## _wp15236 — Section 1–4

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### Abstract and research objective
- Research focus:
  - Analyze tradeoffs between savings, debt and public investment in the Republic of Congo given oil exhaustibility concerns.
- Key messages:
  - Large scaling-up in public investment and oil price volatility pose risks to fiscal and capital sustainability given a projected decline in the oil revenue to GDP ratio.
  - Structural reforms that improve public investment efficiency can enable faster buildup of sustainable public capital and sustain higher non-oil growth without adversely affecting the debt ratio or savings.
  - Even with prudent fiscal policy that preserves resource wealth and debt sustainability, low public investment quality (misallocation of resources) can prevent attainment of sustainable public capital and positive non-oil growth.

### Cross-country perspective and empirical context
- Resource-rich developing-country indicators cited:
  - Poverty headcounts in excess of 55 percent.
  - Human development indicators in the bottom 50 percent.
  - Less than 30 percent of roads are paved.
- Oil production horizons and vulnerabilities:
  - Oil production has a horizon of less than 20 years in several developing countries.
  - African exporters such as Congo, Equatorial Guinea, and Gabon have relatively shorter horizons of remaining hydrocarbon production and relatively larger capital expenditure to non-oil GDP ratios than counterparts in the Middle East and Asia.
- Fiscal risk proxy:
  - The size of the non-oil primary deficit used as proxy for fiscal adjustment needed once oil resources deplete; Equatorial Guinea, Angola, and Congo highlighted as having large non-oil primary deficits despite limited horizons of oil production.

### Model structure, agents, and calibration
- Model type and key features:
  - Medium-scale open-economy DSGE extending Melina, Yang, and Zanna (2014), Buffie and others (2012), and Berg and others (2013).
  - Features: natural resource sector, multiple debt instruments, investment efficiency and absorptive capacity constraints, Dutch Disease effects, and a Sovereign Wealth Fund (SWF).
- Agents and sectors:
  - Households: optimizing (OPT) and non-optimizing (HTM).
  - Firms: non-resource traded goods, non-traded goods, natural resource producers.
  - Government: provides productive investment and consumption; finances via taxes, debt, resource revenues, SWF; access to external and domestic debt.
- Key calibration and Congo-specific baseline (annual data, steady state end-2013; projections 2014–2030):
  - Private investment to GDP: 0.093
  - Export share to GDP: 0.43
  - Import share to GDP: 0.14 (Table 2 later lists imp_share = 0.46 — see Key structural parameter values)
  - Share of oil GDP to total GDP: 88.4 percent
  - Government consumption to GDP: 14 percent
  - Government investment to GDP: 6 percent
  - Size of sovereign wealth fund at end-2013: 66.5 percent of GDP
  - Initial ratio of public concessional debt: 18.9 percent
  - Public domestic and commercial debt to GDP: 1 percent
  - Congo macro facts reported:
    - Oil production accounts for 58 percent of GDP
    - Oil exports account for 78 percent of exports
    - Government revenues from oil represent 74 percent of total fiscal revenues
  - Oil production projection:
    - Peak projected in 2017 at around 118 million barrels (Moho Nord on-stream), surpassing previous peak of 115 million barrels in 2010.
    - Absent new discoveries, production declines steadily over next 15 years.
  - Oil revenues projection:
    - From around 33 percent of GDP in 2013 to less than 4 percent of GDP in 2030.
  - Fiscal baseline:
    - End-2013 non-oil primary deficit: around 26 percent of GDP.
    - Capital expenditures at end-2013: 24 percent of GDP; total expenditures: 38 percent of GDP.
    - Capital expenditures projected to stabilize at around 13 to 14 percent of GDP in the long run.
    - Non-oil GDP growth expected to average around 5 percent per year.
    - Non-oil revenues projected to increase from 12 percent of GDP in 2013 to around 29 percent of GDP at end of 2030.
    - Consolidated effect yields a non-oil primary balance close to zero by 2030.
  - Historical debt context:
    - HIPC and MDRI debt relief reduced external debt stock by $1.9 billion to about 20 percent of GDP in 2010.
    - End-2013 stock of external public debt: 32 percent of GDP (mostly concessional bilateral loans from China).
  - SWF floor and initial:
    - Initial SWF value: 66.5 percent of GDP.
    - SWF floor set at 40 percent of GDP.

### Public capital, efficiency, and absorptive capacity
- Public capital accumulation and inefficiencies:
  - Public capital enters production function; public investment affects non-resource GDP growth.
  - Baseline public investment efficiency ϵ̄ = 0.5 (consistent with evidence that a dollar of investment typically translates to 50 cents of public capital).
  - Absorptive capacity: maximum absorption capacity parameter set to 0.5; when public investment exceeds by 45 percent of initial capital investment investment efficiency falls until lower bound level of 0.2 (per calibration following Pritchett (2000) and eq. (39)).
  - Severity of absorptive capacity constraint ςϵ = 25.
  - Annual depreciation rate of public capital δ_G = 0.05.
- Project selection and quality:
  - Investment allocated between high-productivity g̃IHt and low-productivity g̃ILt with share parameter ς ∈ [0,1]:
    - g̃IHt = ς g̃It
    - g̃ILt = (1 − ς) g̃It
  - Depreciation assumptions: δ_GH = 0.05; δ_GL = 0.1 (δ_GH < δ_GL).
  - Misallocation result: when more than 1/3 of investment is tilted toward “white elephant” (low-productivity) projects, output growth enters negative territory.

