## _wp1444

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---

### Introduction: problem and approach
- Senegal experienced higher fiscal deficits just five years after the Heavily Indebted Poor Countries Initiative (HIPC) reduced public debt from79percent of GDP in 2000 to21 percent in 2006.
- Fiscal deficit increased from2:5percent of GDP in 2001-2006 to an average of 5 percent of GDP in the last five years.
- Public debt has increased two-fold and is now higher than its 2006 level; the country faces a recurring energy crisis and must both reduce the fiscal deficit and finance new public investment in energy and non-energy infrastructure.
- Central research question: are efficiency gains from downsizing an inefficient oil-based energy sector and replacing it with more efficient hydropower, gas-fired, and coal-fired generation large enough to permit larger infrastructure investment while achieving deficit reduction?
- Method: variant of the IMF debt sustainability tool (Buffie et al. 2012 model) extended for Senegal to include wage and profits taxes, government consumption of traded and nontraded goods, controlled energy prices, regional CFA-zone debt, an inefficient oil-based energy sector, and a new low-cost coal/gas/hydropower sector.
- Core model features: sector-specific capital, productivity-enhancing public infrastructure, concessional and commercial external debt, consumption VAT, government transfers, variable public investment efficiency, absorptive capacity constraint, hand-to-mouth consumers, and state-run energy sector with Leontief technologies.
- Key model preview result: coordinated investment in low-cost hydroelectric power with phased contraction of oil-based sector increases total energy supply by70percent, stimulates private investment, and raises real wages and real GDP; short-run fiscal deficit increases by1 percent of GDP but medium-run fiscal gains are on the order of4percent of GDP. A temporary30percent energy price increase ensures continuous deficit reduction but is politically sensitive.

### Macroeconomic developments since 2001: facts and fiscal-energy nexus
- Budget deficit averaged5:1 percent of GDP during 2007-2012, up from2:6percent for 2001-2006.
- Relative to 2001-2006: revenue increased by2.3 percent of GDP, expenditure rose nearly5percent of GDP.
- Average GDP growth:4:3percent during 2007-2012 (compared to4:4for 2001-2006).
- Current expenditure steady at60percent of total expenditure (or15:4percent of GDP) since 2001.
- Key increases during 2007-2012: goods and services, subsidies and other transfers, and energy-related subsidies rose in percent of GDP.
- Energy sector specifics:
  - About90percent of power supply generated using imported oil; remaining10percent from hydropower.
  - Benchmark tariffs set below full cost recovery → tariff gaps and explicit producer/consumer subsidies.
  - Budgetary compensation to SENELEC: CFAF105billion or1:5percent of GDP in 2012.
  - Additional power sector costs: shortfall in tax collection (0:5percent of GDP), renting mobile power generators (0:2percent of GDP), rehabilitation/extension of plants (0:3percent of GDP).
  - Total power sector deficit:2:5percent of GDP in 2012.
  - Power outages in 2011 estimated to subtract 1-1.5 percentage point of GDP growth.
- Public debt: since HIPC reduced debt to21.9 percent of GDP in 2006, total public debt increased more than two-fold and stood at45:4percent of GDP (stock at end-2013).
- Policy implication: reform energy sector by coordinating new investment in efficient production with gradual disinvestment in inefficient oil-based plants to stabilize debt and growth.

### The model: structure and mechanisms
- Production and infrastructure:
  - Two private production sectors (tradables, nontradables) with Cobb-Douglas production; infrastructure is a public good enhancing productivity.
- Energy sector structure:
  - State-run with two technologies:
    - Inefficient oil-based technology: capital ke, output qe;t = ae ke;t-1.
    - Efficient sector (coal/gas/hydro): capital kh, output qh;t = ah kh;t-1.
  - No input substitution; Leontief constraints for energy production inputs.
- Capital/investment pricing:
  - Pk;t = Pmm + ak Pn;t
  - Pz;t = Pmm + az Pn;t
  - Pke;t = Pmm + ake Pn;t
  - Pkh;t = Pmm + akh Pn;t
- Households and markets:
  - Private agents: savers and non-savers (poor, hand-to-mouth). Non-savers consume all income; savers maximize intertemporal utility with bonds that yield non-pecuniary services.
  - Energy prices are controlled and set below shadow price P̃e; rationing binds (shadow price equates marginal value product).
- Public investment and absorptive capacity:
  - Energy capital stock evolution: (1 +g)ke;t = ie;t + (1-δ)ke;t-1 and similarly for kh.
  - Infrastructure stock ~z evolves with potential inefficiency: zt = zo + s(~zt - ~zo) with s ≤ 1.
  - Absorptive capacity modeled via implementation cost multiplier (1 + iz;t/~z t-1 - δ - g)^ψ, with ψ ≥ 0.
- Fiscal policy and debt:
  - Government spending includes transfers, wages, oil imports, energy and infrastructure investment, interest payments, supplemental OMVS imports qf at price Pf, purchases gn and gm.
  - Revenues from user fees, VAT, wage and profits taxes, grants, energy sales.
  - Deficit financed by regional bond issuance b; transfers T can be adjusted to balance budget in scenarios.
  - Regional bond market: inverse loan supply curve r t = r0 + ζ[(bf;t - bf;o)/bf;o], with ζ ≥ 0; Senegal is large in regional market so more borrowing pushes up r.
- Market clearing: labor, nontraded goods, energy rationing condition q e + q h + q f = Ex + En + Es + E1.
- National saving–investment identity and external debt dynamics combine private and government constraints.

