2
  - Real interest rate on public concessional debt 푟_ௗ,௢ = 0.0
  - Real interest rate on public external debt 푟_ௗ௖,௢ = 5.2
  - Disaster fund savings to GDP 픰_௢ = 0.0
  - Consumption tax (VAT) rate 휏_௢௖ = 12.5
  - Private external debt to GDP 푏_௢∗ = 37.2
- Calibrated parameters:
  - Depreciation rate of standard public infrastructure 훿_௭௜ = 6.0
  - Depreciation rate of adaptation public infrastructure 훿_௭௔ = 3.0
  - Additional cost of adaptation public infrastructure ε = 0.25
  - Intertemporal elasticity of substitution in public capital inputs ξ = +∞
  - Depreciation rate of private capital 훿_௞ = 5.0
  - Trend per capita growth rate g = 1.5
- Additional calibration notes:
  - Initial public debt-to-GDP ratio calibrated to 67.7 percent of GDP in 2016 (sum of debt components).
  - Natural disaster calibration: on average each year St. Lucia suffers a loss of public capital of 1 percent of GDP and private capital of 0.5 percent of GDP.
  - Savings fund feedback parameter 휙픰 calibrated so that the savings fund is replenished at the initial level anytime used (픰_௧ = 픰_଴, ∀푡).

### IV. Simulation set-up and policy designs
- Grant assumption:
  - In year t-1, government receives a grant equal to 8 percent of initial GDP to finance one of three policies.
- Policy 1: Debt reduction
  - Use grant to reduce public debt; initial public debt-to-GDP falls from 67.7 percent to 59.7 percent.
  - Annual interest rate on public debt 50 basis points lower.
  - Investment in standard public infrastructure kept at initial level; reconstruction only in private sector; tax rate kept lower.
- Policy 2: Financial protection
  - Government builds natural savings fund equal to 8 percent of initial GDP.
  - Fund used to finance reconstruction of public capital without issuing new debt; government can fully reconstruct destroyed public capital within the year (휙_௭ =1).
  - Accumulation of assets reduces net public debt and sovereign risk premium; annual interest rate on public debt assumed 50 basis points lower than under structural protection.
  - Tax revenues must increase to attain the 60 percent debt target despite lower interest payments.
- Policy 3: Structural protection
  - Government invests 8 percent of GDP in adaptation (resilient) capital.
  - Higher starting debt requires higher tax revenues to meet the debt target.
  - Structural protection does not provide liquidity for full reconstruct-in-year; 휙_௭ <1.
  - Adaptation capital reduces disaster damages and stimulates private investment despite higher unit cost (ε = 0.25).
- Indifference threshold:
  - Fraction of destroyed public capital that government must reconstruct under policy 3 to match output under policy 2 after 15 years is 휙_௭ = 0.92.

### V. Key quantitative findings and scenarios
- Savings fund sizing:
  - A savings fund sized at 0.9 percent of GDP would have a 95 percent chance of non-depletion.
  - In the absence of capacity constraints, a savings fund of this size implies 휙௭ = 1 and that, in year t-1, the share of adaptation capital in the total stock of public capital is 23.5 percent.
- Scenario 1 — above-threshold reconstruction (휙௭ = 0.97):
  - Policy 1 (debt reduction):
    - GDP falls by 2.8 percent after 15 years.
  - Policy 2 (financial protection):
    - After 15 years, GDP is about 1.5 percent lower and tax revenues increase by 0.8 percent of GDP.
  - Policy 3 (adaptation capital):
    - Lowest output loss: about 0.13 percent smaller loss than under policy 2 after 15 years.
    - Required increase in tax revenues to GDP is 0.7 percent.
- Scenario 2 — below-threshold reconstruction (휙௭ = 0.87):
  - Policy 3 leads to lower GDP than policy 2:
    - Loss of about 1.7 percent after 15 years under policy 3 versus a loss of 1.55 percent under policy 2.
- Aggregate impact statements:
  - Both financial protection and structural protection reduce output losses by 1.5 percent over a 15-year period.
  - These measures raise output growth by 0.1 percent per year.
- Reconstruction under debt-reduction policy (robustness):
  - Allowing full reconstruction financed by taxes under Policy 1 reduces output loss after 15 years from 2.81 percent to 2.51 percent.
  - Even with reconstruction, output loss remains about twofold that under either resilience-building policy.