### Simulation scenarios and principal quantitative results
- Simulation horizon: 17 years (2014–2030).
- Scenarios considered:
  - Benchmark (gradual consolidation to eliminate non-oil primary deficit by 2030).
  - Aggressive scaling-up of public investment.
  - Constant-investment (delay consolidation) scenario.
  - Variations: structural reforms improving public investment efficiency; oil price and revenue volatility; project selection improvements.
- Common policy constraint: cap on public debt of 70 percent of GDP (CEMAC convergence criterion).

Benchmark scenario (key outcomes)
- Public capital spending averages 16 percent of GDP during 2014–2030.
- Debt-to-GDP ratio averages 31 percent.
- Oil revenues decrease from 33 percent in 2014 to around 2.5 percent of GDP in 2030.
- Investment efficiency below steady state until 2022; minimum efficiency reached in 2015 when public investment peaks at around 26 percent of GDP.
- Public capital stabilizes by 2024 at about 32 percent higher than steady state.
- SWF accumulates until 2026, topping out at around 150 percent of GDP, then declines to about 125 percent of GDP by 2030.
- Long-run: higher non-oil GDP and private investment; mild but sustainable increase in public debt due to concessional foreign borrowing.

Aggressive investment scenario (key outcomes)
- Public investment peaks at about 35 percent of GDP in 2018 (text also references scaling up to almost 40 percent in discussion).
- Capital expenditures financed first by running down SWF; SWF reaches minimum 40 percent of GDP in 2023, then external borrowing increases.
- Debt-to-GDP ratio projected to top 60 percent by 2030.
- Risk: large initial capital buildup followed by inadequate recurrent funding leads to depreciation of public capital in future periods and unsustainable public capital stock; eroded SWF and unsustainable public debt without beneficial higher non-oil output.

Constant investment scenario (key outcomes)
- Public investment stays constant until 2020 at around 25 percent of GDP, then declines to baseline projected path.
- Outcome: higher capital stock and non-oil output than baseline, but higher fiscal risks — SWF reaches lower bound and public debt increases to over 65 percent of GDP.
- Policy dilemma: allow public capital to depreciate and non-oil output to fall versus sizeable fiscal adjustments (e.g., increase taxes) to sustain capital stock.

Oil-price volatility and confidence bands
- Oil price process estimated using 1970–2012 data:
  - ln(POt) = α0 + αP ln(POt−1) + εpo t, εpo ∼ i.i.d. N(0, σ^2_po)
  - αP = 0.9753; α0 = 0.1370
  - With 95 percent probability, over the simulation period oil prices expected within the [$25,$235] interval.
- Simulation design:
  - Confidence bands based on 500 simulations; solid lines median; light gray one-standard deviation; dark gray two-standard deviation.
- Key outcomes under benchmark with oil-price volatility:
  - Median SWF peaks around 150 percent of GDP in 2026 and is about 120 percent of GDP by 2030.
  - Two-standard-deviations band: SWF can build to 400 percent of GDP when oil prices high; when oil prices reach lower bound SWF hits minimum 40 percent of GDP and public debt can build to levels potentially exceeding 70 percent of GDP.
  - Median non-oil output growth: average growth around 3.5 percentage points; confidence intervals show fluctuations of about ±2 percentage points.
- Comparative finding: aggressive and constant scenarios similarly vulnerable — slower fiscal adjustment with lower oil prices leads to quicker draw-down of savings, larger debt build-up, and lower non-oil growth.

Structural reform timing and magnitude
- Raising maximum absorption capacity parameter to 0.6 (emerging market efficiency) yields:
  - Early implementation: sizable and sustainable increase in public capital and higher non-oil growth.
  - Delayed implementation: by 2030 public capital stock less than 10 percent of GDP above benchmark level and non-oil output growth less than one percentage point above benchmark.
- In aggressive scaling-up, delayed reforms increase unsustainability risk; avoidance requires full investment efficiency (efficiency parameter of 1), characterized as highly improbable.

### Policy implications and recommendations
- Fiscal policy and investment pacing:
  - Gradual reduction in public investment needed to preserve debt sustainability and finance public capital after the resource windfall depletes, including under revenue volatility.
  - Fiscal consolidation important for preserving macroeconomic stability in the medium to long run as oil reserves are exhausted.
- Sovereign Wealth Fund and borrowing:
  - Drawing on the resource fund before extensive borrowing helps limit immediate debt accumulation, but tradeoffs exist between saving and investment given minimum reserve needs and debt market limits.
  - If SWF falls to floor f_floor = 0.4 (40 percent of GDP), fiscal shortfalls covered by borrowing in model; alternatives (raise taxes or cut non-capital spending) noted but not simulated.
- Structural reforms and absorptive capacity:
  - Improving project implementation efficiency and absorptive capacity can raise public capital and non-oil growth without higher spending.
  - Early implementation of reforms yields materially better outcomes than delayed reforms.
- Project selection and governance:
  - Strengthening project selection to favor high-productivity projects is critical; misallocation can negate benefits of prudent fiscal paths.
  - Misallocation threshold: when more than 1/3 of investment goes to low-productivity projects, output growth can become negative.
- Risk management:
  - Investment plans should account for historical commodity price volatility; confidence bands quantify asymmetric risks to debt and savings from oil price fluctuations.