### Model calibration: key parameter values and initial conditions
- Fiscal/tax parameters:
  - Profit tax hp = .059; wage tax hw = .054.
  - Consumption VAT h = .14.
- Consumption and cost shares:
  - Consumption shares of energy at official prices: e = .027; e1 = .004.
  - Cost shares of energy in tradables/nontradables (official price basis): ϕxo = ϕno = .0125.
- Preferences and dynamics:
  - Intertemporal elasticity of substitution ρ = .40.
  - Elasticity of substitution between non-energy consumer goods θ = .50.
  - Depreciation δ = .05.
  - q-elasticity of investment κ = 2.
  - Trend growth rate g = .01.
  - Pure time preference rate ζ1 = .0956.
- Interest rates and returns:
  - Real interest rate on government debt r = .035.
  - Real interest rates on concessional and non-concessional loans rd = 0; rdc = .07.
  - Returns: Return on infrastructure (Rz - δ) = .25; Return on oil-based energy (Re - δ) = .15; Return on efficient coal/hydro (Rh - δ) = .30.
- Other calibration values:
  - Bonds and non-pecuniary services elasticity: ϕ = .40.
  - Factor shares in private production: βJ = .03, βn = .44, βx = .26.
  - Share of poor non-saving households a/(1 + a) = .60.
  - Energy sector cost shares: βe = .30 (capital), βo = .61 (oil).
  - Cost share of capital in planned hydro investment βh = .93.
  - Domestic input cost shares: βk = .50, βne = .30, βnh = .20, βz = .40.
  - Shares of traded goods in non-energy consumption: m = .29; x = .35.
  - Share of total energy supply imported from Mali qf/(qf + qe) = .091; price Pf = .176 (relative unit where Pe;avg = 1).
  - Public investment efficiency s = .70 (i.e., 30percent of public investment fails to increase productive capital).
  - Ratio of user fees to recurrent costs for non-energy infrastructure ϑ = .43.
  - Ratio of revenue from energy sales to O&M in oil-based sector revom = .55 → overall power sector revenue shortfall 1.97 percent modeled (data show 2 percent of GDP shortfall).
  - Shadow price of energy to firms P̃e computed residually with Pe;avg = 1 → P̃e = 2:59 and initial share of energy investment in GDP = .0051 (0.51 percent).
  - Slope of inverse loan supply ζ = .005 (6 percent of GDP additional debt would raise r from 3.5 percent to 5 percent in calibration).
  - Absorptive capacity parameter ψ = 0:00 in baseline.

### Alternative methods of fiscal adjustment: key simulation findings
A. Traditional fiscal instruments
- Raising wage tax by5 percentage points reduces deficit from5:9percent of GDP to slightly below3percent of GDP; raising profit tax is less effective.
- Profit tax increase reduces private investment and capital stock and lowers GDP; long-run real wage declines by2:5percent under higher profit tax due to capital crowding.
- Cutting government consumption of nontraded goods:
  - Raises real wages and reduces fiscal deficit but contracts private investment, capital stock, and real GDP.
- Cutting government consumption of traded goods:
  - Lowers real wages, raises private investment, capital stock, and real GDP; deficit falls from5:9percent to3:5percent of GDP.
- Conclusion: traditional fiscal adjustments can reduce deficits but involve difficult trade-offs (lower real incomes or cuts to valued public services).

