## _wp10116

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### Dynamic Optimizers
- A fraction ˆγ of consumers are dynamic optimizers (superscript d). They own firms and financial assets and maximize lifetime utility:
  - E0 ∑t=0∞ βt u(Cdt, Mdt/Pt, ldt) = E0 ∑t=0∞ βt ( log([θd Cdtη−1/η + (1−θd) Mdt/Pt η−1/η] η/(1−η)) − ς l1+ψ/(1+ψ) (ldt)1+ψ ).
- Labor supply and aggregation:
  - ldt = [αN−1/ρL l dN t 1+ρL /ρL + (1−αN)−1/ρL l dT t 1+ρL /ρL] ρL /(1+ρL)
  - ψ is the inverse of the labor supply elasticity.
  - αN is the share of non-traded employment (value added) in total employment (GDP).
  - ρL is the elasticity of substitution between labor services in traded and non-traded sectors.
- Normalized budget constraint (representative dynamic consumer):
  - cdt + bdc t + mdt + st bd∗ t = (1−τ) wN t l dN t + (1−τ) wT t l dT t + (1 + it−1) bdc t−1 / πt + mdt−1 / πt gT + st (1 + i∗ t−1) bd∗ it−1 / π∗ gT − st ψ∗(bd∗ t) + st rem∗ + 1/ˆγ prN t + $ s t
- Real exchange rate and portfolio adjustment costs:
  - st = St P∗ t / Pt
  - ψ∗(b∗ t) = υ∗/2 (b∗ t − ̄b∗)2
  - Choice of υ∗ permits modeling from closed capital account (υ∗ = +∞) to partially open (0 < υ∗ < +∞).
- Policy-relevant implication:
  - Sterilized exchange rate interventions influence the exchange rate by changing expected returns on foreign assets net of portfolio adjustment costs.

### Static Optimizers and Aggregation
- Static optimizers (fraction (1−ˆγ)) have period utility:
  - u(Cst, Mst/Pt, lst) = log([θs Cst η−1/η + (1−θs) Mst/Pt η−1/η] η/(1−η)) − κs ψ (lst)ψ
- Static budget constraint (normalized):
  - cst + mst = (1−τ) wN t l sN t + (1−τ) wT t l sT t + mst−1 / πt gT + st rem∗ − $d
- Aggregation across consumer types for any variable f:
  - ft = ˆγ f d t + (1−ˆγ) f s t  for f = (c, m, lN, lT, b∗, bc, $)

### Consumption Baskets, Demand, and Price Indices
- Two goods categories: traded (T) and non-traded (N); non-traded varieties aggregated with Dixit-Stiglitz elasticity θ.
- Non-traded consumption and price index:
  - cN t = (∫0 1 cN it θ−1/θ di) θ/(θ−1)
  - cN it = (pN it / pN t)−θ cN t
  - PN t = (∫0 1 PN it 1−θ di)1/(1−θ)
- Law of one price for traded goods:
  - PT t = St P∗ t

### Income components and transfers
- Wages: WN t and WT t are nominal wages in non-traded and traded sectors.
- τ denotes the income tax rate.
- PrN t denotes dynamic optimizer’s share of nominal profits in non-traded sector.
- $d denotes transfers between dynamic and static consumers to ensure identical steady state consumption and labor supply.

### The Aggregate Basket and Goods Demand
- Total consumption CES:
  - c_t = ( n_1 χ_1 (c_N_t)^{χ−1/χ} + (1−n_1) 1/χ (c_T_t)^{χ−1/χ} )^{χ/χ−1}
  - χ is elasticity of substitution between non-traded and traded goods.
  - n_1 measures degree of home bias in consumption.
- Government spending CES:
  - G_t = ( v_1 χ_1 (G_N_t)^{χ−1/χ} + (1−v_1) 1/χ (G_T_t)^{χ−1/χ} )^{χ/χ−1}
- Normalized price indices and demand:
  - 1 = ( n_1 (p_N_t)^{1−χ} + (1−n_1) (s_t)^{1−χ} )^{1/1−χ}
  - p_G_t = ( v_1 (p_N_t)^{1−χ} + (1−v_1) (s_t)^{1−χ} )^{1/1−χ}
  - c_N_t = n_1 (p_N_t)^{−χ} c_t
  - c_T_t = (1−n_1) s_t^{−χ} c_t
  - g_N_t = v_1 (p_N_t / p_G_t)^{−χ} g_t
  - c_T_t = (1−v_1) (s_t / p_G_t)^{−χ} g_t

### Non-Traded and Exportable Sectors, Firms, and Adjustment Costs
- Non-traded firm production (i):
  - Y_N_it = Z_N ( K_N_it−1^{φ_N} Q_N_t−1^{1−φ_N} )^{1−α_N} (T_t L_N_it)^{α_N}
  - Capital accumulation with adjustment costs:
    - K_N_it = (1−δ_n) K_N_it−1 + (1−S_N(X_N_it / X_N_it−1)) X_N_it
    - S_N(X_N_it / X_N_it−1) = κ_N / 2 ( (X_N_it / X_N_it−1 g_T^{−1})^2 )
  - Firm demand and labor demand:
    - y_dN_it = ( p_N_it / p_N_t )^{−θ} y_N_t
    - L_N_it = ( p_N_it / p_N_t )^{−θ α_N} y_N_t^{1/α_N} Z_N^{−1/α_N} k_N_it−1^{φ_N (α_N−1)/α_N} q_N_t^{1−φ_N (α_N−1)/α_N}
  - Price adjustment costs:
    - Γ_N(...) = p_N_t y_N_t (1−$) ζ_p^2 ( π_N_it / π_N_t−1 − 1 )^2
  - Distortion $ reduces firms’ incentives to hire and invest (matches low investment shares).
- Exportable goods sector parallels non-traded specification:
  - y_T_jt = Z_T ( K_T_jt−1^{φ_T} Q_T_t−1^{1−φ_T} )^{1−α_T} (T_t L_T_jt)^{α_T}
  - Capital accumulation and adjustment costs S_T(.) analogous to S_N(.).

