## 6.   Macroeconomic Outcomes Under Alternative Relief Scenarios

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---

### Introduction and motivation
- Recurrent availability of debt relief (HIPC and MDRI) creates a time-consistency / moral-hazard problem: countries may borrow more, increase consumption, and lower investment in expectation of future write-offs.
- Historical context: after the 1970s–1980s commodity shocks many low-income countries borrowed to fill financing gaps; by the early 1990s coordinated relief (HIPC, enhanced 1999; MDRI later) aimed to wipe out unsustainable debt and promote investment-led growth.
- Key research question: How different would low-income country behavior be with and without debt relief? The paper builds a dynamic stochastic general equilibrium small open economy model with a minimum consumption requirement and an endogenous, stochastic donor debt-relief rule to quantify incentive effects.

### Model structure and calibration
- Model features
  - Small open economy with a representative firm and infinitely lived representative consumer.
  - Production: Y_t = Z_t K_t^β L_t^{1−β}, with Z_t = Z̄ e^{z_t}, z_t an AR(1) shock.
  - Preferences: CRRA utility with a survival consumption level c_min ≥ 0; expected utility E_0 Σ β^t ((c_t − c_min)^{1−γ}/(1−γ)).
  - Two saving mechanisms: capital accumulation and one-year, risk-free concessional bond subject to a stochastic debt-relief lottery each period.
  - Debt-relief mechanism: interest rate i_t is either −1 (full write-off) with probability ε_t or ī (concessional rate) with probability 1−ε_t. Donor policy modeled as ε_t = 1/(1 + e^{−(α_1 z_t + α_2 (d_t / Y_t))}), a logistic function of productivity shock z_t and debt-to-GDP ratio d_t/Y_t.
  - Minimum consumption constraint and convex capital and portfolio adjustment costs ensure realistic dynamics and stationarity.
- Calibration highlights (parameters taken or estimated to match Ugandan data, 1979–2006)
  - Capital share β = 0.3.
  - Average productivity Z̄ = 1.
  - Depreciation rate δ = 0.0489 (ensures 2006 consumption-to-output ratio matches data).
  - Discount factor β = 0.95.
  - Risk aversion γ = 0.964.
  - Consumption minimum estimated ≈ 58 percent of average consumption (from literature).
  - Concessional real interest rate ī = 5.88 percent (matches 1983-2006 OECD CIRR average).
  - Debt-relief probability rule parameters (α_1, α_2) chosen by restricted logit to fit Ugandan relief years and ensure steady-state debt matches 1982–2006 average.
  - Capital adjustment and portfolio adjustment cost parameters chosen to match investment volatility and multilateral service-fee equivalents.

### Simulation scenarios
- Baseline simulations
  - Debt-relief (benchmark): Donor relief probability ε_t depends on z_t and d_t/Y_t per the calibrated logistic rule.
  - No-relief (counterfactual): ε_t ≡ 0 (no lottery; no debt relief ever).
- Policy-experiment variants
  - Relief responding to debt-to-GDP ratio only: set α_1 = 0 in the logistic rule.
  - Relief responding to productivity shocks only: set α_2 = 0 in the logistic rule (relief functions as insurance against exogenous bad luck).

