## _wp10215 - 2. Table 2: Sensitivity Analysis Using Valencia (2010)

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### Introduction and motivation
- The global financial and economic crisis renewed interest in the impact of international reserves on macroeconomic stability, balancing costs and benefits of holding liquid foreign reserve assets.
- Reserve accumulation rose notably after the Asian crisis, concentrated in emerging economies, with low-income countries (LICs) following an accelerated pattern that helped cushion the 2008 commodity price shock.
- For The Gambia, a small open economy with exposure to current account shocks, import dependence and limitations on external borrowing, targeting an optimal level of international reserves can:
  - allow gradual adjustment of domestic demand to shocks; and
  - avoid excessively tying up resources in low yielding, low risk foreign assets.
- Combining rule-of-thumb indicators with theoretically grounded optimization models provides a more nuanced reserve adequacy assessment tailored to country-specific shocks.

### Recent evolution of international reserves in The Gambia
- Between 2004 and 2007, increased macroeconomic stability and strengthening foreign inflows (private and official transfers, FDI, tourism) enabled reserve accumulation aligned with regional trends and WAMZ convergence criteria.
- 2008 commodity shock outcomes:
  - nominal depreciation of the average exchange rate against the U.S. dollar of 21 percent during 2008;
  - fall in the real effective exchange rate of 7 percent during 2008;
  - central bank sold about one fifth of its reserve stock in Q4 2008 to support the dalasi;
  - gross international reserves coverage fell from 5.0 months to 3.6 months of imports of goods and services between end-2007 and end-2008.
- 2009 developments:
  - gradual rebuilding of foreign reserves supported by increased budget support and high FDI inflows into the banking system;
  - most substantial boost: SDR allocation and Extended Credit Facility (ECF) disbursement, which together represented about one third of the stock of gross international reserves at end-2009;
  - import coverage reached 6 months of imports of goods and services at end-2009.
- Foreign exchange market and trade features:
  - average foreign exchange transaction volumes of about US$ 130 million during 2007–08 and about US$ 150 million from September 2009 through April 2010;
  - The Gambia is vulnerable to terms of trade shocks and volatility in aid and remittances.
- Opportunity cost of holding reserves:
  - real differential between domestic treasury bill yield and U.S. benchmarks averaged about 8 percent per annum during August 2005–April 2010;
  - average treasury bill yields as high as 8 percent in real terms;
  - interest costs consumed 15 percent of government revenue in 2009.

### Static benchmarks of reserve adequacy (rule-of-thumb metrics)
- Common indicators: reserve coverage of imports, reserves to short-term external debt, reserves to broad money, reserves to GDP.
- Relevance to The Gambia:
  - short-term external debt is negligible, making the Greenspan-Guidotti rule less relevant;
  - reserve coverage of imports is the key indicator for current account shocks.
- Rule-of-thumb guidance and The Gambia’s position:
  - widespread rule-of-thumb: coverage of 3 months of imports considered adequate (often a lower bound for very open economies);
  - The Gambia’s import coverage ratio at end-2009 was within the cross-section of ECOWAS and WAMZ members;
  - the ratio of foreign reserves to GDP and reserves to broad money are also informative; The Gambia’s position appears robust, though broad money coverage has trended downwards as the financial sector developed.

### Optimal reserve models applied to low-income countries
- Models used:
  - Barnichon (2009): small open economy representative agent model embedding precautionary savings motive, two-state Markov shock process (normal and shock states), reserves as insurance, opportunity cost calibrated via interest rate differentials.
  - Valencia (2010): variant of Carroll (2004) precautionary savings model including shocks to terms of trade and export volumes, allows for investment and an optional borrowing constraint reflecting limited access to international capital markets.
- Key model mechanics and comparative points:
  - Barnichon (2009) parameters: shocks reduce output, exports and real exchange rate via factors ηy, ηx, ηε (<1); transition probabilities πns and πsn determine shock dynamics; higher shock probability and larger losses raise optimal reserves-to-imports ratio; higher opportunity cost and larger foreign transfers reduce optimal reserves coverage; effect of export share to output is ambiguous due to utility concavity.
  - Valencia (2010) differences: introduces capital and depreciation (δ), terms of trade shocks (ς) and export volume shocks (γ) modeled as non-negative i.i.d. variables; in original form, borrowing constraint can imply reserves-to-consumption (imports) ratio greater than one, so the borrowing constraint was relaxed for comparability with standard indicators and Barnichon’s model.

