## _wp1450

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### Baseline calibration — overview and purpose
- Purpose: DIGNAR model assesses debt sustainability and growth effects of public investment scaling-ups in resource-rich developing countries that combine resource revenues and borrowing to finance public investment.
- Historical/contextual motivation: risks from resource-financed external borrowing in the 1970s and the empirical literature on natural resource “curse” vs. “blessing.”
- Modeling gap addressed: merges debt-dynamics frameworks without a resource sector and resource-sector frameworks without debt accumulation.

### Model scope and key features
- Model type: Real three-sector DSGE model of a small open economy with multiple public debt instruments, multiple tax and spending variables, and a resource fund.
- Sectors and factors:
  - Composite traded and nontraded goods produced with private capital k, labor L, and government-supplied infrastructure k_G.
  - Separate natural resource sector with exogenous production and prices.
- Time horizon and abstractions:
  - 20+ years horizon; nominal side and New Keynesian features abstracted away.
- Public finance and fiscal institutions:
  - Resource fund as fiscal buffer; can be drawn down or accumulate savings; may be subject to minimal asset level f_floor.
  - Four fiscal instruments to close gaps: consumption tax rate, labor income tax rate, government consumption, and transfers; instruments can be constrained by ceilings/floors.
- Debt instruments: concessional debt, external commercial debt, and domestic debt.
- Other elements: large share of poor/hand-to-mouth households; learning-by-doing externalities; inefficiency and absorptive capacity constraints in public investment; time-varying depreciation of public capital; detailed fiscal specification.

### Policy questions and simulated strategies
- Trade-offs:
  - Fast investment scaling-up raises public capital and non-resource growth but reduces saving and increases vulnerability to negative resource revenue shocks.
  - Saving during the windfall is important to sustain capital after resources are exhausted; resource fund is crucial.
- Investment approaches simulated:
  - Spend-as-you-go (SAYG): invest all resource windfall each period without saving.
  - Delinked approach: combines investment and saving so government spending is a-cyclical with resource revenue flows.
- Variations analyzed:
  - Degree of investment front-loading.
  - Investment efficiency and returns to public capital.
  - Financing mix: concessional borrowing, external commercial borrowing, domestic borrowing.
  - Resource revenue inflow scenarios (two hypothetical scenarios).

### Households — structure and preferences
- Two household types:
  - Intertemporal optimizing (Ricardian) households: fraction ω.
  - Rule-of-thumb (hand-to-mouth) households: fraction 1−ω.
- Consumption aggregator:
  - c_i,t = [φ^{1/χ} (c^N_{i,t})^{(χ−1)/χ} + (1−φ)^{1/χ} (c^T_{i,t})^{(χ−1)/χ}]^{χ/(χ−1)}, for i = OPT, ROT.
  - c^N_{i,t} = φ p_{N,t}^{−χ} c_{i,t}; c^T_{i,t} = (1−φ) s_t^{−χ} c_{i,t}.
  - Price relation: 1 = [φ p_{N}^{1−χ} + (1−φ) s_t^{1−χ}]^{1/(1−χ)}.
- Labor supply aggregator and sectoral labor allocations:
  - L_{i,t} = [δ^{−1/ρ} (L^N_{i,t})^{(1+ρ)/ρ} + (1−δ)^{−1/ρ} (L^T_{i,t})^{(1+ρ)/ρ}]^{ρ/(1+ρ)}.
  - L^N_{i,t} = δ (w_{N,t}/w_t)^{ρ} L_{i,t}; L^T_{i,t} = (1−δ) (w_{T,t}/w_t)^{ρ} L_{i,t}.
  - Wage index: w_t = [δ w_{N,t}^{1+ρ} + (1−δ) w_{T,t}^{1+ρ}]^{1/(1+ρ)}.

### Intertemporal optimizing households — utility and budget
- Utility:
  - E_0 Σ_{t=0}^∞ β^t [1/(1−σ) (c^{OPT}_t)^{1−σ} − κ^{OPT}/(1+ψ) (L^{OPT}_t)^{1+ψ}], where β ≡ [(1 +%)]^{−1}.
- Budget constraint (levels):
  - (1 + τ^C_t) c^{OPT}_t + b^{OPT}_t − s_t b^{OPT,*}_t = (1−τ^L_t) w_t L^{OPT}_t + R_{t−1} b^{OPT}_{t−1} − R^*_{t−1} s_t b^{OPT,*}_{t−1} + Ω_{T,t} + Ω_{N,t} + θ_K τ_K (r^K_{T,t} k_{T,t−1} + r^K_{N,t} k_{N,t−1}) + s_t rm^*_t + z_t − μ k_{G,t−1} − Θ^{OPT,*}_t.
- Portfolio costs and external borrowing premium:
  - Θ^{OPT,*}_t ≡ η/2 (b^{OPT,*}_t − b^{OPT,*})^2; R^*_t = R^{dc}_t + u.

### Rule-of-thumb households
- Utility:
  - U(c_ROT_t, L_ROT_t) = 1/(1−σ) (c_ROT_t)^{1−σ} − κ_ROT 1/(1+ψ) (L_ROT_t)^{1+ψ}.
- Budget constraint:
  - (1+τ_C_t) c_ROT_t = (1−τ_L_t) w_t L_ROT_t + s_t rm*_t + z_t − μ k_G,t−1.
- Labor supply:
  - L_ROT_t = [ 1/κ_ROT (1−τ_L_t)/(1+τ_C_t) (c_ROT_t)^{−σ} w_t ]^{1/ψ}.
- Aggregation:
  - c_t = ω c_OPT_t + (1−ω) c_ROT_t; L_t = ω L_OPT_t + (1−ω) L_ROT_t; b_t = ω b_OPT_t; b^*_t = ω b_OPT*_t.

### Firms — production and capital accumulation
- Three sectors: Nontraded (N), Traded non-resource (T), Natural resource (O; exported).
- Nontraded sector:
  - y_N,t = z_N (k_N,t−1)^{1−α_N} (L_N,t)^{α_N} (k_G,t−1)^{α_G}.
  - Capital law of motion: k_N,t = (1−δ_N) k_N,t−1 + [1 − κ_N/2 (i_N,t/i_N,t−1 − 1)^2] i_N,t.
  - Wage: w_N,t = α_N p_N,t y_N,t / L_N,t.
  - q_N,t and Euler conditions as specified (equations (26)–(27)).
- Traded sector:
  - y_T,t = z_T,t (k_T,t−1)^{1−α_N} (L_T,t)^{α_N} (k_G,t−1)^{α_G}.
  - Learning-by-doing TFP: z_T,t / z_T = (z_T,t−1 / z_T)^{ρ_{zT}} + (y_T,t−1 / y_T)^{ρ_{yT}} with ρ_{zT}, ρ_{yT} ∈ [0,1].
  - Capital law of motion: k_T,t = (1−δ_T) k_T,t−1 + [1 − κ_T/2 (i_T,t/i_T,t−1 − 1)^2] i_T,t.
  - Wage: w_T,t = α s_t y_T,t / L_T,t.
  - q_T,t and Euler conditions as specified (equations (33)–(34)).
- Natural resource sector:
  - Exogenous production: ̃y_O,t / ̃y_O = (̃y_O,t−1 / ̃y_O)^{ρ_{yo}} exp(ε_{yo,t}), ρ_{yo} ∈ (0,1); ε_{yo,t} ∼ iid N(0, σ^2_{yo}).
  - Price process: p^*_O,t / p^*_O = (p^*_O,t−1 / p^*_O)^{ρ_{po}} exp(ε_{po,t}), ρ_{po} ∈ (0,1]; ε_{po,t} ∼ iid N(0, σ^2_{po}).
  - Resource GDP: y_O,t = s_t p^*_O,t ̃y_O,t.
  - Total real GDP: y_t = p_N,t y_N,t + s_t y_T,t + y_O,t.