### Government: Budget, Public Investment, and Rules
- Inter-temporal budget constraint (normalized):
  - p_G_t g_t = τ_w_t (L_d_t + L_s_t) + b_t − b_t−1 / π_t g_T − i_t−1 b_c_t−1 / π_t g_T + s_t ( ̄A^∗ + O^*_t ) − (d_G_t − d_G_t−1 / π_t g_T)
- Government debt decomposition:
  - b_t = b_cb_t + b_c_t
- Public investment and capital accumulation:
  - x_G_t = γ ̄G ̄g + γ_G ( g_t − ̄g )
  - q_G_t g_T = (1−δ_G) q_G_t−1 + ε_s x_G_t
  - q_N_t = %_n q_G_t ; q_T_t = %_e q_G_t
- Government deposits and debt rules:
  - d_g_t = ρ_d d_g_t−1 + (1−ρ_d) ̄d_g + (1−γ) s_t O^*_t
  - b_t = b_t−1 − ς ( b_c_t−1 − ̄b_c )

### Central Bank: Reserves, Balance Sheet, and Policy Rule
- Reserve accumulation:
  - R^*_t = ρ_R R^*_t−1 + (1−ρ_R) ̄R^* + (1−ω) O^*_t − ω_e ( π_S_t − π_S )
  - π_S_t = π_t π^*_s_t s_t−1
  - ω is fraction of oil revenues sold on market; ω <1 implies central bank keeps some oil revenues.
  - ω_e pins down exchange rate level or crawl commitment.
- Central bank balance sheet (nominal):
  - M_t = B_cb_t − D_G_t + NFA_t
  - m_t − m_t−1 / π_t g_T = b_cb_t − b_cb_t / π_t g_T − ( d_G_t − d_G_t−1 / π_t g_T ) + nfa_t − nfa_t−1 / π_t g_T
  - nfa_t − nfa_t−1 / π_t g_T = s_t ( R^*_t − R^*_t−1 / π^* g_T )
- Monetary policy (Taylor rule targeting non-traded inflation):
  - r_t = 1/β ( π_t / ̄π )^{φ_π}
  - ̄π is inflation objective.

### Markets, BoP, and Stochastic Processes
- Non-traded market equilibrium:
  - y_nt = p_nt^{−χ} D_nt
  - D_nt = { n_1 ( c_t + x_N_t + x_T_et + Γ_N( π_nt / π_nt−1 ) ) + v_1 (p_g_t)^{χ} G_t }
- Balance of payments constraint (aggregated budgets):
  - c_t + p_G_t g_t + x_N_t + x_T_t + Γ_N(...) − { p_N_t y_N_t + s_t y_T_t } = s_t { rem^∗ + ω O^*_t + ̄A^∗ − ( π^∗ g_T − ρ_R ) / π^∗ g_T ( ̄R^∗ − R^*_{t−1} ) + ω_e ( π_S_t − π_S ) + (1 + i^*_t−1 ) b^*_t−1 / π^∗ g_T − b^*_t − ψ^∗ ( b^*_t ) }
- Oil revenue AR process:
  - O^*_t = ρ_1 O^*_{t−1} + ρ_2 O^*_{t−2} + ρ_3 O^*_{t−3} + ≤O_t
- Real and nominal GDP:
  - y_t = p_N y_N_t + s y_T_t
  - Y_t = p_N_t y_N_t + s_t y_T_t

### Baseline Calibration (selected parameter values and steady state)
- Preference & structural parameters:
  - α_N = 0.40
  - χ = 1.5
  - θ = 12
  - κ = 0.24
  - ψ = 3
  - θ_d, θ_s = 0.9993, 0.9888
  - η = 1.5
  - α_N (duplicate in Table 1) = 0.61 (Matches share of non-traded production in value added (60 %))
  - ρ_L = 1
  - rem^∗ = 0.4281 (Ensures trade deficit equals 31 percent of GDP)
  - β = 0.9951 (Implies real interest rates equal 8 percent)
  - ˆγ = 0.60
- Technology & rigidities:
  - α_T, α_N = 0.7
  - φ_T, φ_N = 0.33
  - ≤ = 0.00001 (No learning by doing in the baseline)
  - κ_T, κ_N = 25
  - g_T = 1.0171 (Ensures steady state annual growth is (6%))
  - Z_T = 1
  - Z_N = 1.044 (Ensures real exchange rate equals one at steady state)
  - δ_N, δ_T = 0.015
  - ζ_p^N = 30 (Prices sticky on average for 6 moths)
  - $ = 0.3609 (Helps match Ghana’s investment share (19%))
  - ι = 0.091
  - υ = 10ˆ5 (Capital account closed)
  - ̄b_a^∗ = 0.2684
- Policy & aid process:
  - Aid process ρ_1, ρ_2, ρ_3 = 1.33, -0.15, -0.2
  - ̄A^∗ = 0.1764 (Matches current share of aid in GDP (5%))
  - var(≤_O) = 0.0780 (Oil revenue equals 6 percentage points of GDP in the first year)
  - v_1 = 0.62
  - τ = 0.59 (Matches current share of government spending (37%))
  - γ ̄G ̄g = 0.3514 (Matches current share of public investment (12%))
  - γ_G = 0.3514
  - ̄b_c = 0.3068 (Matches stock of outstanding domestic government debt (16%))
  - ̄b_cb = 0.0828
  - δ_g = 0.035
  - ε_s = 0.7
  - ρ_d = 0.95
  - ̄d_g = 0.224
  - γ1 = 1
  - ρ_R = 0.97
  - ̄R^∗ = 0.21 (Matches Ghana’s stock of reserves in % of GDP (11%))
  - ω = 1
  - ω_e = 0
  - π^∗ = 1.04 (Consistent with Ghana’s current inflation (18%))
  - φ_π = 1.5
- Ghana steady state values (percents of GDP unless indicated):
  - Private Consumption 75
    - Traded 45
    - Non-traded 30
  - Private Investment 19
    - Traded 7
    - Non-traded 13
  - Government Spending 37
    - Consumption 24
    - Investment 13
      - Traded 14
      - Non-traded 23
  - Trade Balance −31
  - Value added, Traded sector 27
  - Value added, Non-traded sector 73
  - Government Accounts:
    - Government Spending 37
    - Taxes 26
    - Seignorage 2
    - Aid 9
    - Interest Payments 1
    - Government Debt 14
  - Central Bank Balance Sheet:
    - Government debt held by CB 10
    - Government deposits at CB 2
    - Reserves 11
    - Real money balances 20
  - Private Sector Assets:
    - Net foreign assets 4
    - Government debt 4
  - Other Variables:
    - Annual inflation, nominal depreciation 18
    - Real GDP growth 6

