## Reserve Adequacy in Georgia: How Much is Enough? (sipea2026051)

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### A. Introduction and Key Findings
- Reserves increased markedly in 2025, recovering to 100 percent of the IMF’s Assessing Reserve Adequacy (ARA) threshold by end-2025, supported by strong services exports, higher gold prices, and de-dollarization.
- Continued reserve accumulation facilitated a successful Eurobond refinancing in early 2026.
- Despite higher energy prices linked to the war in the Middle East and potential current account pressures, the exchange rate remained broadly stable, partly reflecting stronger reserve buffers.
- Abstract summary finding:
  - Optimal reserve coverage estimated at around 145–150 percent of the ARA metric under the fully extended framework, compared to about 130 percent under the baseline framework.
  - Current reserves cited in the paper: 102 percent of ARA (paragraph 13); earlier statements note recovery to 100 percent of ARA by end-2025.

### B. Baseline Analytical Framework (Jeanne-Ranciѐre, 2011)
- Conceptual summary:
  - Reserves chosen to trade off insurance benefits in crisis states against opportunity costs in normal times.
  - Calibrated to Georgia, the baseline yields an optimal level of around 130 percent of ARA assuming a 10 percent probability of a sudden stop.
- Key formula elements (as presented):
  - 휌 = 휆 + 훾 − (1 − p^(−1/휎))
  - In reserves-to-output ratio notation: p = 1 + [훿/(휋 (1 − 휹 − 휋))], with 휹 representing the term premium and 휋 the probability of a sudden stop.

### C. Extension 1 — Reserves and Sovereign Risk Premia (Borrowing-Cost Channel)
- Mechanism:
  - Higher reserves can reduce sovereign borrowing costs by improving perceptions of liquidity and rollover risk.
  - Model implementation: allow opportunity cost of reserves to depend on reserve holdings; effective marginal cost expressed as 훿(푅) + 푅⋅훿′(푅).
- Empirical calibration notes:
  - A 10-percentage point increase in the reserves-to-GDP ratio can lower EM borrowing costs by around 30-70 basis points (literature estimate).
- Quantitative impacts for Georgia:
  - Incorporating this channel raises optimal reserves by about 5 percent of ARA at lower crisis probabilities.
  - At a 10 percent crisis probability, the net effect is about 8 percent of ARA lower than the baseline framework (i.e., it reduces optimal reserves relative to baseline at that parameterization).
- Technical setup and first-order condition (borrowing-cost-only case):
  - Opportunity cost: 훿(푅)≣ 푟(푅)−푟∗.
  - Reduced-form specification: 훿(푅)=훿(0)−ɸ ln(1+R/Y), ɸ>0
  - Alternative calibration form: 훿(푅)=푠0−푘 푙표푔(1+푅/푌), with S0 as initial spread and k the spread elasticity.
  - Policy-maker maximizes: (1−휋) u(Y− 훿(푅)푅) + 휋 u(푌−퐿+푅)
  - First-order condition: 휋 u′(푌−퐿+푅) = (1−휋) u′(푌− 훿(푅)푅)[ 훿(푅) + 푅 훿′(푅) ].
  - Normalized (GDP = 1) marginal expressions:
    - Marginal cost: MC = ρ + S0 – k log (1+R/Y) – (k(푅/푌)/ 1+(푅/푌))
    - Marginal benefit: MB = (휋/1−휋) (∆퐶/ 푅)
    - Implicit equation F(R) set and solved numerically with no closed-form solution.
  - Calibration notes:
    - Spread elasticity typical for an EM at 5.75
    - GDP normalized at 1
    - Fix ∆퐶, S0, and Ρ at baseline levels for numerical iteration.