### Government — budget, investment, resource fund, and fiscal gap
- Government flow budget constraint (levels) as in equation (39); resource royalties t_O,t = τ_O s_t p^*_O,t ̃y_O,t.
- Debt instruments:
  - External concessional debt d_t (R_d), external commercial debt d_{c,t} (R_{dc,t}), domestic debt b_t.
  - R_{dc,t−1} = R_f + υ_{dc} exp[ η_{dc} ( (d_t + d_{c,t})/y_t − (d + d_c)/y ) ].
- Government purchases:
  - CES aggregate g_t = g_C_t + g_I_t with g_N,t, g_T,t demands and price index p_G_t as specified.
  - Time-varying ν_t; possible ν_g for additional spending.
- Public investment efficiency and absorptive capacity:
  - Effective public investment ̃g_I_t defined piecewise with threshold γ_GI and efficiency ϕ; ϕ(γ_GI_t) = exp[ −ς_ϕ (γ_GI_t − γ_GI) ] ϕ.
  - Public capital law: k_G,t = (1−δ_G,t) k_G,t−1 + ̃g_I_t.
  - Time-varying depreciation δ_G,t defined in (50) with parameters δ_G, φ, ρ_δ.
- Resource fund:
  - Fund asset f^*_t evolves per (51) with inflows f_in,t and outflows f_out,t and lower bound f_floor.
  - Two investing approaches:
    - Spend-as-you-go (SAYG): f^*_t = f^*, ∀t; p_G_t g_I_t − p_G g_I = (t_O,t s_t − t_O s).
    - Delinked approach: g_I_t / g_I = 1 + [ 1 + exp(−k_1 t) − 2 exp(−k_2 t) ] g_I^{nss}, with k_1, k_2 governing speed and frontloading.
  - MATLAB code allows exogenous public investment paths.

- Fiscal gap:
  - gap_t = f_out,t − f_in,t + s_t ( f^*_t − f^*_{t−1} ) (equation (54)).
  - gap_t decomposed as Δ b_t + s_t Δ d_{c,t} + (τ_C_t − τ_C) c_t + (τ_L_t − τ_L) w_t L_t − p_G_t (g_C_t − g_C) − (z_t − z).
  - If f^*_t > f_floor then gap_t = 0; if f^*_t = f_floor then gap_t > 0 and must be covered by borrowing or fiscal adjustments.

### Covering the fiscal gap — rules and fiscal policy implementation
- Borrowing allocation rule:
  - κ∆b_t = (1−κ)s_t∆d_{c,t}, where κ ∈ [0,1]; κ = 0 → domestic borrowing; κ = 1 → external commercial borrowing.
- Debt-stabilizing target adjustments:
  - τ^C_{target,t} = τ^C + λ_1 gap_t / c_t.
  - τ^L_{target,t} = τ^L + λ_2 gap_t / (w_t L_t).
  - g^C_{target,t} = g + λ_3 gap_t / p^G_t.
  - z_{target,t} = z + λ_4 gap_t.
  - λ_i split burden with ∑_{i=1}^4 λ_i = 1.
- Implementability with ceilings/floors:
  - τ^C_t = min{ τ^C_{rule,t}, τ^C_{ceiling} }; τ^L_t = min{ τ^L_{rule,t}, τ^L_{ceiling} }.
  - g^C_t / g^C = max{ g^C_{rule,t} / g^C, g^C_{floor} }; z_t / z = max{ z_{rule,t} / z, z_{floor} }.
- Fiscal rule dynamics:
  - τ^C_{rule,t} = τ^C_{t−1} + ζ_1(τ^C_{target,t} − τ^C_{t−1}) + ζ_2(x_{t−1} − x).
  - τ^L_{rule,t} = τ^L_{t−1} + ζ_3(τ^L_{target,t} − τ^L_{t−1}) + ζ_4(x_{t−1} − x).
  - g^C_{rule,t} / g^C = g^C_{t−1} / g^C + ζ_5(g^C_{target,t} − g^C_{t−1}) / g^C − ζ_6(x_{t−1} − x).
  - z_{rule,t} / z = z_{t−1} / z + ζ_7(z_{target,t} − z_{t−1}) / z − ζ_8(x_{t−1} − x).
  - x_t ≡ (b_t + s_t d_{c,t}) / y_t is domestic + external commercial debt as share of GDP.
- Market clearing and CA identities:
  - Nontraded goods clearing and balance of payments as in equations (71)–(73).