### Benchmark Simulation: Key Responses to the Oil Windfall
- Assumptions:
  - Oil production front-loaded with peak production broadly over first 5 years.
  - IMF staff predicted cumulative government revenues from oil and gas could reach US 12 billion during 2012–2030; model’s path similar but peaks earlier.
  - Central bank in benchmark:
    - (i) Does not pursue an exchange rate target.
    - (ii) Sells all foreign-exchange inflows related to oil production.
  - Monetary policy raises interest rate if inflation exceeds target; target set to 18 percent.
- Fiscal and macro responses:
  - Government spends oil revenue as it accrues.
  - Aggregate demand increase leads to:
    - Sharp (but short-lived) spike in real GDP growth; persistent effect on real GDP.
    - Moderate inflation increase driven by non-tradable inflation rise and decrease in tradable sector inflation.
    - Short-run nominal wage growth increases.
    - Real exchange rate appreciates (both relative price and CPI-deflated nominal exchange rate).
    - Trade deficits net of oil revenues widen.
- Transmission mechanisms:
  - Inter-sectoral reallocation:
    - 62 percent of additional government spending falls on non-traded goods.
    - Higher government demand raises labor demand in non-traded sector, prompting real exchange rate appreciation and reallocation of labor.
    - Real appreciation shifts private demand toward imports, widening trade deficit net of oil revenues.
    - Low labor mobility increases required real appreciation; with flexible prices, sectoral reallocation has little aggregate effect but large sectoral effects.
  - Nominal rigidities:
    - Sticky non-traded prices imply higher government demand raises aggregate labor demand and firms hire more labor in short run, increasing aggregate employment, GDP, non-traded inflation, and nominal wages.
    - Magnitude depends on labor mobility; low mobility increases wage pressures and inflation.

### Sensitivity Analysis and Dutch Disease
- Labor substitutability:
  - Benchmark ρ_L = 1; alternative examined: 5.
  - With elasticity = 5:
    - Easier labor migration from tradable to non-traded.
    - Larger production impacts in both sectors, reduced demand pressures, smaller first-year output spike, and reduced real appreciation needed.
- Learning-by-doing (Dutch disease channels):
  - Tradable-sector productivity endogenized as Z_T_t = ̄Z_T (y_T_{t−1})^{ε}.
  - Baseline ε = 0.
  - Scenario ε = 0.2:
    - Impact of higher public investment on output smaller.
    - Traded sector contraction more pronounced.
    - Overall GDP remains above baseline in presented simulations.
  - Combining high labor substitutability with ε > 0 can produce substantial Dutch disease effects (output considerably below trend, though still above baseline in simulations).
- Three lessons:
  - Dutch disease magnitude depends on tradable-sector shrinkage and multiple parameters; limited factor substitutability curbs tradable decline but increases wage pressures and inflation.
  - Policy that bolsters tradable sector (e.g., public investment) can limit Dutch disease and may reverse it.
  - Even large Dutch disease effects may not outweigh benefits from oil windfall; alternative formulations of tradable-sector productivity dynamics can alter outcomes.

### Fiscal Policy Options and Effects
- Expenditure smoothing (permanent-income style):
  - Benchmark: full spending of oil windfall as it accrues (increase spending to 6 percent of GDP then gradually decrease).
  - Alternative: increase spending by only 1 of GDP permanently.
  - Effects of smoothing:
    - Small macroeconomic impact.
    - Avoids large demand-driven boom in first two years.
    - Spreads benefits over time; consistent with optimizing consumers.
    - Reduces macroeconomic volatility.
- Expenditure composition (without smoothing):
  - Lower share on non-tradables:
    - Baseline: 62 percent of additional government spending goes to non-tradables; alternative: 40 percent.
    - Effects:
      - Higher import content of spending meets demand via imports, requiring less real appreciation.
      - Dampens short-term non-tradables boom, reduces wage pressures and non-tradables inflation, and yields smaller private investment increase in non-tradables.
      - Real GDP growth response smaller than baseline; smoother macro paths.
  - Increasing public investment share:
    - Oil-financed public investment share increased from 35 percent to 60 percent.
    - Effects:
      - Higher public capital accumulation boosts medium-term growth in both sectors.
      - Raises production potential and private capital productivity (crowding in).
      - Real exchange rate appreciation similar to baseline; inflation higher in first year due to wealth effects.
      - Policy implication: using oil revenue for public investment is powerful for medium-term gains and can offset tradable-sector productivity declines.

### Monetary Policy Options and Effects
- Context: oil revenue increase occurs while inflation at 18 percent.
- Discretionary policy tightening (lowering inflation target):
  - Scenario: central bank reduces inflation target to 10 percent as initial surprise.
  - Effects:
    - Temporary reduction in aggregate demand; short-run GDP growth lower and displaced into second year.
    - More gradual increase in non-traded production; similar real appreciation to baseline.
    - Given small nominal rigidities and relatively quick expectation adjustment, cost of lowering target is relatively small (projections optimistic).
- Reserve accumulation (reducing foreign exchange sales):
  - Scenario: central bank accumulates 50 percent of oil proceeds as reserves while government spends local-currency counterpart.
  - Effects:
    - Smaller real appreciation reduces expenditure switching and aggravates demand pressures from fiscal expansion.
    - Short-run GDP impact higher; medium-term GDP expansion considerably lower.
    - Inflation increases considerably.
    - Sterilized reserve accumulation raises real interest rates, crowding out private investment and consumption, reducing medium-term output expansion.
    - Interpretation: economically akin to domestically-financed fiscal expansion with crowding out.
    - Policy implication: reserve accumulation should be coordinated with fiscal savings; otherwise private sector bears adjustment costs.

