## _wp15164

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---

### Features of the Model
- Model type and purpose:
  - Two-sector open economy dynamic general equilibrium model with three types of public sector debt (external concessional, external commercial and domestic debt).
  - Evaluates public investment scaling-up strategies using a debt-sustainability framework for LICs (Buffie and others (2012) based).
  - Designed to analyze trade-offs and risks across public investment, economic growth and debt sustainability; captures efficiency of public investment, absorptive capacity, return on infrastructure, and fiscal reaction rules.
- Key mechanisms and policy levers:
  - Public capital (effective public capital Z) enters Cobb–Douglas production functions for tradable and non-tradable sectors, complements private capital (K) and labor (L).
  - Financing options: concessional loans and grants exogenously fixed; non-concessional domestic and external borrowing available.
  - Policy instruments: consumption tax (VAT τ), user fees for infrastructure (u), transfers (TR), and choice of debt instruments (domestic D, external commercial C, concessional S).
  - Government budget constraint equates financing (D, C, S, u, T, G) with interest payments, investment I, and transfers TR; interest rates i_D, i_C, i_S; risk premium on external commercial debt depends on public debt-to-GDP deviations.
- Behavioral structure:
  - Firms: two sectors (T, N), imported good for consumption/capital; firms maximize profit choosing labor and capital; labor mobile across sectors.
  - Households: savers (smooth consumption; invest in I_T, I_N, domestic bonds B, foreign debt F) and non-savers (hand-to-mouth consume all income); parameter φ governs saver share; portfolio adjustment costs ψ(F) and parameter ν govern capital mobility.
- Fiscal reaction and constraints:
  - Policy adjustment function maps debt gap G to fiscal instruments; fiscal reaction parameter α divides adjustments between tax increases and transfer cuts (α = 1 all on tax; α = 0 all on transfers).
  - Tax and transfer reaction functions include ceilings/floors: τ̄ (ceiling on tax) and TR̲ (floor for transfers); γ_i are fiscal reaction speeds.
- Important modeling lessons:
  - Timing, maintenance costs, investment efficiency, and absorptive capacity crucial for whether investment scaling-up yields fiscally sustaining growth.
  - High-return investments may still be fiscally unsustainable if benefits accrue too late, user fees/tax rates are low, or efficiency is poor.

### Calibration to Sierra Leone
- Calibration approach and caveats:
  - Parameters set to Sierra Leone where available; otherwise values typical for LICs (Buffie et al. (2012)).
  - Trend per capita growth rate set at 3.3 percent (average 2004–11 WDI).
- Institutional and structural parameters (base case and context):
  - Base case return on infrastructure = 0.25 (25 percent).
  - Efficiency of public investment ξ = 0.60 (60 percent); base case assumes 40 percent of public investment fails to increase productive infrastructure.
  - Absorptive capacity constraint parameter φ = 2.00 (interpreted as approximatively 80 percent execution rate).
  - Portfolio adjustment costs parameter = 1.00.
  - Public debt risk premium parameter (baseline) = 0.00.
- Interest rate and debt calibration:
  - Initial real interest rate on domestic debt: 0.10
  - Initial real interest rate on private external debt: 0.10
  - Real risk free foreign interest rate: 0.04
  - Real interest rate on concessional loans: 0.00
  - Initial real interest rate on public commercial loans: 0.06
- Household and financial parameters:
  - Ratio of supply of labor of non-Ricardian to savers (a) set at 1.5 so that 60 percent of consumers are non-Ricardian.
  - Financial deepening indicators preserved as presented: roughly three bank branches per 100,000 persons; 19 percent of population holds a bank account; 1 percent holds a loan from the banking system.
- Sectoral/import content and other calibration notes:
  - Import content of public capital assumed about 75 percent.
  - Capital’s share in value added: traded sector 0.32 (32 percent); nontradable sector 0.40 (40 percent).
  - Selected base-case parameter table highlights (values preserved exactly):
    - 0.34 Intertemporal elasticity of substitution
    - 0.90 Intratemporal elasticity of substitution across goods
    - 0.32 Capital’s share in value added in the traded sector
    - 0.40 Capital’s share in value added in the nontraded sector
    - 0.49 Cost share of non-traded inputs in the production of private capital
    - 0.43 Cost share of non-traded inputs in the production of public capital
    - 0.05 Depreciation rate
    - 0.00 Capital learning externalities
    - 0.00 Sectoral output learning-by-doing
    - 0.48 Value-added in non-traded sector
    - 0.33 Import to GDP ratio
    - 0.033 Trend growth rate
    - 1.00 The portfolio adjustment costs parameter
    - 0.00 Public debt risk premium parameter
    - 0.10 Initial real interest rate on domestic debt
    - 0.10 Initial real interest rate on private external debt
    - 0.04 Real risk free foreign interest rate
    - 0.00 Real interest rate on concessional loans
    - 0.06 Initial real interest rate on public commercial loans
    - u 0.04 Private debt risk premium
    - 0.02 Public debt risk premium
    - 0.25 Initial return on infrastructure
    - 0.09 Initial public domestic debt to GDP ratio
    - 0.253 Initial public concessional debt to GDP ratio
    - 0.017 Grants to GDP ratio
    - 0.04 Remittances to GDP ratio
    - 0.08 Initial ratio of infrastructure investment to GDP
    - 0.60 Efficiency of public investment
    - 0.15 Initial consumption VAT
    - 2.00 Absorptive capacity parameter
    - 0.25 Fiscal reaction parameters (policy instrument terms)
    - 0.02 Fiscal reaction parameters (debt terms)
    - 0.60 Share of non-saving household
    - 2.00 Tobin’s q-elasticity of investment spending
- Base-case scenario explicitly considered:
  - Return on infrastructure = 0.25; Efficiency = 0.60; Absorptive capacity parameter = 2.00; Portfolio adjustment costs = 1.00; Public debt risk premium parameter = 0.00.

### Base Case Analysis: dynamics and key quantitative outcomes
- Baseline public investment path and financing:
  - Initial public investment: 8 percent of GDP.
  - Peak: 14.1 percent of GDP after 3 years.
  - After 10 years: falls to around 11 percent of GDP and stays permanently.
  - Increase in public investment simulated: nearly 36.67 percent of initial GDP during the first 10 years (22.46 percent during the first 5 years).
  - Financing assumed mainly through grants and highly concessional loans; consumption tax rate permanently maintained at 15 percent.
  - Grant element path: above 5 percent of GDP in first five years; then decelerates to 2.43 percent of GDP and to 1.7 percent of GDP by year 10.
- Short-run effects:
  - Real exchange rate appreciation: about 4 percent from initial level by year 3.
  - Tradable sector: declines by 3 percent below the steady state by year 3.
  - Non-tradable sector: increases by 5 percent by year 3 and by 5.8 percent by year 30 relative to steady state.
  - Public capital increases almost by 22.5 percent by year 5 relative to steady state while private capital stock does not accumulate by same year.
  - Private investment initially declines by about 2.4 percent from steady state by year 3 as interest rate climbs.
- Medium- to long-run effects:
  - Real per capita GDP growth peaks to 4.9 percent by year 4 before declining.
  - By year 14 growth rate is 3.4 percent (0.1 percentage points higher than the assumed long term growth rate of 3.3 percent).
  - By year 20: public effective capital is 29 percent higher and private capital is 4.2 percent higher relative to steady state.
  - Debt: repayment phase of concessional debt starts by year 10; total public debt peaks at 57.6 percent of GDP by year 9 and then declines during repayment phase.
  - Forecasted debt level judged not unreasonably burdensome though debt-to-exports could indicate higher distress given growing dependence on iron ore exports.
- Short-run fiscal-adjustment mechanisms considered:
  - Constrained tax adjustment with unconstrained spending adjustment; constrained spending adjustment with unconstrained tax adjustment.
  - With financing mainly via grants and concessional loans, macro outcomes similar across the two mechanisms in baseline.