### VI. Sensitivity analysis — threshold variations and drivers
- Thresholds (fraction of destroyed public capital reconstructed at which financial and structural protection are equivalent) under alternative calibrations:
  - No sovereign risk premium gain → 0.875
  - Lower public investment efficiency → 0.980
  - Same price of public standard and resilient capital → 0.850
  - Same depreciation rate for standard and resilient capital → 0.960
  - Natural disasters every five years → 0.917
- Interpretation:
  - No sovereign risk premium gain lowers threshold to 0.875.
  - Public investment efficiency 1.5 percent lower raises threshold to 0.980.
  - If ε = 0 (same price), threshold falls to 0.850.
  - Equal yearly depreciation rate of 6 percent raises threshold to 0.960.
  - Less frequent but larger disasters (every five years) lower threshold to 0.917.
- Robustness note: the threshold is somewhat sensitive to these changes, but qualitative trade-offs persist.

### VII. Policy conclusions and recommendations
- Both financial protection (savings fund/liquidity for reconstruction) and structural protection (investment in adaptation capital) are effective in reducing output losses from natural disasters.
- Prioritization guidance:
  - Structural protection is preferable when the government can reconstruct at least 92 percent of destroyed public capital and is not fiscally constrained, because resilient capital reduces damages and improves private investment conditions.
  - Financial protection is favored when fiscal space is limited, borrowing constrained, or external grant financing unavailable, because immediate liquidity for reconstruction is critical.
  - Low public investment efficiency further tilts the balance toward financial protection.
  - An optimal approach combines financial protection (priority under financial constraints and low investment efficiency) with structural protection (superior at the margin when reconstruction capacity and efficiency are sufficient).

*Source: wpiea2019054 - REFERENCES _____________________________________________________________________________________ 18*

### REFERENCES _____________________________________________________________________________________ 18

### REFERENCES _____________________________________________________________________________________ 18

### I. INTRODUCTION
- Small developing states (SDS) face average annual disaster costs of 2 percent of GDP, more than four times that for larger countries (International Monetary Fund, 2016).
- Climate change will disproportionally affect SDS through intensified natural disasters and gradual effects (rising sea levels, droughts).
- Two-pronged resilience strategy:
  - Financial protection: self-insurance, risk-transfer instruments, and financial tools providing immediate liquidity for relief and prompt reconstruction; reduces contingent liabilities and can improve debt sustainability.
  - Structural protection: investment in resilient infrastructure (roadways, water supply systems, land use planning, agriculture) that raises marginal product of private capital and stimulates private investment.
- Trade-offs and costs:
  - Self-insurance carries an opportunity cost versus reducing government debt.
  - Risk-transfer instruments may be expensive in shallow markets.
  - Resilient capital (“building back better”) is significantly more expensive than standard capital.
- Literature context:
  - Bevan and Adam (2016): dynamic general equilibrium model for Jamaica — benefits of disaster risk insurance offset by actuarially unfair premia.
  - Borenzstein, Cavallo, and Jeanne (2017): welfare gains from catastrophe bonds but too costly for vulnerable countries.
  - Marto, Papageorgiou, and Klyuev (2017): investing in resilience gave better output payoff than mixed strategy in Vanuatu Cyclone Pam case.
  - De Janvry, del Valle, and Sadoulet (2016): Mexico’s Fund for Natural Disasters associated with 2-4 percent faster growth for municipalities with access after disasters.
- This paper:
  - Uses a dynamic general equilibrium model incorporating natural disasters to assess macroeconomic impact of financial vs. structural protection and policy trade-offs.
  - Calibrated to St. Lucia; modified from Marto, Papageorgiou, and Klyuev (2017).
  - Key differences: high public debt and ECCU regional debt target of 60 percent of GDP by 2030 constrain borrowing; focus on average disasters; financing simplified by assuming all policies funded by a grant of the same amount; financial protection limited to a savings fund.
- Main headline result:
  - Both financial protection and structural protection significantly reduce output loss from natural disasters. Choice hinges on liquidity constraints and efficiency of public investment.

