## wp17223

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### Introduction and context
- Small developing states are among the most vulnerable countries in the world to natural disasters and climate change; the UN World Risk Index places small developing states at the top of its ranking.
- Cyclone Pam (March 2015) in Vanuatu:
  - Damages and losses of about 60 percent of the archipelago’s GDP.
  - Affected more than 188,000 inhabitants (more than 70 percent of the population).
  - Damages to tourism and transport infrastructure estimated at 11 percent of GDP.
  - Production losses in agriculture and tourism equivalent to 14 percent of GDP.
  - The probability of a natural disaster happening in Vanuatu in any given year is 65 percent and more than 99 percent in a five-year period.
  - EM-DAT estimates: natural disasters caused annual damages equivalent to 2.4 percent of GDP over the 1950-2014 period and affected more than 3 percent of the population.
- Climate change projections for Vanuatu (Burke et al. 2015):
  - GDP per capita is expected to drop by 75 percent by 2100 relative to a world without climate change.
  - There is a 97 percent probability that climate change will reduce GDP per capita by more than 50 percent.

### Model structure and calibration
- Model type and key features:
  - Two-sector small open economy model (traded x and nontraded n).
  - Five disaster channels: permanent damages to public infrastructure; permanent damages to private capital; temporary productivity losses; increased inefficiencies in public investment during reconstruction; damages to sovereign creditworthiness.
  - Government instruments: invest in standard infrastructure and in adaptation capital; combine adaptation and standard public capital in a CES aggregator with elasticity ξ and weight ρz; save in an external contingency fund paying the risk-free rate; finance via grants, concessional debt, external commercial debt, and domestic debt.
  - Adaptation capital reduces damages through scaling πj and νD; firms do not internalize protection benefits of adaptation beyond production-input effects.
- Government and fiscal mechanics:
  - Government rebuilds damaged public infrastructure in about 6 years (assumption used in experiments).
  - Public capital accumulation:
    - zi,t = (1 − δzi) zi,t−1 + (1 − Ds) s t i zi,t.
    - za,t = (1 − δza) za,t−1 + (1 − Ds) s t i za,t.
  - Public investment efficiency s ∈ [0,1]; disaster reduces s by Ds at time of disaster.
  - Sovereign risk channel: rdc,t = (1 + Dr,t) (rf + υg e ηg (dt + dc,t)/yt − ̄d + ̄dc/ ̄y ).
  - Fiscal rule for consumption tax τc,t includes targets to ensure long-run debt sustainability.

### Calibration and Cyclone Pam damages
- Overall damages and allocation:
  - Total damages and losses: 60.8% of GDP (36.7% in damages and 24.2% in losses).
  - Tradable sector: 23.7% of GDP (45% in damages, remainder in losses).
  - Nontradable sector: 24.7% of GDP (57% in damages, remainder in losses).
  - Private housing: 12.4% of GDP.
- Key calibrated parameter values and initial conditions:
  - Initial return on total public infrastructure Rzo = 30.0 percent.
  - Return on public standard investment Rzio = 30.0 percent.
  - Return on public adaptation investment Rzao = 50.0 percent.
  - Implied output elasticities w.r.t public infrastructure: 0.0312.
  - Initial public investment efficiency so = 60.0 percent.
  - Public standard infrastructure investment to GDP izi,o = 1.3 percent.
  - Adaptation infrastructure: iza,o = 0.0 and zao = 0.0.
  - Calibrated severity-of-destruction weights: $z = 0.4 and $k = 0.3.
  - Cyclone causes damages of about 25.8% of public infrastructure and 25.5% of private capital relative to steady state.
  - Productivity losses: 20.9% in the nontradable sector and 20.5% in the tradable sector (deviations from steady state).
  - Public investment efficiency loss (Ds) assumed to be 20% (for every dollar invested an additional 12 cents lost).
  - Disaster impact on external commercial debt real rate: Dr = 0.15.
- Additional calibrated values (Table 1 and Table 2 selections):
  - αn = 40.0 percent; αx = 30.0 percent.
  - Depreciation rate of standard infrastructure δzi = 3.0 percent.
  - Depreciation rate of adaptation infrastructure δza = 7.5 percent.
  - Intertemporal elasticity of substitution ςc = 0.34.
  - Share of liquidity-constrained households a/(1+a) = 12.7 percent.
  - Depreciation rate of private capital δk = 5.0 percent.
  - Intratemporal elasticity of substitution across public capital inputs ξ: +∞ (baseline; perfect substitutes).
  - Real risk-free world interest rate r* = 2.0 percent.
- Initial fiscal and debt positions (selected initial values):
  - Public domestic debt to GDP bo: 7.7
  - Public concessional debt to GDP d o: 12.9
  - Public external (commercial) debt to GDP dc,o: 5.0
  - Real interest rate on public domestic debt r o: 5.0
  - Real interest rate on public concessional debt r d,o: 0.0
  - Real interest rate on public external debt r dc,o: 1.5
  - Savings to GDP s o: 0.0
  - Grants to GDP G o: 11.2
  - Consumption tax (VAT) rate τ c o: 12.5
  - Private external debt to GDP b* o: 0.0
  - Remittances to GDP R o: 3.5

### Reconstruction, recovery dynamics, and baseline outcomes
- Reconstruction intent and recovery paths:
  - Government intent: rebuild damaged infrastructure to pre-Pam level in about five years.
  - Recovery of public investment efficiency, sectoral TFPs, and credit risk premium follows a sigmoid: xt = exp(−γx t) xPam + (1−exp(−γx t)) xpre-Pam.
  - With an accelerated reconstruction program:
    - Public capital recovers to pre-Pam level in less than five years.
    - Public investment peaks at 5.5% of GDP before gradually declining to pre-Pam level 1.3% of GDP in about 10 years.
    - Sectoral TFPs take about 6 years to regain pre-Pam levels.
    - Public investment efficiency recovers in less than 4 years.
    - The 25 basis point increase in the government’s real interest rate on external borrowing fades away after about 5 years.

