## _wp0946

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---

### I. Introduction — objectives and empirical regularities
- Objective: introduce an International Financial Institution (IFI), exemplified by the IMF, into an incomplete-markets sovereign debt model with strategic default on commercial debt to uncover sovereign allocation between private creditors and the IFI and account for cyclical properties of IFI lending.
- Empirical regularities documented:
  - Average correlation of IMF debt flows with output: -0.15.
  - Average correlation of commercial debt flows with output: 0.37.
  - Commercial debt flows are about three times as large as IMF debt flows.
  - Unconditional probability of the use of IMF credit: around 50 percent.
  - All countries in the sample were indebted to private sector creditors at all times.
- Key conceptual elements:
  - “Commercial debt” = debt to private sector creditors; “official debt” = debt to the IFI.
  - Sovereign cannot commit to repay commercial debt (strategic default possible); IFI contracts are enforceable (preferred creditor status).
  - Private creditors: perfectly competitive, risk-neutral; interest rates set by endogenous default probabilities.
  - IFI lending: enforceable repayment; interest rate = risk free rate + charge increasing with IFI borrowing; conditionality captured by a higher sovereign discount factor when indebted to the IFI.

### II. Model mechanisms and quantitative implications
- Sovereign choices and constraints:
  - Sovereign chooses portfolio between commercial debt and IFI debt given output shocks, endogenous default probabilities, and differing creditor contract features.
  - Punishment for default: exclusion from commercial credit markets and direct output losses (output truncated during default: y_def = y if y < ˆy; y_def = ˆy if y > ˆy).
  - IFI lending: higher discount factor while indebted (β(d*') = β_H if d*' > 0; β_L if d*' = 0), interpreted as conditionality → consumption shifted from present to future → lower debt and default probability.
  - Surcharges on IFI loans introduce an interest-rate component increasing with the amount borrowed from the IFI (φ(d*')).
- Quantitative/qualitative outcomes (Argentina calibration):
  - Generates procyclical commercial debt and countercyclical IFI debt.
  - Good times: sovereign borrows more commercially at relatively lower rates, with lower default probability and without IFI costs.
  - Bad times: sovereign reallocates toward IFI borrowing to avoid high private creditor premia.
  - Sovereign default probability increases with both commercial debt and official (IFI) debt.
    - Two opposing IFI effects on default probability:
      1. Higher current IFI debt → higher total debt service next period → higher incentive to default on commercial debt (increasing default probability).
      2. Positive IFI debt → higher discount factor → more prudent behavior (lower default probability).
    - Quantitative finding: the first effect dominates, producing higher country spreads when indebted to the IFI versus when not.
  - Elasticities:
    - Elasticity of interest rates to official debt is lower than to commercial debt.
    - Higher commercial debt more directly increases default probability; higher official debt increases next period debt service and default risk via a less direct channel.

### III. IMF lending institutional details (SBAs) — rates, fees, thresholds
- SBA institutional features:
  - Borrowing up to 25 percent of quota: essentially no conditionality.
  - Any amount beyond 25 percent of quota requires a policy program (letter of intent / IMF arrangement).
  - SBAs usually last 4-6 quarters with repayment in 3-5 years (General Resources Account).
- Components of SBA interest rate and fees:
  - SDR interest rate: weighted average of 3-month U.S. T-bill rate, 3-month UK T-bill rate, Japanese Government 13-week financing bills, and 3-month Eurepo rate.
  - Margin:
    - Average margin from May 1993-September 2008: 62 bps.
    - Margin is currently set at 100 bps.
    - Margin was negative for 1981-May 1993 (imputed negative).
  - Burden sharing adjustment:
    - Average from May 1986-September 2008: 19 bps.
    - Currently set at 2 bps.
  - Service fee: 50 bps charged at disbursement.
  - Commitment fee:
    - 25 bps for loans up to the country’s quota.
    - 10 bps for loans in excess of the quota.
  - Surcharges (SBAs):
    - 100 bps apply to portion greater than 200 percent of quota.
    - 200 bps for portion greater than 300 percent.
- Adjusted rate of charge = SDR interest rate + margin + burden sharing adjustment.
  - Adjusted rate of charge averages comparable to yield on 3-year U.S. government bonds.
  - Adjusted rate and fees do not vary across countries; only surcharges vary by loan size relative to quota.

### IV. Conditionality, discounting, and modeling choices
- Conditionality modeled:
  - Captured via a higher sovereign discount factor when indebted to the IFI (β_H when d*' > 0).
  - Sovereign endogenously chooses to be indebted to IFI and thereby selects more patient/aligned behavior while indebted.
- Abstracted elements:
  - No informational or catalytic role of IMF programs (no signaling or catalytic effects modeled).
  - IFI lends during exclusion from capital markets and serves as alternative funding to avoid high private interest rates in bad times.