### Baseline calibration (average LIC) — exact parameter values and shares
- National accounting:
  - Trade balance = 6 percent of GDP.
  - Government consumption = 14 percent of GDP.
  - Public investment = 6 percent of GDP.
  - Private investment = 15 percent of GDP.
  - Shares of tradable goods: private consumption 50 percent, government purchases 40 percent.
  - Share of natural resources at initial steady state = 1 percent of GDP.
- Assets, debt and grants:
  - RF_share = 0.01 (1 percent of GDP).
  - b_share = 0.20, d_share = 0.50, gr_share = 0.04.
  - b^*_share = 0, d_{c,share} = 0 in baseline.
- Interest rates:
  - Real annual interest rate on domestic debt (R−1) = 10 percent.
  - Net real risk-free rate (R_f − 1) = 4 percent.
  - Real rate on external commercial debt (R_{dc} − 1) = 6 percent.
  - Real rate on concessional loans (R_d − 1) = 0 percent.
  - η_{dc} = 0 (no additional risk premium in baseline).
  - Annual real return on resource fund (R_{RF} − 1) = 2.7 percent.
- Private production:
  - Labor income shares: α_N = 0.45, α_T = 0.60.
  - Depreciation rates: δ_N = δ_T = 0.10.
  - Learning-by-doing externality: ρ_{Y_T} = ρ_{z_T} = 0.10.
  - Investment adjustment costs: κ_N = κ_T = 25.
- Household preferences and shares:
  - σ = 2.94; ψ = 10; ρ = 1; χ = 0.44; η = 1; ω = 0.40.
- Mining parameters:
  - ρ_{yo} = 0.90; ρ_{po} = 1.
  - τ_O = 0.65 (calibrated so resource revenue at peak ≈ 50 percent of total revenues).
- Tax rates and implied revenue:
  - τ_C = 0.10, τ_L = 0.15, τ_K = 0.20.
  - Implied non-resource revenue ≈ 18 percent of GDP at initial steady state.
- Fiscal rules and baseline policy:
  - f_{floor} = 0.
  - g^C_{floor} = z_{floor} = −100000; τ^C_{ceiling} = τ^L_{ceiling} = 100000 (no effective floors/ceilings).
  - Baseline adjustment via external commercial borrowing and consumption taxes: κ = 1, λ_1 = 1, λ_2 = λ_3 = λ_4 = 0.
  - ζ_3 = ζ_5 = ζ_7 = 1; ζ_4 = ζ_6 = ζ_8 = 0; ζ_1 = 0.5; ζ_2 = 0.001.
- Public investment parameters:
  - Public investment efficiency ̄ε = 0.50.
  - δ_G = 0.07.
  - Home bias ν = 0.6; ν_g = 0.4.
  - α_G = 0.15 (implies marginal net return of public capital 28 percent at initial steady state).
  - φ = 1; ρ_δ = 0.8.
  - Absorptive capacity binds when public investment rises above 75 percent from initial steady state: ̄γ_{GI} = 0.75.
  - ς_ε = 25 implies average investment efficiency halves to ≈ 25 percent when public investment spikes to ≈ 200 percent from initial steady state.
  - Planned long-term scaling up g^I_{nss} = 0.80 (public investment at new steady state 80 percent higher than initial steady state).

### Scaling-up public investment with a resource windfall — scenarios and quantitative findings
- Baseline resource assumptions:
  - LNG production reaches full capacity by 2021, declines after 2035; peak production ≈ 1500 millions of cubic feet per year.
  - LNG price path from WEO oil forecast multiplied by conversion factor 0.1724; baseline non-volatile price path.
  - Adverse scenario: from 2025 onwards resource revenue quickly declines due to reduced production and large negative price shocks.
- SAYG versus Delinked approaches (no commercial or domestic borrowing in initial comparison):
  - Spend-as-you-go (SAYG):
    - Entire windfall spent in public investment; stabilization fund remains at initial steady state.
    - Volatile public investment mirroring resource revenue volatility; average investment efficiency can drop from 50 percent to almost 25 percent during accelerations.
    - Under baseline (no negative shocks), SAYG can lead to higher public capital accumulation and higher non-resource output, private consumption and investment than delinked approach.
    - If resource depletes after 2040 and public investment cannot be maintained, public capital and growth benefits revert to initial levels.
  - Delinked approach:
    - Gradual scaling-up (k_1 = 0.20, k_2 = 0.20) with saving in stabilization fund.
    - Stabilization fund can peak around 150 percent of GDP under baseline; around 25 percent of GDP under adverse scenario.
    - Yields more resilient and stable non-resource GDP growth and less volatile real exchange rate; performs better under adverse shocks.
- Front-loading with commercial borrowing (k_1 = 0.20; three k_2 values):
  - Conservative: k_2 = 0.10 (slow scaling; little debt accumulation).
  - Gradual: k_2 = 0.20 (small frontloading).
  - Aggressive: k_2 = 0.70 (pronounced overshooting; public investment ≈ 100 percent above initial level during peaks).
  - Fiscal assumptions: κ = 1; λ_1 = 1; consumption tax ceiling at 12.5 percent; short-run increases difficult beyond 2.5 percentage points.
  - Findings:
    - Front-loading prevents savings in the stabilization fund and raises public debt; most pronounced under aggressive path and adverse scenario.
    - Conservative and gradual paths: public debt as share of GDP does not increase significantly; conservative path can accumulate some resource fund savings even under adverse scenario.
    - Aggressive path: government debt appears explosive under adverse scenario (likely unfeasible).
- Domestic versus external commercial borrowing:
  - κ = 0 (domestic borrowing) shifts domestic resources from private to public sector, raises domestic real interest rate, and crowds-out private investment more than external borrowing (κ = 1).
  - Domestic borrowing: higher interest payments, more public debt accumulation, and on average higher consumption tax rates to stabilize debt.
  - Under adverse scenario: external commercial borrowing → public debt remains stable; domestic borrowing → public debt becomes unsustainable.
- Public investment efficiency and returns (example comparisons under external borrowing and adverse resource path):
  - Baseline: ε = 0.50, α_G = 0.15.
  - Improved efficiency: ε increases to 0.70 (α_G = 0.15).
  - Improved efficiency and higher productivity: ε = 0.70 and α_G = 0.18.
  - Findings:
    - Improving ε and/or α_G produces more public capital for given investment, raising non-resource output, income, and consumption.
    - Combined improvements can double additional long-run non-resource GDP growth in example.
    - With baseline calibration and adverse resource path government debt is explosive; with improved efficiency same investment path can be fiscally sustainable because higher non-resource growth generates sufficient revenues.

### Key mechanisms emphasized
- Resource fund dynamics smooth public and private consumption through saving/drawing tied to investment, concessional borrowing, aid, resource production, prices, and revenues.
- Debt accumulation triggers fiscal adjustments via fiscal rules and constrained instruments (taxes, government consumption, transfers).
- Public investment efficiency, absorptive capacity, returns to public capital, and timing/front-loading materially affect growth outcomes and debt sustainability.
- Dutch disease captured via learning-by-doing externalities and relative sectoral dynamics when resource revenues are spent domestically.

### Conclusions and policy recommendations (model-based)
- Delinked investment with savings in a stabilization fund generally yields more macroeconomic stability and resilience to adverse resource shocks than spend-as-you-go.
- Front-loading financed by commercial borrowing can be feasible if front-loading is moderate and projected returns/efficiencies are sufficiently high; aggressive frontloading risks explosive debt under adverse scenarios.
- External commercial borrowing is less crowding-out than domestic borrowing in the model; however, external debt increases exposure to shocks affecting foreign liabilities.
- Public investment efficiency and returns to public capital are critical for both growth outcomes and debt sustainability; improvements can turn otherwise unsustainable paths into sustainable ones.
- Practical guidance:
  - Calibrate DIGNAR to country-specific parameters.
  - Conduct sensitivity analysis on resource revenue scenarios, investment efficiency, and returns to public capital.
  - Use simulations to determine appropriate scaling-up magnitude that sustains public capital while preserving debt sustainability.
  - DIGNAR can complement IMF-WB DSF for natural resource-rich developing countries.

*Source: _wp1450 (IMF Working Paper chapter).*

### 1.  Baseline calibration ...............................................................................................