### Recovery financing scenarios and quantitative outcomes
- Three broad financing strategies analyzed: tax-financed reconstruction; debt-financed reconstruction; and grants-for-reconstruction.
- Tax-financed reconstruction (government raises consumption tax):
  - Consumption tax rate would need to rise from 12.5% to close to 23% in the short term and to about 14% over the medium term.
  - Private consumption would drop 20% relative to its pre-Pam level.
  - Private investment falls sharply: about 40% in tradable sector and 42% in nontradable sector.
  - Domestic real interest rate spikes (from 5% to 18% for Ricardian households).
  - Political and practical constraints: in practice government suspended VAT and import duties on construction materials and allowed 20% withdrawals from National Provident Fund.
- Debt-financed reconstruction (external borrowing):
  - Private consumption falls less than under tax-financed reconstruction.
  - Public debt rises from 25% pre-Pam to well above 90% of GDP in the medium term and could reach above 105% of GDP in 30 years.
  - Real exchange rate appreciates about 4%; current account deficit worsens to about 9% of GDP.
  - Negative impact on tradable sector is 5 percentage points stronger relative to pre-Pam when government resorts to borrowing versus taxes.
- Grants-for-reconstruction (donor-funded):
  - Donor grants closing government budget constraint would require an additional 50% of pre-Pam GDP in grants over 15 years after the cyclone.
  - Grants peak at 17% of (actual) GDP in the first five years and stay above 12% of GDP over the medium term before returning to 2015 level in long run.
  - Grants allow recovery akin to debt-financed program but without debt-distress concerns; current account stabilizes in about 15 years.
  - Practical note: actual donor disbursements did not match initial commitments in GDP terms, implying reconstruction pace likely slower than envisioned.

### Investing in resilient infrastructure (pre-disaster) — quantitative thought experiment
- Policy experiment: government spends 3% of GDP per year in adaptation infrastructure in the five years prior to Cyclone Pam; expenditures entirely funded by donors; post-disaster accelerated reconstruction identical for comparability.
- Effects on damages and productivity:
  - Reduced damages to standard public infrastructure by 5.2%.
  - Reduced damages to private capital by 9.7%.
  - Reduced productivity losses in the tradable sector by 3.8% and in the nontradable sector by 3.9%.
- Fiscal and debt outcomes:
  - Public debt reaches less than 60% of GDP over the medium term (as opposed to 100% of GDP in the no-adaptation scenario).
  - Tax-financed reconstruction still requires consumption tax rate increase to 21%, yet the tax reverts much faster to its initial value (in about five years) compared with the prolonged tax increase without adaptation investment.
- Macro behavior and private sector responses:
  - Investing in adaptation raises marginal product of private capital, crowding in private investment prior to the disaster and increasing the domestic real interest rate.
  - Short-term contraction of private consumption, particularly among savers.
  - Post-disaster private investment declines by about 23% to 31% (a 10 percentage point difference with no-adaptation scenario).
  - Private consumption decreases by about 10 to 12%.

### Building fiscal buffers (contingency fund) and combined strategies
- Policy considered: reallocate half of the annual 3% of GDP (i.e., 1.5% of GDP) to an external contingency fund and the other half to adaptation investments; donors support both allocations; external borrowing closes remaining fiscal gap.
- Contingency fund accumulation and use:
  - Government accumulates about 8% of GDP in its external contingency fund.
  - Withdrawals amount to 75% of the fund’s remaining balance for three years after the disaster to fund reconstruction.
  - Availability of the fund allows reconstruction to start without additional short-term borrowing.
- Comparative outcomes:
  - Building fiscal buffers yields lower medium-term debt-to-GDP levels compared with only investing in resilient infrastructure, though GDP is more affected in the contingency-fund case.
  - Total public debt reaches 53% of GDP by 2035 in the contingency-fund scenario; gains subside by 2035.
  - Both preemptive policies (only adaptation; adaptation + contingency fund) lead to debt levels about 25 percentage points lower than the post-disaster reactive policy.
  - Coupling adaptation with savings saved the economy 3 percentage points of output less than investing entirely in adaptation (noting adaptation investments are not fully efficient).
- Heuristic for contingency fund contributions:
  - If there is one in five chance every year of a shock that costs 1% of GDP, then 1/4% of GDP should be deposited in the contingency fund every non-disaster year.

### Practical constraints observed and concept of “grant-fathering”
- Observed Vanuatu measures after Cyclone Pam included suspending VAT and import duties on construction materials for two months, deferring vehicle registration fees and VAT payments to the next quarter, subsidies for agricultural seedlings, domestic banks delaying loan repayments for 6 to 12 months and providing additional lending to commence repair work, but limited availability of credit for the government and slow external borrowing.
- Policy conclusion: grant-financing post-disaster is essential to prevent reconstruction from putting the country’s debt sustainability at risk.
- Concept introduced: “grant-fathering” — for small open economies with limited access to external borrowing and high import content of infrastructure projects, substantial grant-financing is required when hit by large shocks to ensure fiscal and debt sustainability over the medium term.