### Alternative Assumptions and Financing Scenarios
- A. Closing financing gap with external commercial borrowing:
  - Baseline concessional loans and grants retained; additional external commercial and domestic borrowing fill gap; consumption VAT allowed to adjust.
  - Short-run: fiscal adjustment easier; private consumption and investment not crowded out and increase initially relative to baseline; real exchange rate appreciates further; traded sector contracts by -5 percent after 3 years (versus -3 percent baseline).
  - Debt outcomes: commercial public debt peaks at 23 percent of GDP; total public debt peaks at 72 percent of GDP; commercial public debt and total public debt gradually decrease after 9 years and return to 10 percent and 39 percent respectively by year 25.
  - Long-run: consumption tax rate must increase rapidly to stabilize debt.
- B. Closing financing gap with domestic borrowing (vs external commercial borrowing):
  - Domestic borrowing competes with private sector resources, crowds out private consumption and investment, and increases volatility in domestic interest rates.
  - Domestic public debt higher under domestic borrowing: 30 percent of GDP in year 11 versus 21 percent of GDP by year 9 in external commercial borrowing case.
  - Domestic debt projected to decline from its peak in year 9 to 26 percent of GDP in year 25.
  - Domestic financing terms more expensive and decline more slowly than external commercial borrowing; private investment contracts and remains negative territory for up to 7 years under domestic borrowing.
  - External commercial debt stock declines to around 10 percent of GDP in year 25.
- Alternative investment strategies:
  - Aggressive scenario: public investment rises from 8 percent to 19 percent of GDP by year 4, then falls to 11 percent permanently by year 10.
    - Consumption tax rate peaks at 23 percent in year 9 (versus 17.5 percent in baseline).
    - Additional fiscal effort represents 5.5 percentage points increase of consumption tax relative to baseline in year 9.
    - Short-to-medium-term: lower private consumption and private investment (private consumption below base for first 13 years).
    - Long-term: external commercial public debt 10 percent of GDP in year 20 versus 14.5 percent in base case (4.5 percentage point lower) due to higher long-term growth benefits.
  - Modest scaling-up scenario: peak investment 1.2 percentage points lower than base case; smaller tax adjustment; short-run marginal improvements in private consumption and investment; risk to long-term growth and sustainable debt path if commercial loans finance gap.

### Baseline strategy with structural reforms and sensitivity analysis
- Parameter sets and scenarios:
  - Baseline: Return on infrastructure = 0.25; Efficiency = 0.60; User fees f = 0.50; Absorptive capacity φ = 2.00.
  - Pessimistic: Return on infrastructure = 0.15; Efficiency = 0.40; User fees f = 0.30; Absorptive capacity φ = 5.00.
  - Optimistic: efficiency improves gradually from 0.6 to 0.75 within 10 years.
- Outcomes:
  - Optimistic scenario: effective public capital and growth rates much higher than baseline; total public debt lower; external commercial public debt peaks around 17.5 percent at t=6 and declines to 1.2 percent at t=30; real per capita GDP growth much higher; fiscal adjustment less painful.
  - Pessimistic scenario: real per capita GDP growth increases below assumed long-run 3.3 percent; private consumption falls into negative territory by year 7 until year 25; private investment below baseline due to sharp fiscal adjustment.
- Policy implication:
  - Institutional reforms that raise return on infrastructure and efficiency of public investment (“investing in investing”) materially enhance growth dividends and debt sustainability.

### Policy conditions: fiscal limits, timing and speed of fiscal adjustment
- Fiscal limit cases and tax caps:
  - Two cases for loans and grants adjustment:
    - Panel A: grant-financing grows disproportionately higher after year 10 (similar to baseline).
    - Panel B: loans and grants permanently proportional to public investment scaling up.
  - Consumption tax caps modeled: 16.0 percent and 16.5 percent by year 8.
  - With cap at 16.0 percent (Panel A) total public debt = 45.6 percent of GDP by year 20.
  - With cap at 16.5 percent (Panel A) total public debt = 42 percent of GDP by year 20.
  - With cap at 16.0 percent (Panel B) total public debt > 79 percent of GDP by year 20.
- Timing and speed of adjustment:
  - Faster adjustment: consumption VAT jumps from 15 percent to 16 percent during years 1–6, then to 16.5 percent by year 7.
  - Slower adjustment: VAT stuck at 15 percent over years 1–6, then to 16 percent by year 7.
  - Finding: faster adjustment implies lower debt levels; delays raise risk of unsustainable debt, especially if loans and grants only grow proportionally to investment.

### Downside risks, shocks, and Box 1 findings
- Terms-of-Trade (TOT) shocks:
  - Two permanent negative TOT shocks at year 9 considered: 10 percent decline and 20 percent decline.
  - Negative TOT shifts can lead to unsustainable debt levels; magnitude of shock matters.
  - If concessional financing increases more than proportionally to investment, debt paths remain manageable; if financing adjusts only proportionally, debt paths can be explosive.
  - Policy implication: prioritize grants and highly concessional loans to cover financing needs.
- Total-Factor Productivity (TFP) shocks:
  - Shock design: unexpected non-permanent (first-three years) TFP declines of 5 percent (year 1), 3 percent (year 2), 1 percent (year 3) across both sectors.
  - Real GDP contractions relative to steady state: 4.3 percent (year 1); 3.1 percent (year 2); 1.1 percent (year 3).
  - Under assumption that concessional loans component of fiscal gap financing is higher in long term, TFP shocks do not induce explosive public debt paths.
- Ebola and short-term fiscal impacts (preserved exactly as presented):
  - Short-term non-programed fiscal impact of Ebola in Sierra Leone is U$79 million (1.8 percent of GDP) according to World Bank (2014).
  - Short-term (2014) economic cost is estimated at 3.3 percentage point of GDP (reducing growth from 11.3 percent to 8 percent) (World Bank, 2014).
  - Immediate financial requirement to halt the epidemic is nearly four times the annual health budget.
- Broad downside risk conclusions:
  - Narrow export base and growing dependence on iron ore exposes Sierra Leone to volatile external shocks and increases debt-service vulnerability.
  - Commercial borrowing amid these risks increases probability of unsustainable debt and debt crises.
  - When grants and concessional lending are secured during ill-times, shocks less likely to generate explosive public debt paths.