### V. Data and documented cyclical properties (sample and summary statistics)
- Sample selection: countries chosen based on quarterly GDP data availability and IMF program participation in the last two decades.
- Key empirical statistics:
  - Commercial debt flows (World Bank Global Development Finance Database):
    - Average correlation of net private lending with real output: 0.37 (range: 0.14 (Peru) to 0.62 (Thailand and Turkey)).
    - Average standard deviation of commercial lending: 3.71.
  - IMF debt flows:
    - Average correlation with output: -0.15.
    - Standard deviation of IMF debt flows: 1.22.
    - Commercial debt flows about three times more variable than IMF debt flows.
  - Mean debt ratios:
    - Mean debt to the IMF reported as 6 percent; private sector creditor debt reported as 16 percent (note: IMF debt ratios use quarterly GDP whereas private sector creditor debt uses annual GDP, implying IMF debt comparable with the 16 percent private sector creditor debt would be around 1.6 percent).
    - On average, IMF debt is around one tenth of private sector creditor debt.
  - IMF countercyclicality holds for all countries except Thailand (Thailand’s average IMF debt to GDP ratio = 0.14 percent for 1993-2006 when quarterly data available).
- Country spreads and IMF borrowing (J.P. Morgan’s EMBI Global spreads from Bloomberg):
  - Mexico and Thailand:
    - Average spreads when using Fund resources: Mexico: 617 bps (199); Thailand: 199 bps (199).
    - Average spreads when not using Fund resources: Mexico: 242 bps; Thailand: 61 bps.
    - Median spreads when indebted to IMF: Mexico: 488 bps; Thailand: 163 bps.
    - Median spreads when not indebted to IMF: Mexico: 214 bps; Thailand: 58 bps.
  - Correlation between spreads and IMF-indebtedness dummy: positive for all countries except Ecuador; average correlation = 0.48.
  - Mody and Saravia (2006) comparison: spreads during IMF programs = 406; spreads without programs = 223.
- Usage probabilities and repayment patterns:
  - Probability of positive use of IMF resources Pr[d* > 0]:
    - 46 percent for 1945-2007 (initial sample of 9 emerging market economies).
    - 55 percent for 1970-2007 when expanded to 17 emerging market economies.
  - Historical repayment: IMF loans to major emerging market economies have essentially been repaid; protracted arrears concentrated in a limited set of countries.

### VI. Model: actors, timing, solution method, and calibration
- Agents and timing:
  - Competitive, risk-neutral private creditors; single non-profit IFI; sovereign maximizing household utility.
  - Sovereign each period chooses default (D) or non-default (N) with associated decisions on borrowing from IFI.
  - Default leads to exclusion from commercial markets for stochastic duration (θ probability of reentry).
- Pricing and budget constraints:
  - IFI lending price q*(d*') = 1 / [1 + r + φ(d*')]; IFI debt non-defaultable.
  - Private sector pricing q(d', d*', y) = [1 − E[λ(d', d*', y)]] / (1 + r).
  - Value functions specified: V(d, d*, y) = max_D { V^D(d*, y), V^N(d, d*, y) }; u(c) = c^{1−σ}/(1−σ).
- Quantitative solution method:
  - State space discretization: commercial debt stationary distribution in [0.30, 0.82] with d = 0 in default periods; IFI debt spans [0, 0.14].
  - Iterative algorithm: conjecture q_old, solve sovereign problem by value function iteration, compute default probabilities, update q_new, iterate until convergence max|q_old − q_new| < ξ.
- Calibration targets and parameter choices:
  - Redemption probability set to 10 percent → average exclusion = 10 periods (2.5 years quarterly).
  - Output AR(1) estimated from Argentine quarterly GDP (1980Q1-2000Q4): ρ = 0.91; σ_z = 0.019; 9-state Markov via Tauchen.
  - φ(d*') assumed linear: φ(d*') = k d*'; k set to match mean IFI debt.
  - β_L and ˆy set to match default frequency; β_H set to match probability of IMF credit use.
  - Defaults counted using Reinhart, Rogoff, and Savastano (2003) plus 2001 default → 5 defaults in 183 years ≈ 70 defaults per 10,000 quarters.