### Key quantitative findings from simulations
- Uganda empirical facts (1979–2006)
  - Uganda received some form of debt relief on seven occasions during 1982–2006 (on average every 3.6 years).
  - Total debt outstanding declined from a 1992 peak of 102 percent of GDP to about 12 percent of GDP in 2007 (U.S. dollar GDP smoothed decline from about 75 percent to 12 percent of smoothed GDP).
  - Annual average external gross borrowing (disbursements, 2005 constant US$): about US$ 100 million in the 1970s rising to about US$ 400 million up to 2001.
- Model fit to Ugandan stylized facts
  - Data: implied debt-relief frequency ≈ 28 percent (one event every 3.6 years); model yields average debt-relief probability 29.6 percent.
  - Model steady-state debt-to-GDP = 52.3 percent vs data average 51.6 percent.
  - Ratio of standard deviation of investment to that of GDP: data 2.74, model 2.02.
  - Portfolio adjustment cost (service-fee analog): data 0.75 percent, model 0.76 percent.
  - Minimum-to-average consumption ratio in model ≈ 57.6 percent (close to literature estimate 58 percent).
- Debt-relief vs no-relief: average outcomes (exact quoted results)
  - Average debt-to-GDP:
    - With debt relief (benchmark): 52.3 percent.
    - Without debt relief: 24.3 percent.
  - Investment-to-GDP:
    - With debt relief: 15.4 percent of GDP.
    - Without debt relief: 24.1 percent of GDP.
  - Consumption-to-GDP:
    - Consumption is "halved" in absence of debt relief relative to the relief scenario (model shows substantially lower consumption-to-GDP when no relief is available).
  - GDP level:
    - GDP is on average 22 percent larger without debt relief than with debt relief.
  - Disposable income (DI) allocation (DI = Y + (1+i_t)d_t − d_{t+1} less adjustment costs)
    - Investment-to-DI averages: 13 percent with debt relief vs 33 percent without debt relief.
    - Consumption-to-DI averages: 87 percent with debt relief vs 67 percent without debt relief.
  - Attribution of additional debt in relief scenario:
    - Estimate: 87 percent of additional debt in the relief scenario due to endogenous borrowing choices, and 13 percent due to exogenous shocks (calculation in text: (52.3−48.6)/(52.3−24.3) = 0.13).

### Welfare and volatility
- Consumption with debt relief: higher mean but significantly more volatile.
- Eliminating aggregate consumption variability in the debt-relief scenario is equivalent to a uniform increase in average consumption of 0.85 percent; the same computation in the no-relief scenario yields 0.01 percent.
- Paper reports a potential welfare gain of 0.84 percent of average consumption from eliminating debt-relief–induced volatility.

### Policy-experiment results (mechanism variants)
- Debt-to-GDP–responsive relief only (α_1 = 0)
  - Productivity shocks explain only a minor part of relief expectations; expectations driven chiefly by debt-to-GDP.
  - Average debt-to-GDP: 48.6 percent vs 52.3 percent benchmark.
  - Resource allocation remains similar to benchmark: about 17 percent of DI invested and 83 percent consumed.
  - Interpretation: a donor policy that focuses on debt ratios (and ignores first-round bad-luck shocks) perpetuates incentive distortions.
- Productivity-shock–responsive relief only (α_2 = 0)
  - Making relief respond only to exogenous productivity shocks (insurance against bad luck) produces equilibrium dynamics of debt, consumption, and investment broadly identical to the no-relief scenario.
  - Quantitative illustration: controlling for initial conditions and the amount of relief granted, the planner chooses an investment level on average 90 percent higher than under the benchmark; this additional capital is on average equivalent to 140 percent of the amount of relief granted.
  - Conclusion: relief that insures against true exogenous shocks is much more effective at encouraging investment and avoids perverse borrowing incentives.

### Main policy implications
- Donor design matters: inclusion of the debt-to-GDP ratio in relief eligibility reinforces perverse incentives for endogenous over-borrowing and consumption smoothing via expected write-offs.
- A simplified debt-relief rule that compensates only for negative productivity shocks (i.e., insures against exogenous bad luck and ignores current debt-to-GDP) would:
  - Provide much better incentives for capital accumulation at roughly the same donor cost.
  - Reduce the distortionary effect on investment and reduce repeated cycles of debt accumulation and relief.
- Credible pre-commitment by donors (to limit future relief) would reduce the incentive for repeated excess borrowing; absent credible pre-commitment, medium-term re-emergence of high debt-to-GDP ratios is likely.
- Most historical large-debt accumulation is attributed to endogenous borrowing choices (domestic policies) rather than bad luck: simulations imply the contribution of adverse productivity shocks to debt accumulation was negligible.