### Policy implications and recommendations
- Donor role:
  - Bilateral and multilateral donors must provide significant financial resources post-disaster to enable smooth recovery without jeopardizing debt sustainability.
  - Donor support for pre-disaster investments in resilient infrastructure and for building contingency funds enhances recovery outcomes and reduces required post-disaster grants.
- Domestic policy tradeoffs:
  - Tradeoff between spending for growth-promoting infrastructure versus vulnerability-reducing resilience.
  - Tradeoff between building physical resilience (adaptation capital) and accumulating financial buffers (contingency fund) given limited access to financial markets.
- Financing options and recommended prioritization:
  - Tax increases are often politically infeasible immediately post-disaster and cause large short-term contractions.
  - Domestic borrowing is limited; external concessional and non-concessional borrowing may be slow or unavailable.
  - Grant financing is identified as essential in many scenarios, particularly for catastrophic events like Cyclone Pam.
- Operational and planning recommendations:
  - Incorporate disaster costs into budget planning (average impact on growth, increased infrastructure depreciation rates, maintenance costs).
  - Build fiscal buffers and invest in infrastructure able to withstand disasters (including urban planning and integrated coastal zone management).
  - Enhance national disaster-response frameworks (national plan, institutions, responsibilities) to accelerate recovery and reduce productivity and investment inefficiencies.
  - Model extensions proposed: study optimal balance between ex ante and ex post policies, consider different damage functions (e.g., temperature or wind speeds), and assess climate change impacts on growth and debt sustainability.

*Source: IMF Working Paper — wp17223 (chapters 2, 3, 4, and 5).*

### References26

### wp17223 - References26

### Introduction and context
- Small developing states are among the most vulnerable countries in the world to natural disasters and climate change; the UN World Risk Index places small developing states at the top of its ranking.
- Cyclone Pam (March 2015) in Vanuatu:
  - Damages and losses of about 60 percent of the archipelago’s GDP.
  - Affected more than 188,000 inhabitants (more than 70 percent of the population).
  - Damages to tourism and transport infrastructure estimated at 11 percent of GDP.
  - Production losses in agriculture and tourism equivalent to 14 percent of GDP.
  - The probability of a natural disaster happening in Vanuatu in any given year is 65 percent and more than 99 percent in a five-year period.
  - EM-DAT estimates: natural disasters caused annual damages equivalent to 2.4 percent of GDP over the 1950-2014 period and affected more than 3 percent of the population.
- Climate change projections for Vanuatu (Burke et al. 2015):
  - GDP per capita is expected to drop by 75 percent by 2100 relative to a world without climate change.
  - There is a 97 percent probability that climate change will reduce GDP per capita by more than 50 percent.

### Model structure and calibration
- Model type: small open economy model calibrated to a small, low-income economy like Vanuatu.
- Government choices in the model:
  - Invest in standard infrastructure (e.g., roads).
  - Invest in adaptation capital (e.g., seawalls) which:
    - Contributes to overall quality of infrastructure used in the production function of private firms.
    - Reduces damages inflicted by a natural disaster.
  - Combine adaptation and standard public capital in a CES function to study degrees of complementarity.
  - Save resources in an external contingency fund held in a major financial center that pays the risk-free interest rate.
- Key calibration/contextual parameters and assumptions from the source:
  - Government intent to rebuild damaged public infrastructure in a relatively short time span (about 6 years).
  - Contingency fund is external and risk-free.

### Research questions addressed
- (i) Considering the government’s intent of rebuilding the damaged public infrastructure in a relatively short time span (about 6 years), how much funding would donors have to provide to ensure debt remains sustainable over the medium term without further fiscal consolidation?
- (ii) If donors had supported investments in resilient infrastructure and helped build up the contingency fund in advance of the disaster, what would Vanuatu’s public debt profile look like?

### Main findings and numerical outcomes emphasized
- Substantial donor support is required post-disaster for a smooth recovery and to ensure steady convergence to peers, even if reasonable resources were dedicated to building resilience prior to the disaster.
- Investing in resilient infrastructure and building a contingency fund are complementary measures that:
  - Smooth the impact of the disaster.
  - Help ensure a swift recovery once reconstruction begins.
- Without strong support from development partners, rebuilding public capital in a short time horizon requires either:
  - Strong fiscal adjustment, or
  - Availability of (domestic or external) borrowing.
- Practical constraints observed in Vanuatu post-disaster:
  - Government measures included suspending VAT and import duties on construction materials for two months after the cyclone, deferring payments of vehicle registration fees and VAT payments to the next quarter, and providing subsidies for agricultural seedlings to affected households.
  - Domestic banks delayed loan repayments for 6 to 12 months for some corporate customers pending insurance payouts and provided additional lending to commence repair work, but availability of credit for the government was small.
  - External borrowing (commercial or otherwise) was either not available or would require more months to negotiate and materialize.
- Policy conclusion emphasized: grant-financing post-disaster is essential to prevent reconstruction from putting the country’s debt sustainability at risk.
- Concept introduced: “grant-fathering” — for small open economies with limited access to external borrowing and high import content of infrastructure projects, substantial grant-financing is required when hit by large shocks to ensure fiscal and debt sustainability over the medium term.

### Policy implications and recommendations
- Donor role:
  - Bilateral and multilateral donors must provide significant financial resources post-disaster to enable smooth recovery without jeopardizing debt sustainability.
  - Donor support for pre-disaster investments in resilient infrastructure and for building contingency funds enhances recovery outcomes.
- Domestic policy tradeoffs:
  - Tradeoff between allocating spending for growth-promoting infrastructure versus vulnerability-reducing resilience.
  - Tradeoff between building physical resilience (adaptation capital) and accumulating financial buffers (contingency fund) given limited access to financial markets.
- Financing options for reconstruction analyzed:
  - Tax increases (politically infeasible in many post-disaster contexts).
  - Domestic borrowing (limited availability).
  - External concessional and non-concessional borrowing (may be slow or unavailable).
  - Grant financing (identified as essential in many scenarios).