### Simulation results (Barnichon baseline and scenarios)
- Baseline calibration choices:
  - coefficient of relative risk aversion set to 2 (consistent with literature);
  - baseline assumes a 20 percent (annual) likelihood of a terms of trade shock (defined as an annual negative change in terms of trade for goods and services of at least –10 percent), consistent with average negative annual changes since 1980;
  - shock lasts about a year with no direct effect on output or exports beyond a real depreciation of 10 percent;
  - current transfers (aid and remittances) decline by 20 percent relative to equilibrium during the shock;
  - opportunity cost initially calibrated to a relatively low yearly value of 3.5 percent (Barnichon, 2009).
- Baseline result:
  - benchmark optimal reserves: 4.6 months of imports of goods and services (broadly in line with actual import coverage at end-2007 of 5 months).
- Alternative parameter scenarios and results:
  - Doubling the opportunity cost parameter to 7 percent (broadly in line with average real interest rate differential between The Gambia and the United States since 2005) yields optimal reserve coverage of 4.2 months of imports.
  - Raising likelihood of terms of trade shocks to 30 percent with shock duration shortened to about 8 months yields import coverage of 5.1 months.
  - Doubling the real depreciation during the shock state to 20 percent yields an indicative coverage of about 7 months of imports.
- Interpretation:
  - Baseline suggests prior CBG accumulation up to end-2007 was prudent.
  - Results are sensitive to parameter choices; parameter sensitivity is an important caveat and calls for cautious interpretation.
  - Combining model simulations with rule-of-thumb indicators supports informed policy choices balancing flexibility and prudence in reserve use.

### Valencia (2010) model simulations — comparability notes
- Original Valencia model implications:
  - With borrowing constraint imposed (consumption not to exceed net foreign assets), the ratio of reserves to consumption (imports) will always be greater than one, making direct comparison with standard import-coverage metrics difficult.
- Adjustments for comparability:
  - Borrowing constraint relaxed to allow comparison with Barnichon (2009) results and rule-of-thumb indicators.
  - Recognized that The Gambia’s access to multilateral concessional debt makes a complete lack of external debt access a strong assumption; hence relaxation is justified.
  - Gross interest factor in Valencia (2010) reflects the real interest benefit of holding the risk free asset (e.g., U.S. T-bills) rather than the full opportunity cost faced by The Gambia.

### Calibration and baseline model (Valencia follow-up)
- Baseline calibration follows Valencia (2010) without investment or external borrowing constraints.
- Discount factor β = 0.9.
- Volatility of the transitory shock to terms of trade matched to standard deviation = 0.16 for The Gambia terms of trade for goods and services over 1980–2010 (World Economic Outlook).
- Volatility of export volume shocks = 0.027, based on the elasticity of The Gambia exports to world import demand over the same period.
- Baseline optimal reserve to import coverage ≈ 6.2 months.

### Role of investment and borrowing constraints
- Introducing investment raises the incentive for precautionary saving because agents must finance consumption and capital accumulation.
- When external borrowing is constrained, a negative shock leaves consumers with fewer resources to finance consumption and replacement of depreciated capital, increasing the optimal reserve coverage.
- In a version augmenting the baseline with a Cobb-Douglas production function (share of capital = 0.2) and annual depreciation = 10 percent, import coverage decreases to 4.6 months compared with the baseline (when borrowing constraints are absent).

### Opportunity cost and impatience
- The opportunity cost of holding reserves is modeled through the degree of impatience via the discount factor β (a lower β indicates more impatience and a higher cost of savings/reserves).
- The paper notes difficulty in modeling opportunity cost and that some benefits of holding reserves (for example, fostering confidence in government policy) are difficult to quantify and are left outside the model.

### Sensitivity analysis (model robustness and caveats)
- Optimization model results hinge on chosen parameter values and are sensitive to alternative parameterizations; models may fail to capture full economic structure and heterogeneity.
- Data quality issues can affect parameter choices and calibration.
- Summary of sensitivity results (both models considered):
  - Higher coefficient of relative risk aversion → need for increased precautionary saving (higher reserves).
  - Reduced degree of impatience (higher β) → need for increased precautionary saving.
  - Higher shock likelihood and higher shock volatility → require higher reserves.
  - Increased opportunity cost → reduces the incentive for reserve accumulation.
- The Appendix contains Tables 1 and 2 presenting sensitivity analysis results for individual parameter changes and model baselines (Valencia (2010) and Barnichon (2009) frameworks), including variations in:
  - Coefficient of relative risk aversion
  - Discount factor
  - Transition probability of terms of trade shock
  - Volatility of terms of trade shock
  - Volatility of export volume shock
  - Export loss, real exchange rate depreciation, and aid/remittances loss

