## _wp1451 — Section 1–3

## Source details

**Canonical URL:** [_wp1451 — Section 1–3](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1451.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1451.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1451.pdf.json)

---

### Introduction: objectives and approach
- Objective: Evaluate macroeconomic consequences of a possible scaling-down of investment in Rwanda while the authorities seek to lower reliance on foreign aid.
- Methodology: Use the model of public investment, growth, and debt sustainability in Buffie et al. (2012) to gauge consequences of different financing mechanisms and investment efficiency levels.
- Key model assumptions and implications:
  - Public capital is complementary to private capital and is productivity enhancing.
  - There is a high return to public investment.
  - In the long run all investment must be paid for by adjusting taxes; in the medium run, borrowing (domestic, international commercial, or concessional) can finance investment.
  - Main policy challenge: structure fiscal adjustment over time to avoid unsustainably high debt.

### Background on Rwanda: recent performance and challenges
- Growth and development targets and recent performance:
  - Goal: middle-income country status (income per capita of just over $1000) by the end of the current decade.
  - GDP growth averaged just over 8.5 percent per year over the last 15 years.
- Historical shocks and recovery:
  - The 1994 genocide killed more than 800,000 Rwandans and cut economic output almost in half; by the turn of the century GDP had rebounded to the pre-genocide level.
- Poverty reduction:
  - Headcount poverty rate (national poverty line) fell from above 60 percent in 2000 to 57 percent in 2005 and below 45 percent in 2010.
- Sources of success:
  - Transparency International rank: 49th out of 183 countries on perception of corruption index for 2011; third among sub-Saharan African countries.
  - World Bank ease of doing business rank: 32nd out of 185 countries (2013).
  - Grant inflows in 2011/12: about 10 percent of Rwandan GDP and 40 percent of public expenditure.
  - Authorities issued US$400 million in 10-year bonds (first international capital markets issuance).
- Remaining vulnerabilities and policy priorities:
  - Rwanda is small, landlocked, with limited natural resources; exports cover less than a third of imports.
  - Infrastructure (transportation and energy) remains inadequate.
  - Over-reliance on donor assistance.
  - Policy responses identified:
    - Increase domestic resource mobilization through tax policy changes and improvements in tax collection.
    - Rationalize and reprioritize government spending to raise efficiency.
    - Attract more foreign investment to diversify the private sector.
    - Judicious recourse to external commercial borrowing consistent with debt sustainability.

### Model features, calibration, and key parameters
- Model type and structure:
  - Two-sector intertemporal macroeconomic model (traded and non-traded goods; an imported traded good is present); Cobb-Douglas production with private capital k_{i,t}, labor L_{i,t}, and effective public capital z_t.
  - Consumers: savers and non-savers (hand-to-mouth); CES consumption bundle governed by parameters ε, ρ_x, ρ_m, and ρ_n; parameter a governs savers/non-savers ratio.
  - Savers face capital adjustment costs AC_{i,t} and portfolio adjustment costs Υ_{t}^s; domestic bonds b_{t}^s and foreign bonds b_{t}^{s*} with interest rates r_t and r_t^*.
  - Public capital accumulation implemented as a two-step process; effective public capital z_t^e is the productivity-enhancing portion.
- Purpose of calibration: reflect low-income, low-capacity economies like Rwanda, including remittances, foreign grants, inefficiencies in public investment, and limited household access to capital markets.
- Key calibration values (preserved exactly):
  - τ 0.34 — Intertemporal elasticity of substitution
  - ε 0.50 — Intratemporal elasticity of substitution across goods
  - α_x 0.40 — Capital’s share in value added – traded sector
  - α_n 0.55 — Capital’s share in value added – non-traded sector
  - α_k, α_z 0.50 — Cost share of non-traded inputs in the production of capital
  - δ_x, δ_n, δ_z 0.05 — Capital depreciation rates
  - ρ_x 0.32 — Distribution parameter – traded goods
  - ρ_n 0.44 — Distribution parameter – non-traded goods
  - g 0.047 — Trend per capita growth rate
  - r_o 0.02 — Initial real interest rate on domestic debt
  - r_dc,o 0.06 — Real interest rate on external commercial debt
  - R_z,o 0.25 — Initial return on public investment
  - b_o 0.053 — Initial public domestic debt to GDP ratio
  - d_o 0.119 — Initial external concessional debt to GDP ratio
  - G_o 0.086 — Initial grants to GDP ratio
  - R_o 0.026 — Remittances to GDP ratio
  - I_z,o 0.134 — Initial ratio of public investment to GDP
  - s 0.60 — Efficiency of public investment
  - h_o 0.18 — Initial consumption VAT rate
  - a 1.50 — Ratio of savers to non-savers
- Assumed per capita potential growth rate: 4.7 percent.
- Return on public investment (R_z,o) set to 0.25 (25 percent); efficiency baseline s = 0.60 (60 percent).