B. Efficient energy investment program (gradual upscaling of efficient sector, downsizing oil-based sector)
- Investment path example (percent of initial GDP):
  - Efficient sector: Pkh o · (Ih - Ih o)/yo rises to 2:5 then phases down to 1:5 over time.
  - Inefficient sector: Pke o · (Ie - Ie o)/yo declines by0:5 each year initially and remains down by0:5.
- Implementation increases total energy supply by70percent.
- Macroeconomic impacts:
  - Real GDP increases ~5 percent.
  - Real wage increases ~2 percent.
  - Private investment and private capital fall short-run then recover; capital stock regains pre-reform level by year18.
  - Short-run fiscal deficit increases by1 percent of GDP for ~5 years (from ~6 to ~6:8 percent of GDP) due to higher investment and differing cost structures; medium-run fiscal gains rise to about3 percent of GDP by year15 and ~4 percent medium-term in some runs.
  - Shadow price of energy and returns on efficient energy investment decline over time but remain above official prices; rationing persists.
- Mechanisms:
  - Short-run rise in public investment raises supply price of capital and induces private consumption smoothing (temporary private investment decline).
  - Medium-run large recurrent cost savings from downsizing oil-based plants produce fiscal dividends and higher GDP that increase tax revenues.

C. Using medium-term fiscal gains to finance non-energy infrastructure
- Delayed infrastructure investment scenario (triggered once fiscal deficit drops below pre-reform level):
  - Permanent increase in non-energy infrastructure of1:7percent of initial GDP by year fifteen.
- Outcomes:
  - Real wages rise ~7 percent.
  - Private investment increases ~6 percent.
  - Real GDP increases ~10 percent.
  - Medium-term fiscal cost of higher infrastructure investment is small: by year20 deficit rises only 0:7 percentage point of GDP relative to the energy-only program (3:2 percent in year20 vs. 2:5 percent baseline).
  - About60percent of extra investment financed by additional user fees and tax revenues in general equilibrium.

D. Financing options for the short-run fiscal cost
- Option 1: temporarily raise official energy prices (example:35percent increase for4 years).
  - Fully covers investment bill for initial years; after year6 fiscal deficit falls rapidly as cost savings and revenue gains materialize.
  - Short-run private investment falls more than in transfer-cutting scenarios because savers bear more burden; transfers are proportional to labor shares and poor non-savers have lower energy shares (e1 = .004 vs e = .027).
  - Political feasibility uncertain because energy prices already high.
- Option 2: temporary borrowing in the regional WAEMU bond market with limited supporting fiscal adjustment (e.g., cut transfers by:5percent of initial GDP).
  - With small transfer cut, program successful:
    - Real wage, real GDP, private investment paths similar to price-increase case.
    - Domestic debt rises from12percent to15percent of GDP; total debt from45percent to48percent.
    - Real interest rate rises modestly to3:64 percent in year6 then declines to3:1 percent in long run.
  - Regional borrowing considered safe and effective; allows frontloading of infrastructure if desired.
- Option 3: more aggressive, frontloaded non-energy infrastructure plus borrowing
  - Frontloaded scenario: infrastructure investment increases rapidly (0:4-0:5percent of GDP annually) to reach cumulative2:1percent of initial GDP by year6; permanent increase ~2:1percent of GDP.
  - Benefits:
    - Little short-run crowding out; additional gains of2-3 percentage points in real wage, private investment, and real GDP at 10- and 20-year horizons relative to delayed scenario.
  - Costs:
    - Domestic debt peaks near30percent of GDP; total debt peaks near60percent of GDP in year11.
    - Increased regional borrowing pushes real interest rate from3:5percent to ~4:5percent.
  - Eurobond alternative:
    - Eurobond borrowing reduces pressure on domestic interest rates but carries higher cost of borrowing (modeled Eurobond yield ~7:5percent), lengthening period of depressed transfers (20 years vs. 17 years for regional borrowing).
    - Conclusion: regional borrowing is generally cheaper at calibration rates; Eurobond issuance is costlier but stabilizes domestic rate.

### Policy recommendations and conclusions
- Primary recommendation: reform the inefficient oil-based energy sector by coordinated investment in low-cost hydro/gas/coal generation and phased contraction of oil plants.
  - This reform increases energy supply by70percent, raises real GDP and real wages, and delivers medium-term fiscal dividends on the order of3-4percent of GDP.
- Given medium-term fiscal gains, Senegal should consider borrowing against future fiscal surpluses to scale up non-energy infrastructure investment (a "big-push"):
  - If supported by efficient public investment implementation, frontloaded infrastructure plus energy reform yields significant additional gains in real GDP, real wages, and private investment.
  - The public debt rises in the short run but the medium-run fiscal dividend (~3percent of GDP) more than offsets costs.
- Financing strategy:
  - Regional WAEMU borrowing is generally more cost-effective at current (calibrated) interest rates (regional r ≈ .035) than Eurobond borrowing (Eurobond r ≈ .07–.075).
  - Temporary supporting fiscal adjustment (small transfer cuts) can keep debt dynamics stable during the frontloading period.
- Caveats:
  - Implementation risk: public investment inefficiencies and absorptive capacity constraints matter (modeled via s and ψ).
  - Political economy: raising official energy prices is effective but politically sensitive given already-high prices.
  - Sensitivity to financing costs: Eurobond borrowing imposes higher recurring costs and longer periods of fiscal compression.
- Net conclusion: energy-sector reform combined with prudent temporary borrowing in the regional market and a disciplined, efficient public investment program is the preferred path to raise infrastructure, boost growth and wages, and produce medium-term fiscal consolidation; a big-push program is justified if implemented efficiently and supported by controlled temporary financing measures.