### Sensitivity, robustness, and limitations
- Simulation assumptions and limits:
  - Oil production and resource revenue paths taken as exogenous.
  - Non-oil taxation held unchanged; implications of increased non-oil revenues outside scope.
  - Model assumes authorities draw on SWF before accumulating further debt; other policy mixes possible in reality.
  - Calibration choices: public investment efficiency baseline ϵ̄ = 0.5; absorptive threshold ̄γ_GI = 0.75; severity ςϵ = 25; δ_G = 0.05.
- Debt ceiling and fiscal space:
  - Simulation enforces public debt cap of 70 percent of GDP; exceeding this poses CEMAC convergence criterion breach and market limits to borrowing.

### Key structural parameter values (selected, as reported)
- exp_share: 0.43
- imp_share: 0.46
- g_C_share: 0.14
- g_I_share: 0.06
- i_share: 0.093
- y_O_share: 0.884
- f_*share: 0.665
- b_share: 0.01
- d_share: 0.189
- d_c,share: 0.01
- gr_share: 0.14
- ρ_z: 0.1
- κ_j: 25
- ψ: 10
- σ: 2.94
- ρ: 1
- ω: 0.4
- χ: 0.44
- η: 1
- f: 0.5
- τ_L: 0.05
- τ_C: 0.1
- τ_K: 0.2
- σ_po: 0.068
- δ_G: 0.05
- R−1 (Domestic net real interest rate): 0.1
- δ_GH: 0.05
- R_RF−1 (Foreign net real interest rate): 0.027
- δ_GL: 0.1
- R_d−1 (Net real int.rate on concessional debt): 0
- f_floor: 0.4
- R_f−1 (Net real risk-free rate): 0.04
- ν: 0.6
- R_dc,0−1: 0.06
- ν_g: 0.4
- η_g: 0
- α_G: 0.15
- α_NT: 0.45
- ̄ϵ (Steady-state efficiency of public investment): 0.5
- α_T: 0.6
- ςϵ: 25
- δ_j (Depreciation rate of private capital): 0.1
- ̄γ_GI: 0.75
- ρ_y: 0.1

*Source: WP/15/236, November 2015, International Monetary Fund*

### Section 1

### _wp15236 - Section 1

### Abstract and research objective
- The paper analyzes the tradeoffs between savings, debt and public investment in the Republic of Congo, a developing country with looming oil exhaustibility concerns.
- Key messages:
  - Large scaling-up in public investment and oil price volatility pose risks to fiscal and capital sustainability given a projected decline in the oil revenue to GDP ratio.
  - Structural reforms that improve public investment efficiency can enable faster buildup of sustainable public capital and sustain higher non-oil growth without adversely affecting the debt ratio or savings.
  - Even with prudent fiscal policy that preserves resource wealth and debt sustainability, low public investment quality (misallocation of resources) can prevent attainment of sustainable public capital and positive non-oil growth.

### Cross-country perspective (major themes and evidence)
- Resource-rich developing countries face large social and infrastructure gaps despite resource revenues; typical indicators cited:
  - Poverty headcounts in excess of 55 percent.
  - Human development indicators in the bottom 50 percent.
  - Less than 30 percent of roads are paved.
- Oil production horizons and vulnerabilities:
  - Oil production has a horizon of less than 20 years in several developing countries.
  - African exporters such as Congo, Equatorial Guinea, and Gabon have relatively shorter horizons of remaining hydrocarbon production and relatively larger capital expenditure to non-oil GDP ratios than counterparts in the Middle East and Asia.
- Cross-country comparison highlights (from Table 1 and Figure 1):
  - Equatorial Guinea, Angola, and Congo stand out as having large non-oil primary deficits despite relatively limited horizons of oil production.
  - The size of the non-oil primary deficit is used as a proxy for the fiscal adjustment needed to attain a sustainable primary deficit once oil resources deplete.

### Model structure and scope
- Model type and lineage:
  - A medium-scale open-economy Dynamic Stochastic General Equilibrium (DSGE) model extending Melina, Yang, and Zanna (2014), Buffie and others (2012), and Berg and others (2013).
  - Features: natural resource sector, multiple debt instruments, investment efficiency and absorptive capacity constraints, Dutch Disease effects, and a Sovereign Wealth Fund (SWF).
- Key modeling choices:
  - Public investment and resource revenue paths are taken as exogenous for simulation experiments.
  - Public capital enters the production function, producing a direct impact of public investment on non-resource GDP growth.
  - The model simulates outcomes for growth, public debt, SWF, and the stock of capital over a period of 17 years (i.e., 2014-2030).
- Fiscal financing assumptions and constraints:
  - Public investment can be financed from resource revenues and by borrowing (domestic or foreign).
  - The model assumes authorities draw on their resource fund before accumulating further debt; in practice other combinations may occur.
  - A minimum acceptable lower bound for savings is imposed corresponding to the reserves needed to ensure the smooth operation of the pegged exchange rate arrangement (Congo is a CEMAC member pegging the CFA franc to the euro).