### Public capital accumulation, fiscal constraint, and investment efficiency
- Public capital accumulation:
  - Public capital evolves according to a standard accumulation equation; effective public capital z_t^e is the portion allocated to productivity-enhancing infrastructure.
  - The parameter s (between zero and one) governs the efficiency of public investment: one dollar spent on public investment yields less than one dollar’s worth of public infrastructure when s < 1.
- Government budget constraint:
  - Financing sources: domestic debt, external commercial debt (d_c,t), concessional debt (d_t), and taxes; expenditures include debt service, investment, transfer spending T_t, and grant aid G_t.
  - The path for concessional debt and public investment spending is exogenous; long-run gaps must be covered by taxes and transfers; short- and medium-term gaps may be closed with borrowing.
- Role of investment efficiency:
  - Separates marginal product of effective public capital net of depreciation from efficiency s.
  - Lower s implies lower return on public spending even if infrastructure productivity is high.
  - Increasing s can:
    - Lower the debt path for a given investment spending.
    - Increase the growth dividend for a given level of investment spending.
    - Allow achieving the same growth dividend with reduced reliance on new tax revenue or commercial borrowing.

### Simulation framing and key tradeoffs
- Tradeoffs explored:
  - Financing public investment via tax adjustments (constrained and unconstrained VAT adjustments), commercial borrowing, additional concessional loans, and hybrid mixes.
  - Effects of declining grants on investment and growth.
  - Impact of increased efficiency of public investment on growth and debt dynamics.
- Empirical context: issuance of US$400 million in 10-year bonds illustrates continued high financing needs.
- Baseline fiscal constraint: without additional financing from higher tax receipts or increased borrowing, authorities would have to lower public investment to remain fiscally solvent—baseline scenario leads to sclerotic growth.

### Simulation results — major scenarios and quantitative outcomes
- Baseline Scenario: Declining Grants, Declining Investment
  - Exogenous assumptions:
    - Public investment starts at 13.4 percent of GDP and falls to 6.8 percent after 10 years.
    - External grants start at 8.6 percent of GDP and fall to 2.9 percent.
  - Macroeconomic effects:
    - Per capita GDP growth slows to just above 3 percent in the long run.
  - Policy implication:
    - To attain per capita growth of even 3 percent, government must increase taxes, cut spending, or borrow.

- Public Investment Buildup Financed with an Unconstrained Tax Adjustment
  - Policy shock:
    - Public investment increases by 5 percentage points to 18.4 percent of GDP for 10 years, then returns to initial level; grant aid declines as in baseline; fiscal gap closed entirely by increasing the consumption VAT.
  - Quantitative outcomes:
    - Traded output rises by just over 12 percent and stays elevated for decades.
    - Per capita GDP growth rises to around 6.5 percent when the investment surge starts, stays around 5.5 percent while investment is elevated, then returns to 4.5 percent after the surge.
    - Consumption VAT must rise to 40 percent during the investment surge; remains nearly 30 percent after the surge.
    - Consumption declines by 13 percent and never returns to its initial level.
    - Private investment declines initially but eventually recovers and rises by 2-3 percent in the long run.
  - Policy implication:
    - The fiscal adjustment required via taxes is likely untenable and imposes large welfare costs; borrowing is necessary to finance a plausible investment buildup.