### VII. Quantitative findings, comparative statics, and fit
- Main quantitative findings:
  - Two opposing channels of IFI debt on commercial default: higher future IFI debt service raises default incentives; higher discount factor while indebted to IFI reduces default incentives. The former dominates quantitatively → higher commercial spreads when indebted to IFI.
  - Price schedule steep: small increases in d' drive significant interest rate increases.
  - Introducing two discount factors yields a fixed cost-like effect: small positive d* almost never optimal → lumpiness in IFI borrowing.
- Empirical fit (selected moments):
  - σ(∆d*/y): model = 2.98 percent; data = 1.34.
  - ρ(∆d*/y, y): model = −0.07; data mean = −0.15.
  - ρ(Id* > 0, s): model = 0.25; data = 0.22.
  - E[d*]: model = 3.27; data E[d*] = 3.36.
  - σ(y): data = 4.32; model = 4.42.
  - σ(∆d/y)A: data = 2.87; model = 2.93.
  - ρ(∆d/y, y)A: data = 0.32; model = 0.28.
  - ρ(s, y): data = −0.59; model = −0.27.
  - No. of defaults: data = 70; model = 69.8.
  - Pr(d* > 0): data = 0.62; model = 0.65.
- Countercyclicality and spreads:
  - Model correlations: ρ(∆d/y, y) = 0.28; ρ(∆d*/y, y) = −0.07.
  - In model, spreads when d* > 0 are 2.8 times spreads when d* = 0; data ratios: Mexico = 2.55; Thailand = 3.25.
  - Argentina in model: E[s | d* > 0] = 2100 bps (driven by outliers).
  - Median spreads ratio in data (d* > 0 vs d* = 0) = 2.32.
- Patterns across regimes:
  - E[d*] when s < 25 pct: data = 1.96; model = 2.98.
  - E[d*] when s > 75 pct: data = 2.05; model = 3.04.
  - E[d*] during default: data = 7.97; model = 7.52.
  - E[d*] when y < −σy (busts): data = 8.55; model = 5.79.
  - E[d*] when y > +σy (booms): data = 1.53; model = 0.83.
- Sensitivity (selected scenarios vs baseline):
  - Baseline Pr(d* > 0) = 0.65; No conditionality Pr(d* > 0) = 0.90; High conditionality Pr(d* > 0) = 0.58; k = 1.43 Pr(d* > 0) = 0.53; k = 1.41 Pr(d* > 0) = 0.68.
  - E[d*] baseline = 3.27; no conditionality = 3.55; high conditionality = 2.96; k = 1.43 = 2.81; k = 1.41 = 3.37.
  - No. of defaults: baseline = 69.8; no conditionality = 69.0; high conditionality = 73.0; k = 1.43 = 60.6; k = 1.41 = 73.4.
- Robustness:
  - Main qualitative results (weak countercyclicality of IFI debt flows and higher spreads when indebted to the IFI) are robust across parameter variations.

### VIII. Conclusion and policy implications
- Framework explains sovereign decisions to default and to allocate borrowing between commercial creditors and IFIs, capturing observed cyclical differences.
- Modeled IFI features critical for results:
  - IFI interest rate largely independent of sovereign risk (depends on loan size via φ(d*')).
  - Higher implied discount factor while indebted to the IFI (conditionality) that induces more prudent behavior.
- Policy relevance:
  - Framework useful to analyze design of IMF lending facilities (e.g., SBAs vs other short-term lending) and to study dynamics and normative questions about IMF lending demand and relevance.

*Source: _wp0946 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   20*

### References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   20

### _wp0946 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   20

### I. Introduction — objectives and empirical regularities
- Objective: introduce an International Financial Institution (IFI), exemplified by the IMF, into an incomplete-markets sovereign debt model with strategic default on commercial debt to uncover sovereign allocation between private creditors and the IFI and account for cyclical properties of IFI lending.
- Key empirical regularities documented:
  - Average correlation of IMF debt flows with output for a group of emerging market economies: -0.15.
  - Average correlation of commercial debt flows with output: 0.37.
  - Variability: commercial debt flows are about three times as large as IMF debt flows.
  - Unconditional probability of the use of IMF credit: around 50 percent.
  - All countries in the sample were indebted to private sector creditors at all times.
- Conceptual elements introduced:
  - “Commercial debt” refers to debt to private sector creditors; “official debt” refers to debt to the IFI.
  - Sovereign cannot commit to repay commercial debt (strategic default is possible); contracts with the IFI are enforceable (preferred creditor status).
  - Private sector creditors: perfectly competitive, risk-neutral; interest rates determined by endogenous default probabilities.
  - IFI lending characteristics modeled: enforceable repayment, interest rate = risk free rate + charge increasing with IFI borrowing, conditionality captured by a higher sovereign discount factor when indebted to the IFI.

### II. Model mechanisms and quantitative implications
- Model ingredients and mechanisms:
  - Sovereign chooses portfolio between commercial debt and IFI debt given output shocks, endogenous default probabilities, and different contract features across creditors.
  - Punishment for default: exclusion from commercial credit markets and direct output losses.
  - IFI lending: higher discount factor while indebted (interpreted as conditionality → consumption shifted from present to future → lower debt and default probability).
  - Surcharges on IFI loans introduce an interest-rate component increasing with the amount borrowed from the IFI.
- Quantitative/qualitative model outcomes (calibrated to Argentina as representative emerging market):
  - Generates procyclical commercial debt and countercyclical IFI debt.
  - In good times: sovereign borrows more commercially at relatively lower rates, with lower default probability and without IFI costs.
  - In bad times: sovereign reallocates toward IFI borrowing to avoid high risk premia from private creditors.
  - Sovereign default probability increases with both commercial debt and official (IFI) debt.
    - Two opposing effects of higher IFI debt on default probability:
      1. Higher current IFI debt → higher total debt service next period → higher incentive to default on commercial debt to avoid low consumption (increasing default probability).
      2. Positive IFI debt → higher discount factor → more prudent behavior → lower default probability.
    - Quantitative finding: the first effect dominates, producing higher country spreads when indebted to the IFI versus when not.
  - Elasticities:
    - Elasticity of interest rates to official debt is lower than to commercial debt.
    - Higher commercial debt more directly increases default probability (benefit of default is forgiven commercial debt).
    - Higher official debt increases next period debt service and default risk via a less direct channel.