### Key quantitative facts and selected figures preserved exactly as in source
- Planned increase in power production by an estimated 475 Mega Watts.
- Cost of the airport project is estimated at US$312 million (6.6 percent of 2013 GDP).
- Government will cover only 8 percent of the total estimated cost of the A4P from own budget; estimated budget support represents 56 percent of total cost with the remaining 36 percent unfunded.
- Public and publicly guaranteed external debt amounted to 142 percent of GDP at end–2005 and declined to 26 percent of GDP in 2007; about 30 percent of GDP at end-2011.
- Total external commercial debt amounted to 7.8 percent of GDP at end-2011.
- Domestic debt amounted to 11 percent of GDP at end-2011.
- Sierra Leone: Debt Stock Evolution, 2007–11 (in percent of GDP):
  - Domestic debt: 2007 — 18.4; 2008 — 17.5; 2009 — 15.2; 2010 — 13.8; 2011 — 11.1
  - External Debt: 2007 — 25.9; 2008 — 25.8; 2009 — 36.9; 2010 — 32.3; 2011 — 29.9
  - Multilateral: 2007 — 12.2; 2008 — 13.3; 2009 — 23.0; 2010 — 21.4; 2011 — 18.4
  - Bilateral: 2007 — 1.8; 2008 — 2.0; 2009 — 4.4; 2010 — 4.1; 2011 — 3.6
  - Commercial: 2007 — 12.0; 2008 — 10.0; 2009 — 10.0; 2010 — 9.1; 2011 — 7.8
- Appendix table (Agenda for Prosperity ESTIMATES, in Millions US$) — total row preserved:
  - Total: 633 1148.9 1450.7 1305.0 1208.7 5747.4 3205.6 464.8 2077.0
- Selected pillar totals from Appendix (values preserved):
  - Pillar 1 total: 1745.2; Partners: 1299.9; GoSL: 57.6; Gap: 387.7
  - Pillar 3 total: 1739.9; Partners: 1004.8; GoSL: 32.0; Gap: 703.1
  - Pillar 4 total: 1553.7; Partners: 734.2; GoSL: 256.2; Gap: 563.3
  - Pillar 6 total: 79.3; GoSL: 3.6; Gap: 75.7
  - Pillar 7 total: 577.4; Partners: 132.6; GoSL: 114.4; Gap: 330.39
  - Pillar 8 total: 11.5; Partners: 0.0; GoSL: 0.0; Gap: 11.5

### Policy recommendations and implications (extracted from analysis)
- Financing composition matters: prioritize grants and highly concessional loans to minimize short-run fiscal distress and long-run debt vulnerabilities.
- Strengthen institutional capacity and “invest in investing”:
  - Raise efficiency of public investment (improve project selection, monitoring and execution).
  - Improve return on infrastructure through regulatory and institutional reforms.
- Manage timing and speed of fiscal adjustment:
  - Faster fiscal adjustment (when feasible) reduces debt accumulation and risk of explosive debt paths.
  - If tax-side rigidities prevail, realistic investment scaling-up should be tempered or accompanied by faster, sustained grant financing.
- Cautious use of non-concessional borrowing:
  - External commercial borrowing can smooth adjustment but raises long-run debt vulnerability, especially under adverse TOT or TFP shocks.
  - Domestic borrowing risks crowding out private investment and increasing domestic interest-rate volatility.
- Prepare for downside shocks:
  - Maintain buffer and prioritize concessional financing to insulate public finances from TOT, TFP and epidemic shocks.

*Source: _wp15164 (excerpt) — IMF PDF content provided*

### 1. Features of the Model ...............................................................................................

### 1. Features of the Model

### Model purpose and scope
- Evaluates public investment scaling-up strategies in Sierra Leone based on the debt sustainability framework constructed by Buffie and others (2012) for LICs.
- Complements the standard IMF-World Bank debt sustainability framework by explicitly modeling and analyzing the links between public investment, economic growth and debt sustainability.
- Designed to analyze trade-offs and risks associated with different investment strategies, including fiscal policy reactions to debt and the use of non-concessional, domestic and concessional debt.
- Captures key structural factors: efficiency of public investment, absorptive capacity, and return on infrastructure.

### Context and policy questions addressed
- Assesses whether long-run growth pay-off from increased public investment accrues fast enough to sustain short- and medium-run increases in debt.
- Useful for evaluating financing mixes (concessional, external commercial, domestic) and fiscal responses (tax increases, spending cuts) needed to support investment scaling-up.
- Relevant for fragile, post-conflict economies with large reconstruction needs and limited fiscal space.

### Features signposted in the document
- Model sections in the source document include detailed treatments of:
  - A. Firms
  - B. Consumers
  - C. Government
- Calibration to Sierra Leone and extensive scenario analysis:
  - Base Case Analysis (short run; medium to long run)
  - Alternative Assumptions (external commercial vs concessional borrowing; domestic vs external commercial borrowing; alternative investment strategies)
  - Baseline investment strategy with structural reforms and policy conditions (structural reforms; fiscal limits; timing and speed of fiscal adjustment)
  - Downside risks (terms-of-trade shocks; total factor productivity shocks)

### Implementation and outputs (as indicated)
- Produces simulation results and figures for:
  - Frontloaded investment scaling-up under constrained and unconstrained tax adjustment.
  - Comparisons of external commercial versus concessional borrowing.
  - Domestic borrowing versus external commercial borrowing.
  - Aggressive and lower public investment scaling-up strategies.
  - Sensitivity to efficiency of public investment and fiscal limits.
  - Effects of negative TOT and TFP shocks and an estimated GDP impact of Ebola (2014-17).

### Relation to Sierra Leone’s policy plans
- The model is applied to evaluate the authorities’ Agenda for Prosperity (A4P) medium-term development plan and its financing implications.

### Key quantitative facts from Sierra Leone background (preserved exactly as in source)
- Planned increase in power production by an estimated 475 Mega Watts.
- Cost of the airport project is estimated at US$312 million (6.6 percent of 2013 GDP).
- Government will cover only 8 percent of the total estimated cost of the A4P from own budget; estimated budget support represents 56 percent of total cost with the remaining 36 percent unfunded.
- Short-term non-programed fiscal impact of Ebola in Sierra Leone is U$79 million (1.8 percent of GDP) according to World Bank (2014).
- Short-term (2014) economic cost is estimated at 3.3 percentage point of GDP (reducing growth from 11.3 percent to 8 percent) (World Bank, 2014).
- Public and publicly guaranteed external debt amounted to 142 percent of GDP at end–2005 and declined to 26 percent of GDP in 2007; about 30 percent of GDP at end-2011.
- Total external commercial debt amounted to 7.8 percent of GDP at end-2011.
- Domestic debt amounted to 11 percent of GDP at end-2011.