- Public Investment Buildup Financed with Commercial Borrowing
  - Policy shock:
    - Investment surge financed by external commercial debt; no tax adjustment.
  - Quantitative outcomes:
    - On impact, exchange rate sharply appreciates; traded output falls by about 5 percent initially, non-traded output rises by about 6 percent.
    - Private investment rises by about 9 percent after 10 years and remains above initial level over three decades.
    - GDP growth falls in the first year but remains above six percent in subsequent years; after the buildup, growth falls back to just below its initial level.
    - Total debt-to-GDP peaks at just under 90 percent after 10 years; repayment over next two decades brings debt down to 75 percent of GDP.
  - Policy implication:
    - Commercial borrowing alone leads to sustained and possibly unsustainable debt levels; a combination of borrowing and fiscal adjustment is required.

- Hybrid Financing (Commercial Borrowing, Concessional Loans, and Constrained VAT Adjustment)
  - Policy shock:
    - Increase in concessional borrowing equal to 3 percent of GDP for first 10 years, then repaid at 1 percent of GDP in years 11–30; VAT increase from 18 percent to 23 percent; additional commercial borrowing to close remaining gap.
  - Quantitative outcomes:
    - Total public debt peaks at around 74 percent of GDP and falls to 57 percent of GDP after 30 years.
    - Per capita GDP growth rises, though not as much as the commercial-borrowing-only scenario.
  - Trade-off:
    - Closing the gap through taxation reduces consumption and GDP growth, while borrowing raises debt to high, potentially unsustainable levels.

- Hybrid Financing with Rapidly Reduced Grant Inflows
  - Policy shock:
    - Rapid decline in grant inflows: foreign grants decline to 3 percent of GDP in the first year (from baseline starter value of 8.6 percent of GDP); public investment held constant; loss in grant aid compensated with additional commercial borrowing and a five percentage point increase in the VAT rate.
  - Dynamics (summary):
    - Two competing effects on the real exchange rate: loss of grants draws the real exchange rate down; commercial borrowing pushes it back up.
    - Net effect: modest fall in the exchange rate in the first five years, followed by a long-term rise back to its original level.
    - Per capita GDP growth increases by about half a percentage point in year two, then gradually declines over the next three decades.
    - Total debt as a share of GDP rises to 70 percent by the end of the simulation.
    - VAT rate is raised to compensate for lost grant aid, producing a sharp decline in consumption: consumption contracts by five percent immediately and continues to decline.
  - Welfare assessment:
    - Scenario yields large and sustained contractions in consumption and long-term private investment for an insignificant growth boost—highly undesirable.

### Effect of increased investment efficiency
- Efficiency shock:
  - Investment efficiency increases linearly from 60 to 100 percent by the end of 10 years.
- Growth and debt impacts:
  - Increased efficiency moderately raises per capita GDP growth; growth peaks near eight percent around year 12.
  - Increased efficiency modestly reduces the debt burden by about five percentage points in years 12 through 30.
- Private sector and consumption effects:
  - Traded output increases by about an additional five percentage points.
  - Non-traded output rises by about four percentage points.
  - Private consumption contracts by only three percent in the short term, then never falls by more than two percent again (compared to a long-term decline of five percent when efficiency does not increase).
  - Result: higher private investment in the long run and smaller sustained consumption losses.
- Interpretation: increasing investment efficiency is a powerful lever—one scenario implies that increasing investment efficiency is worth about half a percentage point of GDP every year for 10 years.

### Growth dividend (ten-year horizon) — exact Table 2 entries
- Baseline Scenario: Declining Grants, Declining Investment — Growth Dividend: -5.1 % ; Growth Dividend Relative to Baseline: 0.0 %
- Public Investment Buildup Financed with an Unconstrained Tax Adjustment — Growth Dividend: 9.0 % ; Growth Dividend Relative to Baseline: 14.1 %
- Public Investment Buildup Financed with Commercial Borrowing — Growth Dividend: 11.7 % ; Growth Dividend Relative to Baseline: 16.8 %
- Public Investment Buildup Financed with Commercial Borrowing, Additional Concessional Loans, and Constrained VAT Adjustment (Hybrid Financing) — Growth Dividend: 11.6 % ; Growth Dividend Relative to Baseline: 16.7 %
- Public Investment Buildup with Hybrid Financing and Reduced Grant Inflows — Growth Dividend: 2.1 % ; Growth Dividend Relative to Baseline: 7.2 %
- Public Investment Buildup Financed with Commercial Borrowing and Increased Efficiency of Investment — Growth Dividend: 18.7 % ; Growth Dividend Relative to Baseline: 23.8 %