### III. IMF lending institutional details (SBAs) — rates, fees, thresholds
- IMF lending context: provides temporary financing to members with balance of payments difficulties; lending involves conditionality aimed at enabling timely repayment.
- SBA institutional features and thresholds:
  - Borrowing up to 25 percent of quota: essentially no conditionality.
  - Any amount beyond 25 percent of quota requires a policy program (letter of intent / IMF arrangement).
  - SBAs usually last 4-6 quarters with repayment in 3-5 years (General Resources Account).
- Components of SBA interest rate and fees:
  - SDR interest rate: weighted average of 3-month U.S. T-bill rate, 3-month UK T-bill rate, Japanese Government 13-week financing bills, and 3-month Eurepo rate.
  - Margin: covers IMF intermediation costs and builds reserves against credit risk.
    - Average margin from May 1993-September 2008: 62 bps.
    - Margin is currently set at 100 bps.
    - Note: margin was negative for 1981-May 1993 (imputed negative).
  - Burden sharing adjustment: covers losses due to overdue obligations; refunded as overdue obligations are repaid.
    - Average burden sharing adjustment from May 1986-September 2008: 19 bps.
    - Currently set at 2 bps.
  - Service fee: 50 bps charged at disbursement to cover intermediation costs.
  - Commitment fee: collected but refunded as loans are withdrawn.
    - Commitment fee: 25 bps for loans up to the country’s quota; 10 bps for loans in excess of the quota.
  - Surcharges (SBAs): 100 bps apply to portion greater than 200 percent of quota; 200 bps for portion greater than 300 percent.
- Adjusted rate of charge = SDR interest rate + margin + burden sharing adjustment.
  - Adjusted rate of charge averages are comparable to yield on 3-year U.S. government bonds (consistent with repayment within 3-5 years and SDR composition).
  - Adjusted rate of charge and the fees do not vary across countries; only surcharges are country/loan-size dependent (determined by loan size relative to quota, not sovereign risk).

### IV. Conditionality, discounting, and modeling choices
- Conditionality:
  - IMF program conditionality covers macroeconomic stabilization, monetary, fiscal, and exchange rate policies, institutional arrangements, and financial system issues.
  - IMF (2002a) core areas quoted; IMF (2002b) structural measure composition (1994-1999): fiscal sector 34 percent; financial sector 16 percent; privatization 14 percent.
- Modeling conditionality:
  - Captured via a higher sovereign discount factor when indebted to the IFI (sovereign behaves as a more patient/aligned type).
  - Difference from other literature: sovereign endogenously chooses to be indebted to IFI and thereby effectively selects the more patient/aligned behavior while indebted (no exogenous stochastic alternation of government types).
- Abstracted elements:
  - The model abstracts from any informational or catalytic role of IMF programs (no signaling or catalytic effects modeled).
  - IFI lends during exclusion from capital markets and serves as alternative funding to avoid high private interest rates in bad times.

### V. Relation to literature and contributions
- Builds on Eaton and Gersovitz (1981) framework and recent quantitative sovereign default extensions (Arellano (2008); Aguiar and Gopinath (2006); Yue (2005)).
- Distinct contributions:
  - Explicitly models an IFI (IMF) as a lender with enforceable contracts, surcharges, and conditionality-induced discounting rather than modeling external bailouts as grants or implicit third-party interventions.
  - Matches observed countercyclical IFI lending and procyclical commercial lending in calibrated model.
  - Demonstrates that being indebted to the IFI can be associated with higher country spreads because the higher debt-service channel dominates the prudence/conditionality channel.
- Comparisons with related extensions:
  - Alfaro and Kanczuk (2007): introduce international reserves; their model often implies zero reserve accumulation due to discounting assumptions, while current paper models sovereign as net IFI debtor allowing a stationary distribution of official debt.
  - Literature on “patient vs. impatient” governments (Cole et al. (1995), Alfaro and Kanczuk (2005), Hatchondo et al. (2007), D’Erasmo (2008)): current modeling of conditionality parallels using different discount factors but differs because the sovereign endogenously chooses indebtedness to the IFI.
- Catalytic role debate:
  - Empirical evidence cited: Cottarelli and Giannini (2002) and Ghosh et al. (2002) find little increase in private sector flows after IMF assistance; Mody and Saravia (2006) find catalytic role depends on likelihood of policy adjustments.
  - Theoretical results (Morris and Shin (2006); Corsetti, Guimaraes, and Roubini (2006)) analyze catalytic conditions using global games.
  - Jeanne and Zettelmeyer (2004) examine IMF effects on debtor moral hazard.
  - This paper abstracts from catalytic effects; IFI modeled as alternative funding during exclusion without signaling.