### Appendix A — The Exact Consumer Price Index With Rationing: setup and solution
- Representative household minimizes cost X = Pc + P̃ec E when the price of energy equals its shadow price:
  - Min {c;E} X = Pc + P̃ec E;(A1) subject to c^(1−1/ξ) + k E^(1−1/ξ) = uo^(1−1/ξ) (A2).
- Optimal choices:
  - c = [X/Pc uo^(1−1/ξ)]^ξ;(A3)
  - E = [k X/P̃ec uo^(1−1/ξ)]^ξ;(A4)
- Expenditure function and CPI:
  - X = [Pc^(1−ξ) + k ξ (P̃ec)^(1−ξ)]^(1/(1−ξ)) [uo^(1−1/ξ)]^(ξ/(1−ξ)) :(A5)
  - Decomposition: X = f(uo) g(P; P̃ec); where g(P; P̃ec) = CPĨ = [Pc^(1−ξ) + k ξ (P̃ec)^(1−ξ)]^(1/(1−ξ)) :(A7)
- Rationing and CPI relation:
  - X̃/Xa = CPĨ / CPI = 1 + [(P̃ec − Pec)/Pec] (Pec Ē / Xa).
  - Therefore CPI = CPĨ / [1 + e (P̃ec − Pec)/Pec];(A8) where e = Pec Ē / Xa is the consumption share of energy measured at the official price Pec.

### Appendix B — Policy Reaction Functions and the Path of Government Debt
- Government budget constraint (full expression) summarized in equation (B1) with all spending and revenue components, including energy-related terms and tax bases.
- Short-run financing and the ex ante financing gap:
  - GAPt defined as the size of revenue shortfall when T, h, hw, hp, gn, and gm equal initial values (expression B2).
- Fiscal adjustment shares, targets, and reaction functions:
  - Transfers and government consumption of traded goods example:
    - Ttarget,t = To − ρ GAPt; 0 ≤ ρ ≤ 1;(B3)
    - gm,target,t = gm;o − (1 − ρ) GAPt / Pm;t; 0 ≤ ρ ≤ 1:(B4)
  - Reaction functions with socio-political constraints:
    - gm;t = Max { gm;t−1 + ϕ1 (gm,target,t − gm;t−1) + ϕ2 (bt−1 − btarget) ; g̲m } ;(B5)
    - Tt = Max { Tt−1 + ϕ3 (Ttarget,t − Tt−1) − ϕ4 (bt−1 − btarget) ; T̲ } ;(B6)
  - Slow adjustment can create a transition phase with T < Ttarget and gm < gm,target to generate surpluses needed to pay down debt.

*Source — Excerpted content from _wp1444 (IMF staff paper content provided).*

### References .............................................................................................................

### _wp1444 - References

### Introduction: problem and approach
- Senegal experienced higher fiscal deficits just five years after the Heavily Indebted Poor Countries Initiative (HIPC) reduced public debt from79percent of GDP in 2000 to21 percent in 2006.
- Fiscal deficit increased from2:5percent of GDP in 2001-2006 to an average of 5 percent of GDP in the last five years.
- Public debt has increased two-fold and is now higher than its 2006 level; the country faces a recurring energy crisis and must both reduce the fiscal deficit and finance new public investment in energy and non-energy infrastructure.
- Central research question: are efficiency gains from downsizing an inefficient oil-based energy sector and replacing it with more efficient hydropower, gas-fired, and coal-fired generation large enough to permit larger infrastructure investment while achieving deficit reduction?
- Method: variant of the IMF debt sustainability tool (Buffie et al. 2012 model) extended for Senegal to include wage and profits taxes, government consumption of traded and nontraded goods, controlled energy prices, regional CFA-zone debt, an inefficient oil-based energy sector, and a new low-cost coal/gas/hydropower sector.
- Core model features: sector-specific capital, productivity-enhancing public infrastructure, concessional and commercial external debt, consumption VAT, government transfers, variable public investment efficiency, absorptive capacity constraint, hand-to-mouth consumers, and state-run energy sector with Leontief technologies.
- Key model result preview: coordinated investment in low-cost hydroelectric power with phased contraction of oil-based sector increases total energy supply by70percent, stimulates private investment, and raises real wages and real GDP; short-run fiscal deficit increases by1 percent of GDP but medium-run fiscal gains are on the order of4percent of GDP. A temporary30percent energy price increase ensures continuous deficit reduction but is politically sensitive.