### II. MODEL
- Base model: DIGNAD, an extension of DIG (Buffie and others, 2012) with traded and non-traded goods, public capital as input alongside private capital and labor, and natural disasters.
- Policy instruments modeled:
  - Standard public capital and adaptation (resilient) public capital as separate inputs.
  - Savings fund provides immediate liquidity for reconstruction.
- Five key extensions in this paper:
  1. Natural disasters as continuous annual shocks with permanent effects on GDP (continuum of average-magnitude disasters).
  2. Endogenous replenishment of the savings fund:
     - Fund law of motion: 픰_௧ = (1+푟_௙)픰_௧ିଵ + 픰_௧_௜௡ − 픰_௧_௢௨௧.
     - Money injection rule: 픰_௧_௜௡ = 휙픰 (픰_௧ିଵ − 픰_଴), with 휙픰 >1 governing injection speed.
     - Momentum calibrated so that the savings fund is restored to initial level after use.
  3. Endogenous reconstruction of public capital constrained by capacity and liquidity:
     - Standard public investment: 푖_௭௜,௧ = 휙_௭ [푧_଴௜ − (1− 훿_௭௜) 푧_௧ିଵ௜].
     - Adaptation public investment: 푖_௭௔,௧ = 휙_௭ [푧_଴௔ − (1− 훿_௭௔) 푧_௧ିଵ௔].
     - 휙_௭ ∈ [0,1] measures reconstruction speed; 휙_௭ =1 implies full reconstruction within the year.
  4. Fiscal reaction function:
     - Government adjusts consumption tax to attain ECCU public debt target of 60 percent of GDP by 2030.
     - Government budget constraint (condensed): P_௭௜,௧ 푖_௭௜,௧ + P_௭௔,௧ 푖_௭௔,௧ + 훵_௧ + 푟_௧ିଵ P_௧ 푏_௧ିଵ + 푟_ௗ,௧ିଵ 푑_௧ିଵ + 푟_ௗ௖,௧ିଵ 푑_௖,௧ିଵ + 훥픰_௧ ≤ P_௧ 훥푏_௧ + 훥푑_௧ + 훥푑_௖,௧ + 푟_௙ 픰_௧ିଵ + 휏_௧௖ P_௧ 푐_௧.
     - Three debt types: domestic 푏_௧, external concessional 푑_௧, external commercial 푑_௖,௧ with net interest rates 푟_௧, 푟_ௗ,௧, 푟_ௗ௖,௧.
     - Government earns (1+푟_௙) on savings and collects VAT 휏_௧௖ on consumption.
  5. Resilient capital more damage-resistant but more expensive:
     - 푃_௭௔,௧ = (1+휀) 푃_௭௜,௧ with ε ∊ [0,1].

### III. CALIBRATION
- Calibrated to St. Lucia at annual frequency; selected initial values and parameters:
  - Public standard investment to GDP 푖_௭௜,௢ = 3.9
  - Public adaptation investment to GDP 푖_௭௔,௢ = 0.0
  - Public domestic debt to GDP 푏_௢ = 35.3
  - Public concessional debt to GDP 푑_௢ = 20.4
  - Public external (commercial) debt to GDP 푑_௖,௢ = 12.0
  - Real interest rate on public domestic debt 푟_௢ = 5.2
  - Real interest rate on public concessional debt 푟_ௗ,௢ = 0.0
  - Real interest rate on public external debt 푟_ௗ௖,௢ = 5.2
  - Disaster fund savings to GDP 픰_௢ = 0.0
  - Consumption tax (VAT) rate 휏_௢௖ = 12.5
  - Private external debt to GDP 푏_௢∗ = 37.2
- Calibrated parameters:
  - Depreciation rate of standard public infrastructure 훿_௭௜ = 6.0
  - Depreciation rate of adaptation public infrastructure 훿_௭௔ = 3.0
  - Additional cost of adaptation public infrastructure ε = 0.25
  - Intertemporal elasticity of substitution in public capital inputs ξ = +∞
  - Depreciation rate of private capital 훿_௞ = 5.0
  - Trend per capita growth rate g = 1.5
- Additional calibration notes:
  - Initial public debt-to-GDP ratio calibrated to 67.7 percent of GDP in 2016 (sum of debt components).
  - Concessional debt real interest rate assumed 0.0 percent; domestic and commercial debt real rates 5.2 percent.
  - Initial tax rate on consumption 12.5 percent.
  - Public capital depreciates at annual rate of 5 percent (note: table lists public standard 훿_௭௜ = 6.0 percent and private capital 훿_௞ = 5.0 percent; text states public capital depreciates at 5 percent).
  - Natural disaster calibration:
    - On average each year St. Lucia suffers a loss of public capital of 1 percent of GDP and private capital of 0.5 percent of GDP.
  - Savings fund feedback parameter 휙픰 calibrated so that the savings fund is replenished at the initial level anytime used (픰_௧ = 픰_଴, ∀푡).