### 1.  Baseline calibration

### Overview and purpose
- Presents motivation and objectives for the DIGNAR model: assess debt sustainability and growth effects of public investment scaling-ups in resource-rich developing countries that combine resource revenues and borrowing to finance public investment.
- Highlights historical context: risks from resource-financed external borrowing in the 1970s leading to debt crises in some oil-exporting countries, and empirical literature on the natural resource “curse” vs. “blessing.”
- Identifies modeling gap: previous frameworks either include debt dynamics without a resource sector (Buffie et al. (2012)) or include a resource sector without debt accumulation (Berg et al. (2013)). DIGNAR merges these approaches.

### Model scope and key features
- Model type: Real three-sector DSGE model of a small open economy with multiple public debt instruments, multiple tax and spending variables, and a resource fund.
- Sectors and factors:
  - Composite of traded and nontraded goods produced with private capital k, labor L, and government-supplied infrastructure k_G.
  - Separate natural resource sector with exogenous production and prices.
- Time horizon: 20+ years; nominal side and New Keynesian features abstracted away.
- Public finance and fiscal institutions:
  - Resource fund acts as a fiscal buffer: drawn down when revenues fall short and accumulates savings when revenues are excessive.
  - Four fiscal instruments to close fiscal gaps: consumption tax rate, labor income tax rate, government consumption, and transfers. Instruments can be constrained by ceilings/floors.
  - Resource fund can be subject to a minimal asset level to serve as a saving commitment device.
- Debt instruments: concessional debt, external commercial debt, and domestic debt.
- Other model elements: large share of poor/hand-to-mouth households, learning-by-doing externalities in traded goods production (to capture potential Dutch disease), inefficiency and absorptive capacity constraints in public investment, time-varying depreciation of public capital that accelerates with lack of maintenance, detailed fiscal specification.

### Policy questions and simulated strategies
- Trade-offs analyzed:
  - Fast investment scaling-up can raise public capital and non-resource growth, but dedicating more resource revenues to investment reduces saving and increases vulnerability to future negative resource revenue shocks.
  - Importance of saving to sustain capital after resources are exhausted; resource fund plays crucial role.
- Investment approaches considered in simulations:
  - Spend-as-you-go: invest all resource windfall each period without saving.
  - Delinked approach: combines investment and saving so that government spending is a-cyclical with resource revenue flows.
- Simulated comparative analyses include variations in:
  - Degree of investment front-loading.
  - Investment efficiency and returns to public capital.
  - Mix of financing: concessional borrowing, external commercial borrowing, domestic borrowing.
  - Scenarios for resource revenue inflows (two hypothetical scenarios similar to patterns of an anticipated resource windfall).
- Country applications referenced: Mozambique (Melina and Xiong, 2013) and Kazakhstan (Minasyan and Yang, 2013).

### Model structure — households
- Two household types (distributed over the unit interval):
  - Intertemporal optimizing (Ricardian) households: fraction ω; have access to capital markets; denoted OPT.
  - Rule-of-thumb (hand-to-mouth) households: fraction 1−ω; financially constrained; denoted ROT.
- Consumption aggregator:
  - c_i,t = [φ^{1/χ} (c^N_{i,t})^{(χ−1)/χ} + (1−φ)^{1/χ} (c^T_{i,t})^{(χ−1)/χ}]^{χ/(χ−1)}, for i = OPT, ROT.
  - Parameters: φ indicates nontraded good bias; χ > 0 is the intra-temporal elasticity of substitution.
- Demand functions stemming from minimization:
  - c^N_{i,t} = φ p_{N,t}^{−χ} c_{i,t}, ∀ i = OPT, ROT.
  - c^T_{i,t} = (1−φ) s_t^{−χ} c_{i,t}, ∀ i = OPT, ROT.
- Price relations:
  - Unit price of consumption basket: 1 = [φ p_{N}^{1−χ} + (1−φ) s_t^{1−χ}]^{1/(1−χ)}.
  - s_t is the real exchange rate (price of foreign consumption basket in domestic units); law of one price holds for traded goods.
- Labor supply aggregator (CES across sectors):
  - L_{i,t} = [δ^{−1/ρ} (L^N_{i,t})^{(1+ρ)/ρ} + (1−δ)^{−1/ρ} (L^T_{i,t})^{(1+ρ)/ρ}]^{ρ/(1+ρ)}, for i = OPT, ROT.
  - Parameters: δ is steady-state share of labor in nontraded sector; ρ > 0 is intra-temporal elasticity of substitution.
- Sectoral labor supply schedules:
  - L^N_{i,t} = δ (w_{N,t}/w_t)^{ρ} L_{i,t}, ∀ i = OPT, ROT.
  - L^T_{i,t} = (1−δ) (w_{T,t}/w_t)^{ρ} L_{i,t}, ∀ i = OPT, ROT.
  - Wage index: w_t = [δ w_{N,t}^{1+ρ} + (1−δ) w_{T,t}^{1+ρ}]^{1/(1+ρ)}.

### Intertemporal optimizing households — preferences and budget
- Utility:
  - E_0 Σ_{t=0}^∞ β^t U(c^{OPT}_t, L^{OPT}_t) = E_0 Σ_{t=0}^∞ β^t [1/(1−σ) (c^{OPT}_t)^{1−σ} − κ^{OPT}/(1+ψ) (L^{OPT}_t)^{1+ψ}],
    where β ≡ [(1 +%)]^{−1}; % is the pure rate of time preference; σ is inverse intertemporal elasticity of substitution of consumption; ψ is inverse intertemporal elasticity of labor supply; κ^{OPT} is labor disutility weight.
- Budget constraint (levels):
  - (1 + τ^C_t) c^{OPT}_t + b^{OPT}_t − s_t b^{OPT,*}_t = (1−τ^L_t) w_t L^{OPT}_t + R_{t−1} b^{OPT}_{t−1} − R^*_{t−1} s_t b^{OPT,*}_{t−1} + Ω_{T,t} + Ω_{N,t} + θ_K τ_K (r^K_{T,t} k_{T,t−1} + r^K_{N,t} k_{N,t−1}) + s_t rm^*_t + z_t − μ k_{G,t−1} − Θ^{OPT,*}_t.
  - Explanatory notes on terms:
    - b^{OPT}_t: government bonds held by optimizing households (pay gross real interest rate R_t).
    - b^{OPT,*}_t: private foreign liabilities (pay interest rate R^*_t).
    - Ω_{T,t}, Ω_{N,t}: firm profits from traded and nontraded sectors.
    - θ_K τ_K (·): tax rebate on firms’ return on capital; θ_K captures the fraction of capital income tax revenue not entering government budget to match observed low private investment in LICs.
    - rm^*_t: remittances from abroad; z_t: government transfers.
    - μ: user fees for public capital services; Θ^{OPT,*}_t ≡ η/2 (b^{OPT,*}_t − b^{OPT,*})^2 are portfolio adjustment costs with parameter η controlling capital account openness and b^{OPT,*} the steady-state private foreign debt.
- First-order conditions (with λ_t as Lagrange multiplier):
  - λ_t (1 + τ^C_t) = (c^{OPT}_t)^{−σ}.
  - κ^{OPT} (L^{OPT}_t)^{ψ} = λ_t (1 − τ^L_t) w_t.
  - λ_t = β E_t (λ_{t+1} R_t).
  - λ_t = β E_t [λ_{t+1} s_{t+1} R^*_t / s_t − η (b^{OPT,*}_t − b^{OPT,*})].
- Private sector external borrowing premium:
  - R^*_t = R^{dc}_t + u, where u is a constant premium over the interest rate the government pays on external commercial debt R^{dc}_t.