### D. Extension 2 — Reserves and Dollarization
- Mechanism:
  - Private-sector dollarization leads agents to hold FX as self-insurance, creating currency mismatches and amplified vulnerabilities.
  - Public reserves and private FX holdings act as partial substitutes; higher reserves can reduce private dollarization and mitigate crisis severity.
  - Model representation: crisis losses depend on reserves via dollarization, ΔC(R) = ΔC(D(R)), where D(R) declines with R.
- Quantitative impacts for Georgia:
  - Incorporating dollarization raises optimal reserve holdings by about 18 percent of ARA at a 10 percent crisis probability.
  - The dollarization channel becomes dominant at reserve levels below 100 percent of ARA.
- Technical specification:
  - Degree of private dollarization D(R) ∈ [0,1], with D′(R) < 0.
  - Crisis losses: ∆퐶(퐷) with ∆퐶′(퐷) > 0, hence ∆퐶(푅) = ∆퐶(퐷(푅)).
  - Social planner welfare (with dollarization lowering opportunity cost):
    - W(R) = - 1(-휋) (ρ+δ)R − 휋 ∆퐶(퐷(푅))
  - First-order condition (marginal condition rewritten):
    - 휋
      1−휋
      ∆퐶 (R)
      R
      = ρ+δ −
      휋
      1−휋
      ∆퐶′ (D) D′(R)
- Functional forms and parameters used in calibration:
  - D(R) = 퐷̅ − 휂 log (1+R), 휂>0
  - 퐷̅ = 0.6 (baseline private dollarization)
  - 휂 = 0.10 (reserve responsiveness)
  - Crisis loss amplification: ∆퐶(퐷) = 훥푐̅̅̅ (1+ 휆퐷)
  - 훥푐̅̅̅ =10푝푒푟푒푛푡표푓퐺퐷푃 (푏푎푠푒푙푖푛푒퐺퐷푃푙표푠푠)
  - 휆 = 0.5 (dollarization amplification parameter)
  - Dollarization term contribution to FOC: δD(R) = 휋
                                                   1−휋
                                                   휆 훥푐̅̅̅
                                                   휂
                                                   1+R

### E. Extension 3 — Reserves and FX Intervention (FXI)
- Mechanism:
  - FXI to smooth excessive exchange rate volatility in shallow FX markets may require additional “working liquidity” above precautionary reserves.
- Empirical context:
  - A 2024 episode deploying FXI before parliamentary elections led to a drawdown of around USD 750 million, approximately 10 percent of the ARA metric.
- Model simulation summary (Chen and others, 2023 framework, estimated on Georgian data 2005–2024):
  - Simulated 10,000 times over a 20-year period with and without FXI and compared reserve drawdowns.
  - FXI may require additional reserves of up to 10 percent of the ARA metric as working liquidity to smooth exchange rate volatility.
  - Caveat: this estimate may partly double-count shocks already captured in broader models; treat as an upper bound.

### F. Combined Model Implementation and Numerical Approach
- The integrated model combines:
  - Lower borrowing costs from higher reserves (spread compression via k and log(1+R/Y))
  - Reduced crisis GDP losses via lower private dollarization D(R)
  - A decline in the effective opportunity cost due to both channels.
- Calibration and solution approach:
  - Endogenize dollarization channel through lower GDP loss and lower opportunity cost.
  - Re-calibrate numerically for different crisis probability levels using the same parameters as in the borrowing-cost extension.

### G. Conclusions and Policy Options
- Main quantitative conclusion:
  - At a 10 percent crisis probability, the fully extended model implies an optimal reserve range of about 145–150 percent of ARA.
- Current position and implications:
  - Georgia’s current reserve position is cited as 102 percent of ARA (paragraph 13) and appears adequate under moderate stress and broadly in line with the sovereign-risk extension, but below the range suggested under higher-risk scenarios.
  - Reserve composition matters: part of recent increases reflect valuation effects (particularly higher gold prices); some assets may be less liquid or more costly to deploy under stress.
- Policy recommendations:
  - Scope for further opportunistic reserve accumulation to strengthen resilience, particularly amid elevated global uncertainty.
  - The existing price-based framework governing the National Bank of Georgia’s FX purchases appears appropriate to calibrate the pace and scale of accumulation, while retaining flexibility for external conditions.
  - FXI can be used to mitigate large swings from market shallowness but should be used sparingly to allow the exchange rate to function as a shock absorber.

*Source: IMF Selected Issues Paper SIP/2026/051, “Reserve Adequacy in Georgia: How Much is Enough?” (Section 1 and Annex I, sipea2026051).*

### Section 1

### Reserve Adequacy in Georgia: How Much is Enough?

### A. Introduction
- Reserves increased markedly in 2025, recovering to 100 percent of the IMF’s Assessing Reserve Adequacy (ARA) threshold by end-2025, supported by strong services exports, higher gold prices, and de-dollarization.
- Continued reserve accumulation facilitated a successful Eurobond refinancing in early 2026.
- Despite higher energy prices linked to the war in the Middle East and potential current account pressures, the exchange rate remained broadly stable, partly reflecting stronger reserve buffers.
- Abstract summary finding:
  - Optimal reserve coverage estimated at around 145–150 percent of the ARA metric under the fully extended framework, compared to about 130 percent under the baseline framework.
  - Current reserves cited in the paper: 102 percent of ARA (paragraph 13); earlier statements note recovery to 100 percent of ARA by end-2025.