### Sierra Leone: Debt Stock Evolution, 2007-11 (in percent of GDP)
- Domestic debt: 2007 — 18.4; 2008 — 17.5; 2009 — 15.2; 2010 — 13.8; 2011 — 11.1
- External Debt: 2007 — 25.9; 2008 — 25.8; 2009 — 36.9; 2010 — 32.3; 2011 — 29.9
- Multilateral: 2007 — 12.2; 2008 — 13.3; 2009 — 23.0; 2010 — 21.4; 2011 — 18.4
- Bilateral: 2007 — 1.8; 2008 — 2.0; 2009 — 4.4; 2010 — 4.1; 2011 — 3.6
- Commercial: 2007 — 12.0; 2008 — 10.0; 2009 — 10.0; 2010 — 9.1; 2011 — 7.8

*Source: _wp15164 - 1. Features of the Model (excerpt) — IMF PDF content provided*

### 1. Features of the Model

### 1. Features of the Model

### Overview
- Model type: two-sector open economy dynamic general equilibrium model with three types of public sector debt (external concessional, external commercial and domestic debt).
- Intended use: long term analysis; does not include money or nominal rigidities.
- Public capital (infrastructure) enters the production function for both tradable and non-tradable goods; effective public capital depends on changes in the investment efficiency parameter.
- Financing options:
  - Concessional loans by official creditors and grants are exogenously determined and fixed.
  - Governments can borrow under non-concessional terms domestically and externally.
- Policy levers: tax policy (modeled as a tax rate on consumption), user fees for capital utilization, and choice of debt instruments.
- Main lesson: need to consider dynamic interactions of public investment, growth, recurrent costs, and fiscal policy; maintenance and timing matter for sustained increases in effective public capital and debt sustainability.

### A. Firms
- Structure: two production sectors (traded and non-traded) plus an imported good used for consumption or capital formation.
- Inputs: private capital (K), labor (L), and effective public capital (Z) used in Cobb-Douglas production functions for each sector (i ∈ {N, T}):

  (1)

- Public capital is non–sector-specific and complements private capital and labor, raising returns to private inputs and boosting growth.
- Sectoral productivities include “learning-by-doing” externality and “static” externality:

  (2) , for

- Firms maximize profit choosing labor and capital; notation includes sector output price (p_i), wage (w), and rental rate of capital (r_i). Labor is mobile across sectors; wage is not sector-specific.

### B. Consumers
- Two consumer types: savers and non-savers (hand-to-mouth).
- Preferences: CES basket of traded, imported, and non-traded goods (equation (3)) with price index (equation (4)).
  - Parameter θ governs the intra-temporal elasticity of substitution.
  - Parameters α_T, α_M, and α_N govern distribution in the basket and sum to one.
- Non-savers:
  - Consume all earned income each period (non-Ricardian behavior).
  - Budget constraint (including VAT τ):

    (5)

  - Non-saver subscript h; the parameter φ governs the ratio of savers to non-savers.
- Savers:
  - Smooth consumption over time via investment in traded and non-traded capital (I_T and I_N), domestic bonds (B), and foreign debt (F).
  - Pay user fees for infrastructure services (u).
  - Face real domestic interest rate r and exogenous real foreign interest rate r*.
  - Maximization is with the same utility as non-savers but subject to three constraints: budget constraint and two capital accumulation equations.
- Budget constraint for savers (in maximization problem):

  (6)

- Capital accumulation equations:

  (7)
  (8)

- Notation/details:
  - r: real interest rate on domestic bonds.
  - r*: interest rate on foreign debt.
  - δ: depreciation rate.
  - ψ(F) : portfolio adjustment costs linked to foreign liabilities (degree of financial account openness).
  - Π: profits for domestic firms.
  - g: trend growth rate of GDP per capita; model is rescaled by a permanent component of sector-wide total factor productivity growing at rate g.
  - κ_i: adjustment costs incurred in changing capital stock in each sector.
- Portfolio adjustment costs capture private sector integration into world capital markets. In log-linearized form, equation (9) implicitly defines private demand for foreign debt; parameter ν governs degree of capital mobility. A low ν appropriate for some emerging markets (open capital account); in LICs ν comparatively big indicating a fairly closed capital account.

  (9)

### C. The Government
- Public capital accumulation:

  (10)

  - Z̄ is public investment in steady state.
  - ξ̄ and ξ denote efficiency parameters of public capital at and off steady state (values between zero and one).
  - I is public investment; ΔZ is additional infrastructure generated by public investment.
  - Interpretation: one dollar of public investment does not necessarily yield one dollar of effective public capital (term ξ I).
- Government budget constraint equates financing (domestic debt D, external commercial debt C, concessional debt S, user fees u with recurrent cost ω, taxes and grants T+G) with expenditures on interest payments, infrastructure investment I, and transfers TR:

  (11)

  - i_D, i_C, and i_S are interest rates on domestic debt, external commercial debt, and concessional debt respectively.
  - Interest rate on concessional debt is exogenous (i_S = ī_S).
  - Interest rate on external commercial debt includes a risk premium depending on deviations of external public debt to GDP from its initial steady-state value B̄:

    (12)

    - r*: risk-free interest rate.
    - μ: public debt risk premium constant.
    - η: public debt risk premium parameter.
    - B: GDP.

- Supply price of infrastructure and private capital (combine one imported machine/equipment with m units of non-traded input) determined by:

  (13)
  (14)

  - p_m is relative price of imported machine/equipment; p_N is relative price of non-traded good.

- Policy adjustment function:

  (15)

  - X corresponds to expenditures (including debt service) less revenue on concessional borrowing when taxes (τ) and transfers (TR) are kept at initial values.
  - Combining (11) with (15) yields:

    (16)

- Public investment outlays include cost overruns due to absorptive capacity constraints (term in equation (14) defined by equation (17)):

  (17)

  - New investment multiplied by υ where:

    (18)

    - ψ captures severity of absorptive capacity constraint in the public sector.
- Fiscal adjustment for debt sustainability:
  - Debt gap denoted by G (the symbol as in text); debt sustainability requires VAT τ and/or transfers TR adjust to cover the debt burden G.
  - Policy makers combine tax increases and transfer cuts; policy parameter α divides fiscal adjustments between VAT and transfers.
  - Targets for debt-stabilizing tax rate and transfers:

    (19)
    (20)

    - When α = 1 all adjustments fall on tax; when α = 0 all adjustments fall on transfers.
- In a given year, taxes and transfers follow reaction functions with ceilings and floors:
  - Tax rule and transfer rule (equations (21) and (22)):

    (21) ,  , with  and

    (22) ,  , with  and

  - τ̄ is a ceiling on tax; TR̲ is a floor for transfers.
  - Variables X, Y or Z depend on whether the rule responds to domestic debt or commercial debt; Y_t is GDP in a given year.
  - Target debt level B̄ is exogenously given.
  - γ_i are fiscal reaction parameters in policy instrument terms (determine speed of fiscal adjustment); their calibration requires realistic assessment of country capacity for fiscal adjustment. γ_j are fiscal reaction parameters in debt terms.