### Conclusions (concise)
- Recurrent debt relief creates quantitatively important incentive problems: higher debt-to-GDP ratios, lower investment-to-GDP ratios, and lower average GDP relative to a no-relief environment (GDP on average 22 percent lower with relief expectations).
- Debt-relief–induced uncertainty magnifies consumption volatility with measurable welfare costs (eliminating the volatility in the debt-relief scenario equivalent to about 0.85 percent higher uniform consumption; paper also cites potential welfare gain of 0.84 percent).
- Policy reform suggestion: target debt relief to compensate for negative productivity shocks only (insurance against exogenous bad luck) rather than conditioning relief on debt-to-GDP ratios; this reform would be welfare enhancing and more effective at promoting investment.

*Source: Chapter 6, "Macroeconomic Outcomes Under Alternative Relief Scenarios", _wp11157 (Uganda-calibrated DSGE analysis of debt relief incentives and alternatives).*

### References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   19

### _wp11157 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   19

### Tables
- 1.   Parameter Values Used in Simulations  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   22
- 2.   Key Data to Be Matched in the Simulation with Debt Relief  . . . . . . . . . . . . . . .   22
- 3.   Summary of Simulation Results  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   22

### Figures
- 1.   Debt-to-GDP Ratio of HIPCs at Completion Point . . . . . . . . . . . . . . . . . . . . . . .   23
- 2.   Uganda: Debt Stocks and Disbursements, 1971-2011 . . . . . . . . . . . . . . . . . . . . .   24
- 3.   Debt-Relief Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   25
- 4.   Debt Ratio and Debt-Relief Episodes  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   25
- 5.   Productivity Shocks and Conditional Debt-Relief Probability . . . . . . . . . . . . . . .   26

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp11157.pdf*

### 6.   Macroeconomic Outcomes Under Alternative Relief Scenarios . . . . . . . . . .   26

### 6.   Macroeconomic Outcomes Under Alternative Relief Scenarios

### Introduction and motivation
- Recurrent availability of debt relief (HIPC and MDRI) creates a time-consistency / moral-hazard problem: countries may borrow more, increase consumption, and lower investment in expectation of future write-offs.
- Historical context: after the 1970s–1980s commodity shocks many low-income countries borrowed to fill financing gaps; by the early 1990s coordinated relief (HIPC, enhanced 1999; MDRI later) aimed to wipe out unsustainable debt and promote investment-led growth.
- Key research question: How different would low-income country behavior be with and without debt relief? The paper builds a dynamic stochastic general equilibrium small open economy model with a minimum consumption requirement and an endogenous, stochastic donor debt-relief rule to quantify incentive effects.

### Model structure and calibration
- Model features
  - Small open economy with a representative firm and infinitely lived representative consumer.
  - Production: Y_t = Z_t K_t^β L_t^{1−β}, with Z_t = Z̄ e^{z_t}, z_t an AR(1) shock.
  - Preferences: CRRA utility with a survival consumption level c_min ≥ 0; expected utility E_0 Σ β^t ((c_t − c_min)^{1−γ}/(1−γ)).
  - Two saving mechanisms: capital accumulation and one-year, risk-free concessional bond subject to a stochastic debt-relief lottery each period.
  - Debt-relief mechanism: interest rate i_t is either −1 (full write-off) with probability ε_t or ī (concessional rate) with probability 1−ε_t. Donor policy modeled as ε_t = 1/(1 + e^{−(α_1 z_t + α_2 (d_t / Y_t))}), a logistic function of productivity shock z_t and debt-to-GDP ratio d_t/Y_t.
  - Minimum consumption constraint and convex capital and portfolio adjustment costs ensure realistic dynamics and stationarity.
- Calibration highlights (parameters taken or estimated to match Ugandan data, 1979–2006)
  - Capital share β = 0.3.
  - Average productivity Z̄ = 1.
  - Depreciation rate δ = 0.0489 (ensures 2006 consumption-to-output ratio matches data).
  - Discount factor β = 0.95.
  - Risk aversion γ = 0.964.
  - Consumption minimum estimated ≈ 58 percent of average consumption (from literature).
  - Concessional real interest rate ī = 5.88 percent (matches 1983-2006 OECD CIRR average).
  - Debt-relief probability rule parameters (α_1, α_2) chosen by restricted logit to fit Ugandan relief years and ensure steady-state debt matches 1982–2006 average.
  - Capital adjustment and portfolio adjustment cost parameters chosen to match investment volatility and multilateral service-fee equivalents.

