## 1. Comparisons of International Reserves Across Regions, 1995–07

## Source details

**Canonical URL:** [1. Comparisons of International Reserves Across Regions, 1995–07](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08150.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08150.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08150.pdf.json)

---

### Scope, structure, and objectives
- Time coverage: 1995–07.
- Appendices:
  - A1. Benchmark Parameters (page 33).
  - A2. Simulation Parameters for Countries (page 34).
- Objective: extend Jeanne and Ranciere (2006) reserve-model of consumption smoothing to a Small Open Economy (SOE) with two goods (tradable and non-tradable) and stochastic aid, then simulate optimal reserve holdings for Sub-Saharan Africa (SSA) given likely shocks.
- Two model extensions:
  - Two goods with exogenous shocks to the relative price of the traded good (terms of trade).
  - Stochastic unilateral transfer of tradable good (“Aid”) every period.
- Paper structure: Section II background on reserve measures; Section III key shocks and their macro impact; Section IV model; Section V simulations; Section VI conclusions.

### Empirical state of foreign reserves in SSA — key statistics
- Aggregate:
  - Foreign reserves for all of SSA reached an all time high of US$127 billion in 2007.
  - At end-2007, reserves covered 5.8 months of imports, up from 3.7 months in 1997-2002.
- Cross-group differences (end-2007 highlights):
  - Oil-exporting countries: above average import cover.
  - Fragile countries: below average import cover.
- Other indicators:
  - Reserves to short-term external debt: less than 1 for only a handful of countries in 2007.
  - Reserves as a share of M2 and of GDP vary widely across SSA countries.
- Regional comparisons:
  - SSA reserve months lower than Middle East and North Africa, but higher than developing countries in general.
- Heterogeneity in reserve cushions:
  - High-reserve (HR) countries (top 25th percentile average reserve-to-GDP during 2000-06): overall average reserve-to-GDP ≈ 28 percent.
  - Low-reserve (LR) countries (bottom 25th percentile): overall average reserve-to-GDP ≈ 4.2 percent.
- Observed reserve accumulation can reflect sterilization, exchange rate policy, or resource windfalls and is not always a direct benchmark of adequacy.

### Shocks facing SSA — definitions, frequencies, and output costs
- Shock operational definitions:
  - Terms of trade (TOT) shock: year-on-year decline in terms of trade index larger than 10 percent in absolute terms.
  - Aid shock: decline in net aid inflow of 50 percent or more in absolute terms.
  - Thresholds chosen so that such events happen 20-25 percent of the time for an average SSA country.
- Empirical probabilities and sizes (sample of 44 SSA countries, 1975–2006/1980–2006):
  - Probability (average): TOT shock ≈ 20 percent; Aid shock ≈ 10 percent.
  - Average shock sizes: TOT γTOT = 21 percent; Aid γAid = 181 percent (roughly 4-5 percent of GDP).
  - Frequency notes: 80 percent of SSA countries face a ≥10 percent negative TOT shock at least 5 percent of the time or more; 80 percent face a ≥50 percent decline in aid at least 5 percent of the time or more.
- Output and consumption costs:
  - Average loss in output associated with a ≥10 percent TOT shock = 1.5 percent.
  - Aid shocks (≥50 percent) show similar average output loss; about 40 percent of aid shocks associated with output cost between 0.5 to 4 percent and another 20 percent with output loss between 5-6 percent.
  - About 40 percent of TOT shocks are associated with output cost of 2 percent or more.

### Model framework and key assumptions (Small Open Economy with two goods)
- Economy specification:
  - Two goods—tradable and non-tradable; deterministic growth path disturbed by exogenous TOT shocks; stochastic aid transfers of tradable good that grow at same rate as output absent shocks.
- Shock mechanics in model:
  - TOT shock interpreted as fall of ten percent or more from normal level (normal T = 1 in model notation).
  - Aid shock interpreted as unforeseen drop in aid flows of five percent or more (authors also operationalize aid-shock definitions earlier as ≥50 percent; model exposition clarifies “5 percent or more” as modeling shorthand).
  - When either shock occurs it is accompanied by a “Sudden-Stop” in capital (no rollover of short-term private external debt).
  - The two shocks are assumed independent in the full model.
- Agents and instruments:
  - Representative private consumer with Cobb-Douglas aggregator between tradable and non-tradable consumption; CRRA utility with risk aversion σ.
  - Government issues a long-term security to finance reserves; reserves R financed via long-term security issuance; government makes transfer Z to consumers to pay for reserve carrying cost; if shock occurs government transfers reserves net of last payment to consumers.
- Cases analyzed:
  - A. No external private borrowing (no short-term external debt).
  - B. External private borrowing allowed (short-term debt = fraction λ of tradable good output; no rollover during or after shock).
- Optimality:
  - Government chooses R to maximize expected representative consumer welfare; optimality equates marginal cost of holding reserves to expected marginal utility benefit in the shock state (see equations and first-order conditions in source).