### Simulation experiments and principal results (themes and findings)
- Scenario types analyzed:
  - Alternative public investment paths (including aggressive scaling up, constant investment, and fiscal consolidation paths).
  - Changes in public investment efficiency and absorptive capacity constraints.
  - Commodity price volatility (historical oil price volatility used to derive confidence bands).
  - Project selection: allocation between low- and high-productivity projects.
- Key quantitative and qualitative findings:
  - Aggressive scaling up of investment:
    - Can lead to fast accumulation of public capital and higher near-term non-oil growth.
    - Devoting more oil revenues to public investment reduces savings, increasing vulnerability to negative oil price shocks and oil depletion.
    - Once savings hit the minimum acceptable lower bound, the government may resort to borrowing; continued borrowing reaches a limit where debt thresholds force downward adjustment of government spending.
    - Postponing fiscal consolidation tends to run up unsustainable public debt and leaves no financial assets to provide a permanent income after oil exhaustibility.
  - Constant-investment (delay consolidation) scenarios:
    - Lead to lower long-run savings and higher long-run debt than baseline consolidation scenarios, increasing vulnerability to negative oil price shocks.
  - Public investment efficiency and absorptive capacity:
    - Base-case public investment efficiency is assumed to be 0.5 (consistent with evidence that a dollar of investment in developing countries typically translates to 50 cents of public capital).
    - Efficiency declines once public investment exceeds a given threshold due to absorptive constraints.
    - Structural reforms that improve efficiency can deliver a higher sustainable level of public capital and higher non-oil output growth without increasing public investment spending.
  - Commodity price volatility:
    - Historical oil price volatility is used to construct confidence bands around resource revenue paths.
    - Volatility produces downside risk and upside potential for public investment plans; the framework quantifies implications for debt and savings under those risks.
  - Project selection (allocation across project productivity types):
    - Introducing low- and high-productivity projects shows that inadequate project selection or misallocation toward lower-yield projects can prevent sustainable public capital accumulation and positive non-oil growth—even when public investment follow paths that preserve resource wealth and debt sustainability.

### Policy implications and recommendations (implicit and explicit)
- Fiscal policy and investment pacing:
  - A gradual reduction in public investment is needed to preserve debt sustainability and to have sufficient financing to sustain public capital after the resource windfall depletes, including under resource revenue volatility.
  - Fiscal consolidation is important for preserving macroeconomic stability in the medium to long run when oil reserves are exhausted.
- Use of Sovereign Wealth Fund and borrowing:
  - Drawing on the resource fund before extensive borrowing helps limit immediate debt accumulation, but there is a tradeoff between saving and investment that must consider minimum reserve needs and debt market limits.
- Structural reforms to raise investment efficiency:
  - Improving project implementation efficiency and absorptive capacity can raise public capital and non-oil growth without higher spending.
- Project selection and governance:
  - Strengthening the project selection process to favor high-productivity projects is critical; misallocation can negate the benefits of prudent fiscal paths and investment preservation strategies.
- Risk management:
  - Investment plans should account for historical commodity price volatility; the model’s confidence bands illustrate the asymmetric risks to debt and savings from oil price fluctuations.

### Research limitations and scope
- The simulations take oil production and revenues as exogenous.
- Non-oil taxation is assumed unchanged; implications of increased reliance on non-oil revenues are outside the scope of this paper.
- The model focuses on a country at the peak of oil production (the Republic of Congo) but findings are intended to be illustrative for similarly oil-dependent developing countries.

*Source: WP/15/236, November 2015, International Monetary Fund*

### Section 2

### _wp15236 - Section 2

### Model structure and agents
- Economy composed of three agents: (i) households, (ii) firms and (iii) government.
- Households split into optimizing (OPT) and non-optimizing (hand-to-mouth, HTM) types:
  - OPT: access financial markets, smooth consumption intertemporally.
  - HTM: consume all disposable income each period.
- Firms: three types — (i) non-resource traded goods producers; (ii) non-traded goods producers; (iii) natural resource producers.
- Government provides productive investment and consumption, finances spending with taxes, debt, natural resource revenues, and sovereign wealth fund savings; has access to different types of debt (external and domestic).

### Household preferences and behavior (key relations)
- Identical preferences for both household types:
  - U(c_it, L_it) = 1/(1−σ) (c_it)^{1−σ} − κ/(1+ψ) (L_it)^{1+ψ}
- Consumption aggregator (Stiglitz–Dixit CES):
  - c_it = [ φ^{1/χ} (c_{iN,t})^{(χ−1)/χ} + (1−φ)^{1/χ} (c_{iT,t})^{(χ−1)/χ} ]^{χ/(χ−1)}
- Price aggregator normalized to 1:
  - 1 = [ φ (p_{N,t})^{χ−1} + (1−φ) (s_t)^{χ−1} ]^{1/(χ−1)}
- Demand functions:
  - c_{iN,t} = φ p_{N,t}^{−χ} c_{i,t}
  - c_{iT,t} = (1−φ) s_t^{−χ} c_{i,t}
- Labor aggregator and sectoral labor shares use a CES specification with parameter δ (share of labor in non-traded sector) and ρ (intratemporal elasticity between sectoral labor).
- Aggregate consumption and labor:
  - c_t = ω c_{OPT,t} + (1−ω) c_{HTM,t}
  - L_t = ω L_{OPT,t} + (1−ω) L_{HTM,t}