### Macroeconomic developments since 2001: facts and fiscal-energy nexus
- Budget deficit averaged5:1 percent of GDP during 2007-2012, up from2:6percent for 2001-2006.
- Relative to 2001-2006: revenue increased by2.3 percent of GDP, expenditure rose nearly5percent of GDP.
- Average GDP growth:4:3percent during 2007-2012 (compared to4:4for 2001-2006).
- Current expenditure steady at60percent of total expenditure (or15:4percent of GDP) since 2001.
- Key increases during 2007-2012: goods and services, subsidies and other transfers, and energy-related subsidies rose in percent of GDP.
- Energy sector specifics:
  - About90percent of power supply generated using imported oil; remaining10percent from hydropower.
  - Benchmark tariffs set below full cost recovery → tariff gaps and explicit producer/consumer subsidies.
  - Budgetary compensation to SENELEC: CFAF105billion or1:5percent of GDP in 2012.
  - Additional power sector costs: shortfall in tax collection (0:5percent of GDP), renting mobile power generators (0:2percent of GDP), rehabilitation/extension of plants (0:3percent of GDP).
  - Total power sector deficit:2:5percent of GDP in 2012.
  - Power outages in 2011 estimated to subtract 1-1.5 percentage point of GDP growth.
- Public debt: since HIPC reduced debt to21.9 percent of GDP in 2006, total public debt increased more than two-fold and stood at45:4percent of GDP (stock at end-2013).
- Policy implication: reform energy sector by coordinating new investment in efficient production with gradual disinvestment in inefficient oil-based plants to stabilize debt and growth.

### The model: structure and mechanisms
- Two private production sectors (tradables, nontradables) with Cobb-Douglas production; infrastructure is a public good enhancing productivity.
- Energy sector is state-run with two technologies:
  - Inefficient oil-based technology (capital ke, output qe;t = ae ke;t-1).
  - Efficient sector (coal/gas/hydro) (capital kh, output qh;t = ah kh;t-1).
  - No input substitution; Leontief constraints for energy production inputs.
- Capital goods and infrastructure produced by combining an imported machine (Pmm) with a units of a nontraded input; supply prices:
  - Pk;t = Pmm + ak Pn;t
  - Pz;t = Pmm + az Pn;t
  - Pke;t = Pmm + ake Pn;t
  - Pkh;t = Pmm + akh Pn;t
- Private agents: savers and non-savers (poor, hand-to-mouth). Non-savers consume all income; savers maximize intertemporal utility with bonds that yield non-pecuniary services.
- Energy prices are controlled and set below shadow price P̃e; rationing binds (shadow price equates marginal value product).
- Public investment:
  - Energy capital stock evolution: (1 +g)ke;t = ie;t + (1-δ)ke;t-1 and similarly for kh.
  - Infrastructure stock ~z evolves with potential inefficiency: zt = zo + s(~zt - ~zo) with s ≤ 1.
  - Absorptive capacity modeled via implementation cost multiplier (1 + iz;t/~z t-1 - δ - g)^ψ, with ψ ≥ 0.
- Fiscal policy and public budget constraint:
  - Government spending includes transfers, wages, oil imports, energy and infrastructure investment, interest payments, supplemental OMVS imports qf at price Pf, purchases gn and gm.
  - Revenues from user fees, VAT, wage and profits taxes, grants, energy sales.
  - Deficit financed by regional bond issuance b; transfers T can be adjusted to balance budget in scenarios.
- Regional bond market: inverse loan supply curve r t = r0 + ζ[(bf;t - bf;o)/bf;o], with ζ ≥ 0; Senegal is large in regional market so more borrowing pushes up r.
- Market clearing: labor, nontraded goods, energy rationing condition q e + q h + q f = Ex + En + Es + E1.
- National saving–investment identity and external debt dynamics combine private and government constraints.