### Key policy conclusions and implications
- Main challenge: Rwanda faces costly public investment needs to accelerate medium-term growth; without additional financing, recent gains may be short-lived.
- Financing trade-offs:
  - Higher consumption taxes reduce the need for external borrowing but depress consumption and welfare.
  - External commercial borrowing reduces immediate tax pressures but risks unsustainable debt buildup (examples: debt-to-GDP peaking just under 90 percent in a commercial-borrowing scenario; hybrid peaks around 74 percent).
  - Replacing commercial debt with concessional debt reduces but does not eliminate debt sustainability risk.
- Overarching policy recommendation:
  - For any given level of investment or financing mix, the surest way to secure sustainable high growth is improved efficiency of public investment (increasing s), which raises growth, reduces debt pressures, and mitigates consumption losses.

*Source: WP/14/51, Surging Investment and Declining Aid: Evaluating Debt Sustainability in Rwanda; Will Clark and Birgir Arnason; March 2014.*

### Section 1

### _wp1451 - Section 1

### Introduction: objectives and approach
- Objective: Evaluate macroeconomic consequences of a possible scaling-down of investment in Rwanda while the authorities seek to lower reliance on foreign aid.
- Methodology: Use the model of public investment, growth, and debt sustainability in Buffie et al. (2012) to gauge consequences of different financing mechanisms and investment efficiency levels.
- Key model assumptions and implications:
  - Public capital is complementary to private capital and is productivity enhancing.
  - There is a high return to public investment.
  - In the long run all investment must be paid for by adjusting taxes; in the medium run, borrowing (domestic, international commercial, or concessional) can finance investment.
  - Main policy challenge: structure fiscal adjustment over time to avoid unsustainably high debt.

### Background on Rwanda: recent performance and challenges
- Growth and development targets:
  - Goal: achieve middle-income country status (income per capita of just over $1000) by the end of the current decade.
  - GDP growth has averaged just over 8.5 percent per year over the last 15 years.
- Historical shocks and recovery:
  - The 1994 genocide killed more than 800,000 Rwandans and cut economic output almost in half.
  - By the turn of the century, GDP had rebounded to the pre-genocide level.
- Poverty reduction:
  - Headcount poverty rate (national poverty line) fell from above 60 percent in 2000 to 57 percent in 2005 and below 45 percent in 2010.
  - The drop in the poverty rate was more pronounced in rural areas than urban; accompanied by narrowing income inequality.
- Sources of success:
  - Good governance: Transparency International ranked Rwanda 49th out of 183 countries on its perception of corruption index for 2011, placing it third among sub-Saharan African countries.
  - Macroeconomic policies: fiscal and monetary policies focused on macroeconomic stability; fiscal deficits kept small; inflation kept low despite external shocks.
  - Structural reforms: ranked 32nd out of 185 countries on the World Bank’s 2013 ease of doing business index; particularly high for ease of starting a business, getting electricity, obtaining credit, paying taxes, and enforcing contracts.
  - Donor support: in 2011/12, grant inflows (about evenly divided between direct budget support and project grants) amounted to about 10 percent of Rwandan GDP and 40 percent of public expenditure.
- Remaining vulnerabilities and policy priorities:
  - Rwanda is small, landlocked, with limited natural resources; exports cover less than a third of imports.
  - Infrastructure (transportation and energy) remains inadequate.
  - Over-reliance on donor assistance.
  - Authorities’ policy responses identified:
    - Increase domestic resource mobilization through tax policy changes and improvements in tax collection.
    - Rationalize and reprioritize government spending to raise efficiency.
    - Attract more foreign investment to diversify the private sector.
    - Judicious recourse to external commercial borrowing consistent with debt sustainability.