### VI. Data and documented cyclical properties (sample and summary statistics)
- Data sample selection: countries chosen based on quarterly GDP data availability and IMF program participation in the last two decades.
- Commercial debt flows (annual, World Bank Global Development Finance Database; includes bonds, commercial banks, other debt to private creditors):
  - Average correlation of net lending by private sector creditors with real output: 0.37 (positive for all sample countries; range: 0.14 (Peru) to 0.62 (Thailand and Turkey)).
  - Average standard deviation of commercial lending: 3.71, with Thailand as an outlier (standard deviation not fully reported in excerpt).
- IMF debt flows:
  - Average correlation with output: -0.15 (countercyclical).
  - Variability substantially lower than commercial debt flows (commercial about three times more variable).
  - Unconditional probability of IMF credit use: around 50 percent (countries do not borrow from IMF at all times).
- Tables and figures referenced (contents summarized in paper; specific numeric table values not fully reproduced in excerpt):
  - Tables listed: Average interest rates; Data Moments: Private Sector Creditor Lending; Data Moments: IMF Lending; Spreads and Use of IMF Credit; Probability of Use of IMF Credit; Parameters; Business Cycle Statistics; IFI Debt During High and Low Spreads; IFI Debt During Booms and Busts; Sensitivity.
  - Figures listed: IMF Interest Rates vs U.S. Government Bond Yields; Commercial Debt Price Schedule, q(d′, d∗′, y); Stationary Bond Distributions for the Simple SOE Model.
- Note on causality: authors establish correlation but not causality between commercial spreads and IFI lending; negative endowment shocks are the modeled underlying driver of both higher commercial spreads and higher IFI lending in the model.

_Italic line: Source: _wp0946 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   20_

### 10.10 percent. Finally, commercial debt stock is around 15 percent of annual GDP on

### _wp0946 - 10.10 percent. Finally, commercial debt stock is around 15 percent of annual GDP on

### Empirical patterns: magnitudes and cyclicalities
- "10.10 percent." Finally, commercial debt stock is around 15 percent of annual GDP on average.
- IMF lending is countercyclical with an average correlation of -0.15 with output.
- Using quarterly IMF credit data from International Financial Statistics (IFS), countercyclicality holds for all countries except Thailand (0.18).
  - Thailand’s average IMF debt to GDP ratio was 0.14 percent in the period for which quarterly GDP data are available (1993-2006).
- Standard deviation of debt flows:
  - IMF debt flows: 1.22
  - Commercial (private sector) debt flows: 3.71
- Mean debt ratios:
  - Mean debt to the IMF reported as 6 percent (note: text asserts "mean debt to the IMF is lower than that to the private sector creditors (16 vs. 6 percent)"; IMF debt ratios use quarterly GDP whereas private sector creditor debt uses annual GDP, implying IMF debt comparable with the 16 percent private sector creditor debt would be around 1.6 percent).
  - Therefore, on average, IMF debt is around one tenth of private sector creditor debt.

### Country spreads and IMF borrowing
- Data source: J.P. Morgan’s EMBI Global spread data from Bloomberg.
- For Mexico and Thailand (the only countries with significant numbers of periods with and without IMF use in the available EMBI sample):
  - Spreads in periods with use of Fund credit are about 3 times the spreads in periods without Fund credit.
  - Average spreads when using Fund resources:
    - Mexico: 617 bps (199)
    - Thailand: 199 bps (199) — (text shows "617 (199) bps when Mexico (Thailand) was using Fund resources" and later "while the average spreads were 242 (61) bps when it was not.")
  - Average spreads when not using Fund resources:
    - Mexico: 242 bps
    - Thailand: 61 bps
  - Median spreads when indebted to IMF:
    - Mexico: 488 bps
    - Thailand: 163 bps
  - Median spreads when not indebted to IMF:
    - Mexico: 214 bps
    - Thailand: 58 bps
- Correlation between spreads and an IMF-indebtedness dummy:
  - Positive for all countries in the sample except Ecuador.
  - Average correlation reported as 0.48.
- Comparison to Mody and Saravia (2006):
  - Their calculations: spreads during IMF programs were 406, while they were 223 in the absence of programs.