### B. Analytical Framework: Baseline and Extensions
- Baseline framework (Jeanne-Ranciѐre, 2011):
  - Reserves chosen to trade off insurance benefits in crisis states against opportunity costs in normal times.
  - Calibrated to Georgia, the baseline yields an optimal level of around 130 percent of ARA assuming a 10 percent probability of a sudden stop.
  - Key formula elements (as presented):
    - 휌 = 휆 + 훾 − (1 − p^(−1/휎))
    - In reserves-to-output ratio notation: p = 1 + [훿/(휋 (1 − 휹 − 휋))], with 휹 representing the term premium and 휋 the probability of a sudden stop.
- Extension 1 — Reserves and Sovereign Risk Premia:
  - Higher reserves can reduce sovereign borrowing costs by improving perceptions of liquidity and rollover risk.
  - Empirical estimates (literature): a 10-percentage point increase in the reserves-to-GDP ratio can lower EM borrowing costs by around 30-70 basis points.
  - Model implementation: allow opportunity cost of reserves to depend on reserve holdings; effective marginal cost expressed as 훿(푅) + 푅⋅훿′(푅).
  - Quantitative impact for Georgia:
    - Incorporating this channel raises optimal reserves by about 5 percent of ARA at lower crisis probabilities.
    - At a 10 percent crisis probability, the net effect is about 8 percent of ARA lower than the baseline framework (i.e., it reduces optimal reserves relative to baseline at that parameterization).
- Extension 2 — Reserves and Dollarization:
  - Private-sector dollarization leads agents to hold FX as self-insurance, creating currency mismatches and amplified vulnerabilities.
  - Public reserves and private FX holdings act as partial substitutes; higher reserves can reduce private dollarization and mitigate crisis severity.
  - Model representation: crisis losses depend on reserves via dollarization, ΔC(R) = ΔC(D(R)), where D(R) declines with R.
  - Quantitative impact for Georgia:
    - Incorporating dollarization raises optimal reserve holdings by about 18 percent of ARA at a 10 percent crisis probability.
    - The dollarization channel becomes dominant at reserve levels below 100 percent of ARA.
- Extension 3 — Reserves and FX Intervention (FXI):
  - FXI to smooth excessive exchange rate volatility in shallow FX markets may require additional “working liquidity” above precautionary reserves.
  - Empirical context:
    - A 2024 episode deploying FXI before parliamentary elections led to a drawdown of around USD 750 million, approximately 10 percent of the ARA metric.
  - Model simulation (Chen and others, 2023 framework, estimated on Georgian data 2005–2024):
    - Simulated 10,000 times over a 20-year period with and without FXI and compared reserve drawdowns.
    - FXI may require additional reserves of up to 10 percent of the ARA metric as working liquidity to smooth exchange rate volatility.
    - Caveat: this estimate may partly double-count shocks already captured in broader models; treat as an upper bound.

### C. Conclusions and Policy Options
- Main quantitative conclusion:
  - At a 10 percent crisis probability, the fully extended model implies an optimal reserve range of about 145–150 percent of ARA.
- Current position and implications:
  - Georgia’s current reserve position is cited as 102 percent of ARA (paragraph 13) and appears adequate under moderate stress and broadly in line with the sovereign-risk extension, but below the range suggested under higher-risk scenarios.
  - Reserve composition matters: part of recent increases reflect valuation effects (particularly higher gold prices); some assets may be less liquid or more costly to deploy under stress.
- Policy recommendations:
  - Scope for further opportunistic reserve accumulation to strengthen resilience, particularly amid elevated global uncertainty.
  - The existing price-based framework governing the National Bank of Georgia’s FX purchases appears appropriate to calibrate the pace and scale of accumulation, while retaining flexibility for external conditions.
  - FXI can be used to mitigate large swings from market shallowness but should be used sparingly to allow the exchange rate to function as a shock absorber.

*Source: IMF Selected Issues Paper SIP/2026/051, “Reserve Adequacy in Georgia: How Much is Enough?” (Section 1, completed May 19, 2026).*

### Section 2

### Annex I. Technical Details — Borrowing Cost and Dollarization Channels

### Borrowing Cost Channel: setup and functional form
- Return on reserve assets equals the risk-free rate r*; sovereign borrowing rate in international markets is r(R).
- Opportunity cost of reserves: 훿(푅)≣ 푟(푅)−푟∗.
- Sovereign spread reduced by reserves; reduced-form specification:
  - 훿(푅)=훿(0)−ɸ ln(1+R/Y), ɸ>0
  - Alternative reduced-form used for calibration from sovereign spread literature:
    - 훿(푅)=푠0−푘 푙표푔(1+푅/푌)
    - S0 represents the initial spread for Georgia and k the spread elasticity.