### Key model purposes and mechanisms (summary)
- Captures dynamic interactions among:
  - Public investment (including absorptive capacity and efficiency of converting investment to effective public capital),
  - Growth (via complementarity and externalities),
  - Recurrent costs (maintenance and user fees),
  - Fiscal policy (taxes, transfers, debt composition, and reaction rules).
- Emphasizes timing and transitional fiscal risks: even high-return investments may not pay for themselves fiscally if tax rates and user fees are low, benefits accrue more to private sector, or benefits materialize after debt repayment is due.
- Allows assessment of debt sustainability under varying financing mixes (concessional vs. commercial vs. domestic) and fiscal reaction speeds.

*Source: _wp15164 - 1. Features of the Model*

### 2. Calibration to Sierra Leone

### 2. Calibration to Sierra Leone

### Calibration approach and caveats
- The model’s parameters are calibrated to match Sierra Leone-specific estimates where available; otherwise frequently used parameter values for low income countries (similar to Buffie and others (2012)) are used.
- The calibration is a rough approximation of the Sierra Leonean economy, not a replica; this limitation should be addressed in future applications of the model.
- The trend per capita growth rate is 3.3 percent, matching the average of 2004-11 reported in World Development Indicators.

### Institutional parameters governing public investment and debt dynamics
- Key parameters underpinning the institutional environment for scaling up public investment include:
  - Return on public investment (marginal product of effective public capital net of depreciation).
    - No Sierra Leone-specific estimate is available; literature for sub-Saharan Africa suggests upper bounds ranging from 20 percent to 30 percent for countries with good governance.
    - Base case return on infrastructure is set at 0.25 (25 percent).
  - Efficiency of public investment (fraction of public investment that becomes productive public capital).
    - Base case assumes 40 percent of public investment fails to increase productive infrastructure and the efficiency parameter is set at 0.60 (60 percent).
    - Alternative scenarios investigate higher efficiency (“investing to invest”) and implications for growth dividends and debt sustainability.
  - Absorptive capacity constraint (budget execution/execution rate of investment projects).
    - Empirical evidence: sub-Saharan Africa budget execution ratios ranged from 28 percent to 89 percent with an average of 66 percent.
    - For Sierra Leone baseline, execution rates are assumed to be approximatively 80 percent and the absorptive capacity constraint parameter is set at 2.00 (interpreted in text as 20 percent constraint).
    - Alternative scenarios investigate reduced or no constraint.

### Macroeconomic and financial parameters
- Parameters capturing borrowing costs and international financial integration shape reaction to debt and public capital accumulation:
  - Portfolio adjustment cost parameter is calibrated to reflect limited private sector access to international capital markets; set at 1.00.
  - Private and public debt risk premia are modeled as increasing functions of the debt-to-GDP ratio when nonconcessional borrowing is allowed; in the baseline the public debt risk premium parameter is set at 0.00.
  - At the steady state, the risk premium parameter equals the difference between the interest rate on public commercial debt and the risk-free foreign interest rate.
  - Initial real interest rates and related rates used in calibration:
    - Initial real interest rate on domestic debt: 0.10
    - Initial real interest rate on private external debt: 0.10
    - Real risk free foreign interest rate: 0.04
    - Real interest rate on concessional loans: 0.00
    - Initial real interest rate on public commercial loans: 0.06

### Household, savings, and financial deepening features
- Reflecting limited private savings and liquidity-constrained consumers:
  - World Bank data: roughly three bank branches per 100,000 persons in Sierra Leone; 19 percent of population holds a bank account; 1 percent holds a loan from the banking system (textual data preserved as presented).
  - Distinction between Ricardian and non-Ricardian households is incorporated.
  - Ratio of supply of labor of non-Ricardian to savers (a) is set at 1.5 so that 60 percent of consumers are non-Ricardian.
- Initial fiscal and balance-sheet shares used from available recent Sierra Leone data (2005-12 flows; 2011-12 stocks) include:
  - Tax rates on consumption, private consumption and trade/GDP shares, share of remittances to GDP, share of grants to GDP, initial public investment to GDP ratio, initial external and domestic debt to GDP ratios (these specific numeric initial values are provided in Table 2).

### Sectoral and import-content assumptions
- Cost shares of non-tradable input in production of public capital reflect high import content of public capital in Sierra Leone:
  - Import content of public capital assumed about 75 percent of total public capital (textual assumption).
- Capital’s share in value added for traded and nontraded sectors were chosen based on a Sierra Leone social accounting matrix by Fofana et al. (2014); due to poor national accounts data, gross operating surplus (GOS) shares were demeaned in calibration to:
  - 0.32 in the tradable sector (32 percent)
  - 0.40 in the nontradable sector (40 percent)

### Parameters set equal to Buffie and others (2012) due to lack of Sierra Leone-specific data
- Fiscal reaction parameters in policy instrument terms and in debt terms, private debt risk premium (u), public debt risk premium (), capital adjustment cost parameter (), Tobin’s q elasticity of investment spending parameter (), intertemporal elasticity of substitution (τ), intratemporal elasticity of substitution across goods (), and the real risk-free foreign interest rate () are set at the same values as in Buffie and others (2012).

### Key scenarios explicitly considered
- Base case: return on infrastructure = 0.25; efficiency of public investment = 0.60; absorptive capacity constraint parameter = 2.00 (approximatively 80 percent execution rate); portfolio adjustment costs parameter = 1.00; public debt risk premium parameter = 0.00.
- Alternative scenarios:
  - Higher efficiency of public investment (improved “investing to invest”).
  - Reduced or removed absorptive capacity constraints (higher execution rates).
  - Scenarios affect growth dividends, fiscal resource generation, and debt sustainability.

### Table 2: Calibration of Main Parameters (Base Case) — Selected parameter values
- 0.34 Intertemporal elasticity of substitution
- 0.90 Intratemporal elasticity of substitution across goods
- 0.32 Capital’s share in value added in the traded sector
- 0.40 Capital’s share in value added in the nontraded sector
- 0.49 Cost share of non-traded inputs in the production of private capital
- 0.43 Cost share of non-traded inputs in the production of public capital
- 0.05 Depreciation rate* ;
- 0.00 Capital learning externalities ;
- 0.00 Sectoral output learning-by-doing
- 0.48 Value-added in non-traded sector
- 0.33 Import to GDP ratio
- 0.033 Trend growth rate
- 1.00 The portfolio adjustment costs parameter
- 0.00 Public debt risk premium parameter
- 0.10 Initial real interest rate on domestic debt
- 0.10 Initial real interest rate on private external debt
- 0.04 Real risk free foreign interest rate
- 0.00 Real interest rate on concessional loans
- 0.06 Initial real interest rate on public commercial loans
- u 0.04 Private debt risk premium
- 0.02 Public debt risk premium
- 0.25 Initial return on infrastructure
- 0.09 Initial public domestic debt to GDP ratio
- 0.253 Initial public concessional debt to GDP ratio
- 0.017 Grants to GDP ratio
- 0.04 Remittances to GDP ratio
- 0.08 Initial ratio of infrastructure investment to GDP ;
- 0.60 Efficiency of public investment
- 0.15 Initial consumption VAT
- 2.00 Absorptive capacity parameter ;
- 0.25 Fiscal reaction parameters (policy instrument terms) ;
- 0.02 Fiscal reaction parameters (debt terms)
- 0.60 Share of non-saving household
- 2.00 Tobin’s q-elasticity of investment spending

*Note: Several parameters are reported with symbolic punctuation in the source (e.g., semicolons and parentheses) that reflect their presentation in the calibration table.