### Key mechanisms emphasized
- Resource fund dynamics enable smoothing of public and private consumption through saving/drawing behavior tied to exogenous paths of public investment, concessional borrowing, aid, resource production, prices, and revenues.
- Debt accumulation triggers fiscal adjustments via fiscal rules governing speed and instruments of adjustment (taxes, government consumption, transfers); constraints on adjustment instruments capture institutional and political feasibility.
- Public investment efficiency, absorptive capacity, returns to public capital, and degree/timing (front-loading) of scaling-up materially affect growth outcomes and debt sustainability.
- The model includes mechanisms to capture Dutch disease via learning-by-doing externalities and relative sectoral dynamics when resource revenues are spent domestically.

*Source: _wp1450 - 1.  Baseline calibration*

### 2.  Rule-of-thumb Households

### 2.  Rule-of-thumb Households

### Rule-of-thumb household preferences and behavior
- Utility:
  - U(c_ROT_t, L_ROT_t) = 1/(1−σ) (c_ROT_t)^{1−σ} − κ_ROT 1/(1+ψ) (L_ROT_t)^{1+ψ}. (16)
- Budget constraint (consumption determined by):
  - (1+τ_C_t) c_ROT_t = (1−τ_L_t) w_t L_ROT_t + s_t rm*_t + z_t − μ k_G,t−1. (17)
- Labor supply from static maximization:
  - L_ROT_t = [ 1/κ_ROT (1−τ_L_t)/(1+τ_C_t) (c_ROT_t)^{−σ} w_t ]^{1/ψ}. (18)

### Aggregation with optimizing households
- Aggregate variables with share ω of optimizing households:
  - c_t = ω c_OPT_t + (1−ω) c_ROT_t. (19)
  - L_t = ω L_OPT_t + (1−ω) L_ROT_t. (20)
  - b_t = ω b_OPT_t; b*_t = ω b_OPT*_t. (21)

---

### B.  Firms

### Production structure overview
- Three production sectors:
  - Nontraded good sector (N).
  - Traded good sector (T) (non-resource traded goods).
  - Natural resource sector (O) — assumed whole resource output exported.

### 1. Nontraded Good Sector
- Technology (Cobb-Douglas):
  - y_N,t = z_N (k_N,t−1)^{1−α_N} (L_N,t)^{α_N} (k_G,t−1)^{α_G}. (22)
  - z_N: total factor productivity; k_N,t: end-of-period private capital; k_G,t: end-of-period public capital; α_N: labor share; α_G: output elasticity w.r.t. public capital.
- Capital accumulation with investment adjustment costs:
  - k_N,t = (1−δ_N) k_N,t−1 + [1 − κ_N/2 (i_N,t/i_N,t−1 − 1)^2] i_N,t. (23)
  - Investment adjustment costs follow Christiano et al. (2005).
- Representative firm maximizes discounted lifetime profits weighted by λ_t:
  - Ω_T,0 = E_0 Σ_{t=0}^{∞} β^t λ_t [ p_N,t y_N,t − w_N,t L_N,t − i_N,t − τ_K r_K_N,t k_N,t−1 ]. (24)
  - r_K_N,t = (1−α_N) p_N,t y_N,t / k_N,t−1.
- First-order conditions:
  - w_N,t = α_N p_N,t y_N,t / L_N,t. (25)
  - q_N,t = E_t [ β λ_{t+1}/λ_t ( (1−δ_N) q_N,t+1 + (1−τ_K)(1−α_N) p_N,t+1 y_N,t+1 / k_N,t ) ]. (26)
  - 1/q_N,t = [ 1 − κ_N/2 (i_N,t/i_N,t−1 − 1)^2 − κ_N (i_N,t/i_N,t−1 − 1) i_N,t/i_N,t−1 ] + E_t [ β λ_{t+1}/λ_t κ_N q_N,t+1/q_N,t (i_N,t+1/i_N,t − 1) (i_N,t+1/i_N,t)^2 ]. (27)

### 2. Traded Good Sector
- Technology mirrors nontraded sector:
  - y_T,t = z_T,t (k_T,t−1)^{1−α_N} (L_T,t)^{α_N} (k_G,t−1)^{α_G}. (28)
- Learning-by-doing externalities in TFP to capture Dutch disease:
  - z_T,t / z_T = (z_T,t−1 / z_T)^{ρ_{zT}} + (y_T,t−1 / y_T)^{ρ_{yT}}. (29)
  - ρ_{zT}, ρ_{yT} ∈ [0,1].
  - Specification implies no permanent effects but persistent productivity effects from deviations.
- Private capital accumulation:
  - k_T,t = (1−δ_T) k_T,t−1 + [1 − κ_T/2 (i_T,t/i_T,t−1 − 1)^2] i_T,t. (30)
- Representative firm profits:
  - Ω_T,0 = E_0 Σ_{t=0}^{∞} β^t λ_t [ y_T,t − w_T,t L_T,t − i_T,t − τ_K r_K_T,t k_T,t−1 ]. (31)
- First-order conditions:
  - w_T,t = α s_t y_T,t / L_T,t. (32)
  - q_T,t = E_t [ β λ_{t+1}/λ_t ( (1−δ_T) q_T,t+1 + (1−τ_K)(1−α_T) s_{t+1} y_T,t+1 / k_T,t ) ]. (33)
  - 1/q_T,t = [ 1 − κ_T/2 (i_T,t/i_T,t−1 − 1)^2 − κ_T (i_T,t/i_T,t−1 − 1) i_T,t/i_T,t−1 ] + E_t [ β λ_{t+1}/λ_t κ_T q_T,t+1/q_T,t (i_T,t+1/i_T,t − 1) (i_T,t+1/i_T,t)^2 ]. (34)

### 3. Natural Resource Sector
- Resource production exogenous:
  - ̃y_O,t / ̃y_O = (̃y_O,t−1 / ̃y_O)^{ρ_{yo}} exp(ε_{yo,t}). (35)
  - ρ_{yo} ∈ (0,1); ε_{yo,t} ∼ iid N(0, σ^2_{yo}).
- International commodity price process (taken as given):
  - p^*_O,t / p^*_O = (p^*_O,t−1 / p^*_O)^{ρ_{po}} exp(ε_{po,t}). (36)
  - ρ_{po} ∈ (0,1]; ε_{po,t} ∼ iid N(0, σ^2_{po}).
- Resource GDP in domestic consumption units:
  - y_O,t = s_t p^*_O,t ̃y_O,t. (37)
- Total real GDP:
  - y_t = p_N,t y_N,t + s_t y_T,t + y_O,t. (38)