### Relationship to existing literature
- Macroeconomic effects of public investment and fiscal/debt sustainability: Barro (1990); Barro and Sala-i-Martin (1992); Futagami et al. (1993); Turnovsky (1999); Buffie et al. (2012); Adam and Bevan (2006).
- Macroeconomic effects of natural disasters: Cavallo and Noy (2011); Noy (2009); Bevan and Cook (2015); Cavallo et al. (2013); Becerra et al. (2014); Bakkensen and Barrage (2017); Borensztein et al. (2017); Bevan and Adam (2016); Ikefuji and Horii (2012).

### Paper organization (as stated)
- Section II: Model.
- Section III: Data used to calibrate the model and experiments conducted.
- Section IV: Macroeconomic impact of the natural disaster.
- Section V: Policies that could have been implemented prior to the disaster.
- Section VI: Conclusion and policy implications.

*Source: wp17223 - References26 (PDF chapter/section).*

### 2.    The Model

### 2.    The Model

### Overview
- Two-sector small open economy with traded (x) and nontraded (n) goods.
- Five channels through which a natural disaster affects the economy:
  - Permanent damages to public infrastructure.
  - Permanent damages to private capital.
  - Temporary losses of productivity from economic and social disruption.
  - Increased inefficiencies in public investment during reconstruction.
  - Damages to the sovereign’s creditworthiness.
- Government instruments for preparedness and recovery: domestic and external debt, grants, consumption taxes, government investment in adaptation infrastructure, and fiscal buffers (savings abroad).
- Adaptation infrastructure and standard infrastructure enter public capital via a CES aggregator with elasticity ξ and weight ρz.

### Firms
- Output in sector j (j = n,x):
  - yj,t = Aj,t zj,t−1^ψj kj,t−1^αj lj,t^(1−αj). (equation (2))
- Production uses public infrastructure zt, which is a CES of standard infrastructure zi and adaptation capital za with productivity νa:
  - zt = [ρz^(1/ξ) zi,t^(ξ−1)/ξ + (1−ρz)^(1/ξ) (νa za,t)^(ξ−1)/ξ]^(ξ/(ξ−1)). (equation (3))
- Natural disaster damages Dj,t ∈ [0,1] permanently destroy public and private capital and induce a transitory productivity loss; public adaptation investment za reduces damages through scaling πj and νD.
- Decomposition of damages:
  - (1 − Dz_j) = (1 − Dj (1 + πj za)^(νD))^$z
  - (1 − Dk_j) = (1 − Dj (1 + πj za)^(νD))^$k
  - (1 − DA_j) = (1 − Dj (1 + πj za)^(νD))^(1−$z ψj − $k αj)
  - Constraint: 1 − $z ψj − $k αj ≥ 0.
- Firm profit maximization (sector j):
  - Φj,t = Pj,t (1 − Dj,t (1 + πj za,t−1)^(νD)) yj,t − wt lj,t − rj,t kj,t−1. (equation (1))
- Factor demand conditions:
  - Pj,t αj yj,t / kj,t−1 = rj,t. (equation (4))
  - Pj,t (1 − αj) yj,t / lj,t = wt. (equation (5))
- Output elasticity w.r.t. public capital:
  - Pj,t ψj yj,t / zt−1 = Rz,t. (equation (6))
  - Rz,t decomposed into Rzi,t and Rza,t with arguments involving zi,t−1, za,t−1, νa, ρz, and zt−1.
- Firms do not internalize protection benefits of adaptation (only production input benefits).
- Prices of capital and public infrastructure depend on imported machinery price Pmm and nontradable input price Pn:
  - Pk,t = Pmm,t + akis Pn,t.
  - Pzi,t = Pmm,t + az i Pn,t.
  - Pza,t = (1 + pr) Pmm,t + az a Pn,t.

### Government
- Government expenditures: Pzi,t izi,t + Pza,t iza,t, transfers Tt, and servicing domestic and external debt.
- Revenues: VAT on consumption τc,t Pt ct and fees on Ricardian households’ usage of standard public infrastructure μzei t−1 (μ = f δzi Pzi o).
- Public investment efficiency s ∈ [0,1]; s is time-varying and reduced by disaster through Ds at time of disaster.
- Public capital accumulation:
  - zi,t = (1 − δzi) zi,t−1 + (1 − Ds) s t i zi,t. (equation (7))
  - za,t = (1 − δza) za,t−1 + (1 − Ds) s t i za,t. (equation (8))
  - δzi > δza (adaptation infrastructure depreciates more slowly).
- Real interest rate on concessional debt held constant: rd,t = rd.
- Sovereign risk channel: disaster weakens rating by Dr,t and external commercial debt rate:
  - rdc,t = (1 + Dr,t) (rf + υg e ηg (dt + dc,t)/yt − ̄d + ̄dc/ ̄y ). (equation (9))
- Government can build foreign savings st (paying rf), drawn down only in major disasters.
- Financing instruments: external grants G, external concessional debt ∆d_t, domestic ∆b_t, external commercial ∆dc,t with rule (1 − υ) ∆b_t = υ ∆dc,t.
- Government budget constraint (nominal terms):
  - Pzi,t izi,t + Pza,t iza,t + Tt + rt−1 Pt bt−1 + rd,t−1 dt−1 + rdc,t−1 dc,t−1 + ∆s_t ≤ Pt ∆b_t + ∆d_t + ∆dc,t + rf st−1 + τc,t Pt ct + μz e t−1 + Gt.
- Fiscal gap formulation:
  - Gapt = Pt ∆b_t + ∆dc,t + (τc,t − τc,o) Pt ct − ∆s_t. (equation (10))
  - Gapt = Expt − Revt, where
    - Expt = Pzi,t izi,t + Pza,t iza,t + Tt + rt−1 Pt bt−1 + rdc,t−1 dc,t−1 + (1 + rd) dt−1 − dt.
    - Revt = rf st−1 + τc,o Pt ct + μz e t−1 + Gt.
- Fiscal rule for consumption tax τc,t:
  - τc,t = τc,t−1 + λ1 ((τc,t)target − τc,t−1) + λ2 (Pt−1 bt−1 + dc,t−1 − (Pb + dc)target / yt)  for λ1, λ2 ≥ 0. (equation (11))
  - Tax target: (τc,t)target = τc,o + Gap t / (Pt ct), ensuring long-run debt sustainability.
- Scenario choices in analysis:
  - τc,t = τc,o if government finances reconstruction entirely with borrowing.
  - τc,t = (τc,t)target if reconstruction is entirely financed with taxes.