### Simulation scenarios
- Two baseline simulations:
  1. Debt-relief (benchmark): Donor relief probability ε_t depends on z_t and d_t/Y_t per the calibrated logistic rule.
  2. No-relief (counterfactual): ε_t ≡ 0 (no lottery; no debt relief ever).
- Two policy-experiment variants:
  - Relief responding to debt-to-GDP ratio only: set α_1 = 0 in the logistic rule.
  - Relief responding to productivity shocks only: set α_2 = 0 in the logistic rule (relief functions as insurance against exogenous bad luck).

### Key quantitative findings from simulations
- Uganda empirical facts (1979–2006, context)
  - Uganda received some form of debt relief on seven occasions during 1982–2006 (on average every 3.6 years).
  - Total debt outstanding declined from a 1992 peak of 102 percent of GDP to about 12 percent of GDP in 2007 (U.S. dollar GDP smoothed decline from about 75 percent to 12 percent of smoothed GDP).
  - Annual average external gross borrowing (disbursements, 2005 constant US$): about US$ 100 million in the 1970s rising to about US$ 400 million up to 2001.
- Model fit to Ugandan stylized facts
  - Data: implied debt-relief frequency ≈ 28 percent (one event every 3.6 years); model yields average debt-relief probability 29.6 percent.
  - Model steady-state debt-to-GDP = 52.3 percent vs data average 51.6 percent.
  - Ratio of standard deviation of investment to that of GDP: data 2.74, model 2.02.
  - Portfolio adjustment cost (service-fee analog): data 0.75 percent, model 0.76 percent.
  - Minimum-to-average consumption ratio in model ≈ 57.6 percent (close to literature estimate 58 percent).
- Debt-relief vs no-relief: average outcomes (exact quoted results)
  - Average debt-to-GDP:
    - With debt relief (benchmark): higher (benchmark steady-state value cited as 52.3 percent).
    - Without debt relief: average debt-to-GDP declines to 24.3 percent (less than one half of the benchmark scenario).
  - Investment-to-GDP:
    - With debt relief: 15.4 percent of GDP.
    - Without debt relief: 24.1 percent of GDP.
  - Consumption-to-GDP:
    - Consumption is "halved" in absence of debt relief relative to the relief scenario (model shows substantially lower consumption-to-GDP when no relief is available).
  - GDP level:
    - GDP is on average 22 percent larger without debt relief than with debt relief.
  - Disposable income (DI) allocation (DI = Y + (1+i_t)d_t − d_{t+1} less adjustment costs)
    - Investment-to-DI averages: 13 percent with debt relief vs 33 percent without debt relief.
    - Consumption-to-DI averages: 87 percent with debt relief vs 67 percent without debt relief.
  - Attribution of additional debt in relief scenario:
    - Estimate: 87 percent of additional debt in the relief scenario due to endogenous borrowing choices (domestic policies), and 13 percent due to exogenous shocks (calculation in text: (52.3−48.6)/(52.3−24.3) = 0.13).
- Welfare and volatility
  - Consumption with debt relief: higher mean but significantly more volatile.
  - Eliminating aggregate consumption variability in the debt-relief scenario is equivalent to a uniform increase in average consumption of 0.85 percent; the same computation in the no-relief scenario yields 0.01 percent.
  - Paper also reports a potential welfare gain of 0.84 percent of average consumption from eliminating debt-relief–induced volatility (conclusion).
- Policy-experiment results (mechanism variants)
  - Debt-to-GDP–responsive relief only (α_1 = 0)
    - Productivity shocks explain only a minor part of relief expectations; expectations driven chiefly by debt-to-GDP.
    - Average debt-to-GDP in this modified rule: 48.6 percent vs 52.3 percent benchmark (stated as "only slightly lower").
    - Resource allocation remains similar to benchmark: about 17 percent of DI invested and 83 percent consumed (closely mirroring benchmark distortions).
    - Interpretation: a donor policy that focuses on debt ratios (and ignores first-round bad-luck shocks) perpetuates incentive distortions.
  - Productivity-shock–responsive relief only (α_2 = 0)
    - Making relief respond only to exogenous productivity shocks (insurance against bad luck) produces equilibrium dynamics of debt, consumption, and investment broadly identical to the no-relief scenario.
    - Quantitative illustration: controlling for initial conditions and the amount of relief granted, the planner chooses an investment level on average 90 percent higher than under the benchmark; this additional capital is on average equivalent to 140 percent of the amount of relief granted. Conclusion: relief that insures against true exogenous shocks is much more effective at encouraging investment and avoids perverse borrowing incentives.