### Conclusions and policy implications
- Improved macroeconomic stability and increasing foreign exchange inflows through 2007 allowed The Gambia to accumulate international reserves that buffered the commodity price shock of 2008.
- Baseline scenarios indicate a central range between 4.5 months to 7 months of import coverage.
- Actual coverage of 6 months of imports of goods and services at end 2009 suggests international reserve adequacy in The Gambia is broadly in line with optimal levels derived from the theoretical models, with caution due to model caveats.
- Conditional on macroeconomic developments, authorities could consider foregoing short-run reserve accumulation given the actual reserve coverage ratio.
- Simulations that incorporate The Gambia–specific data support maintaining reserve coverage well in excess of 3 months of imports of goods and services (higher than a traditional rule-of-thumb).
- The one-off nature of the 2009 reserve increase from the SDR allocation strengthens the case for continued prudence in reserve policy.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10215.pdf*

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

### _wp10215 - References ...............................................................................................................

### Figures

- 1. Gross Reserves in Percent of GDP ....................................................................................... 3
- 2. Gross International Reserves ................................................................................................ 5
- 3. Import Coverage of Gross International Reserves ................................................................  5
- 4. Gross International Reserves and Exchange Rates ............................................................... 6
- 5. Exchange Market Pressure Index .......................................................................................... 6
- 6. Trade in Percent of GDP ....................................................................................................... 6
- 7. Behavior of Terms of Trade and Current Transfers .............................................................. 6
- 8. Cost of Holding Reserves ..................................................................................................... 7
- 9. Standard Metrics of Reserve Coverage ................................................................................. 8

### Appendix

- 1. Table 1: Sensitivity Analysis Using Barnichon (2009) ...................................................... 16

*Source: _wp10215 - References .............................................................................................................*

### 2. Table 2: Sensitivity Analysis Using Valencia (2010) ......................................................... 16

### _wp10215 - 2. Table 2: Sensitivity Analysis Using Valencia (2010)

### Introduction and motivation
- The global financial and economic crisis renewed interest in the impact of international reserves on macroeconomic stability, balancing costs and benefits of holding liquid foreign reserve assets.
- Reserve accumulation rose notably after the Asian crisis, concentrated in emerging economies, with low-income countries (LICs) following an accelerated pattern that helped cushion the 2008 commodity price shock.
- For The Gambia, a small open economy with exposure to current account shocks, import dependence and limitations on external borrowing, targeting an optimal level of international reserves can:
  - allow gradual adjustment of domestic demand to shocks; and
  - avoid excessively tying up resources in low yielding, low risk foreign assets.
- Combining rule-of-thumb indicators with theoretically grounded optimization models provides a more nuanced reserve adequacy assessment tailored to country-specific shocks.

### Recent evolution of international reserves in The Gambia
- Between 2004 and 2007, increased macroeconomic stability and strengthening foreign inflows (private and official transfers, FDI, tourism) enabled reserve accumulation aligned with regional trends and WAMZ convergence criteria.
- 2008 commodity shock outcomes:
  - nominal depreciation of the average exchange rate against the U.S. dollar of 21 percent during 2008;
  - fall in the real effective exchange rate of 7 percent during 2008;
  - central bank sold about one fifth of its reserve stock in Q4 2008 to support the dalasi;
  - gross international reserves coverage fell from 5.0 months to 3.6 months of imports of goods and services between end-2007 and end-2008.
- 2009 developments:
  - gradual rebuilding of foreign reserves supported by increased budget support and high FDI inflows into the banking system;
  - most substantial boost: SDR allocation and Extended Credit Facility (ECF) disbursement, which together represented about one third of the stock of gross international reserves at end-2009;
  - import coverage reached 6 months of imports of goods and services at end-2009.
- Foreign exchange market and trade features:
  - average foreign exchange transaction volumes of about US$ 130 million during 2007–08 and about US$ 150 million from September 2009 through April 2010;
  - The Gambia is vulnerable to terms of trade shocks and volatility in aid and remittances.
- Opportunity cost of holding reserves:
  - real differential between domestic treasury bill yield and U.S. benchmarks averaged about 8 percent per annum during August 2005–April 2010;
  - average treasury bill yields as high as 8 percent in real terms;
  - interest costs consumed 15 percent of government revenue in 2009.