### Households
- Two types: Ricardian (r) and liquidity-constrained (c).
- Consumption composite for household type i (i = r,c):
  - ci,t = [ρx^(1/ε) (cix,t)^(ε−1)/ε + ρm^(1/ε) (cim,t)^(ε−1)/ε + (1 − ρx − ρm)^(1/ε) (cin,t)^(ε−1)/ε]^(ε/(ε−1)). (equation (12))
  - Consumer price index:
    - Pt = [ρx Px,t^(1−ε) + ρm Pm,t^(1−ε) + (1 − ρx − ρm) Pn,t^(1−ε)]^(1/(1−ε)). (equation (13))
  - Foreign CPI P∗t is the numeraire.
- Ricardian household maximization:
  - max Σt=0^∞ β^t (cr_t)^(1−1/ςc) / (1 − 1/ςc).
- Ricardian decisions: invest in private tradable and nontradable capital ix and in, adjustment costs ACrj,t ≡ v/2 (irj,t / krj,t−1 − δ)^2 / krj,t−1; pay infrastructure levies μz i t−1; save through domestic bonds b and external private debt br∗ with interest r∗ and portfolio adjustment costs Θr∗t ≡ η/2 (br∗t − b s∗)^2.
- Ricardian household budget constraint:
  - (1 + τc,t) Pt cr_t + μz i t−1 + Pt br_t + (1 + r∗t−1) br∗t−1 + Θr∗t + Pk,t (irn,t + irx,t + ACrn,t + ACrx,t)
    ≤ wt lr_t + rn,t krn,t−1 + rx,t krx,t−1 + (1 + rt−1) Pt br_t−1 + br∗t + 1/(1 + a) (Rt + Tt) + Φr_t. (equation (14))
- Private capital accumulation (j = n,x):
  - krj,t = (1 − δk) krj,t−1 + irj,t. (equation (15))
- Euler and non-arbitrage conditions:
  - Consumption Euler (Ricardian):
    - cr_t = cr_t+1 [β (1 + rt) (1 + τc,t)/(1 + τc,t+1)]^(−ςc). (equation (16))
  - Returns on capital equate to return on domestic bonds with adjustment terms (equation (17)).
  - Return on domestic bonds equates to return on external private debt:
    - (1 + rt) Pt+1 / Pt = (1 + r∗t) [1 − η (br∗t − ̄br∗)]. (equation (18))
  - r∗t = rdc,t + u where u is a premium over sovereign commercial rate; η governs private sector integration abroad.
- Liquidity-constrained households:
  - Same preferences as Ricardian but cannot save/borrow domestically or externally.
  - Budget: (1 + τc,t) Pt cc_t = wt lc_t + a/(1 + a) (Rt + Tt). (equation (19))

### Aggregation and Market-Clearing Conditions
- Aggregation across households and firms: x_t = Σi=r,c Σj=n,x x_i,j,t for variables x_i,j,t ∈ {c_i j,t, l_i j,t, i_i,t, k_i j,t, AC_i j,t, b_i,t, b_i,∗t, y_j,t, Φ_i j,t}.
- Labor markets: lx,t + ln,t = lr_t + lc_t = lt.
- Nontradable goods market clearing:
  - yn,t = ρn (Pn,t / Pt)^(−ε) ct + ak (in,t + ix,t + ACn,t + ACx,t) + azi izi,t + aza iza,t. (equation (20))
  - ak and az i define nontradable content of private and public investment.
- Balance of payments (capital and current account relation):
  - ∆b∗t + ∆dc,t + ∆dt + Gt + Rt − ∆st =
    − [Pn,t yn,t + Px,t yx,t − r∗t−1 b∗t−1 − Θs∗t − rdc,t−1 dc,t−1 − rd dt−1 + rf st−1 − Pt ct − Pzi,t izi,t − Pza,t iza,t − Pk,t (in,t − ix,t − ACn,t − ACx,t)]. (equation (21))
  - Current account: cat = −∆b∗t − ∆dc,t − ∆dt − Gt − Rt + ∆st.

*Source: IMF Working Paper — chapter 2, "The Model", wp17223 - 2.    The Model*

### 3.    Calibration

### 3.    Calibration

### Calibration overview
- Model tailored to Vanuatu’s economy at the time of the natural disaster (2015).
- Parameters and initial values calibrated using literature and data provided by the authorities, the IMF, and other partners during late-2016 Article IV consultations.
- Initial values and parameters are reported in Table 1 and Table 2 (see text).