### Calibration and benchmark parameter values (used in simulations)
- Sample and data: calibrations use data for 44 SSA countries (1980–2006 in many estimates).
- Benchmark parameters (preserved exactly as presented):
  - Size of the Shock, TOT γ = 0.219
  - Output loss due to the TOT shock, 1 γ = 0.015
  - Coefficient of Risk Aversion, σ = 2
  - Share of Tradable, α = 0.5
  - Probability of TOT Shock, TOT π = 0.209
  - Term Premium, δ = 0.015
  - Potential Output Growth, g = 0.05
  - Risk free Rate of Return, r = 0.05
  - Short Term Debt as a Share of Output, λ = 0.204
  - Aid as a share of GDP = 0.04
  - Size of Aid Shock, Aid γ = 1.81
  - Output loss due to Aid shock, 2 γ = 0.015
  - Probability of Aid Shock, Aid π = 0.10
- Additional calibration notes:
  - Aid as share of GDP = 4 percent (average aid-to-GDP ratio for 44 SSA countries 1975–2005).
  - Potential output growth, g = 5 percent (average growth rate for Africa over last 5 years per authors).
  - Risk-free short-term rate r = 5 percent.
  - Term premium δ = 1.5 percent (same value used by Jeanne and Ranciere (2005)); authors note δ may be higher in low-income African countries.

### Simulation results — main findings and quantitative outcomes
- Two-Good model vs Jeanne-Ranciere (one-good) model:
  - Two-Good model suggests a higher optimal reserve level than the Jeanne-Ranciere model for relevant parameter ranges (difference under benchmark ≈ 2 percent of GDP).
  - Illustrative consumption paths with optimal reserves:
    - Single-good model consumption falls by ≈4 percent at shock.
    - Two-good model consumption falls by ≈1.5 percent at shock.
- Full model with both TOT and Aid shocks:
  - Optimal reserves increase with probability and size of both TOT and Aid shocks.
  - Optimal reserves decrease with higher term premium δ.
  - For benchmark parameters, Two-Good model optimal reserves ≈ 11 to 12 percent of total output for a typical SSA country facing both TOT and aid shocks.
- Cross-country and end-2007 comparison:
  - Many SSA countries had adequate or more-than-adequate reserves by the model benchmark at end-2007.
  - A few countries had reserves significantly below the model optimum (examples identified in the source: Burundi, Democratic Republic of Congo).
- Reserve gap dynamics:
  - The reserve gap increased by some 4 percent of GDP over the last 8 years (as reported).
  - Example country dynamics:
    - Angola: reserve gap declines significantly because optimal reserves fell with falling short-term debt while actual reserves rose owing to oil revenue windfalls; Angola held more reserves than the two-good model suggested in 2006–07.
    - Congo, D.R.: maintained roughly constant reserve-to-GDP ratio in the period illustrated.
- Sensitivity:
  - Optimal reserves sensitive to probability and size of TOT shocks, output cost of shocks, and term premium δ (Figures 13 and 14).
  - Aid-parameter sensitivity smaller for most countries because aid is a small percentage of output; sensitivity larger for aid-dependent countries.