### Model features and calibration (overview)
- Model type:
  - Two-sector intertemporal macroeconomic model designed for long-run analysis (no money or nominal rigidities).
  - Sectors: traded goods and non-traded goods; an imported traded good is also present.
- Production technology:
  - In each sector (i = n, x) firms use private capital (k_{i,t}), labor (L_{i,t}), and effective public capital (z_t) in a Cobb-Douglas production function.
  - Public capital is non–sector-specific and increases output, raising returns on private capital and labor.
- Consumers:
  - Two types: savers and non-savers (hand-to-mouth).
  - Consumption bundle: CES basket with price index; parameters ε, ρ_x, ρ_m, and ρ_n govern elasticities and distribution.
  - Non-savers consume all earned income after taxes in the period earned; hand-to-mouth behavior creates non-Ricardian outcomes typical of low-income countries.
  - The parameter a governs the ratio of savers to non-savers.
- Savers:
  - Utility-maximizing agents who smooth consumption by investing in traded or non-traded capital or borrowing in domestic/international debt markets.
  - Face capital adjustment costs AC_{i,t} and portfolio adjustment costs Υ_{t}^s which capture financial account openness.
  - Domestic bonds b_{t}^s and foreign bonds b_{t}^{s*} with interest rates r_t and r_t^*, respectively.
  - Depreciation rate δ applies to capital accumulation.
- Public capital accumulation:
  - Implemented as a two-step process (described in the model; details in Buffie et al. (2012)).
- Purpose of calibration:
  - Model is calibrated to reflect low-income, low-capacity economies like Rwanda, including remittances, foreign grants as a government financing source, inefficiencies in public investment, and limited household access to capital markets.

### Policy tradeoffs and simulation framing (from Section IV preview)
- Key tradeoffs explored:
  - Financing public investment via:
    - Tax adjustments (including constrained and unconstrained VAT adjustments).
    - Commercial borrowing.
    - Additional concessional loans.
    - Hybrid financing mixes.
  - Effects of declining grants on investment and growth.
  - Impact of increased efficiency of public investment on growth and debt dynamics.
- Empirical context influencing simulations:
  - Rwanda issued US$400 million in 10-year bonds (country’s first international capital markets issuance), illustrating continued high financing needs.
  - Without additional financing from higher tax receipts or increased borrowing, authorities would have to lower public investment to remain fiscally solvent—baseline scenario leads to sclerotic growth.

### Key numeric and ranked facts (preserved exactly)
- GDP growth averaged just over 8.5 percent per year over the last 15 years.
- Goal: middle-income country status (income per capita of just over $1000) by the end of the current decade.
- Genocide: killed more than 800,000 Rwandans.
- Poverty headcount: above 60 percent in 2000; 57 percent in 2005; below 45 percent in 2010.
- Transparency International rank: 49th out of 183 countries on perception of corruption index for 2011; third among sub-Saharan African countries.
- World Bank ease of doing business rank: 32nd out of 185 countries (2013).
- Grant inflows in 2011/12: about 10 percent of Rwandan GDP and 40 percent of public expenditure.
- Issuance: US$400 million in 10-year bonds (authorities’ first foray into international capital markets).

*Source: WP/14/51, Surging Investment and Declining Aid: Evaluating Debt Sustainability in Rwanda; Will Clark and Birgir Arnason; March 2014.*

### Section 2

### _wp1451 - Section 2

### Public capital accumulation and fiscal constraint
- Public capital evolves according to a standard accumulation equation (equation (9) in the source).
- Effective public capital (z_t^e) is the portion of public capital allocated to productivity-enhancing infrastructure (equation (10) in the source).
- The parameter s governs the efficiency of public investment and takes a value between zero and one; one dollar spent on public investment yields less than one dollar’s worth of public infrastructure.
- z_t^e enters directly into the representative firm’s production function.
- The government budget constraint equates government financing from domestic debt, external commercial debt (d_c,t), concessional debt (d_t), and taxes with expenditures on debt service, investment, transfer spending (T_t), and grant aid (G_t) (equation (11) in the source).
- The path for concessional debt and public investment spending is exogenous to the model; the budget constraint can be rewritten as a gap between spending and revenues (equation (12) in the source).
- Debt sustainability requires that the long-run gap be covered by adjustments in taxes and transfers; short- and medium-term gaps may be closed with additional borrowing.