*Source: 2. Calibration to Sierra Leone (extracted from the provided IMF content unit)._

### 1.00 Elasticities of sectoral output with respect to infrastructure

### 1.00 Elasticities of sectoral output with respect to infrastructure

### IV. The Base Case Analysis
- Public finances can appear sound now but be vulnerable to shocks: terms-of-trade shifts, sudden stops in capital inflows, natural disasters, and aid shortfalls.
- Ebola outbreak implications for Sierra Leone:
  - Immediate financial requirement to halt the epidemic is nearly four times the annual health budget.
  - Government revises downward public infrastructure investment scaling-up relative to Agenda for Prosperity (A4P).
- Baseline public infrastructure investment path:
  - Initial level: 8 percent of GDP.
  - Peak: 14.1 percent of GDP after 3 years.
  - After 10 years: falls to around 11 percent of GDP and stays permanently.
  - Increase in public investment simulated amounts to nearly 36.67 percent of initial GDP during the first 10 years (22.46 percent during the first 5 years).
- Financing and fiscal assumptions:
  - Financing assumed to be covered mainly through grants and highly concessional loans.
  - Consumption tax rate permanently maintained at 15 percent.
  - Grant element of borrowing expected to remain above 5 percent of GDP in the first five years; then projected to decelerate to 2.43 percent of GDP before petering out to 1.7 percent of GDP by year 10.
  - Total public investment exceeds 90 percent of initial GDP over the 5 years of the country’s medium-term development strategy (footnote).
  - GoSL expectation: public infrastructure investment covered 43 percent by development partners’ commitment, 15 percent through own budget, with a funding gap of 42 percent (footnote).

### Fiscal adjustment parameterization (baseline scenarios)
- Two fiscal-adjustment mechanisms considered:
  - Constrained tax adjustment with unconstrained spending adjustment (figure 1).
  - Constrained spending adjustment with unconstrained tax adjustment (figure 2).
- Financing mainly via grants and concessional loans makes macroeconomic outcomes under the two mechanisms similar in the baseline.

### A. Short-Run Effects
- Real exchange rate:
  - Scenario produces a real exchange rate appreciation of about 4 percent from its initial level by year three.
- Public infrastructure import intensity:
  - Assumed nearly 75 percent of total public capital is import-intensive.
- Sectoral impacts:
  - Tradable sector declines by 3 percent below the steady state by year 3.
  - Non-tradable sector increases by 5 percent by year 3 and by 5.8 percent by year 30 relative to the steady state.
- Wages and Dutch disease:
  - Reallocation to non-tradable bids up wages, reflecting Dutch Disease effects.
- Factor reallocation sensitivity:
  - If sectors have very similar factor composition, even small appreciation reduces export sector significantly.

### B. Medium-to Long-Run Effects
- Role of grant-financed infrastructure:
  - Can halt short-run downside when medium-to long-term productivity improvements raise GDP growth, incomes, and debt sustainability.
- Consumption dynamics:
  - Euler consumption smoothing governs ricardian household consumption; consumption tax rate held constant.
  - 60 percent of households live hand to mouth; overall consumption path driven mainly by non-ricardian (transfer-driven) consumption.
  - Private consumption projected to decline slightly in year 4 (consumption tax rate increases by 2 percentage point and transfer declines by 1.5 percentage point in the same year), then increase gradually after five years.
  - Total private consumption is 5 percent higher relative to the steady state by year 25 when consumption tax rate and transfers converge to steady state.
- Private investment and capital:
  - Private investment initially declines by about 2.4 percent from the steady state by year 3 as interest rate climbs.
  - Public capital increases almost by 22.5 percent by year 5 relative to steady state while private capital stock does not accumulate by the same year.
  - By year 20: public effective capital is 29 percent higher and private capital is 4.2 percent higher relative to steady state.
- Real per capita GDP growth:
  - Peaks to 4.9 percent by year 4 before declining.
  - By year 14 growth rate is 3.4 percent, which is 0.1 percentage points higher than the assumed long term growth rate of 3.3 percent.
- Debt dynamics:
  - Repayment phase of concessional debt starts by year 10.
  - Total public debt peaks at 57.6 percent of GDP by year 9 and then declines during repayment phase.
  - Forecasted debt level judged not unreasonably burdensome, though debt-to-exports could indicate higher debt distress given growing dependence on iron ore exports.

### V. Alternative Assumptions
A. Closing the financing gap with external commercial borrowing
- Scenario setup:
  - Baseline concessional loans and grants path retained; additional external commercial borrowing and domestic borrowing used to fill gap.
  - Consumption VAT allowed to adjust.
- Short-run effects:
  - Fiscal adjustment easier in initial years; private consumption and investment not crowded out and increase in initial years relative to baseline.
  - Capacity constraints bind; real exchange rate appreciates further initially.
  - Traded sector contracts further: -5 percent after 3 years compared to -3 percent in baseline.
- Long-run effects and debt:
  - Commercial public debt peaks at 23 percent of GDP and total public debt peaks at 72 percent of GDP.
  - In the long run, consumption tax rate must increase rapidly.
  - Commercial public debt and total public debt gradually decrease after 9 years and return to 10 percent and 39 percent respectively in year 25.

B. Closing the financing gap with domestic borrowing versus external commercial borrowing
- Domestic borrowing scenario assumes broadening of investor base and domestic market capable of absorbing part of public borrowing requirements.
- Historical domestic debt stock reference:
  - Domestic debt was 18.4 percent of GDP at end-2007 (text cuts off at this point).

*Source: _wp15164 - 1.00 Elasticities of sectoral output with respect to infrastructure*

### 9.2 percent of GDP at end-2012), the rise in interest rate and the maturity structure highlight

### _wp15164 - 9.2 percent of GDP at end-2012), the rise in interest rate and the maturity structure highlight

### Domestic versus external borrowing: risks and dynamics
- Domestic borrowing:
  - Competes against private sector on available resource; produces a crowding-out effect on private consumption and investment.
  - Adds volatility to domestic interest rates (Buffie et al. 2012).
  - Domestic public debt is higher under domestic borrowing: 30 percent of GDP in year 11 versus 21 percent of GDP by year 9 in the external commercial borrowing case only.
  - Domestic debt stock is projected to decline from its peak level in year 9 to 26 percent of GDP in year 25.
  - Financing terms are more expensive for domestic borrowing than for external commercial borrowing; declines more slowly over time.
  - When government borrows domestically, domestic interest rate is volatile and private investment is crowded-out, especially for the first five years (investment contracts and remains in the negative territory for up to 7 years).
- External commercial borrowing:
  - External commercial debt stock declines to a level around 10 percent of GDP in year 25.
  - Both types of debt accumulations are expected to remain moderate over the long run.
- Short-run policy implication:
  - Alternative financing secured for public investment indicates that in the short run policymakers can enjoy both higher growth (economic efficiency) and welfare improvement (unpainful fiscal adjustment).
- Long-run trade-off:
  - Policymakers face a trade-off between fiscal sustainability and social-friendly goals; the need for debt sustainability and fiscal tightening measures are more likely to damage investment, growth and social indicators.