### Conclusions and Policy Implications
- Short-run:
  - An oil-driven fiscal expansion similar in size to the expected windfall likely generates a moderate demand-led expansion in output and a moderate increase in non-traded goods inflation.
  - Aggregate inflation impact can be minimal if real exchange rate is allowed to appreciate.
  - Frictions in labor and financial markets amplify inflationary impacts; reducing frictions improves the economy’s response.
- Medium-term:
  - Competitiveness could be negatively affected if sizable learning externalities exist in the tradable sector; higher public capital can reverse negative effects.
  - Public investment financed by oil revenue is a powerful tool to boost medium-term output and can offset Dutch disease.
- Policy design:
  - Smoother fiscal responses and higher import content in government spending reduce demand pressures.
  - Discretionary monetary tightening can reduce inflation but requires credible commitment to price stability.
  - If government saves part of oil windfall domestically while central bank accumulates foreign-currency proceeds, real exchange rate appreciation is smaller but inflation higher—even if sterilized—highlighting the role of foreign-currency supply from oil proceeds.
  - Fiscal and central bank coordination is critical; reserve accumulation without fiscal savings amplifies inflation and crowds out private investment.
- Institutional capacity caveat:
  - Analysis abstracts from formal modeling of fiscal institutions and assumes capacity to absorb large increases in public investment; in practice, implementation constraints could reduce public capital accumulation.

*Source: _wp10116 - 1. Dynamic Optimizers; 1. The Aggregate Basket; 5. Baseline Scenario: Macroeconomic Impact of the Oil Windfall (PDF chapter).*

### 1. Dynamic Optimizers....................................................................9

### 1. Dynamic Optimizers

### Overview and role in the model
- A fraction ˆγ of all consumers are dynamic optimizers (superscript d). These consumers own the firms and the financial assets in the economy and maximize lifetime utility:
  - E0 ∑t=0∞ βt u(Cdt, Mdt/Pt, ldt) = E0 ∑t=0∞ βt ( log([θd Cdtη−1/η + (1−θd) Mdt/Pt η−1/η] η/(1−η)) − ς l1+ψ/(1+ψ) (ldt)1+ψ ).
- The dynamic consumer supplies labor across exportable and non-traded sectors with labor aggregator:
  - ldt = [αN−1/ρL l dN t 1+ρL /ρL + (1−αN)−1/ρL l dT t 1+ρL /ρL] ρL /(1+ρL)
- Parameter definitions used explicitly in the model:
  - ψ is the inverse of the labor supply elasticity.
  - αN is the share of non-traded employment (value added) in total employment (GDP).
  - ρL is the elasticity of substitution between labor services provided in the traded and non-traded sector.

### Dynamic optimizer budget constraint (normalized)
- The nominal (non-stationary) budget constraint includes consumption, domestic nominal bonds, money holdings, foreign assets, labor income, bond returns, portfolio adjustment costs, profits and transfers. After stationarization and normalization (lower case variables), the representative dynamic consumer faces:
  - cdt + bdc t + mdt + st bd∗ t = (1−τ) wN t l dN t + (1−τ) wT t l dT t + (1 + it−1) bdc t−1 / πt + mdt−1 / πt gT + st (1 + i∗ t−1) bd∗ it−1 / π∗ gT − st ψ∗(bd∗ t) + st rem∗ + 1/ˆγ prN t + $ s t
- Real exchange rate definition used:
  - st = St P∗ t / Pt
- Portfolio adjustment costs (to model capital account openness) are specified as:
  - ψ∗(b∗ t) = υ∗/2 (b∗ t − ̄b∗)2
  - Choice of υ∗ permits modeling from a closed capital account (υ∗ = +∞) to a partially open one (0 < υ∗ < +∞).
- Implication noted in the model text: sterilized exchange rate interventions influence the exchange rate by changing expected returns on foreign assets net of portfolio adjustment costs.

### Income components and transfers
- Wages: WN t and WT t are nominal wages in the non-traded and traded sectors respectively.
- τ denotes the income tax rate.
- PrN t denotes the dynamic optimizer’s share of nominal profits of domestic firms in the non-traded sector.
- $d refers to transfers between dynamic and static consumers; transfers ensure steady state consumption and labor supply are the same for both consumer types.

---

### 2. Static Optimizers

### Definition and preferences
- The remaining fraction (1−ˆγ) of consumers are static optimizers (superscript s). They do not own firms and receive income only from labor.
- Period utility:
  - u(Cst, Mst/Pt, lst) = log([θs Cst η−1/η + (1−θs) Mst/Pt η−1/η] η/(1−η)) − κs ψ (lst)ψ

### Budget constraint (normalized)
- cst + mst = (1−τ) wN t l sN t + (1−τ) wT t l sT t + mst−1 / πt gT + st rem∗ − $d

### Aggregation
- Aggregation across consumer types for any consumer variable f:
  - ft = ˆγ f d t + (1−ˆγ) f s t  for f = (c, m, lN, lT, b∗, bc, $)

---

### 3. Consumption Baskets, Demand Functions, and Price Indices

### Goods structure
- Two types of goods: traded (superscript T) and non-traded (superscript N).
- Non-traded goods are a continuum of varieties over [0,1]; their aggregation uses a Dixit-Stiglitz aggregator with elasticity θ between varieties.