### Interpretation of investment efficiency and return
- The model separates return on public investment (marginal product of effective public capital net of depreciation) from efficiency of transforming public investment into effective public capital (s).
- In low-income country stylized facts (Hulten (1996), Pritchett (2000)): high productivity of infrastructure while return on public spending is low—captured by low s.
- Lower s implies lower return on public spending even if productivity of infrastructure is high.
- Increasing s (investment efficiency) can:
  - Lower the debt path for a given investment spending.
  - Increase the growth dividend for a given level of investment spending.
  - Allow achieving the same growth dividend with reduced reliance on new tax revenue or commercial borrowing.
- One scenario in the simulations increases s over time to show effects of increased investment efficiency.

### Calibration to Rwanda — key assumptions and parameter values
- Calibration draws on the joint IMF-World Bank debt sustainability analysis (DSA) macroeconomic framework for Rwanda.
- Assumed per capita potential growth rate: 4.7 percent.
- Initial public investment level: 13 percent of GDP.
- Return on public investment (R_z,o) set to 0.25 (25 percent) — no Rwanda-specific estimate available; based on Sub-Saharan Africa estimates.
- Efficiency of public investment (s) baseline: 0.60 (60 percent), informed by Pritchett (2000) and the estimate that around half of government investment spending does not actually create capital.
- Proportion of savers to non-savers (a) set to 1.50, using Buffie et al. (2012) estimate.
- Other parameters use values from Buffie et al. (2012) for Sub-Saharan Africa.

- Table 1: Model Calibration for Baseline Scenarios (parameter — value — definition)
  - τ 0.34 — Intertemporal elasticity of substitution
  - ε 0.50 — Intratemporal elasticity of substitution across goods
  - α_x 0.40 — Capital’s share in value added – traded sector
  - α_n 0.55 — Capital’s share in value added – non-traded sector
  - α_k, α_z 0.50 — Cost share of non-traded inputs in the production of capital
  - δ_x, δ_n, δ_z 0.05 — Capital depreciation rates
  - ρ_x 0.32 — Distribution parameter – traded goods
  - ρ_n 0.44 — Distribution parameter – non-traded goods
  - g 0.047 — Trend per capita growth rate
  - r_o 0.02 — Initial real interest rate on domestic debt
  - r_dc,o 0.06 — Real interest rate on external commercial debt
  - R_z,o 0.25 — Initial return on public investment
  - b_o 0.053 — Initial public domestic debt to GDP ratio
  - d_o 0.119 — Initial external concessional debt to GDP ratio
  - G_o 0.086 — Initial grants to GDP ratio
  - R_o 0.026 — Remittances to GDP ratio
  - I_z,o 0.134 — Initial ratio of public investment to GDP
  - s 0.60 — Efficiency of public investment
  - h_o 0.18 — Initial consumption VAT rate
  - a 1.50 — Ratio of savers to non-savers

### Simulation results — Baseline Scenario: Declining Grants, Declining Investment
- Exogenous assumptions:
  - Public investment starts at 13.4 percent of GDP and falls to 6.8 percent after 10 years.
  - External grants start at 8.6 percent of GDP and fall to 2.9 percent.
- Macroeconomic effects:
  - Decline in grant inflows leads to depreciation of the exchange rate and a temporary increase in competitiveness of the export/traded sector.
  - Investment increases in the short run due to traded goods sector strength; non-traded output and private consumption fall sharply.
  - In the long run, as the exchange rate stabilizes, traded output and investment fall; per capita GDP growth slows to just above 3 percent (consistent with the DSA framework).
- Policy implication:
  - To attain per capita growth of even 3 percent, the government must increase taxes, cut spending, or borrow to offset declining grants.
  - Timing of fiscal adjustment is critical: too slow and debt explodes due to rising interest payments; too fast and it is politically/policy painful.