### Model calibration: key parameter values and initial conditions
- Fiscal/tax parameters:
  - Profit tax hp = .059; wage tax hw = .054.
  - Consumption VAT h = .14.
- Consumption shares of energy at official prices: e = .027; e1 = .004.
- Cost shares of energy in tradables/nontradables (official price basis): ϕxo = ϕno = .0125.
- Preferences and dynamics:
  - Intertemporal elasticity of substitution ρ = .40.
  - Elasticity of substitution between non-energy consumer goods θ = .50.
  - Depreciation δ = .05.
  - q-elasticity of investment κ = 2.
  - Trend growth rate g = .01.
  - Pure time preference rate ζ1 = .0956.
- Interest rates:
  - Real interest rate on government debt r = .035.
  - Real interest rates on concessional and non-concessional loans rd = 0; rdc = .07.
- Bonds and non-pecuniary services elasticity: ϕ = .40.
- Factor shares in private production: βJ = .03, βn = .44, βx = .26.
- Share of poor non-saving households a/(1 + a) = .60.
- Energy sector cost shares: βe = .30 (capital), βo = .61 (oil).
- Cost share of capital in planned hydro investment βh = .93.
- Domestic input cost shares: βk = .50, βne = .30, βnh = .20, βz = .40.
- Shares of traded goods in non-energy consumption: m = .29; x = .35.
- Share of total energy supply imported from Mali qf/(qf + qe) = .091; price Pf = .176 (relative unit where Pe;avg = 1).
- Returns:
  - Return on infrastructure (Rz - δ) = .25 (effective return on infrastructure investment).
  - Return on oil-based energy (Re - δ) = .15.
  - Return on efficient coal/hydro (Rh - δ) = .30.
- Public investment efficiency s = .70 (i.e., 30percent of public investment fails to increase productive capital).
- Ratio of user fees to recurrent costs for non-energy infrastructure ϑ = .43.
- Ratio of revenue from energy sales to O&M in oil-based sector revom = .55 → overall power sector revenue shortfall 1.97 percent modeled, data show 2 percent of GDP shortfall.
- Shadow price of energy to firms P̃e computed residually with Pe;avg = 1 → P̃e = 2:59 and initial share of energy investment in GDP = .0051 (0.51 percent).
- Slope of inverse loan supply ζ = .005 (6 percent of GDP additional debt would raise r from 3.5 percent to 5 percent in calibration).
- Absorptive capacity parameter ψ = 0:00 in baseline.

### Alternative methods of fiscal adjustment: key simulation findings
A. Traditional fiscal instruments
- Raising wage tax by5 percentage points reduces deficit from5:9percent of GDP to slightly below3percent of GDP; raising profit tax is less effective.
- Profit tax increase reduces private investment and capital stock and lowers GDP; long-run real wage declines by2:5percent under higher profit tax due to capital crowding.
- Cutting government consumption of nontraded goods:
  - Raises real wages and reduces fiscal deficit but contracts private investment, capital stock, and real GDP.
- Cutting government consumption of traded goods:
  - Lowers real wages, raises private investment, capital stock, and real GDP; deficit falls from5:9percent to3:5percent of GDP.
- Conclusion: traditional fiscal adjustments can reduce deficits but involve difficult trade-offs (lower real incomes or cuts to valued public services).

B. Efficient energy investment program (gradual upscaling of efficient sector, downsizing oil-based sector)
- Investment path example (percent of initial GDP):
  - Efficient sector: Pkh o · (Ih - Ih o)/yo rises to 2:5 then phases down to 1:5 over time (see Table 3).
  - Inefficient sector: Pke o · (Ie - Ie o)/yo declines by0:5 each year initially and remains down by0:5.
- Implementation increases total energy supply by70percent.
- Macroeconomic impacts (Figure 4 summary):
  - Real GDP increases ~5 percent.
  - Real wage increases ~2 percent.
  - Private investment and private capital fall short-run then recover; capital stock regains pre-reform level by year18.
  - Short-run fiscal deficit increases by1 percent of GDP for ~5 years (from ~6 to ~6:8 percent of GDP) due to higher investment and differing cost structures; medium-run fiscal gains rise to about3 percent of GDP by year15 and ~4 percent medium-term in some runs.
  - Shadow price of energy and returns on efficient energy investment decline over time but remain above official prices; rationing persists.
- Mechanisms: short-run rise in public investment raises supply price of capital and induces private consumption smoothing (temporary private investment decline); medium-run large recurrent cost savings from downsizing oil-based plants produce fiscal dividends and higher GDP that increase tax revenues.

C. Using medium-term fiscal gains to finance non-energy infrastructure
- Delayed infrastructure investment scenario (triggered once fiscal deficit drops below pre-reform level) (Table 4):
  - Permanent increase in non-energy infrastructure of1:7percent of initial GDP by year fifteen.
  - Outcomes (Figure 5):
    - Real wages rise ~7 percent.
    - Private investment increases ~6 percent.
    - Real GDP increases ~10 percent.
    - Medium-term fiscal cost of higher infrastructure investment is small: by year20 deficit rises only 0:7 percentage point of GDP relative to the energy-only program (3:2 percent in year20 vs. 2:5 percent baseline).
    - About60percent of extra investment financed by additional user fees and tax revenues in general equilibrium.