### Largely episodic IMF lending; usage probabilities and repayment patterns
- IMF borrowing displays lumpiness: spikes after entering an arrangement, with nested periods of no borrowing.
- Probability of positive use of IMF resources (Pr[d* > 0]) — unconditional probabilities:
  - 46 percent for 1945-2007 (sample of 9 emerging market economies as initial sample).
  - 55 percent for 1970-2007 when sample expanded to 17 emerging market economies (additional countries: Chile, Colombia, Egypt, India, Korea, Malaysia, Singapore, and Venezuela).
  - Note: probabilities are higher for the original sample of 9 countries (selection bias due to choosing countries with significant IMF borrowing).
- Historical repayment:
  - Essentially, all IMF loans to major emerging market economies have been repaid.
  - Zettelmeyer (2005): historically IMF has virtually always been repaid; possibility remains that open lending relationships may eventually result in arrears or debt forgiveness.
  - Jeanne and Zettelmeyer (2001): most open lending relationships with emerging market countries are statistically similar to past lending cycles that eventually ended in repayment.
  - Eichengreen (2003) and Saravia (2004): IMF loans are typically repaid; only during the 1980s debt crises was there an increase in non-repayment cases.
  - Zettelmeyer (2005): 13 countries in protracted arrears to the IMF (Cambodia, Guyana, Haiti, Honduras, Liberia, Panama, Peru, Sierra Leone, Somalia, Sudan, Vietnam, Zaire, and Zambia); most have repaid and Peru repaid (only emerging market among these).

### Section summary (textual bullets as in source)
- The IMF lending rate under SBAs can be approximated by the sum of the risk free rate and a charge that increases with the amount borrowed.
- Lending by private sector creditors is procyclical whereas IMF lending is countercyclical.
- Debt to the private sector creditors is about three times more variable than that to the IMF.
- The average debt stock to the IMF is about one tenth of the debt to private sector creditors.
- Country spreads are higher in periods when countries are indebted to the IMF.
- The unconditional probability of the use of IMF resources is about 50 percent for emerging markets.
- IMF has almost always been repaid particularly by emerging market economies.

### Model: actors, timing, and strategic considerations
- Agents:
  - Competitive, risk-neutral private sector creditors.
  - An IFI (single non-profit international financial institution).
  - A sovereign maximizing household utility.
- Sovereign states each period: default (D) or non-default (N) vis-a-vis private sector creditors.
  - If in N, sovereign observes output, decides whether to default and whether to borrow from the IFI.
  - If defaults, it does not repay existing commercial debt and loses access to commercial borrowing for a stochastic, exogenously determined period.
  - During exclusion, the sovereign can still borrow from the IFI.
- IFI lending terms:
  - IFI lends at the risk free rate plus a debt-elastic component capturing IMF surcharges.
  - IFI debt is non-defaultable (preferred creditor status); sovereign does not face a commitment problem repaying IFI.
- Role of IFI: provides an instrument to smooth consumption, especially when commercial default probability is high or when sovereign is excluded from commercial markets.
- Sovereign's choice rule (value function):
  - V(d, d*, y) = max_D { V^D(d*, y), V^N(d, d*, y) }
  - Default chosen iff V^D > V^N.
- Value of default:
  - V^D(d*, y) = max_{d*'} { u(c) + β(d*') Σ_{y'} [ θ V(0, d*', y') + (1−θ) V^D(d*', y') ] π(y'|y) }
  - u(c) = c^{1−σ}/(1−σ)
  - θ: exogenously determined probability of entry back to credit market after default (average duration of exclusion).
  - Budget constraint during exclusion: y_def = c + d* − q* d*'
  - q*(d*') = 1 / [1 + r + φ(d*')]
- Output process:
  - y = e^z, z_t = ρ z_{t−1} + ε_t, ε ∼ N(0, σ_z^2)
  - AR(1) approximated by Markov chain with S states and transition matrix π.
  - Output truncated during default: y_def = y if y < ˆy; y_def = ˆy if y > ˆy (direct output cost of default increases with output).
- Non-default value:
  - V^N(d, d*, y) = max_{d', d*'} { u(c) + β(d*') Σ_{y'} V(d', d*', y') π(y'|y) }
  - Budget constraint: c = y − d + q d' − d* + q* d*'
- Private sector pricing:
  - q(d', d*', y) = [1 − E[λ(d', d*', y)]] / (1 + r)
  - Spread s = 1/q − 1 − r
- Conditionality modeling:
  - Sovereign faces a higher discount factor (lower discount rate) while indebted to IFI to capture conditionality and the empirical regularity of non-permanent IMF borrowing.
  - β(d*') = β_H if d*' > 0; β_L if d*' = 0
- Competitive equilibrium conditions:
  1. Sovereign maximizes utility taking prices as given.
  2. Given implied default probabilities, private creditors lend at q(d', d*', y) and IFI lends at q*(d*').
  3. Goods market clears.