### Country-specific parameter table excerpt (simulation inputs preserved verbatim)
- Table A2 selected entries and averages (preserved exactly as in source):
  - Angola              39.37.156.860.037
  - Benin28.67.120.540.027
  - Botswana            25.021.437.730.350
  - Burkina Faso        25.03.622.160.021
  - Burundi             35.73.632.220.120
  - Cameroon            25.03.627.560.078
  - Cape Verde          28.63.641.550.118
  - Central African Rep.17.93.620.740.279
  - Chad                17.93.650.000.000
  - Comoros35.714.323.910.063
  - Congo, Dem. Rep. of10.77.148.050.126
  - Congo, Republic of17.921.4101.790.032
  - Côte d'Ivoire       14.37.143.650.000
  - Equatorial Guinea   32.114.388.280.001
  - Eritrea3.63.627.810.029
  - Ethiopia            28.67.127.010.019
  - Gabon               10.732.149.830.048
  - Gambia, The         17.910.744.830.293
  - Ghana               21.47.148.790.022
  - Guinea              17.910.730.820.083
  - Guinea-Bissau       21.414.341.590.194
  - Kenya               17.93.630.100.032
  - Lesotho             3.67.170.110.024
  - Madagascar35.77.141.220.007
  - Malawi              25.07.133.450.025
  - Mali17.93.631.590.032
  - Mauritius3.628.664.690.022
  - Mozambique          14.37.141.760.151
  - Namibia             25.010.747.730.253
  - Niger               28.63.627.900.019
  - Nigeria             25.032.132.650.008
  - Rwanda              39.33.624.620.011
  - São Tomé & Príncipe32.110.745.000.000
  - Senegal10.77.136.370.019
  - Seychelles39.325.0117.340.074
  - Sierra Leone        3.614.326.380.074
  - South Africa        3.63.633.700.221
  - Swaziland           0.039.370.580.000
  - Tanzania            32.13.631.950.003
  - Togo                21.40.051.920.023
  - Uganda              35.77.126.800.012
  - Zambia32.17.139.480.007
  - Average21.510.442.510.094

### Policy implications and recommendations
- Reserve adequacy assessment should explicitly account for exogenous TOT and aid shocks for LICs/SSA; the Two-Good model that incorporates these shocks indicates higher optimal reserves than single-good models in benchmark calibration.
- Key determinants of optimal reserves:
  - Probability and size of TOT and aid shocks (higher → higher optimal reserves).
  - Output cost associated with shocks (higher → higher optimal reserves).
  - Term premium δ (higher → lower optimal reserves because carrying reserves is costlier).
- Practical recommendations:
  - Maintain adequate foreign reserves as part of reducing macroeconomic volatility, especially where alternative financing sources are limited.
  - Use country-specific calibration: optimal reserve recommendations are sensitive to country-specific probabilities, tradable shares, short-term debt shares, and country-specific term premia.
  - Apply the Two-Good model as a benchmark but complement with country-level analysis and judgement given parameter sensitivity.

### Model limitations and suggested extensions
- Limitations noted:
  - Current model assumes no saving in terms of non-tradable good.
  - No capital accumulation and production are included in the base specification.
- Suggested extensions:
  - Relax the restriction of no-saving-in-terms-of non-tradable good.
  - Introduce capital accumulation and production in the economy.
  - Extend the model to incorporate other shocks besides terms of trade and aid shocks.

*Source: _wp08150 (IMF Working Paper content provided in the supplied PDF excerpt).*

### 1. Comparisons of International Reserves Across Regions, 1995–07 .......................................5

### 1. Comparisons of International Reserves Across Regions, 1995–07

### Scope and Structure
- Time coverage: 1995–07
- Appendices:
  - A1. Benchmark Parameters (page 33)
  - A2. Simulation Parameters for Countries (page 34)
- Focus: cross-regional comparisons of international reserves and associated model analyses and simulations.

### Figures and Analytical Components
- Figure 1: Reserves in Months of Imports
- Figure 3: Reserves to Short-Term Debt <2, 2007
- Figure 4: Frequency Distributions of Key Parameters
- Figure 5: Frequency Distributions of Key Parameters
- Figure 6: Response of Key Macro Economic Variables to a Large TOT Schock
- Figure 7: Response of Key Macroeconomic Variables to a Large Aid Shock
- Figure 8: Optimal Reserve Behavior – Jeanne-Ranciere v.s. Two-Good
- Figure 9: Path of Consumption—Ranciere vs. Two-Good Model
- Figure 10: Optimal Reserve Behavior—Two Good Model with both TOT and Aid Shock [I]
- Figure 11: Optimal Reserve Behavior—Two Good Model with both TOT and Aid Shock [II]
- Figure 12: Actual Level of Reserves to GDP ratio for SSA countries
- Figure 13: Sensitivity of Optimal Reserves to Key Parameters
- Figure 14: Sensitivity of Optimal Reserves to Key Parameters
- Figure 15: Reserve Adequacy for African Countries Using Two-Good Model /1
- Figure 16: Country Specific Application—Illustrative Examples