### Main policy implications
- Donor design matters: inclusion of the debt-to-GDP ratio in relief eligibility reinforces perverse incentives for endogenous over-borrowing and consumption smoothing via expected write-offs.
- A simplified debt-relief rule that compensates only for negative productivity shocks (i.e., insures against exogenous bad luck and ignores current debt-to-GDP) would:
  - Provide much better incentives for capital accumulation at roughly the same donor cost.
  - Reduce the distortionary effect on investment and reduce repeated cycles of debt accumulation and relief.
- Credible pre-commitment by donors (to limit future relief) would reduce the incentive for repeated excess borrowing; absent credible pre-commitment, medium-term re-emergence of high debt-to-GDP ratios is likely.
- Most historical large-debt accumulation is attributed to endogenous borrowing choices (domestic policies) rather than bad luck: simulations imply the contribution of adverse productivity shocks to debt accumulation was negligible.

### Conclusions (concise)
- Recurrent debt relief creates quantitatively important incentive problems: higher debt-to-GDP ratios, lower investment-to-GDP ratios, and lower average GDP relative to a no-relief environment (GDP on average 22 percent lower with relief expectations).
- Debt-relief–induced uncertainty magnifies consumption volatility with measurable welfare costs (eliminating the volatility in the debt-relief scenario equivalent to about 0.85 percent higher uniform consumption; paper also cites potential welfare gain of 0.84 percent).
- Policy reform suggestion: target debt relief to compensate for negative productivity shocks only (insurance against exogenous bad luck) rather than conditioning relief on debt-to-GDP ratios; this reform would be welfare enhancing and more effective at promoting investment.

*Source: Chapter 6, "Macroeconomic Outcomes Under Alternative Relief Scenarios", _wp11157 (Uganda-calibrated DSGE analysis of debt relief incentives and alternatives)._