### Optimizing households: financial access and first-order conditions
- OPT households maximize lifetime utility E_0 Σ_{t=0}^∞ β^t U(c_{OPT,t}, L_{OPT,t}) subject to a comprehensive budget constraint (including consumption taxes τ_c, labor taxes τ_L, domestic bonds b_{OPT,t}, international bonds b_{OPT,t}^*, remittances rm_t, transfers z_t, user fees μ k_{G,t−1}, profits Ω_{T,t}, Ω_{NT,t}, portfolio adjustment costs Θ_{OPT}^* = η/2 (b_{OPT}^* − b_{OPT}^*)^2, and a premium on external debt R_t^* = R_{dc,t} + u).
- Capital accumulation with adjustment costs: k_{j,t} = (1−δ_j) k_{j,t−1} + [ 1 − κ_j/2 (i_{j,t}/i_{j,t−1} − 1)^2 ] i_{j,t} for j = T, NT.
- Key first-order conditions include:
  - λ_t (1 + τ_{c,t}) = (c_{OPT,t})^{−σ}
  - κ (L_t)^{ψ} = λ_t (1 − τ_{L,t}) w_t
  - Euler conditions for domestic and foreign bonds with portfolio adjustment costs and capital return equations for q_{j,t}.

### Non-optimizing households (HTM)
- Maximize current-period utility U(c_{HTM,t}, L_{HTM,t}) subject to period budget constraint:
  - (1 + τ_{c,t}) c_{HTM,t} = (1 − τ_{L,t}) w_t L_{HTM,t} + s_t rm_t + z_t + μ k_{G,t−1}
- Static labor supply (aggregate form):
  - L_t = [ 1/κ (1−τ_{L,t})/(1+τ_{c,t}) (c_t)^{−σ} w_t ]^{1/ψ}

### Firms: production and factor pricing
- Goods production (traded and non-traded) uses Cobb–Douglas:
  - y_{j,t} = z_{j} (k_{j,t−1})^{1−α_j} (L_{j,t})^{α_j} (k_{G,t−1})^{α_G} for j = T, NT
- Traded sector subject to learning-by-doing externalities:
  - z_{T,t}/z_T = (z_{T,t−1}/z_T)^{ρ_z} (y_{T,t−1}/y_T)^{ρ_y}
- Factor prices (profit maximization):
  - Traded: r_{T,K,t} = (1−α_T) s_t y_{T,t} / k_{T,t−1}; w_{T,t} = α_T s_t y_{T,t} / L_{T,t}
  - Non-traded: r_{NT,K,t} = (1−α_{NT}) p_{NT,t} y_{NT,t} / k_{NT,t−1}; w_{NT,t} = α_{NT} p_{NT,t} y_{NT,t} / L_{NT,t}

### Natural resource sector
- Resource production exogenous:
  - y_{O,t}/y_O = (y_{O,t−1}/y_O)^{ρ_{yO}} exp(ε_{yO,t})
- World resource price exogenous:
  - p_{O,t}/p_O = (p_{O,t−1}/p_O)^{ρ_{pO}} exp(ε_{pO,t})
- Resource GDP in consumption-basket units:
  - y_{O,t} = s_t p_{O,t} y_{O,t}
- Producer profits after output tax τ_{O,t}:
  - Ω_{O,t} = (1 − τ_{O,t}) y_{O,t}

### Government budget, public investment, and sovereign wealth fund (SWF)
- Government budgets include consumption, investment, transfers, debt service; revenues from consumption, labor, capital taxes, user fees, grants, resource royalties, and SWF interest.
- Interest on commercial debt r_{dc,t} = r_{f,t} + ν_{dc} e^{η_g ( (d_t + d_{c,t})/y_t − (d + d_c)/y ) }.
- Government consumption and investment: g_t = g_{C,t} + g_{I,t}; government consumption price index p_{G,t} defined by CES of p_N and s_t with parameter ν_t.
- Public capital accumulation with inefficiencies and absorptive capacity:
  - k_{G,t} = (1−δ_G) k_{G,t−1} +  ̃g_{I,t}
  - Effective investment ̃g_{I,t} defined piecewise: baseline efficiency ϵ ∈ [0,1] and threshold γ_GI; for deviations above γ_GI the efficiency of additional investment decreases with exp[−ς_ϵ (γ_GI_t − γ_GI)] capturing absorptive capacity constraints; ς_ϵ ∈ [0, ∞).
- Sovereign wealth fund evolution (with floor f_{floor} ≥ 0):
  - f_{*,t} − f_* = max{ f_{floor} − f_*, (f_{*,t−1} − f_*) + f_{in,t} s_t − f_{out,t} s_t }
  - Fiscal inflows f_{in,t} and outflows f_{out,t} defined explicitly (see model).
- If SWF falls to floor, fiscal shortfalls covered by borrowing (paper notes government could alternatively raise taxes or cut non-capital spending).