### Non-traded demand and price index
- Aggregate non-traded consumption:
  - cN t = (∫0 1 cN it θ−1/θ di) θ/(θ−1)
- Demand for variety i:
  - cN it = (pN it / pN t)−θ cN t
- Non-traded price index:
  - PN t = (∫0 1 PN it 1−θ di)1/(1−θ)

### Traded goods pricing
- Law of one price (LOP) for traded goods:
  - PT t = St P∗ t

---

### 4. Key model features and policy-relevant insights (from the paper’s summary)
- The model is a DSGE framework tailored to low-income countries with:
  - Limited access to international capital markets (captured via portfolio adjustment costs).
  - Limited participation by residents in the domestic financial market.
  - Varying degrees of labor mobility across sectors (ρL).
- Short-term and medium-term channels are explicitly modeled:
  - Short-term: aggregate-demand pressures from fiscal expansion — effects on inflation, output gap, and real exchange rate.
  - Medium-term: effects of higher public spending on the productivity of private capital (public capital impacts).
- Summary findings presented in the source:
  - In the short term, an oil-driven fiscal expansion similar in size to the expected oil windfall is likely to generate a moderate demand-led expansion in output and a moderate increase in non-traded goods inflation.
  - The impact on aggregate inflation would be minimal provided that the real exchange rate is allowed to appreciate.
  - Medium-term competitiveness could be negative if there are sizeable learning externalities in the traded sector; this negative effect could be reversed if fiscal expansion raises public capital.
  - Smoother fiscal responses to the oil windfall and a higher import component in government spending reduce demand pressures.
  - A discretionary monetary policy tightening—to reduce inflation from current high levels to a new, lower steady state—would reduce inflationary pressures but requires a strong commitment to price stability.
  - If the government saves part of the oil windfall domestically while the central bank accumulates foreign-currency proceeds, real exchange rate appreciation will be smaller but inflation will be higher, even if sterilized. This underscores the role of the supply of foreign currency from oil proceeds in stabilizing aggregate demand and containing inflationary pressures.
  - Frictions in the labor market and the financial market amplify inflationary impacts; reducing these frictions improves the economy’s response to the shock.

*Source: _wp10116 - 1. Dynamic Optimizers.*

### 1.    The Aggregate Basket

### 1.    The Aggregate Basket

### Consumption and Government Baskets
- Total consumption basket (CES):
  - c_t = ( n_1 χ_1 (c_N_t)^{χ−1/χ} + (1−n_1) 1/χ (c_T_t)^{χ−1/χ} )^{χ/χ−1}  (equation (6))
  - Parameter χ is the elasticity of substitution between non-traded goods and traded goods.
  - n_1 measures the degree of home bias in consumption.
- Government spending basket (CES):
  - G_t = ( v_1 χ_1 (G_N_t)^{χ−1/χ} + (1−v_1) 1/χ (G_T_t)^{χ−1/χ} )^{χ/χ−1}  (equation (7))
- Normalized price indices:
  - 1 = ( n_1 (p_N_t)^{1−χ} + (1−n_1) (s_t)^{1−χ} )^{1/1−χ}  (equation (8))
  - p_G_t = ( v_1 (p_N_t)^{1−χ} + (1−v_1) (s_t)^{1−χ} )^{1/1−χ}  (equation (9))
- Demand for traded and non-traded goods:
  - c_N_t = n_1 (p_N_t)^{−χ} c_t
  - c_T_t = (1−n_1) s_t^{−χ} c_t  (equation (10))
  - g_N_t = v_1 (p_N_t / p_G_t)^{−χ} g_t
  - c_T_t = (1−v_1) (s_t / p_G_t)^{−χ} g_t  (equation (11)

### C. Non-Traded Goods Sector
- Production function (firm i):
  - Y_N_it = Z_N ( K_N_it−1^{φ_N} Q_N_t−1^{1−φ_N} )^{1−α_N} (T_t L_N_it)^{α_N}  (equation (12))
  - L_N_it: labor employed by firm i.
  - K_N_it−1: private capital.
  - Q_N_t−1: public capital in the non-traded sector (common to all firms).
  - α_N and φ_N indicate production shares of labor and public/private capital.
  - Z_N is aggregate efficiency; T_t is Hicks-neutral productivity.
- Capital accumulation with adjustment costs:
  - K_N_it = (1−δ_n) K_N_it−1 + (1−S_N(X_N_it / X_N_it−1)) X_N_it
  - S_N(X_N_it / X_N_it−1) = κ_N / 2 ( (X_N_it / X_N_it−1 g_T^{−1})^2 ) (Christiano et al. (2005) form)
- Firm demand:
  - y_dN_it = ( p_N_it / p_N_t )^{−θ} y_N_t  (equation (13))
- Labor demand (normalized):
  - L_N_it = ( p_N_it / p_N_t )^{−θ α_N} y_N_t^{1/α_N} Z_N^{−1/α_N} k_N_it−1^{φ_N (α_N−1)/α_N} q_N_t^{1−φ_N (α_N−1)/α_N}
- Firm profit maximization (normalized):
  - Objective includes sales distorted by $ (sales value reduced by $), wage costs, price adjustment costs Γ_N(p_N_t, y_N_t, π_N_it, π_N_t−1), investment x_N_it, and capital accumulation constraint via multiplier λ_nt.
  - Price adjustment costs:
    - Γ_N(...) = p_N_t y_N_t (1−$) ζ_p^2 ( π_N_it / π_N_t−1 − 1 )^2
    - π_N_it = π_t p_N_it / p_N_it−1 ; π_N_t−1 = π_t−1 p_N_t−1 / p_N_t−2
  - Distortion $ reduces firms’ incentive to hire and invest (used to match low investment shares in many low-income countries).

### D. Exportable Goods Sector
- Production function (firm j):
  - y_T_jt = Z_T ( K_T_jt−1^{φ_T} Q_T_t−1^{1−φ_T} )^{1−α_T} (T_t L_T_jt)^{α_T}  (equation (14))
- Profit maximization (normalized):
  - Objective includes foreign-currency exports priced at s_t, distortion $, wage costs, investment x_T_jt, capital accumulation (with S_T of same form as S_N), and multiplier λ_T_jt.
  - S_T(.) has same form as S_N(.).