### References

### _wp11157 - References

### Citations and literature base
- Alvarez-Pelaez, M. J. and A. Diaz (2005), "Minimum Consumption and Transitional Dynamics in Wealth Distribution," Journal of Monetary Economics, 52, 633-667.
- Arellano, C., A. Bulír, T. Lane, and L. Lipschitz (2009), "The Dynamic Implications of Foreign Aid and Its Variability," Journal of Development Economics, 88, 87-102.
- Arslanalp, S. and P. B. Henry (2005), "Debt Relief," Journal of Economic Perspectives, 20, 207-220.
- Atkenson, A. and M. Ogaki (1996), "Wealth-varying Intertemporal Elasticities of Substitution: Evidence from Panel and Aggregate Data," Journal of Monetary Economics, 38, 507-534.
- Atkenson, A. and M. Ogaki (1997), "Rate of Time Prefences, Intertemporal Elasticity of Substitution, and Level of Wealth," Review of Economics and Statistics, 79, 564-572.
- Chatterjee, S (1994), "Transitional Dynamics and the Distribution of Wealth in a Neoclassical Growth Model," Journal of Public Economics, 54, 97-119.
- Chatterjee, S. and B. Ravikumar (1999), "Minimum Consumption Requirements: Theoretical and Quantitative Implications for Growth and Distribution," Macroeconomic Dynamics, 3, 482-505.
- Chauvin, D. N. and A. Kraay (2007), "Who Gets Debt Relief," Journal of the European Economics Association, 5, 2-3, 333-342.
- Christensen, J. (2004), "Domestic Debt Markets in Sub-Sahara Africa," IMF Working Paper No. 04/46.
- Easterly, W. (2002), "How Did Heavily Indebted Poor Countries Become Heavily Indebted? Reviewing Two Decades of Debt Relief," World Development, 30, 1677-1696.
- Green, J. (1989), "External Debt Problem of Sub-Saharan Africa," in Analytical Issues of Debt, ed. by Jacob A. Frenkel, Michael P. Dooley, and Peter Wickham. Washington, DC: International Monetary Fund, 38-74.
- Hubbard, R. G., J. Skinner, and S. P. Zeldes (1995), "Precautionay Savings and Social Insurance," Journal of Political Economy, 103, 2, 360-399.
- International Monetary Fund (various years), World Economic Outlook.
- International Monetary Fund (2004), "Enhanced HIPC Initiative: Possible Options Regarding the Sunset Clause," (Washington, DC: International Monetary Fund and International Development Association). Available at: www.imf.org/external/np/hipc/2004/070704.pdf.
- International Monetary Fund (2007), Debt Relief Under the Heavily Indebted Poor Countries (HIPC) Initiative Fact sheet, IMF Website. Available at http://www.imf.org/external/np/exr/facts/hipc.htm. Accessed July 4, 2008.
- International Monetary Fund (2009), "Staff Report for the 2008 Article IV Consultation and Fourth Review Under the Policy Support Instrument," IMF Country Report No. 09/79.
- International Monetary Fund (2010), "Preserving Debt Sustainability in Low-Income Countries in the Wake of the Global Crisis," (Washington, DC: International Monetary Fund). Available at: www.imf.org/external/np/pp/eng/2010/040110.pdf.
- Kehoe, T. and K. Ruhl (2003), "Recent Great Depressions: Aggregate Growth in New Zealand and Switzerland," Mimeo.
- Koeda, J. (2006), "A Debt Overhang Model for Low-Income Countries: Implications for Debt Relief," IMF Working Paper 06/224.
- Lucas, R. E. JR (1987), Models of Business Cycles, New York, NY: Basil Blackwell, 20-31.
- Mendoza, E. (1991), "Real Business Cycles in a Small Open Economy," The American Economic Review, 81 (4), 797-818.
- Obiols-Homs, F. and C. Urrutia (2005), "Transitional Dynamics and the Distribution of Assets," Economic Theory, 25, 381-400.
- Ogaki, M., J. D. Ostry, and C. M. Reinhart (1996), "Saving Behavior in Low- and Middle-Income Developing Countries," IMF Staff Papers, 43, (1), 38-71.
- Organisation for Economic Co-operation and Development (2009), Historic Commercial Interest Reference Rates (CIRR), OCDE Website. Available at http://www.oecd.org/statisticsdata/0,3381,en_2649_34171_1_119656_1_1_1,00.html.
- Pallage, S., M. A. Robe, and C. Bérubé (2006), "The Potential of Foreign Aid as Insurance," IMF Staff Papers, 53, 3, 453–475.
- Paris Club (2008), Annual Report 2007. Available at: http://www.clubdeparis.org/sections/communication/rapport-annuel-d/rapport-annuel-du-club/downloadFile/Öle/RA_Club_de_Paris_anglais.pdf.
- Paris Club (2009), Annual Report 2008. Available at: http://www.clubdeparis.org/sections/communication/rapport-annuel-d/annual-report-2008/downloadFile/Öle/AnnualReport2008.pdf.
- Paris Club (2010), Annual Report 2009. Available at: http://www.clubdeparis.org/sections/communication/rapport-annuel-d/2009-rapport-annuel1218/downloadFile/Öle/RapportAnnuel_AnnualReport_2009.pdf.
- Rosenzweig, M. R. and K. Wolpin (1993), "Credit Market Constrains, Consumption Smoothing, and the Accumulation of Durable Production Assets in Low-Income Countries: Investment in Bullocks in India," The Journal of Political Economy, 101, 223-244.
- Schmitt-Grohe, S. and M. Uribe (2003), "Closing Small Open Economy Models," Journal of International Economics, 61, 163-185.
- Uribe, M. and V. Z. Yue (2006), "Country Spreads and Emerging Countries: Who Drives Whom?," Journal of International Economics, 69, 6-36.
- World Bank (2001), IDA Eligibility, Terms and Graduation Policies. Mimeo.
- World Bank (various years), World Development Indicators.