---

### C.  The Government

### Government budget constraint and revenues
- Flow budget constraint:
  - τ_C_t c_t + τ_L_t w_t L_t + (1−θ_K) τ_K (r_K_T,t k_T,t−1 + r_K_N,t k_N,t−1) + s_t gr^*_t + μ k_G,t−1 + t_O,t + b_t + s_t d_t + s_t d_{c,t} + s_t R^{RF} f^*_t−1 = p_G_t (g_C_t + g_I_t) + z_t + R_{t−1} b_{t−1} + s_t R_d d_{t−1} + s_t R_{dc,t−1} d_{c,t−1} + s_t f^*_t. (39)
- Resource royalties:
  - t_O,t = τ_O s_t p^*_O,t ̃y_O,t. (40)
  - τ_O is a constant royalty rate (can be time-varying if necessary).
- Government debt instruments:
  - External concessional debt d_t (exogenous; constant gross real interest rate R_d).
  - External commercial debt d_{c,t} (gross real rate R_{dc,t−1} includes risk premium).
  - Domestic debt b_t.
- External commercial debt rate with risk premium depending on deviation of total external public debt-to-GDP from initial steady state:
  - R_{dc,t−1} = R_f + υ_{dc} exp[ η_{dc} ( (d_t + d_{c,t})/y_t − (d + d_c)/y ) ]. (41)
  - R_f is constant risk-free world interest rate; υ_{dc}, η_{dc} are structural parameters.

### 1. Government purchases
- Government purchases g_t = g_C_t + g_I_t are CES aggregate of domestic traded g_T,t and nontraded g_N,t goods:
  - g_t = [ ν_t^{1/χ} (g_N,t)^{(χ−1)/χ} + (1−ν_t)^{1/χ} (g_T,t)^{(χ−1)/χ} ]^{χ/(χ−1)}. (42)
  - ν_t is weight on nontraded goods; χ > 0 is intra-temporal elasticity of substitution (same as private consumption).
- Public demand functions from cost minimization:
  - g_N,t = ν_t (p_N,t / p_G_t)^{−χ} g_t. (43)
  - g_T,t = (1−ν_t) (s_t p_G_t)^{−χ} g_t. (44)
  - Government consumption price index:
    - p_G_t = [ ν_t p_N,t^{1−χ} + (1−ν_t) s_t^{1−χ} ]^{1/(1−χ)}. (45)
- Time-varying ν_t; for additional government spending weight ν_g may differ from steady state ν:
  - ν_t = (p_G_g)^{ν} + (p_G_t g_t − p_G_g g_t)^{ν_g} / (p_G_t g_t). (46)

### 2. Public investment efficiency, absorptive capacity, and public capital depreciation
- Effective public investment ̃g_I_t (γ_GI_t) depends on public investment growth γ_GI_t ≡ g_I_t / g_I − 1 relative to steady state:
  - ̃g_I_t = { ϕ g_I_t, if γ_GI_t ≤ γ_GI; (1+γ_GI) ̄g_I + ϕ(γ_GI_t) [1 + γ_GI_t − γ_GI] ̄g_I, if γ_GI_t > γ_GI }. (47)
  - ϕ ∈ [0,1] is steady-state efficiency; ϕ(γ_GI_t) ∈ (0,1] governs efficiency of portion exceeding threshold γ_GI.
  - ϕ(γ_GI_t) = exp[ −ς_ϕ (γ_GI_t − γ_GI) ] ϕ. (48)
  - ς_ϕ ∈ [0,∞) governs severity of absorptive capacity constraints.
- Public capital law of motion:
  - k_G,t = (1−δ_G,t) k_G,t−1 + ̃g_I_t. (49)
- Time-varying depreciation (maintenance effects):
  - δ_G,t = { φ δ_G δ_G k_G,t−1 / ̃g_I_t, if ̃g_I_t < δ_G k_G,t−1; ρ_δ δ_G,t−1 + (1−ρ_δ) δ_G, if ̃g_I_t ≥ δ_G k_G,t−1 }. (50)
  - δ_G is steady-state depreciation; φ ≥ 0 determines extent poor maintenance increases depreciation; ρ_δ ∈ [0,1) controls persistence.

### 3. The Resource Fund
- Resource windfall defined as t_O,t − t_O (deviation above initial steady-state level).
- Foreign financial asset in resource fund: f^*_t. Fund earns (R_rf − 1) f^*_t−1 with constant gross real rate R_rf.
- Resource fund evolution:
  - f^*_t − f^* = max { f_floor − f^*, (f^*_t−1 − f^*) + f_in,t s_t − f_out,t s_t }. (51)
  - f_in,t: total fiscal inflow; f_out,t: total fiscal outflow; f_floor ≥ 0 lower bound government maintains.
  - If fiscal inflow > outflow, fund value increases; if fund > f_floor and outflow > inflow, fund absorbs gap via withdrawal. If floor binds, fiscal gap covered via borrowing and/or tax increases or cuts in non-capital expenditures.
- Two investing approaches for resource windfall:
  - Spend-as-you-go (SAYG):
    - f^*_t = f^*, ∀t; entire windfall spent in public investment:
    - p_G_t g_I_t − p_G g_I = (t_O,t s_t − t_O s). (52)
  - Delinked investment approach:
    - A scaling-up path specified as a second-order delay function:
    - g_I_t / g_I = 1 + [ 1 + exp(−k_1 t) − 2 exp(−k_2 t) ] g_I^{nss}. (53)
    - g_I^{nss} is scaling-up target expressed as percentage deviation from initial steady state; k_1 > 0 speed of adjustment; k_2 ≥ k_1 degree of frontloading.
    - Special cases: k_1 = k_2 = 0 → g_I_t = g_I ∀t; k_1 → ∞ → immediate jump; k_2 = k_1 → gradual non-frontloaded increase.
  - MATLAB code allows exogenously specified public investment paths.

### 4. The Fiscal Gap
- Fiscal gap representation (from manipulation of (39)):
  - gap_t = f_out,t − f_in,t + s_t ( f^*_t − f^*_{t−1} ). (54)
- Definitions:
  - gap_t = Δ b_t + s_t Δ d_{c,t} + (τ_C_t − τ_C) c_t + (τ_L_t − τ_L) w_t L_t − p_G_t (g_C_t − g_C) − (z_t − z). (55)
  - f_in,t = τ_C c_t + τ_L w_t L_t + (1−θ_K) τ_K ( r_K_T,t k_T,t−1 + r_K_N,t k_N,t−1 ) + t_O,t + μ k_G,t−1 + s_t a^*_t + s_t gr^*_t + s_t (R^{RF} − 1) f^*_t−1 + s_t Δ d_t. (56)
  - f_out,t = p_G_t g_I_t + p_G_t g_C + z + (s_t R_d − 1) d_{t−1} + (R_{dc,t−1} − 1) s_t d_{c,t−1} + (R_{t−1} − 1) b_{t−1}. (57)
- Interpretation:
  - Covering the fiscal gap involves domestic and/or external commercial borrowing or adjustments in fiscal instruments.
  - If f^*_t > f_floor then gap_t = 0 (resource fund absorbs gap; no fiscal adjustments needed).
  - If f^*_t = f_floor then gap_t > 0 and must be covered by fiscal adjustments.