### E. The Government
- 1. Inter-Temporal Budget Constraint (normalized):
  - p_G_t g_t = τ_w_t (L_d_t + L_s_t) + b_t − b_t−1 / π_t g_T − i_t−1 b_c_t−1 / π_t g_T + s_t ( ̄A^∗ + O^*_t ) − (d_G_t − d_G_t−1 / π_t g_T)  (equation (15))
  - Financing: labor income taxes τ_w_t(L_d_t + L_s_t); domestic debt b_t − b_t−1 / π_t g_T; domestic currency value of foreign aid and oil proceeds s_t( ̄A^∗ + O^*_t ); drawing down deposits at central bank −(d_G_t − d_G_t−1 / π_t g_T).
  - Government pays interest on lagged government debt held by private sector b_c; government debt decomposition:
    - b_t = b_cb_t + b_c_t  (equation (16))
- Public investment and public capital accumulation:
  - Share of public investment out of steady state spending and when spending increases:
    - x_G_t = γ ̄G ̄g + γ_G ( g_t − ̄g )
  - Public capital accumulation:
    - q_G_t g_T = (1−δ_G) q_G_t−1 + ε_s x_G_t
    - ε_s measures efficiency of public investment.
  - Public capital allocation between sectors:
    - q_N_t = %_n q_G_t
    - q_T_t = %_e q_G_t

- 2. Government Deposits and Debt Rules
  - Government deposits rule (response to additional oil revenues):
    - d_g_t = ρ_d d_g_t−1 + (1−ρ_d) ̄d_g + (1−γ) s_t O^*_t  (equation (17))
    - Parameter γ: fraction of new oil revenues spent immediately; if γ <1 revenues accumulate as central bank deposits and are gradually spent at speed ρ_d.
  - Government debt rule:
    - b_t = b_t−1 − ς ( b_c_t−1 − ̄b_c )  (equation (18))
    - ς is small but positive; ensures open market operations do not permanently affect private sector holdings and steady state interest payments.

### F. The Central Bank
- 1. Reserve Accumulation (normalized foreign currency value of reserves):
  - R^*_t = ρ_R R^*_t−1 + (1−ρ_R) ̄R^* + (1−ω) O^*_t − ω_e ( π_S_t − π_S )  (equation (19))
  - π_S_t (nominal depreciation) = π_t π^*_s_t s_t−1  (equation (20))
  - Interpretation:
    - ω measures fraction of additional oil revenues (in dollars) sold on the market by central bank; ω <1 implies central bank keeps some oil revenues.
    - ω_e pins down commitment to nominal exchange rate level or crawl; depending on steady state inflation, authorities may target exchange rate level (if π_t = π^*) or rate of crawl (if π_t > π^*).
    - Central bank targets long run reserves ̄R^* (provided ω_e not infinite).
- 2. Central Bank Balance Sheet (nominal):
  - M_t = B_cb_t − D_G_t + NFA_t  (equation (21))
  - First-difference normalized:
    - m_t − m_t−1 / π_t g_T = b_cb_t − b_cb_t / π_t g_T − ( d_G_t − d_G_t−1 / π_t g_T ) + nfa_t − nfa_t−1 / π_t g_T  (equation (22))
  - Changes in nfa related to reserves:
    - nfa_t − nfa_t−1 / π_t g_T = s_t ( R^*_t − R^*_t−1 / π^* g_T )  (equation (23))
- 3. Monetary Policy Rule (Taylor rule targeting non-traded inflation):
  - r_t = 1/β ( π_t / ̄π )^{φ_π}  (equation (24))
  - ̄π is inflation objective.

### G. Non-Traded Goods Market Equilibrium and Balance of Payments
- Non-traded sector equilibrium:
  - y_nt = p_nt^{−χ} D_nt  (equation (25))
  - D_nt = { n_1 ( c_t + x_N_t + x_T_et + Γ_N( π_nt / π_nt−1 ) ) + v_1 (p_g_t)^{χ} G_t }  (equation (26))
- Balance of payments constraint (aggregated budgets):
  - c_t + p_G_t g_t + x_N_t + x_T_t + Γ_N(...) − { p_N_t y_N_t + s_t y_T_t } = s_t { rem^∗ + ω O^*_t + ̄A^∗ − ( π^∗ g_T − ρ_R ) / π^∗ g_T ( ̄R^∗ − R^*_{t−1} ) + ω_e ( π_S_t − π_S ) + (1 + i^*_t−1 ) b^*_t−1 / π^∗ g_T − b^*_t − ψ^∗ ( b^*_t ) }  (equation (27))
- Labor market clearing: demand for labor by firms in both sectors equals sector-specific supply.

### H. Stochastic Processes for O^*_t (Oil Revenues)
- Oil revenue AR process:
  - O^*_t = ρ_1 O^*_{t−1} + ρ_2 O^*_{t−2} + ρ_3 O^*_{t−3} + ≤O_t  (equation (28))

### I. Aggregate GDP
- Real GDP (value added sum at steady state prices):
  - y_t = p_N y_N_t + s y_T_t  (equation (29))
- Nominal GDP (deflated by CPI):
  - Y_t = p_N_t y_N_t + s_t y_T_t  (equation (30))