### Simulation: Public Investment Buildup Financed with an Unconstrained Tax Adjustment
- Policy shock:
  - Public investment increases by 5 percentage points to 18.4 percent of GDP, stays elevated for 10 years, then returns to initial level.
  - Grant aid declines as in baseline.
  - Fiscal gap closed entirely by increasing the consumption VAT; no additional borrowing.
- Quantitative outcomes:
  - Traded output rises by just over 12 percent from its initial level and stays elevated for decades.
  - Non-traded output declines modestly; net impact on growth positive.
  - Per capita GDP growth rises to around 6.5 percent when the investment surge starts, stays around 5.5 percent while investment is elevated, then returns to 4.5 percent after investment returns to initial level.
  - Consumption VAT must rise to 40 percent during the investment surge; remains nearly 30 percent even after the surge.
  - Consumption declines by 13 percent and never returns to its initial level.
  - Private investment declines initially but eventually recovers and rises by 2-3 percent in the long run.
- Policy implication:
  - The fiscal adjustment required via taxes is likely untenable and imposes large welfare costs; borrowing is necessary to finance a plausible investment buildup.

### Simulation: Public Investment Buildup Financed with Commercial Borrowing
- Policy shock:
  - Investment surge financed by external commercial debt; no tax adjustment.
- Quantitative outcomes:
  - On impact, exchange rate sharply appreciates; traded output falls by about 5 percent initially, non-traded output rises by about 6 percent.
  - Private investment rises by about 9 percent after 10 years and remains above initial level over three decades.
  - Consumption dips only slightly over the long term.
  - GDP growth falls in the first year but remains above six percent in subsequent years; after the buildup, growth falls back to just below its initial level.
  - Total debt-to-GDP peaks at just under 90 percent after 10 years; repayment over next two decades brings debt down to 75 percent of GDP.
- Policy implication:
  - Commercial borrowing alone leads to sustained and possibly unsustainable debt levels; a combination of borrowing and fiscal adjustment is required.

### Simulation: Hybrid Financing (Commercial Borrowing, Concessional Loans, and Constrained VAT Adjustment)
- Policy shock:
  - Increase in concessional borrowing equal to 3 percent of GDP (extended for the first 10 years to finance the buildup, then repaid at 1 percent of GDP in years 11-30).
  - VAT increase from 18 percent to 23 percent (constrained tax adjustment).
  - Additional commercial borrowing to close remaining financing gap.
- Quantitative outcomes:
  - Increased foreign exchange inflows cause exchange rate appreciation, temporarily reducing traded output and boosting non-traded output.
  - Over time, both traded and non-traded output rise, but non-traded output eventually declines below its initial level—likely due to the VAT-induced drop in consumption.
  - Debt dynamics:
    - Total public debt peaks at around 74 percent of GDP.
    - Debt falls to 57 percent of GDP after 30 years (repayment aided by concessional debt structure), which remains unsustainably high.
  - Per capita GDP growth rises, though not as much as the commercial-borrowing-only scenario.
- Trade-off:
  - A trade-off exists between debt and growth: closing the gap through taxation reduces consumption and GDP growth, while borrowing raises debt to high, potentially unsustainable levels.
- Policy implication:
  - Even with access to concessional financing and constrained tax adjustments, a 5 percentage point increase in public investment can push debt to levels that may harm welfare.

### Simulation: Hybrid Financing with Rapidly Reduced Grant Inflows
- Policy shock:
  - Rapid decline in grant inflows: foreign grants decline to 3 percent of GDP in the first year (from baseline starter value of 8.6 percent of GDP).
  - Public investment held constant at its initial level to reflect a drastic shock to the government budget constraint.
  - Loss in grant aid compensated with additional commercial borrowing and a five percentage point increase in the VAT rate.
- Modeling comparison:
  - Compared to scenario where grants fall modestly (as in the current DSA) and public investment remains constant, this scenario examines effects of an abrupt aid decline.
- Dynamics:
  - Two competing effects act on the real exchange rate (text breaks off at this point in the provided content).