### Market clearing and external balance
- Non-traded goods market clearing:
  - y_{N,t} = φ p_{N,t}^{−χ} (c_t + i_{N,t} + i_{T,t}) + ν_t (p_{N,t}/p_{G,t})^{−χ} g_t
- Aggregate budget/foreign asset identity: growth in net foreign debt equals national spending minus national income, expressed in detailed account identity linking changes in b^*, d, d_c, f^* to domestic absorption, government spending, remittances, and interest flows.

### Calibration and Congo-specific baseline (key calibration and projections)
- Model calibrated to Congo with annual data; initial steady state based on macro developments at end of 2013; projections over 2014-2030 (close to complete depletion of natural resource windfall).
- Calibration and initial values:
  - Private investment to GDP: 0.093
  - Export share to GDP: 0.43
  - Import share to GDP: 0.14
  - Share of oil GDP to total GDP: 88.4 percent
  - Government consumption to GDP: 14 percent
  - Government investment to GDP: 6 percent
  - Size of sovereign wealth fund at end-2013: 66.5 percent of GDP
  - Initial ratio of public concessional debt: 18.9 percent
  - Public domestic and commercial debt to GDP: 1 percent
- Congo macro facts (as stated in the section):
  - Oil production accounts for 58 percent of GDP
  - Oil exports account for 78 percent of exports
  - Government revenues from oil represent 74 percent of total fiscal revenues
- Oil production and revenue projections:
  - Oil production projected to peak in 2017 at around 118 million barrels (Moho Nord on-stream), surpassing previous peak of 115 million barrels in 2010.
  - Absent new discoveries, oil production projected to decline steadily over next 15 years.
  - Oil revenues expected to decline from around 33 percent of GDP in 2013 to less than 4 percent of GDP in 2030.
  - Oil prices calibrated to IMF WEO price forecast.
- Fiscal and investment projections under the benchmark scenario:
  - End-2013 non-oil primary deficit: around 26 percent of GDP.
  - Capital expenditures at end-2013: 24 percent of GDP; total expenditures: 38 percent of GDP.
  - As oil revenues deplete, capital expenditures projected to stabilize at around 13 to 14 percent of GDP in the long run.
  - Non-oil GDP growth expected to average around 5 percent per year.
  - Non-oil revenues projected to increase from 12 percent of GDP in 2013 to around 29 percent of GDP at end of 2030.
  - Consolidated effect yields a non-oil primary balance close to zero by 2030—interpreted as sustainable under the benchmark.
- Historical context and policy buffer:
  - HIPC and MDRI debt relief reduced external debt stock by $1.9 billion to about 20 percent of GDP in 2010; end-2013 stock of external public debt: 32 percent of GDP (mostly concessional bilateral loans from China).
  - Initial SWF value taken as 66.5 percent of GDP reflecting gross official reserves; SWF floor set at 40 percent of GDP to maintain reserve coverage and fiscal buffers.

*Source: _wp15236 - Section 2*

### Section 3

### _wp15236 - Section 3

### Efficiency and absorptive capacity constraints
- Congo ranked 178th out of 189 countries in the 2015 World Bank’s Doing Business Survey.
- Key constraints identified: limited access to electricity, time and costs of cross-border trade and starting a business, limited access to financial services.
- Low PIMI score and references to Dabla‑Norris and others (2012) imply absorptive capacity constraints and government inefficiency.
- Calibration and assumptions:
  - Maximum absorption capacity parameter set to 0.5 (following Pritchett (2000) estimates for sub-Saharan Africa).
  - When public investment exceeds by 45 percent of the initial capital investment, investment efficiency (absorptive capacity) is assumed to fall until it reaches the lower bound level of 0.2 depending on magnitude of public investment (see eq. (39)).
  - Annual depreciation rate of public capital assumed to be 5 percent (Hurlin and Arestoff (2010) and Gupta, Alvar, and Papageorgiou (2011) estimate depreciation in a range of 2.5 - 4.3 percent; given low PIMI rank and limited maintenance, 5 percent is used).

### Model simulations — overview
- Four sets of simulations considered:
  - Three public investment path scenarios (Benchmark, Aggressive, Constant).
  - Each of these anchors simulations exploring:
    - (i) structural reforms improving public investment efficiency;
    - (ii) oil price and revenue volatility;
    - (iii) improvements in project selection capacity.
- Simulation constraint: cap on public debt of 70 percent of GDP, in line with current CEMAC convergence criteria.

### Investment profiles — scenarios and key quantitative outcomes
- Benchmark scenario
  - Objective: eliminate the non-oil primary deficit by 2030.
  - Public capital spending adjusts as oil revenues decline.
  - Public capital investment averages 16 percent of GDP during 2014–2030.
  - Debt-to-GDP ratio averages 31 percent.
  - Oil revenues decrease from 33 percent in 2014 to around 2.5 percent of GDP in 2030.
  - Investment efficiency below steady state until 2022; minimum efficiency reached in 2015 when public investment peaks at around 26 percent of GDP.
  - Public capital stabilizes by 2024 at about 32 percent higher than steady state.
  - Sovereign wealth fund (SWF) accumulates until 2026, topping out at around 150 percent of GDP, then declines to about 125 percent of GDP by 2030.
  - Long-run effects: higher non-oil GDP and private investment; mild but sustainable increase in public debt due to concessional foreign borrowing.