### IV. Model Simulations — A. Baseline Calibration (selected parameter values)
- Preference and structural parameters (Table 1 excerpts):
  - α_N = 0.40
  - χ = 1.5
  - θ = 12
  - κ = 0.24
  - ψ = 3
  - θ_d, θ_s = 0.9993, 0.9888
  - η = 1.5
  - α_N (in Table 1 duplicate) = 0.61 (Matches the share of non-traded production in value added (60 %))
  - ρ_L = 1
  - rem^∗ = 0.4281 (Ensures trade deficit equals 31 percent of GDP)
  - β = 0.9951 (Implies real interest rates equal 8 percent)
  - ˆγ = 0.60
- Technology and rigidities (Table 2 excerpts):
  - α_T, α_N = 0.7
  - φ_T, φ_N = 0.33
  - ≤ = 0.00001 (No learning by doing in the baseline)
  - κ_T, κ_N = 25
  - g_T = 1.0171 (Ensures steady state annual growth is (6%))
  - Z_T = 1 (Normalization)
  - Z_N = 1.044 (Ensures the real exchange rate equals one at steady state)
  - δ_N, δ_T = 0.015
  - ζ_p^N = 30 (Implies prices are sticky for 6 moths on average)
  - $ = 0.3609 (Helps match Ghana’s investment share (19%))
  - ι = 0.091 (Eliminates monopolistic distortion at steady state)
  - υ = 10ˆ5 (Implies the capital account is closed)
  - ̄b_a^∗ = 0.2684
- Policy parameters and aid process (Table 3 excerpts):
  - Aid process ρ_1, ρ_2, ρ_3 = 1.33, -0.15, -0.2 (Helps match the path of oil revenue)
  - ̄A^∗ = 0.1764 (Matches current share of aid in GDP (5%))
  - var(≤_O) = 0.0780 (Oil revenue equals 6 percentage points of GDP in the first year)
  - v_1 = 0.62
  - τ = 0.59 (Matches the current share of government spending (37%))
  - γ ̄G ̄g = 0.3514 (Matches the current share of public investment (12%))
  - γ_G = 0.3514
  - ̄b_c = 0.3068 (Matches the stock of outstanding domestic government debt (16%))
  - ̄b_cb = 0.0828 (Helps match real money balances)
  - δ_g = 0.035
  - ε_s = 0.7
  - ρ_d = 0.95
  - ̄d_g = 0.224
  - γ1 = 1 (Policy parameter for the experiments)
  - ρ_R = 0.97
  - ̄R^∗ = 0.21 (Matches Ghana’s stock of reserves in % of GDP (11%))
  - ω = 1 (Policy parameter for the experiments)
  - ω_e = 0 (Policy parameter for the experiments)
  - π^∗ = 1.04 (Consistent with Ghana’s current inflation (18%))
  - φ_π = 1.5
- Ghana steady state values (Table 4 excerpts, percents of GDP unless otherwise indicated):
  - Private Consumption 75
    - Traded 45
    - Non-traded 30
  - Private Investment 19
    - Traded 7
    - Non-traded 13
  - Government Spending 37
    - Consumption 24
    - Investment 13
      - Traded 14
      - Non-traded 23
  - Trade Balance −31
  - Value added, Traded sector 27
  - Value added, Non-traded sector 73
  - Government Accounts:
    - Government Spending 37
    - Taxes 26
    - Seignorage 2
    - Aid 9
    - Interest Payments 1
    - Government Debt 14
  - Central Bank Balance Sheet:
    - Government debt held by CB 10
    - Government deposits at CB 2
    - Reserves 11
    - Real money balances 20
  - Private Sector Assets:
    - Net foreign assets 4
    - Government debt 4
  - Other Variables:
    - Annual inflation, nominal depreciation 18
    - Real GDP growth 6

- Benchmark scenario assumptions (text):
  - Oil production is expected to be front-loaded with peak production broadly over the first 5 years.
  - IMF staff calculation predicted government revenues from oil and gas could reach a cumulative amount of US 12 billion during production period 2012–2030; the model’s oil revenue path is similar but peaks a couple of years earlier.
  - Central bank foreign exchange operations in benchmark:
    - (i) Does not pursue an exchange rate target.
    - (ii) All foreign-exchange inflows related to oil production are sold.
  - Monetary policy: central bank raises interest rate if inflation exceeds target; tightening modest. Target set to 18 percent (identical to base year inflation).

### IV. Model Simulations — B. Benchmark Simulation (key responses to oil windfall)
- Fiscal and macro responses (Figure 5 narrative):
  - The government spends the oil revenue as it accrues (panel 2).
  - Increase in aggregate demand leads to a sharp (but short-lived) spike in real GDP growth (panel 3); persistent effect on real GDP (panel 4).
  - Inflation increases moderately:
    - Increase driven by non-tradable inflation rise combined with a decrease in tradable sector inflation (panel 5).
    - Nominal wage growth increases in the short run (panel 6).
  - Real exchange rate appreciates (both measured as ratio of tradable to non-tradable prices and nominal exchange rate deflated by CPI) (panel 7).
  - Trade deficits net of oil revenues widen (panel 8), consistent with oil windfall.
- Mechanisms identified:
  - Inter-sectoral reallocation channel:
    - Higher government spending increases relative demand for non-traded goods (62 percent of additional government spending falls on non-traded goods).
    - Labor demand in non-traded sector increases, prompting real exchange rate appreciation to reallocate labor across sectors.
    - Real appreciation shifts private demand away from non-traded toward imports, increasing trade deficit net of oil revenues.
    - Difficulty of labor reallocation increases required real appreciation; with flexible prices, reallocation has little effect on aggregate variables but large sectoral output effects.
  - Nominal rigidities channel:
    - Sticky prices in non-traded sector imply higher government demand raises aggregate labor demand; firms hire more labor in short run regardless of real exchange rate.
    - Aggregate employment and GDP increase; inflationary pressures in non-traded sector rise; nominal wages increase.
    - Magnitude of effects depends on labor mobility; low labor mobility increases sectoral labor supply steepness and real wage pressure.

_Italic: Source: _wp10116 - 1.    The Aggregate Basket (PDF chapter)._

### 5. Baseline Scenario: Macroeconomic Impact of the Oil Windfall

### 5. Baseline Scenario: Macroeconomic Impact of the Oil Windfall

### Transmission mechanism and medium-term effects
- Aggregate-demand pressures from rapid spending increases interact critically with the monetary policy reaction function.
- Higher inflation and the real appreciation are important parts of the required macroeconomic adjustment when the monetary policy rule is held constant.
- An increase in inflation is not inevitable; it results from aggregate-demand pressures arising from rapid spending and the monetary policy stance.
- Medium-term GDP effects depend on the impact of public investment on productive capacity; under the paper’s calibration, both tradable and non-tradable sectors benefit from public investment.

### Sensitivity analysis: labor substitutability
- Benchmark elasticity of labor substitutability between tradable and non-tradable sectors: 1.
- Alternative elasticity examined: 5.
- With elasticity = 5:
  - Labor migrates more easily from the tradable to the non-tradable sector.
  - Impacts on production in both tradable and non-tradable sectors are more significant than in the benchmark.
  - Easier reallocation reduces demand pressures and produces a smaller spike in output growth in the first year.
  - Real appreciation required for reallocation is reduced.