D. Financing options for the short-run fiscal cost
- Option 1: temporarily raise official energy prices (example:35percent increase for4 years).
  - Fully covers investment bill for initial years; after year6 fiscal deficit falls rapidly as cost savings and revenue gains materialize.
  - Short-run private investment falls more than in transfer-cutting scenarios because savers bear more burden; transfers are proportional to labor shares and poor non-savers have lower energy shares (e1 = .004 vs e = .027).
  - Political feasibility uncertain because energy prices already high.
- Option 2: temporary borrowing in the regional WAEMU bond market with limited supporting fiscal adjustment (e.g., cut transfers by:5percent of initial GDP).
  - With small transfer cut, program successful:
    - Real wage, real GDP, private investment paths similar to price-increase case.
    - Domestic debt rises from12percent to15percent of GDP; total debt from45percent to48percent.
    - Real interest rate rises modestly to3:64 percent in year6 then declines to3:1 percent in long run.
  - Regional borrowing considered safe and effective; allows frontloading of infrastructure if desired.
- Option 3: more aggressive, frontloaded non-energy infrastructure plus borrowing
  - Frontloaded scenario (Table 5): infrastructure investment increases rapidly (0:4-0:5percent of GDP annually) to reach cumulative2:1percent of initial GDP by year6; permanent increase ~2:1percent of GDP.
  - Benefits (Figure 8):
    - Little short-run crowding out; additional gains of2-3 percentage points in real wage, private investment, and real GDP at 10- and 20-year horizons relative to delayed scenario.
  - Costs:
    - Domestic debt peaks near30percent of GDP; total debt peaks near60percent of GDP in year11.
    - Because Senegal is large in regional bond market, increased regional borrowing pushes real interest rate from3:5percent to ~4:5percent.
  - Eurobond alternative (Figure 9):
    - Eurobond borrowing reduces pressure on domestic interest rates but carries higher cost of borrowing (modeled Eurobond yield ~7:5percent), lengthening period of depressed transfers (20 years vs. 17 years for regional borrowing).
    - Conclusion: regional borrowing is generally cheaper at calibration rates; Eurobond issuance is costlier but stabilizes domestic rate.

### Policy recommendations and conclusions
- Primary recommendation: reform the inefficient oil-based energy sector by coordinated investment in low-cost hydro/gas/coal generation and phased contraction of oil plants.
  - This reform increases energy supply by70percent, raises real GDP and real wages, and delivers medium-term fiscal dividends on the order of3-4percent of GDP.
- Given medium-term fiscal gains, Senegal should consider borrowing against future fiscal surpluses to scale up non-energy infrastructure investment (a "big-push"):
  - If supported by efficient public investment implementation, frontloaded infrastructure plus energy reform yields significant additional gains in real GDP, real wages, and private investment.
  - The public debt rises in the short run but the medium-run fiscal dividend (~3percent of GDP) more than offsets costs.
- Financing strategy:
  - Regional WAEMU borrowing is generally more cost-effective at current (calibrated) interest rates (regional r ≈ .035) than Eurobond borrowing (Eurobond r ≈ .07–.075).
  - Temporary supporting fiscal adjustment (small transfer cuts) can keep debt dynamics stable during the frontloading period.
- Caveats:
  - Implementation risk: public investment inefficiencies and absorptive capacity constraints matter (modeled via s and ψ).
  - Political economy: raising official energy prices is effective but politically sensitive given already-high prices.
  - Sensitivity to financing costs: Eurobond borrowing imposes higher recurring costs and longer periods of fiscal compression.
- Net conclusion: energy-sector reform combined with prudent temporary borrowing in the regional market and a disciplined, efficient public investment program is the preferred path to raise infrastructure, boost growth and wages, and produce medium-term fiscal consolidation; a big-push program is justified if implemented efficiently and supported by controlled temporary financing measures.

*Italic: Source — Excerpted content from _wp1444 (IMF staff paper content provided).*

### Appendix A: The Exact Consumer Price Index With Rationing

### _wp1444 - Appendix A: The Exact Consumer Price Index With Rationing

### Appendix A — Exact Consumer Price Index with Rationing: setup and solution
- Representative household minimizes cost X = Pc + P̃ec E when the price of energy equals its shadow price:
  - Min {c;E} X = Pc + P̃ec E;(A1)
  - Subject to utility constraint:
    - c^(1−1/ξ) + k E^(1−1/ξ) = uo^(1−1/ξ) (A2)
- Optimal choices:
  - c = [X/Pc uo^(1−1/ξ)]^ξ;(A3)
  - E = [k X/P̃ec uo^(1−1/ξ)]^ξ;(A4)
- Substituting into (A1) yields the expenditure function:
  - X = [Pc^(1−ξ) + k ξ (P̃ec)^(1−ξ)]^(1/(1−ξ)) [uo^(1−1/ξ)]^(ξ/(1−ξ)) :(A5)
- Expenditure function decomposed:
  - X = f(uo) g(P; P̃ec);(A6)
  - where g(P; P̃ec) is the exact consumer price index (CPĨ):
    - g(P; P̃ec) = CPĨ = [Pc^(1−ξ) + k ξ (P̃ec)^(1−ξ)]^(1/(1−ξ)) :(A7)