### Implied Analytical Themes (based on figure titles and appendices)
- Measurement of reserve adequacy using months of imports and reserves-to-short-term-debt ratios (including threshold <2, 2007).
- Use of frequency distributions to characterize key model parameters.
- Dynamic responses of macroeconomic variables to commodity terms-of-trade (TOT) shocks and aid shocks.
- Comparison of optimal reserve behavior between Jeanne-Rancière framework and a Two-Good model, including consumption paths.
- Sensitivity analysis of optimal reserves to model parameters.
- Application of the Two-Good model to assess reserve adequacy for African countries and country-specific illustrative examples.
- Benchmark and country-level simulation parameterization documented in appendices A1 and A2.

*Source: _wp08150 - 1. Comparisons of International Reserves Across Regions, 1995–07*

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

### _wp08150 - References..............................................................................................................

### Introduction and purpose
- Objective: extend Jeanne and Ranciere (2006) reserve-model of consumption smoothing to a Small Open Economy (SOE) with two goods (tradable and non-tradable) and stochastic aid, then simulate optimal reserve holdings for Sub-Saharan Africa (SSA) given likely shocks.
- Rationale: SSA faces distinct exogenous shocks (terms of trade and aid flows) that standard single-good reserve models do not explicitly incorporate.
- Two model extensions: (1) two goods with exogenous shocks to the relative price of the traded good (terms of trade); (2) stochastic unilateral transfer of tradable good (“Aid”) every period.
- Paper structure: Section II background on reserve measures; Section III key shocks and their macro impact; Section IV model; Section V simulations; Section VI conclusions.

### Foreign reserves in Sub‑Saharan Africa — state and comparative indicators
- Aggregate and pattern:
  - Foreign reserves for all of SSA reached an all time high of US$127 billion in 2007.
  - At end-2007, reserves covered 5.8 months of imports, up from 3.7 months in 1997-2002.
- Cross-group differences (end-2007 highlights):
  - Oil-exporting countries: above average import cover.
  - Fragile countries: below average import cover.
- Other reserve indicators:
  - Reserves to short-term external debt: less than 1 for only a handful of countries in 2007.
  - Reserves as a share of M2 and of GDP vary widely across SSA countries (figures and country listings provided in source).
- Regional comparisons:
  - SSA reserve months lower than Middle East and North Africa, but higher than developing countries in general (Table 1).
- Cautions: observed reserve accumulation can reflect sterilization, exchange rate policy, or resource windfalls and is not always a direct benchmark of adequacy.

### Shocks facing SSA — definitions, frequency, and output costs
- Shock definitions (operationalized for analysis):
  - Terms of trade (TOT) shock: year-on-year decline in terms of trade index larger than 10 percent in absolute terms.
  - Aid shock: decline in net aid inflow of 50 percent or more in absolute terms.
  - Thresholds chosen so that such events happen 20-25 percent of the time for an average SSA country (per authors’ calibration).
- Empirical summary (sample of 44 SSA countries and 1975–2006/1980–2006 periods used in analyses):
  - Probability (average): terms of trade shock ≈ 20 percent; aid shock ≈ 10 percent.
  - Average shock sizes: average size of a terms of trade shock = 21 percent; average size of aid shock = 181 percent (roughly 4-5 percent of GDP).
  - Frequency: 80 percent of SSA countries face a ≥10 percent negative TOT shock at least 5 percent of the time or more; 80 percent face a ≥50 percent decline in aid at least 5 percent of the time or more.
- Output and consumption costs:
  - Average loss in output (reduction in GDP growth) associated with a ≥10 percent TOT shock = 1.5 percent (based on sample).
  - Aid shocks (≥50 percent) show similar average output loss; about 40 percent of aid shocks are associated with an output cost between 0.5 to 4 percent and another 20 percent with output loss between 5-6 percent.
  - About 40 percent of TOT shocks are associated with output cost of 2 percent or more.
- Reserves cushion heterogeneity:
  - High-reserve (HR) countries (top 25th percentile average reserve-to-GDP during 2000-06): overall average reserve-to-GDP ≈ 28 percent.
  - Low-reserve (LR) countries (bottom 25th percentile): overall average reserve-to-GDP ≈ 4.2 percent.
  - Empirical event-window findings (1980-2006): LR countries suffer larger declines in GDP growth and much larger declines in per capita absorption following shocks than HR countries. LR countries draw down reserves less (cumulative two-year reduction ≈ 0.98 percent of GDP) versus HR countries (≈ 3 percent of GDP) following a TOT shock — indicating LR countries cannot or do not draw reserves as much to smooth consumption.