### Quantitative solution method
- State space discretization:
  - Commercial debt stationary distribution in [0.30, 0.82]; impose d = 0 in default periods and place (NB−1) equally spaced nodes in [0.30, 0.82], concatenate with d_NB = 0.
  - IFI debt state space spans [0, 0.14].
- Algorithm to find equilibrium:
  1. Discretize state space.
  2. Conjecture private sector price schedule q_old(d', d*', y) = 1/(1 + r).
  3. Solve sovereign’s problem by value function iteration taking q_old and q* as given to obtain D(d, d*, y), policy functions d'(·), d*'(·), and c(·).
  4. Compute default probability λ(d', d*', y).
  5. Compute q_new(d', d*', y) = [1 − E[λ(d', d*', y)]] / (1 + r).
  6. Update q_old as weighted average of q_old and q_new; iterate until max|q_old − q_new| < ξ (ξ very small).
- Note: computation of q* does not require a fixed point; for given φ(d*') evaluate q*(d*') and plug into sovereign budget.

### Calibration, data, and targeted moments
- Parameters: three sets — those from sovereign debt literature, estimated from data, and calibrated to match model statistics. (All parameters reported in Table 6 in source.)
- Redemption probability: set to 10 percent implying average exclusion of 10 periods (2.5 years with quarterly calibration).
- Output process estimation:
  - Estimated from quarterly Argentine GDP for 1980Q1-2000Q4 (Neumeyer and Perri (2005)).
  - Series deseasonalized, logged, HP filtered with smoothing parameter 1600.
  - AR(1) estimates: ρ = 0.91; σ_z = 0.019.
  - Markov process with 9 states via Tauchen’s algorithm.
- Parameters set to match default frequency and mean IFI debt and IMF credit usage probability:
  - β_L and ˆy set to match default frequency.
  - φ(d*') assumed linear: φ(d*') = k d*' ; k set to match mean IFI debt.
  - β_H set to match probability of use of IMF credit.
- Data treatment: private sector creditor debt is annual; simulated private borrowing statistics are annualized for comparison. Defaults counted using Reinhart, Rogoff, and Savastano (2003) plus 2001 default, yielding 5 defaults in 183 years ≈ 70 defaults per 10,000 quarters.

### Quantitative findings and comparative statics
- Standard sovereign debt model forces persist: high commercial debt strengthens incentives to default; high output strengthens repayment incentives.
- In two-creditor setting:
  - Default probability on commercial debt increases with the level of IFI debt, but less steeply than with commercial debt.
  - Price schedule is steep: small increases in d' drive significant interest rate increases.
  - IFI debt affects commercial default probability via two opposing channels:
    1. Higher IFI debt raises future IFI debt service, reducing resources to repay commercial debt → raises commercial default probability.
    2. Positive IFI debt induces a higher discount factor (β_H) → more prudent behavior, lowering default probability.
  - Quantitatively, the first effect dominates: commercial interest rates increase with IFI debt.

*Italic: Source document content as provided from the IMF PDF unit.*

### Introduction of two different discount factors generates a fixed cost-like effect making it

### Introduction of two different discount factors generates a fixed cost-like effect making it

### Model mechanism and key intuition
- Introducing two discount factors (a low and a relatively high discount factor when indebted to an IFI) generates a fixed cost-like effect: when output is not low the sovereign prefers d* = 0 keeping the discount factor low; when output is low the sovereign chooses relatively high values of d*.
- As a consequence, small but positive values for d* are almost never optimal, producing lumpiness in IFI borrowing and matching the probability of Fund credit use in the data.
- The fixed cost-like effect is confirmed in a stripped-down small open economy consumption-savings model (Appendix): with β(b) = {βH if b < 0; βL if b = 0} and a constant interest rate, bond positions in [−0.04, 0] are almost never chosen in the calibrated example.

### Empirical fit: non-target moments and aggregate statistics
- Model matches non-target moments related to IFI borrowing (with some exceptions):
  - σ(∆d*/y) generated by the model = 2.98 percent; data = 1.34.
  - ρ(∆d*/y, y) in model = −0.07; data mean reported = −0.15.
  - ρ(Id* > 0, s) in model = 0.25; data = 0.22.
- Commercial debt-related statistics also well matched by the model (see Table 7 comparisons):
  - E[d*] model = 3.27; data E[d*] = 3.36.
  - σ(y) data = 4.32; model = 4.42.
  - σ(∆d/y)A data = 2.87; model = 2.93.
  - ρ(∆d/y, y)A data = 0.32; model = 0.28.
  - ρ(s, y) data = −0.59; model = −0.27.
  - No. of defaults data = 70; model = 69.8.
  - Pr(d* > 0) data = 0.62; model = 0.65.