### Natural disaster: Cyclone Pam — damages and losses
- Total damages and losses: 60.8% of GDP (36.7% in damages and 24.2% in losses).
- Damages and losses by sector:
  - Tradable sector (agriculture, industry, tourism): 23.7% of GDP (45% in damages, remainder in losses).
  - Nontradable sector (education and health, communication, energy, environment, transport, water): 24.7% of GDP (57% in damages, remainder in losses).
  - Private housing: 12.4% of GDP.
- Distribution among public/private capital destruction and productivity losses depends on:
  - Output elasticities w.r.t public infrastructure (ψn and ψx).
  - Private capital shares in value added (αn and αx).
  - Severity of damages to public and private capital ($z and $k).
- Initial return on total public infrastructure Rzo = 30.0 percent; gross return on standard public investment Rzio = 30.0 percent.
- Initial gross return on public adaptation investment Rzao = 50.0 percent.
- Implied output elasticities w.r.t public infrastructure: 0.0312 (low elasticities reflecting high inefficiencies).
- Initial efficiency of public investment so = 60.0 percent (calibrated).
- Public standard infrastructure investment to GDP izi,o = 1.3 percent (set to 2015 levels).
- Adaptation infrastructure: iza,o = 0.0 and zao = 0.0 (practically nonexistent at time of Pam).
- Depreciation rates reported in text and table (see “Remaining Calibration” and Table 2 for calibrated values and potential notation differences):
  - Text: standard and adaptation capital depreciate at different rates with δzi = 7.5% and δzi = 3% (text discussion).
  - Table 2 entries: Depreciation rate of standard infrastructure (%) δzi = 3.0; Depreciation rate of adaptation infrastructure (%) δza = 7.5.
- Private capital shares in value added:
  - αn (nontradable) set to 30.0 percent in text discussion; Table 2 lists αn = 40.0 percent and αx = 30.0 percent — preserve table values where tabulated.
- Calibrated severity-of-destruction weights: $z = 0.4 and $k = 0.3.
- Cyclone causes damages of about 25.8% of public infrastructure and 25.5% of private capital relative to steady state.
- Productivity losses: deviations from steady state of 20.9% in the nontradable sector and 20.5% in the tradable sector.
- Public investment efficiency loss (Ds) assumed to be 20% (for every dollar invested an additional 12 cents lost).
- Disaster impact on real interest rate on external commercial debt: Dr = 0.15 (15% aggravation).
- Credit-rating channel: assumed ηg = 0 given limited exposure to international capital markets; S&P (2015) discussion noted largest natural disasters could lead to downgrades of around 1.5 notches.

### Reconstruction and recovery: assumptions and dynamic paths
- Government intent: rebuild damaged infrastructure to pre-Pam level in about five years.
- Recovery of public investment efficiency, sectoral TFPs, and credit risk premium follows a sigmoid function:
  - xt = exp(−γx t) xPam + (1−exp(−γx t)) xpre-Pam, where x ∈ {zi, s, A, j, Dr}, γx controls speed of transition, and t is time vector.
  - Note: Dpre-Pam r = 0.
- Public investment path for accelerated reconstruction:
  - i_reconstruction zi,t = zi t − (1−δzi) zi t−1 / s_t (formula as given in text).
- Key dynamic outcomes (with accelerated reconstruction program):
  - Public capital recovers to pre-Pam level in less than five years.
  - Public investment peaks at 5.5% of GDP before gradually declining to pre-Pam level 1.3% of GDP in about 10 years.
  - Without accelerated reconstruction, public capital remains well below pre-Pam level for a prolonged period.
  - Sectoral TFPs take about 6 years to regain pre-Pam levels.
  - Public investment efficiency recovers in less than 4 years.
  - The 25 basis point increase in the government’s real interest rate on external borrowing fades away after about 5 years.

### Remaining calibration and initial conditions (selected)
- Public debt levels (bo, do, and dc,o) taken from IMF 2016 debt sustainability analysis.
- Public external commercial debt corresponds to public semi-concessional debt (e.g., bilateral donors).
- Private external debt (b*o) from World Bank long-term private nonguaranteed external debt series.
- Grants and remittances (Go and Ro) taken from IMF based on Reserve Bank of Vanuatu and Ministry of Finance estimates; initial grants include significant 2015 inflows.
- Real interest rates:
  - Real interest rate on concessional debt r d is assumed 0.0 percent.
  - Real interest rate on public external debt r dc,o matches semi-concessional lending: 1.5 percent.
  - Real interest rate on public domestic debt r o = 5.0 percent.
- Initial consumption tax (VAT) rate τc o = 12.5 percent.

### Table 1 — Selected initial values (%)
- Public standard investment to GDP izi,o: 1.3
- Public adaptation investment to GDP iza,o: 0.0
- Return on public standard infrastructure investment Rzi o: 30.0
- Return on public adaptation infrastructure investment Rza o: 50.0
- Public domestic debt to GDP bo: 7.7
- Public concessional debt to GDP d o: 12.9
- Public external (commercial) debt to GDP dc,o: 5.0
- Real interest rate on public domestic debt r o: 5.0
- Real interest rate on public concessional debt r d,o: 0.0
- Real interest rate on public external debt r dc,o: 1.5
- Savings to GDP s o: 0.0
- Grants to GDP G o: 11.2
- Consumption tax (VAT) rate τ c o: 12.5
- Private external debt to GDP b* o: 0.0
- Remittances to GDP R o: 3.5

### Public capital technology and substitutability
- Baseline intratemporal elasticity of substitution between public capital inputs ξ such that (ξ−1)/ξ = 1 (or ξ = +∞), making standard and adaptation infrastructure perfect substitutes and zt = zi t + νa za t.
- Marginal rate of technical substitution between public capital inputs in baseline: Rza t / Rzi t = νa.
- Alternative specifications discussed (no experiments here):
  - Perfect complements (Leontief): total public capital = min(zi t ρz, νa za t 1−ρz) with ξ → 0.
  - Cobb-Douglas: zt = (zi t)ρz (νa za t)1−ρz with ξ → 1.
- Discussion on policy implication: with perfect substitutability, social planner would prefer adaptation infrastructure due to scarcity, lower depreciation rate, and disaster-reduction benefits.