- Aggressive investment scenario
  - Public investment peaks at about 35 percent of GDP in 2018 (text also references scaling up to almost 40 percent in discussion of effects).
  - Capital expenditures financed first by running down the SWF; once SWF reaches minimum level for pegged exchange rate operation (assumed 40 percent of GDP) in 2023, government increases external borrowing.
  - Debt-to-GDP ratio projected to increase and top 60 percent by 2030.
  - Risk: large initial capital buildup followed by inadequate recurrent funding leads to depreciation of public capital in future periods and unsustainable public capital stock.
  - Long-term: eroded SWF and unsustainable public debt without beneficial higher non-oil output.

- Constant investment scenario
  - Public investment stays constant until 2020 at around 25 percent of GDP, then declines to baseline projected path.
  - Outcome: higher capital stock and non-oil output than baseline, but higher fiscal risks — SWF reaches lower bound and public debt increases to over 65 percent of GDP, constraining external borrowing and fiscal space.
  - Policy dilemma: either allow public capital to depreciate and non-oil output to fall versus sizeable fiscal adjustments (e.g., increase taxes) to sustain capital stock.

### Project implementation efficiency (structural reform timing and magnitude)
- Simulated structural reforms raise the maximum absorption capacity (efficiency) parameter to 0.6 (consistent with emerging market efficiency).
  - Early implementation scenario (benchmark with improvements): sizable and sustainable increase in public capital, positive spillovers, higher non-oil growth.
  - Delayed implementation scenario: missed opportunity — by 2030 public capital stock is less than 10 percent of GDP above the benchmark level and non-oil output growth is less than one percentage point above the benchmark rate.
- In the aggressive scenario, delayed reforms plus scaling-up increase likelihood of unsustainable capital. Avoidance of unsustainability requires achieving full investment efficiency (efficiency parameter of 1), which is characterized as highly improbable for a developing country.
- Conclusion: benchmark scenario with early implementation of structural reforms yields best outcomes for public capital accumulation and non-oil GDP growth by 2030.

### Oil revenue shock (simulated price paths and fiscal risk)
- Oil revenues computed as price × production × government share; production path and government share held constant while prices are simulated.
- Oil price process specification:
  - ln(POt) = α0 + αP ln(POt−1) + εpo t, where εpo ∼ i.i.d. N(0, σ^2_po) (equation (46)).
  - Estimated parameters using 1970–2012 data: αP = 0.9753 and α0 = 0.1370.
  - With 95 percent probability, over the simulation period oil prices expected within the [$25,$235] interval.
- Simulation design: confidence bands based on 500 simulations; solid lines are median paths; light gray = one-standard deviation; dark gray = two-standard deviation.
- Key outcomes under benchmark scenario with oil-price volatility:
  - Median SWF peaks at around 150 percent of GDP in 2026 and is about 120 percent of GDP by 2030.
  - Two-standard-deviations confidence interval: SWF builds up to 400 percent of GDP when oil prices are high; when oil prices are at the lower bound, SWF reaches minimum imposed threshold of 40 percent of GDP and public debt can build up to unsustainable levels, potentially exceeding the CEMAC convergence criterion of 70 percent of GDP.
  - Median non-oil output growth shows an average growth of around 3.5 percentage points; confidence intervals for growth show relative fluctuations from the baseline in the order of ±2 percentage points.
- Comparative note: aggressive and constant scenarios yield similar findings — slower fiscal adjustment with lower oil prices leads to quicker draw-down of savings, larger build-up in debt, and lower non-oil growth, highlighting vulnerability to adverse oil shocks.

### Project selection (allocation across high- and low-productivity projects)
- Government allocates investment between high-productivity projects (g̃IHt) and low-productivity projects (g̃ILt):
  - g̃IHt = ς g̃It
  - g̃ILt = (1 − ς) g̃It
  - ς represents share of total government investment in high-productivity projects; ς ∈ [0,1].
- Capital stocks evolve with different depreciation rates:
  - kGHt = (1 − δGH) kGHt−1 + g̃IHt
  - kGLt = (1 − δGL) kGLt−1 + g̃ILt
  - Assumption: δGH < δGL (higher quality projects have lower obsolescence).
- Output production incorporates variable elasticity of public capital depending on project mix (see equation (52)).
- Simulation result:
  - Misallocation toward low-productivity projects reduces capital stock and output growth.
  - When more than 1/3 of investment is tilted towards “white elephant” (low-productivity) projects, output growth enters negative territory.
- Implication: project selection quality crucial to realize positive spillovers from public investment.