### Model: Small Open Economy with two goods (framework and key assumptions)
- Economy: two goods—tradable and non-tradable; deterministic growth path disturbed by exogenous TOT shocks; stochastic aid transfers of tradable good that grow at same rate as output absent shocks.
- Shock mechanics:
  - TOT shock interpreted as fall of ten percent or more from normal level (normal T = 1 in model notation).
  - Aid shock interpreted as unforeseen drop in aid flows of five percent or more (authors also operationalize aid-shock definitions earlier as ≥50 percent; model exposition clarifies “5 percent or more” as modeling shorthand—use the source text’s parameterization).
  - When either shock occurs it is accompanied by a “Sudden-Stop” in capital (no rollover of short-term private external debt).
  - The two shocks are assumed independent in the full model.
- Agents and instruments:
  - Representative private consumer with Cobb-Douglas aggregator between tradable and non-tradable consumption; CRRA utility with risk aversion σ.
  - Government issues a long-term security (pays one unit of good each period until shock, then falls to zero) to finance reserves. Price of the security before the shock: P = 1/(r + δ + sπ − …) (model gives closed-form expression; see equation 1.7 and 1.21 for the derived constant price p and connection to r, δ, and shock probability sπ).
  - Reserves R are financed via long-term security issuance; government makes transfer Z to consumers to pay for reserve carrying cost; if shock occurs government transfers reserves net of last payment to consumers.
- Two cases analyzed:
  - A. No external private borrowing (no short-term external debt).
  - B. External private borrowing allowed (short-term debt = fraction λ of tradable good output; debt must be repaid even during shocks; no rollover during or after shock).
- First-order conditions and optimization:
  - Government chooses reserves R to maximize expected representative consumer welfare; optimality equates marginal cost of holding reserves (pre-shock consumption cost proportional to term premium δ and shock probability) to expected marginal utility benefit in the shock state. See equations (1.19)–(1.21) and related expressions for marginal conditions.

### Calibration and benchmark parameter choices (for simulations)
- Sample and data: calibrations use data for 44 SSA countries (1980–2006 in many estimates); aggregate statistics used to set several parameters.
- Key benchmark parameter values used in simulations:
  - Average size of TOT shock, γTOT = 21 percent (average size of a terms of trade shock).
  - Average size of aid shock, γAid = 181 percent (roughly 4-5 percent of GDP).
  - Average probabilities: πTOT ≈ 20 percent; πAid ≈ 10 percent.
  - Aid as share of GDP = 4 percent (average aid-to-GDP ratio for 44 SSA countries 1975–2005).
  - Potential output growth, g = 5 percent (average growth rate for Africa over last 5 years per authors).
  - Short-term debt share in GDP, λ: calibrated using country-specific data for the 44 SSA countries for 2007.
  - Risk-free short-term rate of return, r = 5 percent.
  - Term premium (cost of holding reserves), δ = 1.5 percent (same value used by Jeanne and Ranciere (2005)).
  - Note: authors acknowledge δ may be higher in low-income African countries and country-specific δ preferred where available.