- Policy-maker maximizes expected utility:
  - (1−휋) u(Y− 훿(푅)푅) + 휋 u(푌−퐿+푅)
  - 휋: probability of a sudden stop
  - L: output loss in crisis states
  - Preferences: CRRA with coefficient of relative risk aversion 훾.

### First-order condition (borrowing-cost-only case) and marginal terms
- Optimality condition equating marginal insurance benefit to marginal cost:
  - 휋 u′(푌−퐿+푅) = (1−휋) u′(푌− 훿(푅)푅)[ 훿(푅) + 푅 훿′(푅) ].
- Effective marginal cost is decreasing in R because MC = 훿(푅) + 푅 훿′(푅).
- For the reduced calibration (normalized GDP at 1), first-order condition expressed with defined MC and MB:
  - Marginal cost: MC = ρ + S0 – k log (1+R/Y) – (k(푅/푌)/ 1+(푅/푌))
  - Marginal benefit: MB = (휋/1−휋) (∆퐶/ 푅)
  - First-order condition:
    - (휋/1−휋) (∆퐶/ 푅) = ρ + S0 – k log (1+R/Y) − (k(푅/푌)/ 1+(푅/푌))
  - Implicit equation for R:
    - F(R) = (휋/1−휋) (∆퐶/ 푅)  – [ρ + S0 – k log (1+R/Y) – (k(푅/푌)/ 1+(푅/푌)))]
    - No closed-form solution; numerical iteration performed for each crisis probability starting from 1.

- Calibration notes retained from source:
  - Spread elasticity typical for an EM at 5.75
  - GDP normalized at 1
  - Fix ∆퐶, S0, and Ρ at baseline levels for numerical iteration.

### Dollarization Channel: specification and effect on crisis losses and opportunity cost
- Degree of private dollarization D(R) ∈ [0,1], declining with reserves:
  - D′(R) < 0
- Crisis consumption losses increase with dollarization:
  - ∆퐶(퐷) with ∆퐶′(퐷) > 0
  - Therefore ∆퐶(푅) = ∆퐶(퐷(푅))
- Social planner welfare (with dollarization channel lowering opportunity cost):
  - W(R) = - 1(-휋) (ρ+δ)R − 휋 ∆퐶(퐷(푅))
- First-order condition (derivative of W with respect to R):
  - dW / dR = - 1(-휋) (ρ+δ) − 휋 ∆퐶′(퐷′(R)) = 0
  - Rewritten marginal condition:
    - 휋
      1−휋
      ∆퐶 (R)
      R
      = ρ+δ −
      휋
      1−휋
      ∆퐶′ (D) D′(R)

- Incorporating endogenous spread compression (borrowing-cost effects) and dollarization:
  - 휋
    1−휋
    ∆퐶 (R)
    R
    = ρ+δ (R) + R δ′(R) −
    휋
    1−휋
    ∆퐶′ (D) D′(R)
  - Right-hand side: net cost of holding reserves reduced by dollarization benefits and endogenous spread compression.

### Functional forms, parameters, and crisis-loss amplification used in dollarization calibration
- Dollarization functional form:
  - D(R) = 퐷̅ − 휂 log (1+R), 휂>0
  - 퐷̅ = 0.6 (baseline private dollarization)
  - 휂 = 0.10 (reserve responsiveness)
- Crisis loss amplification specification:
  - ∆퐶(퐷) = 훥푐̅̅̅ (1+ 휆퐷)
  - 훥푐̅̅̅ =10푝푒푟푒푛푡표푓퐺퐷푃 (푏푎푠푒푙푖푛푒퐺퐷푃푙표푠푠)
  - 휆 = 0.5 (dollarization amplification parameter)

- Dollarization term contribution to first-order condition:
  - δD(R) = 휋
            1−휋
            휆 훥푐̅̅̅
            휂
            1+R

### Implementation summary and recalibration approach
- The model combines:
  - Lower borrowing costs from higher reserves (spread compression via k and log(1+R/Y))
  - Reduced crisis GDP losses via lower private dollarization D(R)
  - A decline in the effective opportunity cost due to both channels.
- Calibration approach:
  - Use same parameters as in the lower borrowing cost extension, endogenize dollarization channel through lower GDP loss and lower opportunity cost, and re-calibrate for different crisis probability levels numerically.

*Source: sipea2026051 - Section 2*

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_Source: https://www.imf.org/-/media/files/publications/selected-issues-papers/2026/english/sipea2026051.pdf_