*Key figure references*: Figure 4 (Domestic borrowing versus external commercial borrowing) demonstrates volatile real interest rate, higher public debt under domestic borrowing, and crowding out of private investment.

### Alternative case investment strategies: aggressive and modest scenarios
- Common assumptions:
  - Same economic structure as baseline, similar level of grants as baseline.
  - No additional financing from concessional borrowing assumed for more aggressive investment strategy.
  - Government accesses external commercial loans to finance part of the fiscal gap.
  - Coping with public investment plans requires domestic fiscal stance adjustments; rigidity in spending adjustment implies adjustments mainly on the tax side.
- Aggressive public investment scaling up scenario:
  - Public investment projected to rise from 8 percent of GDP to 19 percent of GDP by year 4, then falls gradually to 11 percent of GDP permanently by year 10.
  - Consumption tax rate reaches a peak of 23 percent in year 9 compared to 17.5 percent in the baseline.
  - Additional fiscal effort necessary represents 5.5 percentage points increase of the consumption tax relative to the baseline in year 9.
  - Short-to-medium-term effects: lower private consumption and private investment (private consumption path below base case in the first 13 years; private investment lower compared to baseline, marginally).
  - Long-term effects: external commercial public debt is 10 percent of GDP in year 20 in the aggressive case versus 14.5 percent of GDP in the base case (4.5 percentage point lower); favorable debt dynamics partly result from higher long-term growth benefits.
- Lower public investment (modest scaling up) scenario:
  - Peak investment level is 1.2 percentage point lower compared to the base case.
  - Leads to smaller adjustment in tax rates.
  - Private consumption and private investment expand marginally in the short run relative to baseline.
  - Risk: jeopardizes long-term goals such as higher GDP growth rate and sustainable debt path, especially when commercial loans finance part of the fiscal gap.

*Key figure references*: Figure 5 (Aggressive public investment scaling up); Figure 6 (Lower public investment scaling up).

### Baseline investment strategy with structural reforms and sensitivity analysis
- Structural parameters and scenarios:
  - Parameters considered: return on infrastructure (), efficiency of public investment (), user fees on infrastructure (f), absorptive capacity (φ).
  - Two alternative scenarios versus baseline: optimistic and pessimistic.
  - Baseline parameter values: Return on infrastructure () = 0.25; Efficiency () = 0.60; User fees (f) = 0.50; Absorptive capacity (φ) = 2.00.
  - Pessimistic scenario values: Return on infrastructure () = 0.15; Efficiency () = 0.40; User fees (f) = 0.30; Absorptive capacity (φ) = 5.00.
  - Optimistic scenario: gradual improvement in efficiency from baseline value 0.6 to 0.75 within 10 years (figure 7).
- Outcomes under optimistic scenario:
  - Effective public capital and growth rate reach much higher levels compared to baseline.
  - Total public debt is at a lower level; external commercial public debt peaks at around 17.5 percent at t=6 and declines to 1.2 percent at t=30, below the base case.
  - Real per capita GDP growth rate reaches a much higher level compared to base case.
  - Fiscal adjustment (revenue side) is not painful; paths notably better in the long run.
- Outcomes under pessimistic scenario:
  - Real per capita GDP growth rate increases below the assumed long-run growth rate of 3.3 percent.
  - Total public debt stock reaches a much lower level compared to the base case (context indicates worse outcomes for growth and social indicators despite lower debt).
  - Private consumption path falls into negative territory by year 7 until year 25.
  - Private investment is below baseline due to sharp fiscal adjustment.
- Policy implication:
  - Good institutional factors (return on infrastructure, efficiency of public investment) contribute significantly to public investment effectiveness, economic growth, and sustainability.
  - Authorities should pursue structural reforms aimed at improving institutional and regulatory frameworks of project selection and monitoring, including “investing in investing” or investment in capacities that foster new investments and institutional capacities (Collier, 2008).

*Key figure references*: Figure 7 (Efficiency of public investment in optimistic scenario); Figure 8 (Higher efficiency and commercial public debt); Figure 9 (Lower structural conditions and commercial public debt).

### Policy conditions: fiscal limits, timing and speed of fiscal adjustment
- Fiscal limits and grant-financing cases:
  - Two cases for loans and grants adjustment:
    - Panel A: grant-financing proportional to degree of public investment scaling up during first 10 years while growing disproportionately higher after 10 years (similar to baseline assumed path).
    - Panel B: loans and grants permanently proportional to the degree of public investment scaling up.
  - To capture tax adjustment rigidities, the consumption tax rate is capped at 16 percent (red line) and at 16.5 percent (green line) by year 8.
- Impact of tax caps on total public debt:
  - With cap at 16 percent, total public debt amounts to 45.6 percent of GDP by year 20 in Panel A.
  - With cap at 16.5 percent, total public debt amounts to 42 percent of GDP by year 20 in Panel A.
  - When loans and grants grow quickly relative to scaled-up investment (Panel A), debt is more manageable than when loans and grants grow proportionately (Panel B).
  - For a tax rate restricted to 16 percent: total public debt reaches 45.6 percent of GDP by year 20 in Panel A versus more than 79 percent of GDP in Panel B.
- Timing and speed of fiscal adjustment:
  - Faster fiscal adjustment (discrete jumps in consumption VAT) vs slower adjustment:
    - Faster adjustment: consumption VAT jumps from initial 15 percent to 16 percent from year 1 to 6, then to 16.5 percent by year 7.
    - Slower adjustment: consumption VAT stuck at 15 percent over years 1–6, then to 16 percent by year 7.
  - When concessional loans and grants grow fast compared to scaled-up public investment (Panel A), postponing fiscal adjustment poses less risk of debt distress; debt trajectory does not explode.
  - When loans and grants grow proportionately to scaled-up investment (Panel B), delays in adjustment cause debt to blow up.
  - General finding: faster adjustment entails lower debt level; delays increase risk of unsustainable debt trajectories.

*Key figure references*: Figure 10 (Different fiscal limits); Figure 11 (Speed of tax adjustments).