### Countercyclicality of IFI debt and spreads
- Weak countercyclicality of IFI debt arises because the IFI interest rate is decoupled from default probability and output shocks:
  - Sovereign reallocates toward IFI debt in bad times because commercial borrowing costs increase with negative shocks while IFI cost does not.
  - Measured correlations: ρ(∆d/y, y) = 0.28 and ρ(∆d*/y, y) = −0.07 (model).
- Result persists under ‘no conditionality’ suggesting inelasticity of IFI interest rate to output shocks and commercial debt levels is central.
- Spreads and IFI borrowing:
  - In model, spreads in periods with d* > 0 are 2.8 times those when d* = 0.
  - Data ratios for Mexico and Thailand: 2.55 and 3.25, respectively.
  - For Argentina, E[s | d* > 0] = 2100 bps (driven by a few outliers).
  - Ratio of median spreads conditional on being and not being indebted to the IMF in data = 2.32.
- Portfolio composition: replacing commercial debt with IFI debt (for given total debt) lowers spreads because interest rates are more elastic to commercial debt than to IFI debt; however, switching to IFI debt does not suffice to reduce spreads overall since any debt raises interest rates.

### Patterns across regimes (high/low spreads, booms/busts)
- IFI debt during spreads and default (Table 8):
  - E[d*] when s < 25 pct: data = 1.96; model = 2.98.
  - E[d*] when s > 75 pct: data = 2.05; model = 3.04.
  - E[d*] during default: data = 7.97; model = 7.52.
- IFI debt during booms and busts (Table 9):
  - E[d*] when y < −σy (busts): data = 8.55; model = 5.79.
  - E[d*] when y > +σy (booms): data = 1.53; model = 0.83.
- Model tends to generate higher variability in trade balance and IFI debt flows than the data, partly because the two-discount-factor specification produces few small positive d* realizations (more pronounced lumpiness in the model than in the data).

### Sensitivity analysis (conditionality and k)
- Scenarios examined: baseline; no conditionality (βH = βL = 0.884); higher conditionality; higher k (k = 1.43); lower k (k = 1.41).
- Key outcomes reported in Table 10 (selected comparisons vs baseline):
  - Baseline Pr(d* > 0) = 0.65; No conditionality Pr(d* > 0) = 0.90; High conditionality Pr(d* > 0) = 0.58; k = 1.43 Pr(d* > 0) = 0.53; k = 1.41 Pr(d* > 0) = 0.68.
  - E[d*] baseline = 3.27; no conditionality = 3.55; high conditionality = 2.96; k = 1.43 = 2.81; k = 1.41 = 3.37.
  - σ(∆d*/y) baseline = 2.98; no conditionality = 2.81; high conditionality = 3.11; k = 1.43 = 2.69; k = 1.41 = 2.92.
  - No. of defaults: baseline = 69.8; no conditionality = 69.0; high conditionality = 73.0; k = 1.43 = 60.6; k = 1.41 = 73.4.
- Interpretation:
  - Removing conditionality increases average official debt holdings (E[d]A rises from 12.38 to 12.57) and raises frequency of d* > 0 (65 percent to 90 percent), reducing variability of IFI flows.
  - Higher conditionality lowers average IFI debt and frequency but increases variability of IFI flows and raises defaults (73 vs 70).
  - Increasing k lowers average IFI debt and its frequency and reduces variability (smoother flows) and can decrease defaults.
  - Lower k raises average IFI debt and frequency and increases defaults relative to baseline.
- Main qualitative results (weak countercyclicality of IFI debt flows and higher spreads when indebted to the IFI) are robust across these parameter variations.

### Conclusion and policy implications
- Framework explains sovereign decisions to default and to allocate borrowing between commercial creditors and IFIs, capturing differences in cyclical properties of these debts.
- Key modeled IFI features: interest rate charged independent of sovereign risk (depends only on loan size) and a higher implied discount factor (more prudent policies) while indebted to the IFI.
- Model accounts for weak countercyclicality of IFI debt flows and higher IFI debt stocks in periods of high spreads; results robust to key parameter changes.
- The framework can be used to analyze policy questions regarding the design of IMF lending facilities (e.g., comparing SBAs to other facilities such as short-term lending) and to study dynamics and normative questions about IMF lending demand and relevance.

### Appendix — Simple Small Open Economy (SOE) model (illustration)
- Setup:
  - max_{ct} E0 Σ_{t=0}^∞ β(bt+1)^t u(ct) subject to ct + bt+1 = yt + bt(1 + r).
  - β(b) = {βH, if b < 0; βL, if b = 0}.
  - CRRA utility; β(1 + r) < 1; constant r; commitment technology (no default).
- Calibration example:
  - Baseline: βH = βL = 0.98.
  - Two-β case: βH = 0.98, βL = 0.979965.
  - Standard deviation of output set to 4.5 percent.
  - βL set so that b′ < 0 is chosen around 60 percent of the time.
- Findings:
  - βH − βL must be very small to obtain the 60 percent probability of negative bond position; larger differences lead to autarky.
  - The switch-to-higher-β requirement induces the country not to choose small negative bond positions; bond positions in [−0.04, 0] are almost never chosen in the illustrated stationary distribution.

*Source: _wp0946 - Introduction of two different discount factors generates a fixed cost-like effect making it; IMF working paper PDF content provided.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0946.pdf_