### Simulation results — key findings
- Two-Good model vs Jeanne-Ranciere (one-good) model:
  - For relevant parameter ranges, the Two-Good model suggests a higher optimal reserve level than the Jeanne-Ranciere model (difference under benchmark ≈ 2 percent of GDP).
  - Intuition:
    - Two-Good model captures direct income effect: a TOT fall reduces tradable output and thus import capacity directly, so reserves to insure tradable consumption are more valuable (raises optimal reserves).
    - Offsetting effects: lower marginal utility return to reserves (since TOT shock affects both tradable and non-tradable output) and easier substitution of tradable consumption between states (tradables may be only part of total consumption) tend to lower optimal reserves. For benchmark parameters, the direct income effect dominates.
  - Illustrative consumption paths: with optimal reserves chosen, single-good model consumption falls by ≈4 percent at shock; two-good model consumption falls by ≈1.5 percent.
- Full model with both TOT and Aid shocks:
  - Optimal reserves increase with probability and size of both TOT and Aid shocks.
  - Optimal reserves decrease with higher term premium δ (higher carrying cost reduces optimal reserves).
  - For benchmark parameters, Two-Good model optimal reserves ≈ 11 to 12 percent of total output for a typical SSA country facing both TOT and aid shocks.
- Cross-country comparison (end-2007):
  - Figure 12 and Figure 15 compare actual reserves-to-GDP (end 2007) for 44 SSA countries with model-optimal reserves.
  - Many SSA countries had adequate or more-than-adequate reserves by the model benchmark at end-2007; a few countries had reserves significantly below the model optimum (examples given in text: Burundi, Democratic Republic of Congo among those noted as well below optimal).
- Sensitivity and country-specific applications:
  - Optimal reserve levels sensitive to choice of key parameters: probability and size of TOT shocks, output cost of shocks, and term premium δ (shown in Figures 13 and 14).
  - Aid-parameter sensitivity smaller for most countries because aid is a small percentage of output; but for aid-dependent countries sensitivity increases.
  - Country-specific estimates: authors compute country-specific shock probabilities (1980–2006) and tradable-good share α for each of 44 SSA countries; use common δ = 1.5 and other common parameters to produce country optimal reserves-to-GDP over time and generate a “reserve gap” = optimal minus actual reserves (examples provided for Angola and Congo, D.R.).
- Time dynamics and reserve behavior examples:
  - Angola: reserve gap declines significantly because optimal reserves fell with falling short-term debt while actual reserves rose owing to oil revenue windfalls; Angola had more reserves than the two-good model suggested in recent years (2006–07).
  - Congo, D.R.: maintained roughly constant reserve-to-GDP ratio (around values shown in detailed figures in source).

### Policy-relevant conclusions and implications
- Reserve adequacy assessment should explicitly account for exogenous TOT and aid shocks for LICs/SSA: Two-Good model that incorporates these shocks indicates higher optimal reserves than single-good models in benchmark calibration.
- Key determinants of optimal reserves include:
  - Probability and size of TOT and aid shocks (higher → higher optimal reserves).
  - Output cost associated with shocks (higher → higher optimal reserves).
  - Term premium δ (higher → lower optimal reserves because carrying reserves is costlier).
- Practical implications:
  - Many SSA countries may hold reserve stocks consistent with model benchmarks, but some countries hold reserves significantly below the model-implied optimal, posing vulnerability to shocks.
  - Country-specific calibration matters: optimal reserve recommendations are sensitive to country-specific probabilities, tradable shares, short-term debt shares, and country-specific term premia.
  - Results are illustrative and depend on parameter choices; application requires judgement and country-level analysis.

*Source: Authors’ computations based on I.M.F, International Financial Statistics and World Bank, World Development Indicators; content from _wp08150 - References (PDF) provided in prompt.*

### 2.5 percent) but saw an increase in the optimal level of reserves, with the reserve gap

### _wp08150 - 2.5 percent) but saw an increase in the optimal level of reserves, with the reserve gap

### Summary of substantive findings
- The reserve gap increased by some 4 percent of GDP over the last 8 years.
- The consumption smoothing role of reserves is particularly important in SSA countries; countries with very low levels of reserves are more strongly affected by exogenous shocks than others.
- A few SSA countries do not currently carry reserves consistent with the expected output costs associated with expected terms-of-trade or aid shocks.
- There is no one-size-fits-all level of reserves for all SSA countries; reserve adequacy depends on country-specific factors such as vulnerability to shocks, magnitude of shocks, and opportunity cost of holding reserves.

### Model, methodology, and benchmark approach
- Uses a small open economy two-goods model with exogenous terms of trade and aid shocks as a benchmark for reserve adequacy.
- The model compares the insurance value of foreign reserves against their "carrying costs" by simulating optimal reserve levels across a spectrum of shocks and output costs.
- The optimal level of reserves is sensitive to key parameters such as term premium and probability of shocks; results based on average parameter values can be misleading.
- Country-specific information is used to obtain optimal reserve levels for SSA countries to reflect heterogeneity in shocks and structural factors.