### Downside risks
- Prevalent downside risks will have adverse effects on debt sustainability and other measures such as debt-to-revenue and debt-to-exports.
- Key risk factors:
  - Volatility in external and domestic outlook due to growing dependence on iron ore export and undiversified, narrow export base; economy prone to extreme vulnerability to terms of trade shock.
  - Protracted civil war historically damaged human capital and infrastructure; flight of qualified workers.
  - Current Ebola epidemic risks to morbidity could halt momentum and reverse post-conflict gains; economic costs felt in foregone productivity and foregone output.
  - These risks undermine public finances and may increase public debt risk premium.
- Implication for borrowing:
  - Commercial borrowing in presence of these risks is likely to induce unsustainable debt levels.
  - When grants and concessional lending are secured during ill-times, shocks are less prone to generate explosive public debt paths.

*Key figure references*: Figures in Section VII illustrate vulnerability and potential debt distress under downside scenarios.

*Source: _wp15164 - 9.2 percent of GDP at end-2012), the rise in interest rate and the maturity structure highlight — https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15164.pdf*

### Box 1: Speed of Fiscal Adjustment

### Box 1: Speed of Fiscal Adjustment

### Error Correction Model (ECM) representation and interpretation
- The equation of the tax rate dynamic (21) can be expressed in the form of Error Correction Model (ECM) as follows:
  - (21)
- Where  is the speed of adjustment parameter. It tells us by how many percent the tax rate deviation  from its target () is corrected every year.
- The lag in  entails that the adjustment is sluggish.
- Following Chiang (1984), (21) indicates that tax rate evolves sluggishly toward its target level at a constant speed () proportional to its distance from :
  - , or using the adjustment time t: .
- We define the adjustment ratio  as: ,
- From (21),
- The time it takes to close  percent of the gap is therefore:
- When  the speed of adjustment, , then it takes two to three years to cut half (i.e. ) the gap between the current tax rate and its target value.
- However, it takes one to two years to cut it half when the adjustment is speed up (e.g:).

### Terms-of-Trade (TOT) shock scenarios and debt implications
- Two scenarios of unexpected and permanent negative terms-of-trade shock hitting the economy at year 9 (a time of higher economic vulnerability):
  - 10 percent decline in the TOT.
  - 20 percent decline in the TOT.
- Findings:
  - Negative terms-of-trade shifts can lead to unsustainable debt levels; the magnitude of the shock matters for the debt level.
  - The scale and speed at which loans and grants adjust to the scale of public investment matters.
  - Assumption used: concessional financing increases more than proportionally compared to public investment. If financing adjusted only proportionally, debt paths would be explosive.
  - Conclusion drawn: Sierra Leone’s debt distress is moderate, but narrow export base and dependence on iron ore volatility could reverse that finding.
- Policy implication:
  - Need to continue seeking mostly grants and highly concessional loans to cover financing needs.

### Total-Factor Productivity (TFP) shock scenarios and GDP impacts
- Shock design:
  - Unexpected non-permanent (first-three years) negative TFP shocks modeled as a gradual, equal and simultaneous decline in productivity scale factors in tradable and nontradable sectors over the first three years.
  - Assumed simultaneous and equal decrease of 5 percent, 3 percent and 1 percent in the TFP scale factors in “year 1”, “year 2” and “year 3”, respectively.
- GDP impact (relative to the steady state):
  - Real GDP contracts by 4.3 percent in “year 1”.
  - Real GDP contracts by 3.1 percent in “year 2”.
  - Real GDP contracts by 1.1 percent in “year 3”.
- Comparison with World Bank estimates:
  - At the beginning of the year 2014, the World Bank forecasted that GDP growth in 2014 would amount to 11.3 percent for Sierra Leone.
  - In mid-August 2014 the World Bank revised these estimates to 8.0 percent, which is 3.3 percentages point decline.
  - In January 2015, the actual GDP growth (7.3) points to 4 percentages point decline of GDP growth in 2014.
  - The World Bank forecasts that GDP growth in 2015 would contract by 2 percent.
- Public debt implications:
  - TFP shocks do not induce explosive paths for public debt when the government contracts commercial loans, under the assumption that the concessional loans component of fiscal gap financing is higher in the long term.
  - Long-term path of concessional loans assumed slightly more than proportional to the path of public investment, which rules out risks to larger debt burden.

### Policy and structural conclusions (selected)
- Transforming Sierra Leone to achieve middle income status requires forceful steps to address structural and policy bottlenecks that impede the intended effect of public investment.
- More ambitious investment strategies, even with loans and grants similar to baseline, will require unrealistic and unachievable fiscal adjustment in the short term if tax-side rigidities prevail.
  - Potential adjustments could include cutting current spending to cover financing gaps, recurrent spending and interest payments—measures that may incur high political costs and conflict with the Agenda for Transformation.
- Intermediate investment scenario similar to the baseline:
  - Provides more feasible fiscal adjustment when accompanied by a sustained and faster trajectory of grant-financing.
- External commercial borrowing:
  - Could complement concessional loans and allow smoothing of fiscal adjustment, but poses risks to debt distress and debt crisis, especially given vulnerability to TOT shocks and Ebola-induced productivity shortfalls.
- Domestic borrowing:
  - Would normally play a limited role due to crowding-out effects in this framework.
- Institutional factors:
  - Good institutional factors contribute significantly to the returns from public investment, economic growth and sustainability.
  - Authorities should improve structural factors such as the return of infrastructure and the efficiency of public investment through reforms to project selection and monitoring—“investing in investing” (capacity building).

### Key numeric values and specific figures cited
- Terms-of-Trade shock magnitudes: 10 percent decline, 20 percent decline.
- TFP shock magnitudes (by year): 5 percent (year 1), 3 percent (year 2), 1 percent (year 3).
- Real GDP contraction relative to steady state: 4.3 percent (year 1), 3.1 percent (year 2), 1.1 percent (year 3).
- World Bank forecasts and observations:
  - Forecast at beginning of 2014: 11.3 percent (GDP growth in 2014).
  - Revised mid-August 2014: 8.0 percent (GDP growth in 2014).
  - Revision magnitude: 3.3 percentages point decline.
  - Actual GDP growth (January 2015): 7.3 (implying 4 percentages point decline in 2014).
  - World Bank forecast for 2015: contract by 2 percent.
- Appendix table total row (Agenda for Prosperity ESTIMATES, in Millions US$):
  - Total: 633 1148.9 1450.7 1305.0 1208.7 5747.4 3205.6 464.8 2077.0
- Specific pillar figures (selected examples from Appendix):
  - Pillar 1 total: 1745.2 (Total), Partners: 1299.9, GoSL: 57.6, Gap: 387.7
  - Pillar 3 total: 1739.9, Partners: 1004.8, GoSL: 32.0, Gap: 703.1
  - Pillar 4 total: 1553.7, Partners: 734.2, GoSL: 256.2, Gap: 563.3
  - Pillar 6 total: 79.3, GoSL: 3.6, Gap: 75.7
  - Pillar 7 total: 577.4, Partners: 132.6, GoSL: 114.4, Gap: 330.39
  - Pillar 8 total: 11.5, Partners: 0.0, GoSL: 0.0, Gap: 11.5

*Source: _wp15164 - Box 1: Speed of Fiscal Adjustment*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15164.pdf_