*Source: _wp1450 - 2.  Rule-of-thumb Households*

### 5.  Covering the Fiscal Gap

### 5.  Covering the Fiscal Gap

### Split of government borrowing between domestic and external commercial debt
- Rule for allocating borrowing:
  - κ∆b_t = (1−κ)s_t∆d_{c,t}, (58) where κ ∈ [0,1].
  - κ = 0: supplement concessional borrowing exclusively with domestic markets.
  - κ = 1: supplement concessional borrowing with external commercial debt.

### Debt-stabilizing (target) fiscal instruments
- Target adjustments required to cover the fiscal gap gap_t:
  - τ^C_{target,t} = τ^C + λ_1 gap_t / c_t, (59)
  - τ^L_{target,t} = τ^L + λ_2 gap_t / (w_t L_t), (60)
  - g^C_{target,t} = g + λ_3 gap_t / p^G_t, (61)
  - z_{target,t} = z + λ_4 gap_t, (62)
- Allocation of burden:
  - λ_i, i = 1,...,4 split the fiscal burden with ∑_{i=1}^4 λ_i = 1.
- Policy reaction functions (implementability with ceilings/floors):
  - τ^C_t = min{ τ^C_{rule,t}, τ^C_{ceiling} }, (63)
  - τ^L_t = min{ τ^L_{rule,t}, τ^L_{ceiling} }, (64)
  - g^C_t / g^C = max{ g^C_{rule,t} / g^C, g^C_{floor} }, (65)
  - z_t / z = max{ z_{rule,t} / z, z_{floor} }, (66)
  - τ^C_{ceiling}, τ^L_{ceiling} = maximum implementable tax levels.
  - g^C_{floor}, z_{floor} = minimum deviations from initial steady-state values.
- Fiscal rules determining τ^C_{rule,t}, τ^L_{rule,t}, g^C_{rule,t}, z_{rule,t}:
  - τ^C_{rule,t} = τ^C_{t−1} + ζ_1(τ^C_{target,t} − τ^C_{t−1}) + ζ_2(x_{t−1} − x), with ζ_1, ζ_2 > 0, (67)
  - τ^L_{rule,t} = τ^L_{t−1} + ζ_3(τ^L_{target,t} − τ^L_{t−1}) + ζ_4(x_{t−1} − x), with ζ_3, ζ_4 > 0, (68)
  - g^C_{rule,t} / g^C = g^C_{t−1} / g^C + ζ_5(g^C_{target,t} − g^C_{t−1}) / g^C − ζ_6(x_{t−1} − x), with ζ_5, ζ_6 > 0, (69)
  - z_{rule,t} / z = z_{t−1} / z + ζ_7(z_{target,t} − z_{t−1}) / z − ζ_8(x_{t−1} − x), with ζ_7, ζ_8 > 0, (70)
- Definition:
  - x_t ≡ (b_t + s_t d_{c,t}) / y_t is the sum of domestic and external commercial debt as a share of GDP.
- ζ parameters control speed and responsiveness of fiscal adjustments.

### Identities and market clearing conditions
- Goods market clearing for nontraded goods:
  - y_{N,t} = φ p^{−χ}_{N,t} (c_t + i_{N,t} + i_{T,t}) + ν_t (p_{N,t} / p^G_t) − χ g_t. (71)
- Balance of payments condition:
  - ca^d_t s_t = gr^*_t − ∆f^*_t + ∆d_t + ∆d_{c,t} + ∆b^*_t, (72)
  - Current account deficit ca^d_t:
    - ca^d_t = c_t + i_{N,t} + i_{T,t} + p^G_t g_t + Θ^{OPT*}_t − y_t − s_t rm^*_t
      + (R^d_{t−1} − 1) s_t d_{t−1}
      + (R^{dc}_{t−1} − 1) s_t d_{c,t−1}
      + (R^*_{t−1} − 1) s_t b^*_{t−1}
      − (R^{RF} − 1) s_t f^*_{t−1}. (73)

### Calibration (baseline to an average LIC)
- National accounting:
  - Trade balance = 6 percent of GDP.
  - Government consumption = 14 percent of GDP.
  - Public investment = 6 percent of GDP.
  - Private investment = 15 percent of GDP.
  - Shares of tradable goods: private consumption 50 percent, government purchases 40 percent.
  - Share of natural resources at initial steady state = 1 percent of GDP.
- Assets, debt and grants:
  - Government savings initially small: RF_share = 0.01 (1 percent of GDP).
  - b_share = 0.20, d_share = 0.50, gr_share = 0.04.
  - b^*_share = 0, d_{c,share} = 0 in baseline to highlight constraints.
- Interest rates:
  - Real annual interest rate on domestic debt (R−1) = 10 percent.
  - Net real risk-free rate (R_f − 1) = 4 percent.
  - Real rate on external commercial debt (R_{dc} − 1) = 6 percent.
  - Real rate on concessional loans (R_d − 1) = 0 percent.
  - No additional risk premium in baseline: η_{dc} = 0.
  - Annual real return on resource fund (R_{RF} − 1) = 2.7 percent.
- Private production:
  - Labor income shares: α_N = 0.45, α_T = 0.60.
  - Depreciation rates: δ_N = δ_T = 0.10.
  - Learning-by-doing externality: ρ_{Y_T} = ρ_{z_T} = 0.10.
  - Investment adjustment costs: κ_N = κ_T = 25.
- Households preferences:
  - Risk aversion σ = 2.94 (implies inter-temporal elasticity of substitution 0.34).
  - Frisch labor elasticity inverse ψ = 10 (Frisch elasticity 0.10).
  - Labor mobility ρ = 1.
  - Elasticity between traded and nontraded goods χ = 0.44.
  - Portfolio adjustment elasticity η = 1.
- Measure of optimizers:
  - ω = 0.40 (40 percent optimizers; 60 percent rule-of-thumb).
- Mining:
  - Persistence of resource production shock ρ_{yo} = 0.90.
  - Resource price follows a random walk ρ_{po} = 1.
  - Royalty tax rate τ_O = 0.65 (calibrated so resource revenue at peak ≈ 50 percent of total revenues).
- Tax rates:
  - τ_C = 0.10, τ_L = 0.15, τ_K = 0.20.
  - Implied non-resource revenue ≈ 18 percent of GDP at initial steady state.
- Fiscal rules and baseline policy parameter choices:
  - f_{floor} = 0.
  - No effective floors/ceilings in baseline: g^C_{floor} = z_{floor} = −100000, τ^C_{ceiling} = τ^L_{ceiling} = 100000.
  - Baseline fiscal adjustment occurs entirely via external commercial borrowing and consumption taxes:
    - κ = 1, λ_1 = 1, λ_2 = λ_3 = λ_4 = 0.
    - ζ_3 = ζ_5 = ζ_7 = 1; ζ_4 = ζ_6 = ζ_8 = 0.
    - Smoothing: ζ_1 = 0.5, ζ_2 = 0.001.
- Public investment:
  - Public investment efficiency ̄ε = 0.50.
  - Depreciation rate of public capital δ_G = 0.07.
  - Home bias ν = 0.6; for additional spending ν_g = 0.4.
  - Output elasticity to public capital α_G = 0.15 (implies marginal net return of public capital 28 percent at initial steady state).
  - Severity of public capital depreciation φ = 1.
  - Persistence of change in public capital depreciation ρ_δ = 0.8.
  - Absorptive capacity binds when public investment rises above 75 percent from initial steady state: ̄γ_{GI} = 0.75.
  - Absorptive capacity severity ς_ε = 25 implies average investment efficiency halves to ≈ 25 percent when public investment spikes to ≈ 200 percent from initial steady state.
  - Planned long-term scaling up of investment g^I_{nss} = 0.80 (public investment at new steady state 80 percent higher than initial steady state).