### Static benchmarks of reserve adequacy (rule-of-thumb metrics)
- Common indicators: reserve coverage of imports, reserves to short-term external debt, reserves to broad money, reserves to GDP.
- Relevance to The Gambia:
  - short-term external debt is negligible, making the Greenspan-Guidotti rule less relevant;
  - reserve coverage of imports is the key indicator for current account shocks.
- Rule-of-thumb guidance and The Gambia’s position:
  - widespread rule-of-thumb: coverage of 3 months of imports considered adequate (often a lower bound for very open economies);
  - The Gambia’s import coverage ratio at end-2009 was within the cross-section of ECOWAS and WAMZ members;
  - The ratio of foreign reserves to GDP and reserves to broad money are also informative; The Gambia’s position appears robust, though broad money coverage has trended downwards as the financial sector developed.

### Optimal reserve models applied to low-income countries
- Models used:
  - Barnichon (2009): small open economy representative agent model embedding precautionary savings motive, two-state Markov shock process (normal and shock states), reserves as insurance, opportunity cost calibrated via interest rate differentials.
  - Valencia (2010): variant of Carroll (2004) precautionary savings model including shocks to terms of trade and export volumes, allows for investment and an optional borrowing constraint reflecting limited access to international capital markets.
- Key model mechanics and comparative points:
  - Barnichon (2009) parameters: shocks reduce output, exports and real exchange rate via factors ηy, ηx, ηε (<1); transition probabilities πns and πsn determine shock dynamics; higher shock probability and larger losses raise optimal reserves-to-imports ratio; higher opportunity cost and larger foreign transfers reduce optimal reserves coverage; effect of export share to output is ambiguous due to utility concavity.
  - Valencia (2010) differences: introduces capital and depreciation (δ), terms of trade shocks (ς) and export volume shocks (γ) modeled as non-negative i.i.d. variables; in original form, borrowing constraint can imply reserves-to-consumption (imports) ratio greater than one, so the borrowing constraint was relaxed for comparability with standard indicators and Barnichon’s model.

### Simulation results (Barnichon baseline and scenarios)
- Baseline calibration choices:
  - coefficient of relative risk aversion set to 2 (consistent with literature);
  - baseline assumes a 20 percent (annual) likelihood of a terms of trade shock (defined as an annual negative change in terms of trade for goods and services of at least –10 percent), consistent with average negative annual changes since 1980;
  - shock lasts about a year with no direct effect on output or exports beyond a real depreciation of 10 percent;
  - current transfers (aid and remittances) decline by 20 percent relative to equilibrium during the shock;
  - opportunity cost initially calibrated to a relatively low yearly value of 3.5 percent (Barnichon, 2009).
- Baseline result:
  - benchmark optimal reserves: 4.6 months of imports of goods and services (broadly in line with actual import coverage at end-2007 of 5 months).
- Alternative parameter scenarios and results:
  - Doubling the opportunity cost parameter to 7 percent (broadly in line with average real interest rate differential between The Gambia and the United States since 2005) yields optimal reserve coverage of 4.2 months of imports.
  - Raising likelihood of terms of trade shocks to 30 percent with shock duration shortened to about 8 months yields import coverage of 5.1 months.
  - Doubling the real depreciation during the shock state to 20 percent yields an indicative coverage of about 7 months of imports.
- Interpretation:
  - Baseline suggests prior CBG accumulation up to end-2007 was prudent.
  - Results are sensitive to parameter choices; parameter sensitivity is an important caveat and calls for cautious interpretation.
  - Combining model simulations with rule-of-thumb indicators supports informed policy choices balancing flexibility and prudence in reserve use.

### Valencia (2010) model simulations — comparability notes
- Original Valencia model implications:
  - With borrowing constraint imposed (consumption not to exceed net foreign assets), the ratio of reserves to consumption (imports) will always be greater than one, making direct comparison with standard import-coverage metrics difficult.
- Adjustments for comparability:
  - Borrowing constraint relaxed to allow comparison with Barnichon (2009) results and rule-of-thumb indicators.
  - Recognized that The Gambia’s access to multilateral concessional debt makes a complete lack of external debt access a strong assumption; hence relaxation is justified.
  - Gross interest factor in Valencia (2010) reflects the real interest benefit of holding the risk free asset (e.g., U.S. T-bills) rather than the full opportunity cost faced by The Gambia.