### Conclusions — policy implications and tradeoffs
- The model highlights tradeoffs for a highly oil-dependent country with large social and infrastructure gaps, absorptive and implementation constraints, and near peak oil production.
- Key policy messages:
  - Fiscal consolidation is important to preserve macroeconomic stability in the medium to long run as oil reserves are exhausted.
  - Aggressive scaling-up of investment can produce rapid public capital accumulation and higher non-oil growth but increases vulnerability to oil-price declines because less can be saved.
  - As oil revenues decline, public investment will increasingly be financed by drawing down the SWF; once SWF hits a minimum acceptable lower bound (here, level of reserves needed for smooth operation of pegged exchange rate), borrowing may be used, but market limits exist.
  - Postponing fiscal consolidation risks unsustainable public debt and depletion of financial assets that would provide permanent income after oil reserves are exhausted.
- Practical note: simulations assume authorities draw on the resource fund before accumulating further debt; in reality, authorities may borrow and preserve gross savings or use a mix of drawing savings and borrowing.

*Source: _wp15236 - Section 3*

### Section 4

### _wp15236 - Section 4

### Intermediate public investment maintenance scenario
- Maintaining public investment constant for a period before fiscal consolidation:
  - Leads to a lower build up of savings in the long run than the baseline fiscal consolidation scenario.
  - Leads to a higher build up of debt than the baseline fiscal consolidation scenario.
  - Increases the vulnerability of the economy to negative oil price shocks.

### Sensitivity to oil price shocks and fiscal implications
- Budgetary revenues are highly sensitive to oil price shocks, with implications for:
  - Government spending.
  - Potential non-oil output growth.
- Importance of fiscal adjustment when oil prices decline is emphasized by the simulations.

### Public investment efficiency and outcomes
- Improving public investment efficiency has a positive impact:
  - Can contribute to a sustainable and higher-level of public capital.
  - Does not adversely affect fiscal sustainability in the simulations.
- This is particularly important for Congo where public investment efficiency is lower than the average for Low Income Developing Countries (see IMF(2015)).

### Investment project misallocation
- Misallocation of investment projects has negative effects:
  - Reduces output growth.
  - Reduces public capital accumulation.

### Confidence-intervaled scenario simulations (figures)
- Figures present simulated responses to oil shocks with confidence bands:
  - Confidence bands are based on 500 simulations.
  - Solid lines refer to the median paths.
  - Light gray areas represent one-standard deviation confidence intervals.
  - Dark gray areas represent two-standard deviation confidence intervals.
- Two scenario labels shown in figures:
  - "Aggressive scenario: oil shocks (confidence intervals)"
  - "Constant scenario: oil shocks (confidence intervals)"

### Key structural parameter values (Table 2)
- exp_share (Export (share of GDP)): 0.43
- imp_share (Imports (share of GDP)): 0.46
- g_C_share (Government consumption (share of GDP)): 0.14
- g_I_share (Government investment (share of GDP)): 0.06
- i_share (Private investment (share of GDP)): 0.093
- y_O_share (Oil GDP (share of GDP)): 0.884
- f_∗share (Sovereign wealth fund (share of GDP)): 0.665
- b_share (Domestic public debt (share of GDP)): 0.01
- b_∗share (Private foreign debt (share of GDP)): 0
- d_share (Public concessional debt (share of GDP)): 0.189
- d_c,share (Commercial debt (share of GDP)): 0.01
- gr_share (Grants (share of GDP)): 0.14
- exp (Export (share of GDP)): 0.43
- ρ_z (Persistence of TFP in traded sector): 0.1
- κ_j (Investment adjustment cost): 25
- ψ (Inverse of Frisch labor elasticity): 10
- σ (Inverse of intertemp. elasticity of substitution): 2.94
- ρ (Intertemporal substitution elasticity of labor): 1
- ω (Measure of optimizers in the economy): 0.4
- χ (Substitution elasticity traded/non-traded goods): 0.44
- η (Elast. of portfolio adjustment costs): 1
- f (User fee of public infrastructure): 0.5
- τ_L (Tax rate of labor income): 0.05
- τ_C (Tax rate on consumption): 0.1
- τ_K (Tax rate on capital): 0.2
- σ_po (Standard deviation of oil price shock): 0.068
- δ_G (Depreciation rate of public capital): 0.05
- R−1 (Domestic net real interest rate): 0.1
- δ_GH (Depreciation rate of capital in high prod. proj.): 0.05
- R_RF−1 (Foreign net real interest rate): 0.027
- δ_GL (Depreciation rate of capital in low prod. proj.): 0.1
- R_d−1 (Net real int.rate on concessional debt): 0
- f_floor (Lower bound for the stabilization fund): 0.4
- R_f−1 (Net real risk-free rate): 0.04
- ν (Home bias of government purchases): 0.6
- R_dc,0−1 (Net real int. rate on commercial debt): 0.06
- ν_g (Home bias of additional spending): 0.4
- η_g (Elasticity of sovereign risk): 0
- α_G (Output elasticity of public capital): 0.15
- α_NT (Labor income share in non-traded sector): 0.45
- ̄ (Steady-state efficiency of public investment): 0.5
- α_T (Labor income share in traded sector): 0.6
- ς (Severity of absorptive capacity constraint): 25
- δ_j (Depreciation rate of private capital): 0.1
- ̄γ_GI (Threshold of absorptive capacity): 0.75
- ρ_y (Learning by doing in the traded sector): 0.1
- χ (Substitution elasticity traded/non-traded goods): 0.44
- κ_j (Investment adjustment cost): 25

*Source: _wp15236 - Section 4*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15236.pdf_