### Table 2 — Calibrated parameters (selected)
Firms
- Capital share in value added in the nontraded goods sector (%) αn: 40.0
- Capital share in value added in the traded goods sector (%) αx: 30.0
- Cost share of nontraded inputs in the production of private and public capital (%) ak, a zi, a za: 50.0

Households
- Intertemporal elasticity of substitution of consumption ςc: 0.34
- Intratemporal elasticity of substitution across consumption goods ϕ: 0.50
- Share of liquidity-constrained households (%) a/(1+a): 12.7
- Portfolio adjustment costs parameter η1: 0.0
- Depreciation rate of private capital (%) δk: 5.0

Government
- Intratemporal elasticity of substitution across public capital inputs ξ: +∞
- Depreciation rate of standard infrastructure (%) δzi: 3.0
- Depreciation rate of adaptation infrastructure (%) δza: 7.5
- User fees fraction of recurrent spending (%) μ: 50.0
- Premium on imported machinery for adaptation infrastructure (%) pr: 0.0
- Public debt risk premium parameter ηg: 0.0
- Risk-free world real interest rate (%) r*: 2.0

Additional calibration notes:
- Share of liquidity-constrained households calibrated from latest World Bank reported poverty headcount ratio (national poverty lines) — figure may understate lack of credit access.
- Government charges households a fee fraction μ = 50% of recurrent costs.
- Imports to GDP used for CES consumption basket share parameters: imports of goods = 54% (IMF).
- CES public capital definition tilted in favor of standard public infrastructure: 90% (share parameter).
- Value added in nontradable sectors used to compute share of output in nontraded sector: 48% (national accounts estimates).

### 4. Recovering with fiscal and debt sustainability — key scenarios and findings
- Two financing scenarios analyzed for the government-financed accelerated reconstruction (no donor support):
  1. Tax-financed (increase consumption tax).
  2. Debt-financed (external borrowing).
- Main findings:
  - Both financing schemes produce similar impacts on real GDP, but different distributional and sustainability outcomes.
  - Tax-financed reconstruction:
    - Consumption tax rate would need to rise from 12.5% to close to 23% in the short term and to about 14% over the medium term.
    - Private consumption would drop 20% relative to its pre-Pam level.
    - Private investment falls sharply (about 40% in tradable sector and 42% in nontradable sector).
    - Domestic real interest rate spikes (from 5% to 18% for Ricardian households), exacerbating intertemporal consumption effects.
    - Increasing taxes conflicts with authorities’ goal to smooth household consumption; in practice, government suspended VAT and import duties on construction materials and allowed 20% withdrawals from National Provident Fund.
  - Debt-financed reconstruction:
    - Private consumption falls less than under tax-financed reconstruction.
    - But debt-financed reconstruction pushes public debt to well above 90% of GDP in the medium term and could reach above 105% of GDP in 30 years (from 25% pre-Pam).
    - Real exchange rate appreciates about 4%, reducing tradable sector competitiveness; current account deficit worsens to about 9% of GDP.
    - Negative impact on tradable sector is 5 percentage points stronger relative to pre-Pam when government resorts to borrowing versus taxes.
  - Both strategies leave capital stocks about 20% below pre-Pam level for more than 10 years; both entail significant risks and challenging medium-term recovery.
- Grants-for-reconstruction scenario (donor-funded)
  - Donor grants closing government budget constraint (no additional taxes or borrowing) would require:
    - An additional 50% of pre-Pam GDP in grants over 15 years after the cyclone.
    - Grants peak at 17% of (actual) GDP in the first five years and stay above 12% of GDP over the medium term before returning to 2015 level in long run.
  - Grants-financed reconstruction benefits:
    - Allows recovery akin to debt-financed program but without debt-distress concerns.
    - Current account stabilized in about 15 years after the cyclone due to lower debt levels.
    - Grants often include technical assistance, procurement rules, and institutional strengthening that sustain public investment efficiency and accelerate productivity recovery—implying stronger recovery of private consumption and investment if modeled.
  - Practical note: actual donor disbursements did not match initial commitments in GDP terms, implying reconstruction pace likely slower than envisioned; “aid fatigue” concerns could dampen government incentives for tax collection over prolonged donor support.