### IV. SIMULATION RESULTS — SET-UP AND POLICY DESIGNS
- Grant assumption:
  - In year t-1, government receives a grant equal to 8 percent of initial GDP to finance one of three policies.
- Policy 1: Debt reduction
  - Use grant to reduce public debt, immediately reaching 60 percent of GDP instead of building resilience.
  - Grant reduces initial public debt-to-GDP from calibrated 67.7 percent to 59.7 percent.
  - Annual interest rate on public debt 50 basis points lower.
  - Investment in standard public infrastructure kept at initial level; reconstruction only in private sector.
  - Tax rate kept lower, but higher damages and public capital deterioration lead to large output losses.
- Policy 2: Financial protection
  - Government builds a natural savings fund equal to 8 percent of initial GDP.
  - Fund used exclusively to finance reconstruction of public capital without issuing new debt.
  - Government can fully reconstruct destroyed public capital within the year (휙_௭ =1).
  - Accumulation of assets reduces net public debt and sovereign risk premium.
  - Annual interest rate on public debt assumed 50 basis points lower than under structural protection.
  - Despite lower interest payments, tax revenues must increase to attain the 60 percent debt target.
  - Lack of resilient capital implies large disaster damages, but rapid reconstruction contains output losses.
- Policy 3: Structural protection
  - Government invests the same 8 percent of GDP in adaptation (resilient) capital.
  - Higher starting debt level requires increases in tax revenues to meet debt target.
  - Structural protection does not provide liquidity for full reconstruct-in-year; 휙_௭ <1.
  - Building resilient capital reduces disaster damages and stimulates private investment, reducing output losses despite higher initial price (ε = 0.25).
- Indifference threshold between financial and structural protection:
  - Fraction of destroyed public capital that government must be able to reconstruct under policy 3 to match output under policy 2 after 15 years is 휙_௭ = 0.92 (the “threshold”).
  - Simulations examine scenarios with 휙_௭ above and below 0.92.

*Source: wpiea2019054 - REFERENCES _____________________________________________________________________________________ 18*

### 0.9 percent of GDP would have a 95 percent chance of non-depletion.

### wpiea2019054 - 0.9 percent of GDP would have a 95 percent chance of non-depletion.

### Key calibration and baseline statement
- A savings fund sized at 0.9 percent of GDP would have a 95 percent chance of non-depletion.
- In the absence of capacity constraints, a savings fund of this size implies 휙௭ = 1 and that, in year t-1, the share of adaptation capital in the total stock of public capital is 23.5 percent.
- The model assumes the economy grows at a steady rate of 1.5 percent per year independently of natural disasters.