### Scaling up public investment with a resource windfall (scenarios and findings)
- Baseline scenario assumptions:
  - LNG production reaches full capacity by 2021, declines after 2035; peak production ≈ 1500 millions of cubic feet per year.
  - LNG price path constructed from WEO oil price forecast multiplied by conversion factor 0.1724; baseline assumes non-volatile price path.
  - Adverse scenario: from 2025 onwards resource revenue quickly declines due to reduced production and large negative price shocks.
- Two investment approaches (no commercial or domestic borrowing):
  - Spend-as-you-go (SAYG):
    - Government spends all resource windfall each period; stabilization fund remains at initial steady state.
    - Results in volatile public investment mirroring resource revenue volatility; fiscal volatility → macroeconomic instability; average investment efficiency can drop from 50 percent to almost 25 percent during accelerations.
    - In baseline (no negative shocks), SAYG can lead to higher public capital accumulation and higher non-resource output, private consumption and investment than delinked approach.
    - If resource depletes after 2040 and public investment cannot be maintained, public capital and growth benefits revert to initial levels.
  - Delinked investment approach:
    - Combines investment spending with savings in a resource fund.
    - Scales up public investment gradually with no overshooting (k_1 = 0.20, k_2 = 0.20); can build a stabilization fund and maintain stable spending path without major fiscal adjustments.
    - Under baseline, stabilization fund can peak around 150 percent of GDP; under adverse scenario it peaks around 25 percent of GDP.
    - Delinked approach yields more resilient and stable non-resource GDP growth and less volatile real exchange rate; performs better under adverse shocks.
- Front-loading public investment financed with commercial borrowing:
  - Three frontloading degrees (all reach long-run investment level 80 percent higher than initial steady state, k_1 = 0.20):
    - Conservative: k_2 = 0.10 (slow scaling; little debt accumulation).
    - Gradual: k_2 = 0.20 (small frontloading).
    - Aggressive: k_2 = 0.70 (pronounced overshooting; public investment ≈ 100 percent above initial level during peaks).
  - Fiscal assumptions for these exercises:
    - Use external commercial borrowing when stabilization fund lower bound reached: κ = 1.
    - Consumption tax used to stabilize debt: λ_1 = 1.
    - Ceiling on consumption tax rate at 12.5 percent; short-run increases difficult beyond 2.5 percentage points.
  - Findings:
    - Front-loading results in no savings in stabilization fund and rising public debt; most pronounced under aggressive path and adverse scenario.
    - Conservative and gradual paths: public debt as share of GDP does not increase significantly; conservative path can accumulate some resource fund savings even under adverse scenario.
    - Aggressive path signals likely unfeasible path: government debt appears explosive under adverse scenario.
- Domestic versus external commercial borrowing:
  - Comparison with aggressive frontloading path:
    - κ = 0 (domestic borrowing) shifts domestic resources from private to public sector, raising domestic real interest rate and crowding-out private investment more than external borrowing (κ = 1).
    - Domestic borrowing results in higher interest payments, more public debt accumulation, and on average higher consumption tax rates to stabilize debt.
    - Under adverse scenario: external commercial borrowing → public debt remains stable; domestic borrowing → public debt becomes unsustainable.
- Public investment efficiency, return on public capital, and debt sustainability:
  - Scenarios compared (external commercial borrowing, adverse resource scenario):
    - Baseline: ε = 0.50, α_G = 0.15.
    - Improved efficiency: ε increases from 0.50 to 0.70 (α_G = 0.15).
    - Improved efficiency and higher productivity: ε increases to 0.70 and α_G = 0.18.
  - Findings:
    - Improving ε and/or α_G produces more public capital for given investment, raising non-resource output, income, and consumption.
    - Combined improvements can double additional long-run non-resource GDP growth in example.
    - Fiscal implications: with baseline calibration and adverse resource path government debt is explosive; with improved efficiency same investment path can be fiscally sustainable because higher non-resource growth generates sufficient revenues to close the fiscal gap.

### Conclusions and model use
- DIGNAR model capabilities:
  - Assesses debt sustainability and growth effects of public investment scaling-ups in resource-abundant developing countries.
  - Integrates public investment inefficiencies, absorptive capacity constraints, learning-by-doing externalities, and flexible fiscal policy structure (domestic and external commercial borrowing; multiple fiscal instruments).
  - Includes a resource fund as fiscal buffer and savings device with configurable minimal savings.
- Policy-analytic insights:
  - Delinked investment with savings in a stabilization fund generally yields more macroeconomic stability and resilience to adverse resource shocks than spend-as-you-go.
  - Front-loading financed by commercial borrowing can be feasible if degree of front-loading is moderate and projected returns/efficiencies are sufficiently high; aggressive frontloading risks explosive debt under adverse scenarios.
  - External commercial borrowing is less crowding-out than domestic borrowing in the model; however, external debt increases exposure to shocks affecting foreign liabilities.
  - Public investment efficiency and returns to public capital are critical for both growth outcomes and debt sustainability; improvements can turn otherwise unsustainable paths into sustainable ones.
- Practical application:
  - DIGNAR can be calibrated to country-specific parameters; where uncertainty exists, sensitivity analysis is essential (e.g., resource revenue scenarios, investment efficiency, return to public capital).
  - Simulations can guide the determination of appropriate scaling-up magnitude that sustains public capital while preserving debt sustainability.
  - DIGNAR can complement IMF-WB DSF for natural resource-rich developing countries.

*Source: _wp1450 - 5.  Covering the Fiscal Gap (IMF Working Paper chapter).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1450.pdf_