### Table 1 — Parameter Values Used in Simulations
- Depreciation rate (in percent): 4:89
- Capital's share of income: 0:3
- Average productivity level: Z1
- Time preference: 0:95
- Risk aversion coefficient: 0:964
- Capital adjustment cost constant: 2:9
- Debt adjustment cost constant: 6:5
- Real interest rate (in percent) i: 5:88
- Productivity shock constant in debt relief function 1: -28:64
- Debt/GDP constant in debt relief function 2: -36:77
- Relief probability constant a1: 0:999
- Relief probability adjustment factor a2: -24:1
- Note: "The last four parameters are used to transform a standard logistic function into equation (8)."

### Table 2 — Key Data to Be Matched in the Simulation with Debt Relief
- Average debt-relief probability (in percent): 29:56 (Paris Club and World Economic Outlook; authors' calculations)
- Average debt/GDP ratio (in percent): 52:32
- Relative standard deviation of investment and GDP: 2:02
- Ratio of minimum to average consumption (in percent): 57:55 (Chatterjee and Ravikumar (1999))
- Portfolio adjustment cost of average debt (in percent): 0:76 (Service fee charged by multilateral development banks)
- Note: "All variables are in natural logarithms and filtered by a linear trend."

### Table 3 — Summary of Simulation Results
- Relief scenario:
  - Debt/GDP (in percent): 52:32
  - Investment/GDP (in percent): 15:41
  - Investment/Disposable income (in percent): 13
  - Consumption/Disposable income (in percent): 8
- No Relief scenario:
  - Debt/GDP (in percent): 24:29
  - Investment/GDP (in percent): 24:14
  - Investment/Disposable income (in percent): 33
  - Consumption/Disposable income (in percent): 67
- Note: "Disposable income is defined as GDP plus net debt inflows as in equation (11)."

### Figures and captions (selected)
- Figure 1. Debt-to-GDP Ratio of HIPCs at Completion Point
  - Source: World Economic Outlook 2010. Excludes Afghanistan and the Republic of Congo.
  - Note: "We aggregate total debt outstanding at year-end and GDP series in current US$ to compute average debt-to-GDP ratios of 28 countries in the completion point group of the HIPC initiative as of September 2010."
- Figure 2. Uganda: Debt Stocks and Disbursements, 1971-2011
  - Source: World Economic Outlook and Global Development Finance. Data for 2010-2011 are WEO projections.
  - Notes:
    - "Total debt in current US$; the GDP series is smoothed with the Hodrick-Prescott filter to limit volatility in Ugandan US dollar GDP. Domestic debt was less than 10 percent of GDP."
    - "Total external debt disbursements in millions of US$; available only until 2008."
- Figure 3. Debt-Relief Function
- Figure 4. Debt Ratio and Debt-Relief Episodes
  - Axis/labels excerpt: r*; Debt/GDP; Debt/GDP relief scenario; Shocks; Debt relief
  - Numeric label shown: 5.88
- Figure 5. Productivity Shocks and Conditional Debt-Relief Probability
- Figure 6. Macroeconomic Outcomes Under Alternative Relief Scenarios

*Source: _wp11157 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp11157.pdf_