### Simulation results — Scenario 1 (above-threshold reconstruction)
- Threshold condition: investing in adaptation capital is preferable if the government can rebuild more than 92 percent of the destroyed capital.
- Baseline scenario for policy 3: 휙௭ = 0.97 (5 percent above the 92 percent threshold).
- Policy 1 (debt reduction, blue line):
  - Immediately reduces public debt to the target of 60 percent of GDP.
  - With no government efforts to reconstruct, public capital is eroded by natural disasters.
  - GDP falls by 2.8 percent after 15 years.
- Policy 2 (financial protection, red line):
  - Uses initial grant to build financial protection and provides liquidity to promptly reconstruct destroyed public capital.
  - Stock of public standard capital stabilizes at a lower level due to continuous shocks.
  - After 15 years, GDP is about 1.5 percent lower and tax revenues increase by 0.8 percent of GDP.
- Policy 3 (adaptation capital, yellow line):
  - Lowest output loss among the three policies: about 0.13 percent smaller loss than under policy 2 after 15 years.
  - Required increase in tax revenues to GDP is slightly lower than under financial protection: 0.7 percent.
  - Joint effects: lower damages from resilient capital and near-complete reconstruction (97 percent) make this policy preferable in this scenario.

### Simulation results — Scenario 2 (below-threshold reconstruction)
- Alternate assumption for policy 3: 휙௭ = 0.87 (5 percent below the 92 percent threshold).
- Under this constraint, policy 3 leads to lower GDP than policy 2:
  - Loss of about 1.7 percent after 15 years under policy 3 versus a loss of 1.55 percent under policy 2.
- Conclusion: constraints on public capital reconstruction can reverse the preference and make structural protection less preferable.

### Sensitivity analysis — alternative calibrations and implied thresholds
- The analysis checks sensitivity to: sovereign risk premium effects, public investment efficiency under structural resilience, relative price of resilient vs standard capital, depreciation rates of resilient capital, and shock frequency/magnitude.
- Table of calibration outcomes (thresholds of public capital reconstruction at which policies are equivalent):
  - Policy 2: no gain in sovereign risk premium → 0.875
  - Policy 3: lower public investment efficiency → 0.980
  - Policy 3: same price of public standard and resilient capital → 0.850
  - Policy 3: same depreciation rate of public standard and resilient capital → 0.960
  - All policies: Natural disasters every five years → 0.917
- Interpretation of specific calibrations:
  - No sovereign risk premium gain: threshold lowers to 87.5 percent (i.e. 0.875).
  - Lower public investment efficiency under policy 3 (assumed 1.5 percent lower) raises threshold from 92 percent to 98 percent (i.e. 0.980).
  - Same price of resilient and standard capital (ε = 0) lowers threshold to 85 percent (i.e. 0.850).
  - Equal yearly depreciation rate of 6 percent for standard and adaptation capital raises threshold to 96 percent (i.e. 0.960).
  - Less frequent but larger disasters (every five years) lower threshold to 91.7 percent (i.e. 0.917).
- Robustness note: the threshold is slightly sensitive to these changes, but qualitative policy trade-offs continue to hold.

### Additional robustness check: reconstruction under debt-reduction policy
- Relaxing the assumption of no reconstruction under Policy 1 and allowing full reconstruction financed by taxes:
  - Output loss after 15 years is reduced from 2.81 percent to 2.51 percent (red-dashed vs blue-solid line).
  - Despite mitigation, the output loss remains about twofold that suffered under either resilience-building policy.

### Policy conclusions and implications
- Building resilience with both structural protection (adaptation capital) and financial protection (savings fund/financial tools) is key to coping with natural disasters.
- Quantitative simulation findings:
  - Both financial protection and structural protection reduce output losses by 1.5 percent over a 15-year period.
  - These measures raise output growth by 0.1 percent per year.
- Trade-offs and recommended prioritization:
  - If the government can reconstruct at least 92 percent of destroyed public capital and is not fiscally constrained, structural protection is the best strategy due to reduced damages and improved private investment conditions.
  - If fiscal space is limited, borrowing constrained, or external grant financing unavailable, the availability of liquidity for reconstruction favors financial protection.
  - Low public investment efficiency further tilts the balance in favor of financial protection.
  - Overall, an optimal strategy is a mix of financial protection (priority under financial constraints and low investment efficiency) and structural protection (superior at the margin).

*Source: IMF working paper content (wpiea2019054).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019054.pdf_