### Dutch disease effects (learning-by-doing externalities)
- The model’s baseline did not include learning-by-doing; tradable sector productivity was exogenous in the benchmark.
- Productivity in the tradable sector is endogenized via Z_T_t = ̄Z_T (y_T_{t−1})^{ε} (equation notation as presented), so the larger the tradable sector, the larger multifactor productivity in that sector; shrinkage reduces productivity.
- Benchmark parameter for learning-by-doing (epsilon) set to zero.
- Scenario with epsilon = 0.2:
  - Impact on output from higher public investment is smaller.
  - Contraction in the traded sector is more pronounced.
  - While GDP effect is smaller, overall GDP remains above baseline levels in simulations shown.
- Combining high labor substitutability with large learning-by-doing effects:
  - Produces a more substantial Dutch disease effect, with output considerably below its trend, though still above baseline in the presented simulation.

- Three lessons from the simulations:
  - Dutch disease effects do not necessarily need to be large; they depend on the extent of tradable sector shrinkage, which itself depends on multiple parameters. Limited substitutability of production factors between sectors curbs tradable sector decline but implies larger wage pressures, higher inflation, and a more pronounced real appreciation.
  - Policy measures that bolster the tradable sector limit Dutch disease effects. In the benchmark, public investment eventually increases the size of the tradable sector relative to baseline, eliminating Dutch disease effects via the same mechanism that generates them when the sector shrinks.
  - Even if large Dutch disease effects occur, they do not necessarily outweigh the benefits from the oil windfall. Alternative mechanisms (e.g., linking tradable sector size to productivity growth rate instead of the level) could yield much larger effects where Dutch disease might outweigh benefits.

### Fiscal policy options

- Expenditure smoothing (permanent income–style scenario):
  - Benchmark assumption: full spending of all oil windfall revenue as soon as it accrues (increase spending to 6 percent of GDP and then gradually decreasing it).
  - Alternative: increase spending by only 1 of GDP but permanently sustain it (textual formulation preserved).
  - Effects of expenditure smoothing:
    - Small macroeconomic impact.
    - Avoids the large demand-driven boom in the first two years seen in the benchmark.
    - Spreads benefits of the oil windfall over time; consistent with optimizing, forward-looking consumers.
    - Avoids macroeconomic volatility characterizing early years of the benchmark.

- Expenditure composition variations (without smoothing):
  - Lower government spending on non-tradables:
    - Baseline government spending on non-tradables out of oil revenue: 62 percent.
    - Alternative share considered: 40 percent.
    - Effects:
      - Increasing import content of spending makes higher government demand easier to meet via imports.
      - Requires less real appreciation for shifting resources from tradable to non-tradable sectors and for redirecting private demand to imports.
      - Dampens short-term non-tradables output boom, reduces wage pressures and non-tradables inflation, and yields smaller private investment increase in non-tradables.
      - Overall real GDP growth response is smaller than baseline; smoother paths for key macro variables.
      - Policy implication: focusing spending on projects with high import content can be useful if real appreciation or non-tradable sector bottlenecks are concerns.
  - Increasing the public investment share:
    - Oil-financed government spending share on productive investment increased from 35 percent to 60 percent.
    - Effects:
      - Higher public capital accumulation boosts medium-term growth response, benefiting both tradable and non-tradable sectors.
      - Direct effect: higher capital accumulation raises production potential.
      - Indirect effect: increased public capital lifts private capital productivity and triggers higher private investment (crowding in).
      - Real exchange rate appreciation is similar to baseline; aggregate-demand wealth effects raise inflation in the first year relative to baseline.
      - Policy implication: using oil revenue for public investment is powerful for boosting medium-term output gains and can offset tradable-sector productivity declines from Dutch disease.

### Monetary policy options

- Context: projected oil revenue increase occurs while inflation remains high at 18 percent.
- Discretionary policy tightening (lowering inflation target):
  - Scenario: central bank reduces inflation target to 10 percent as an initial surprise (discretionary tightening), then credibility achieved once inflation reaches new target.
  - Effects:
    - Temporary reduction in aggregate demand; short-run GDP growth lower and displaced into the second year.
    - More gradual increase in non-traded production; similar real exchange rate appreciation compared to baseline.
    - Model features (small nominal rigidities, relatively quick adjustment of inflation expectations after one year) imply the cost of reducing the inflation target is relatively small in these projections.
    - Projections are optimistic and should be interpreted with caution.
- Reducing foreign exchange sales (reserve accumulation):
  - Scenario: central bank accumulates 50 percent of oil proceeds as reserves while government spends the local-currency counterpart.
  - Effects:
    - Smaller real appreciation reduces expenditure switching, aggravating demand pressures from fiscal expansion.
    - Short-run GDP impact is higher; medium-term GDP expansion is considerably lower.
    - Inflation increases considerably.
    - Sterilized reserve accumulation raises real interest rates, crowding out private investment and consumption, reducing medium-term output expansion.
    - Interpretation: akin to a domestically-financed fiscal expansion with similar aggregate-demand and private-sector crowding out implications.
    - Policy implication: fiscal/central bank coordination is critical—reserve accumulation should be supported by fiscal savings; otherwise private sector bears adjustment costs.

### Conclusion: overall findings and policy implications
- Ghana is on the verge of becoming an oil producer; oil production expected by the end of 2010 (context in the text).
- Using a dynamic general equilibrium model calibrated to Ghana, the paper assesses short- and medium-term macroeconomic effects of oil revenues accruing directly to government and translating into higher government spending.
- Key findings:
  - Short-run increase in government spending need not raise inflation beyond its current level under the current spending composition between tradable and non-tradable sectors; however, risks are high if the government increases the non-tradable component of spending.
  - The real exchange rate plays a central role in adjustment; real appreciation can, in principle, lead to persistent productivity declines if learning-by-doing externalities exist in the traded sector, but increases in productive public capital can offset this.
  - Simultaneous monetary tightening to bring inflation to a lower target would lower short-run output growth and slightly increase real appreciation.
  - Reserve accumulation when government spending increases amplifies aggregate-demand pressures and results in higher inflation unless supported by fiscal savings.
- Institutional capacity caveat:
  - Analysis abstracts from formally modeling fiscal institutions for managing oil wealth and implicitly assumes the country can absorb relatively large increases in public investment.
  - In practice, implementation capacity limitations could result in smaller public capital accumulation.

*Source: 5. Baseline Scenario: Macroeconomic Impact of the Oil Windfall (chapter/section as provided)*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10116.pdf_