### Policy implications and caveats
- Policy implications:
  - CBG’s gradual reserve accumulation through end-2007 matched a model-based benchmark of roughly 4.6–5 months of import coverage under baseline assumptions.
  - High domestic borrowing costs (treasury bill yields up to 8 percent real; interest costs at 15 percent of government revenue in 2009) imply a material opportunity cost of holding reserves and justify careful evaluation of reserve use versus domestic debt reduction.
  - Asset management strategies that increase reserve yields while preserving maturity and risk profiles consistent with reserve definitions could positively affect optimal reserves.
- Caveats:
  - Parameter sensitivity is substantial; optimal coverage estimates vary with shock probability, shock severity (real depreciation), shock duration, and assumed opportunity cost.
  - Models abstract from some real-world features (e.g., market depth, access to multilateral concessional finance) that affect optimal reserve choices for The Gambia.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10215.pdf*

### 3.5 percent on the 10-year U.S. treasury bonds over 1967–2007. As discussed in the text, we also experiment

### 3.5 percent on the 10-year U.S. treasury bonds over 1967–2007. As discussed in the text, we also experiment

### Calibration and baseline model
- Baseline calibration follows Valencia (2010) without investment or external borrowing constraints.
- Discount factor β = 0.9.
- Volatility of the transitory shock to terms of trade matched to standard deviation = 0.16 for The Gambia terms of trade for goods and services over 1980–2010 (World Economic Outlook).
- Volatility of export volume shocks = 0.027, based on the elasticity of The Gambia exports to world import demand over the same period.
- Baseline optimal reserve to import coverage ≈ 6.2 months.

### Role of investment and borrowing constraints
- Introducing investment raises the incentive for precautionary saving because agents must finance consumption and capital accumulation.
- When external borrowing is constrained, a negative shock leaves consumers with fewer resources to finance consumption and replacement of depreciated capital, increasing the optimal reserve coverage.
- In a version augmenting the baseline with a Cobb-Douglas production function (share of capital = 0.2) and annual depreciation = 10 percent, import coverage decreases to 4.6 months compared with the baseline (when borrowing constraints are absent).

### Opportunity cost and impatience
- The opportunity cost of holding reserves is modeled through the degree of impatience via the discount factor β (a lower β indicates more impatience and a higher cost of savings/reserves).
- The paper notes difficulty in modeling opportunity cost and that some benefits of holding reserves (for example, fostering confidence in government policy) are difficult to quantify and are left outside the model.

### Sensitivity analysis (model robustness and caveats)
- Optimization model results hinge on chosen parameter values and are sensitive to alternative parameterizations; models may fail to capture full economic structure and heterogeneity.
- Data quality issues can affect parameter choices and calibration.
- Summary of sensitivity results (both models considered):
  - Higher coefficient of relative risk aversion → need for increased precautionary saving (higher reserves).
  - Reduced degree of impatience (higher β) → need for increased precautionary saving.
  - Higher shock likelihood and higher shock volatility → require higher reserves.
  - Increased opportunity cost → reduces the incentive for reserve accumulation.
- The Appendix contains Tables 1 and 2 presenting sensitivity analysis results for individual parameter changes and model baselines (Valencia (2010) and Barnichon (2009) frameworks), including variations in:
  - Coefficient of relative risk aversion
  - Discount factor
  - Transition probability of terms of trade shock
  - Volatility of terms of trade shock
  - Volatility of export volume shock
  - Export loss, real exchange rate depreciation, and aid/remittances loss

### Conclusions and policy implications
- Improved macroeconomic stability and increasing foreign exchange inflows through 2007 allowed The Gambia to accumulate international reserves that buffered the commodity price shock of 2008.
- Baseline scenarios indicate a central range between 4.5 months to 7 months of import coverage.
- Actual coverage of 6 months of imports of goods and services at end 2009 suggests international reserve adequacy in The Gambia is broadly in line with optimal levels derived from the theoretical models, with caution due to model caveats.
- Conditional on macroeconomic developments, authorities could consider foregoing short-run reserve accumulation given the actual reserve coverage ratio.
- Simulations that incorporate The Gambia–specific data support maintaining reserve coverage well in excess of 3 months of imports of goods and services (higher than a traditional rule-of-thumb).
- The one-off nature of the 2009 reserve increase from the SDR allocation strengthens the case for continued prudence in reserve policy.

*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/2010/_wp10215.pdf_