*Source: IMF working paper (section 3, “Calibration”, and related discussion in section 4) — wp17223 - 3.    Calibration (PDF).*

### 5.    Building  Resilience  with  Adaptation  Infrastructure  and  Fiscal

### 5.    Building  Resilience  with  Adaptation  Infrastructure  and  Fiscal Buffers

### Investing in Resilient Infrastructure
- Thought experiment: government spends 3% of GDP per year in adaptation infrastructure in the five years prior to Cyclone Pam; expenditures entirely funded by donors; post-disaster accelerated reconstruction path assumed identical for comparability.
- Effects on damages and productivity:
  - Reduced damages to standard public infrastructure (e.g. roads) by 5.2%.
  - Reduced damages to private capital by 9.7%.
  - Reduced productivity losses in the tradable sector by 3.8% and in the nontradable sector by 3.9%.
- Fiscal and debt outcomes:
  - Investing in adaptation attenuates fiscal and debt sustainability concerns.
  - Public debt reaches less than 60% of GDP over the medium term (as opposed to 100% of GDP in the no-adaptation scenario).
  - Tax-financed reconstruction requires a consumption tax rate increase to 21%, yet the tax reverts much faster to its initial value (in about five years) compared with the prolonged tax increase without adaptation investment.
- Macro behavior and private sector responses:
  - Investing in adaptation raises the marginal product of private capital, crowding in private investment prior to the disaster and increasing the domestic real interest rate.
  - Short-term contraction of private consumption, particularly among savers.
  - Post-disaster outcomes relative to initial steady state:
    - Private investment declines by about 23% to 31% (a 10 percentage point difference with the no-adaptation scenario).
    - Private consumption decreases by about 10 to 12%.

### Building Fiscal Buffers
- Policy considered: reallocate half of the annual 3% of GDP (i.e., 1.5% of GDP) to an external contingency fund and the other half to adaptation investments; donors support both allocations; external borrowing closes remaining fiscal gap.
- Accumulation and use of contingency fund:
  - Government accumulates about 8% of GDP in its external contingency fund.
  - Withdrawals amount to 75% of the fund’s remaining balance for three years after the disaster to fund reconstruction.
  - Availability of the fund allows reconstruction to start without additional short-term borrowing.
- Comparative outcomes (contingency fund + adaptation vs only adaptation vs no resilience):
  - Building fiscal buffers yields lower medium-term debt-to-GDP levels compared with only investing in resilient infrastructure, though GDP is more affected in the contingency-fund case.
  - Total public debt reaches 53% of GDP by 2035 in the contingency-fund scenario; gains subside by 2035.
  - Both preemptive policies (only adaptation; adaptation + contingency fund) lead to debt levels about 25 percentage points lower than the post-disaster reactive policy.
- Trade-offs and macro effects:
  - Diverting part of adaptation investment to the contingency fund reduces the stock of resilient infrastructure and thus increases destruction of public and private capital in the event.
  - Scarcity of adaptation capital raises its marginal benefit and sustains crowding in of private investment prior to the disaster.
  - Relative to investing entirely in adaptation, coupling adaptation with savings (contingency fund) saved the economy 3 percentage points of output less (i.e., investing entirely in adaptation saved the economy 3 percentage points of its output relative to the coupling strategy), noting adaptation investments are not fully efficient.
  - With tax rate fixed in the contingency-fund strategy, private consumption still drops 12% below its initial value upon the shock; the domestic real interest rate reaches negative values.
  - Given low real interest rates and expectation of the storm, private consumption rebounds immediately but stays below pre-Pam level for several decades.
  - Adjusting taxes to finance reconstruction would have further dampened the contraction of private consumption.

- Heuristic for contingency fund contributions:
  - If there is one in five chance every year of a shock that costs 1% of GDP, then 1/4% of GDP should be deposited in the contingency fund every non-disaster year.

- Practical considerations and normative conclusions:
  - For relatively frequent, manageable events (e.g., damages ~1% of GDP), accumulating a contingency fund can be welfare-improving if development partners are unlikely to provide major post-disaster assistance.
  - For truly catastrophic events like Cyclone Pam, relying on donor support (grant-fathering) is essential; small developing states cannot credibly or rationally accumulate enough in a contingency fund to self-insure against cataclysmic events without stunting development.
  - Small states may find catastrophe insurance unattractive because donors could offset insurance payouts by reducing post-disaster aid.
  - A modest contingency fund can help finance immediate needs while donor packages are assembled, but many post-disaster needs (food, potable water, shelter, electricity, and logistics) require donor organization and in-kind support, not just cash.
  - For donors, financing resilient infrastructure ex ante in small developing states may be cheaper in the long run than post-disaster assistance, though political dynamics may favor post-disaster mobilization.

### Conclusions (policy implications and extensions)
- Main findings:
  - Small developing states hit by natural disasters face long-lasting economic scars from infrastructure destruction and productivity impacts, placing large strains on government finances.
  - Grant-fathering by bi- and multilateral partners is key for debt sustainability and a smooth recovery after a major disaster.
  - The government can and should invest in resilient infrastructure and build fiscal buffers to attenuate disaster impacts, but these require creating fiscal space (raising taxes, reducing other expenditures) or resorting to borrowing.
  - Donor support for preemptive investments in resilience reduces the need for larger post-disaster financial contributions.
  - Even with reasonable adaptation infrastructure, recovering from a highly damaging disaster will still demand significant donor contributions.
- Suggested policy dialogue topics and model extensions:
  - Incorporate disaster costs into budget planning (average impact on growth, increased infrastructure depreciation rates, maintenance costs).
  - Build fiscal buffers and invest in infrastructure able to withstand disasters (including urban planning and integrated coastal zone management).
  - Enhance the framework for coping with natural disasters (national plan, institutions, responsibilities) to accelerate recovery and reduce productivity and investment inefficiencies.
  - Model extensions could study optimal balance between ex ante and ex post policies for policymakers and donors, consider different damage functions (e.g., temperature or wind speeds), and assess climate change impacts on growth and debt sustainability.

*Italicized source: IMF Working Paper, chapter 5, "Building Resilience with Adaptation Infrastructure and Fiscal Buffers."*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17223.pdf_