### Rationing, shadow price, and relation between CPI measures
- Actual energy consumption is rationed at Ē and the actual, artificially low price is Pec.
- Define X̃ and Xa as expenditure measured at the shadow price of energy versus the actual price.
- Relationship between shadow-price expenditure and actual-price expenditure:
  - X̃ = Pc + P̃ec Ē = Xa + (P̃ec − Pec) Ē;
  - => X̃/Xa = 1 + [(P̃ec − Pec)/Pec] (Pec Ē / Xa).
- Since energy consumption is the same for X̃ and Xa, non-energy consumption is the same and both are associated with the same level of utility uo.
- Ratio of exact consumer price indices:
  - X̃/Xa = f(uo) g(P; P̃ec) / f(uo) g(P; Pec) = g(P; P̃ec) / g(P; Pec) = CPĨ / CPI.
- It follows that:
  - CPĨ / CPI = 1 + [(P̃ec − Pec)/Pec] (Pec Ē / Xa);
  - => CPI = CPĨ / [1 + e (P̃ec − Pec)/Pec];(A8)
  - where e = Pec Ē / Xa is the consumption share of energy measured at the official price Pec.

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### Appendix B — Policy Reaction Functions and the Path of Government Debt

### Government budget constraint (full expression)
- Government budget constraint:
  - bt − bt−1 = Pz;t { [1 + i z;t ~z t−1 − ĝ] (i z;t − i z;o) + i z;o } + Pke;t ie;t + Pkh;t ih;t + Pn;t gn;t + Pm;t gm;t
    + rd − g 1+gd t−1 + rdc − g 1+gdc t−1 + rt−1 − g 1+gb t−1 + To + wt (Le;t + Lh;t)
    + Po;t Ot + Pf;t qf;t − Pec;t (Ēs;t + E1;t) − Pe;t (Ex;t + En;t) − ho P t (cs;t + c1;t) − xt − τt z t−1 − hw;t w t L(1 + a) − hp;t [Px qx;t + Pn;t qn;t − Pe;t (En;t + Ex;t) − w t (Lx;t + Ln;t)] :(B1)

### Short-run financing and the ex ante financing gap
- In the short run, the deficit can be financed by issuing debt. Eventually policy variables must adjust to cover the ex ante financing gap.
- GAPt is defined as the size of the revenue shortfall when T, h, hw, hp, gn, and gm in (B1) equal their initial values:
  - GAPt = Pz;t { [1 + i z;t ~z t−1 − ĝ] (i z;t − i z;o) + i z;o } + Pke;t ie;t + Pkh;t ih;t + Pn;t gn;o + Pm;t gm;o
    + rd − g 1+gd t−1 + rdc − g 1+gdc t−1 + rt−1 − g 1+gb t−1 + To + wt (Le;t + Lh;t) + Po;t Ot + Pf;t qf;t
    − Pec;t (Ēs;t + E1;t) − Pe;t (Ex;t + En;t) − ho P t (cs;t + c1;t) − xt − τt z t−1 − hw;o w t L(1 + a)
    − hp;o [Px qx;t + Pn;t qn;t − Pe;t (En;t + Ex;t) − w t (Lx;t + Ln;t)] :(B2)

### Fiscal adjustment shares, targets, and reaction functions
- Policy makers specify the share of fiscal adjustment borne by each policy variable, determining long-run target values.
- Example: transfers and government consumption of traded goods adjust:
  - Ttarget,t = To − ρ GAPt; 0 ≤ ρ ≤ 1;(B3)
  - gm,target,t = gm;o − (1 − ρ) GAPt / Pm;t; 0 ≤ ρ ≤ 1:(B4)
- Reaction functions incorporate targets and socio-political constraints:
  - gm;t = Max { gm;t−1 + ϕ1 (gm,target,t − gm;t−1) + ϕ2 (bt−1 − btarget) ; g̲m } ;(B5)
  - Tt = Max { Tt−1 + ϕ3 (Ttarget,t − Tt−1) − ϕ4 (bt−1 − btarget) ; T̲ } ;(B6)
  - g̲m and T̲ are lower bounds on gm and T. Parameters ϕ1–ϕ4 govern speed of adjustment.
- Transition dynamics under slow adjustment:
  - If adjustment is slow, the debt instrument that varies endogenously may rise above its target while gm and T converge to their targets.
  - This can create a transition phase with T < Ttarget and gm < gm,target to generate surpluses needed to pay down debt.

*Source: _wp1444 - Appendix A: The Exact Consumer Price Index With Rationing (IMF).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1444.pdf_