*Source: _wp1451 - Section 2 (PDF chapter/section).*

### Section 3

### _wp1451 - Section 3

### Impact of Lost Grant Aid and Hybrid Financing
- Real exchange rate dynamics:
  - The loss of grant aid draws the real exchange rate down, but the influx of foreign money from commercial borrowing pushes it back up.
  - Net effect: a modest fall in the exchange rate in the first five years of the simulation, followed by a long-term rise back to its original level.
- Sectoral output effects:
  - Currency movement leads to growth in the traded goods sector and contraction in the non-traded goods sector.
- Aggregate growth and per capita outcomes:
  - On balance, the economy grows, although very slightly, and the growth is short-lived.
  - Per capita GDP growth increases by about half a percentage point in year two of the simulation, then gradually declines over the next three decades.
- Fiscal and consumption effects:
  - Government balances the budget constraint by additional concessional borrowing; the debt burden rises substantially.
  - Total debt as a share of GDP rises to 70 percent by the end of the simulation (still unsustainably high).
  - VAT rate is raised to compensate for lost grant aid, producing a sharp decline in consumption:
    - Consumption contracts by five percent immediately and continues to decline over the duration of the simulation.
- Welfare assessment:
  - A simple cost-benefit analysis suggests the scenario is highly undesirable: large and sustained contractions in consumption and long-term private investment for an insignificant growth boost.

### Effect of Increased Investment Efficiency on Debt and Growth
- Efficiency assumption:
  - Investment efficiency increases linearly from 60 to 100 percent by the end of 10 years.
  - Definition preserved: for every dollar of spending directed to public infrastructure, higher efficiency means a greater share of the dollar is turned into productive (productivity-enhancing) public capital that enters as an input to firm production.
- Growth and debt impacts:
  - Increased efficiency moderately raises per capita GDP growth:
    - Growth peaks near eight percent around year 12.
  - Increased efficiency modestly reduces the debt burden by about five percentage points in years 12 through 30.
- Private sector and consumption effects:
  - Private investment increases more and the sharp contraction in private consumption is significantly reduced:
    - Traded output increases by about an additional five percentage points.
    - Non-traded output rises by about four percentage points.
    - Private consumption contracts by only three percent in the short term, then never falls by more than two percent again (compared to a long-term decline of five percent when efficiency does not increase).
  - Result: higher private investment in the long run and smaller sustained consumption losses.

### Growth Dividend: Table 2 Findings (Ten-Year Horizon)
- Table 2 reports cumulative year-on-year GDP growth above or below an initial value of 4.7 percent over 10 years (first column) and cumulative differences relative to the baseline simulation (second column).
- Exact entries from Table 2:
  - Baseline Scenario: Declining Grants, Declining Investment — Growth Dividend: -5.1 % ; Growth Dividend Relative to Baseline: 0.0 %
  - Public Investment Buildup Financed with an Unconstrained Tax Adjustment — Growth Dividend: 9.0 % ; Growth Dividend Relative to Baseline: 14.1 %
  - Public Investment Buildup Financed with Commercial Borrowing — Growth Dividend: 11.7 % ; Growth Dividend Relative to Baseline: 16.8 %
  - Public Investment Buildup Financed with Commercial Borrowing, Additional Concessional Loans, and Constrained VAT Adjustment (Hybrid Financing) — Growth Dividend: 11.6 % ; Growth Dividend Relative to Baseline: 16.7 %
  - Public Investment Buildup with Hybrid Financing and Reduced Grant Inflows — Growth Dividend: 2.1 % ; Growth Dividend Relative to Baseline: 7.2 %
  - Public Investment Buildup Financed with Commercial Borrowing and Increased Efficiency of Investment — Growth Dividend: 18.7 % ; Growth Dividend Relative to Baseline: 23.8 %
- Interpretation highlight:
  - The difference between the commercial-borrowing row and the increased-efficiency row implies that increasing investment efficiency is worth about half a percentage point of GDP every year for 10 years.

### Concluding Remarks and Policy Implications
- Main challenge:
  - Rwanda faces costly public investment needs to accelerate medium-term growth; without additional financing, recent gains may be short-lived.
- Financing trade-offs:
  - Higher consumption taxes reduce the need for external borrowing but depress consumption.
  - External commercial borrowing reduces tax repression but risks unsustainable debt buildup.
  - Replacing commercial debt with concessional debt would reduce, but not eliminate, the debt sustainability risk.
- Key policy recommendation:
  - For any given level of investment or financing mix, the surest way to secure sustainable high growth is improved efficiency of public investment.

*Source: _wp1451 - Section 3*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp1451.pdf_