### Key quantitative results and illustrative examples
- Reserve gap change: "increasing by some 4 percent of GDP over the last 8 years."
- Figures illustrate country-specific trajectories (examples named in text): Angola and Congo, D.R. showing series for Optimal Reserves, Actual Reserves, and Reserves Gap for years 2000–2007 (figures sourced from WEO).
- Table A1. Benchmark Parameters (Terms of Trade Shock):
  - Size of the Shock, TOT γ = 0.219
  - Output loss due to the TOT shock, 1 γ = 0.015
  - Coefficient of Risk Aversion, σ = 2
  - Share of Tradable, α = 0.5
  - Probability of TOT Shock, TOT π = 0.209
  - Term Premium, δ = 0.015
  - Potential Output Growth, g = 0.05
  - Risk free Rate of Return, r = 0.05
  - Short Term Debt as a Share of Output, λ = 0.204
  - Aid as a share of GDP = 0.04
  - Size of Aid Shock, Aid γ = 1.81
  - Output loss due to Aid shock, 2 γ = 0.015
  - Probability of Aid Shock, Aid π = 0.10

- Table A2. Simulation Parameters for Countries (selected entries and averages preserved exactly as in source):
  - Angola              39.37.156.860.037
  - Benin28.67.120.540.027
  - Botswana            25.021.437.730.350
  - Burkina Faso        25.03.622.160.021
  - Burundi             35.73.632.220.120
  - Cameroon            25.03.627.560.078
  - Cape Verde          28.63.641.550.118
  - Central African Rep.17.93.620.740.279
  - Chad                17.93.650.000.000
  - Comoros35.714.323.910.063
  - Congo, Dem. Rep. of10.77.148.050.126
  - Congo, Republic of17.921.4101.790.032
  - Côte d'Ivoire       14.37.143.650.000
  - Equatorial Guinea   32.114.388.280.001
  - Eritrea3.63.627.810.029
  - Ethiopia            28.67.127.010.019
  - Gabon               10.732.149.830.048
  - Gambia, The         17.910.744.830.293
  - Ghana               21.47.148.790.022
  - Guinea              17.910.730.820.083
  - Guinea-Bissau       21.414.341.590.194
  - Kenya               17.93.630.100.032
  - Lesotho             3.67.170.110.024
  - Madagascar35.77.141.220.007
  - Malawi              25.07.133.450.025
  - Mali17.93.631.590.032
  - Mauritius3.628.664.690.022
  - Mozambique          14.37.141.760.151
  - Namibia             25.010.747.730.253
  - Niger               28.63.627.900.019
  - Nigeria             25.032.132.650.008
  - Rwanda              39.33.624.620.011
  - São Tomé & Príncipe32.110.745.000.000
  - Senegal10.77.136.370.019
  - Seychelles39.325.0117.340.074
  - Sierra Leone        3.614.326.380.074
  - South Africa        3.63.633.700.221
  - Swaziland           0.039.370.580.000
  - Tanzania            32.13.631.950.003
  - Togo                21.40.051.920.023
  - Uganda              35.77.126.800.012
  - Zambia32.17.139.480.007
  - Average21.510.442.510.094

### Policy implications and recommendations
- Reserve policy should be informed by country-specific vulnerability to shocks, magnitude of shocks, and opportunity cost of holding reserves.
- Maintaining adequate foreign reserves can be an important element in reducing macroeconomic volatility, especially where alternative sources of financing are limited.
- The choice of reserve levels should be studied within the context of the overall macroeconomic policy framework of a country, accounting for factors such as exchange rate regime and degree of monetization.
- Use the Two-Good model as a benchmark but complement it with country-specific information and other determinants of reserve accumulation behavior.

### Extensions, limitations, and suggested further work
- Model limitations noted:
  - Current model assumes no saving in terms of non-tradable good.
  - No capital accumulation and production are included in the base specification.
- Suggested extensions:
  - Relax the restriction of no-saving-in-terms-of non-tradable good.
  - Introduce capital accumulation and production in the economy.
  - Extend the model to incorporate other shocks besides terms of trade and aid shocks.

### Appendix: analytical expressions and solution highlights
- Equations 1.20, 1.23 and 1.24 are combined and rewritten (exact algebraic expressions presented in source).
- Using consumption aggregator (equation 1.22) leads to further specified forms for aggregate consumption terms (expressions shown in source).
- In the special case with no aid shocks, the optimal level of reserves can be written as:
  - 11,  2 T ttbt RkY  k A − =×+×
  - where k1 and k2 are defined in terms of model primitives (explicit expressions provided in source).
- The derivation solves for 1t R − as a function of pre-shock tradable output and aid flow.

*Source: IMF Working Paper content provided in the supplied PDF excerpt.*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08150.pdf_