## 1. Countries and Debt-Crisis Episodes in the Full Sample

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---

### Scope and methodology
- Sample: panel dataset for 47 market access countries for the 1970–2002 period.
- Crisis definitions: outright default (Standard & Poor’s), coercive restructuring, and near-default episodes avoided through large-scale official financing by the IMF (large nonconcessional IMF loan in excess of 100 percent of quota; sensitivity checks at 50 percent and 150 percent).
- Empirical techniques:
  - Logit models of debt crisis (early-warning system, EWS).
  - Binary recursive tree technique (CART).
  - Combination of logit EWS and tree EWS.
- Additional analyses: event study analysis, sensitivity checks, and examination of entry into versus exit from crisis episodes.
- Estimation details:
  - Robust variance estimator (Huber White sandwich estimator) with country-specific variances.
  - Regressors lagged by one period to reduce endogeneity.
  - Separate coefficients for entry versus remaining in crisis via interaction with lagged GSP indicator.

### Stylized facts and context
- Trend: As more countries adopt flexible exchange rates, currency crises from fixed-rate collapse have become less frequent; sovereign debt-servicing difficulties (outright defaults, rollover/liquidity crises) have become more common.
- Forms observed:
  - Outright defaults (examples: Russia, Ecuador, Argentina).
  - Semi-coercive restructuring under implicit threat of default (examples: Ukraine 2000, Pakistan 1999, Uruguay 2003).
  - Near-default/lack-of-rollover episodes where official support avoided default (examples: Mexico 1994–95; Korea and Thailand 1997–98; Brazil 1999 and 2002; Turkey 2001; Uruguay 2002).
- Liquidity as recurrent issue: short maturities and unwillingness of investors to roll over liabilities are key sources of recent debt-servicing difficulties.

### Key empirical findings — predictors, persistence, heterogeneity
- Predictors of entry into a debt crisis:
  - Solvency measures: high foreign debt (relative to GDP or ability-to-pay measures) increases default probability.
  - Illiquidity measures: short-term debt (relative to foreign reserves) and debt-service obligations are significant predictors.
  - Macroeconomic variables with predictive power:
    - Low GDP growth.
    - Current account imbalances.
    - Low trade openness.
    - Tight liquidity and monetary conditions in the Group of seven countries (e.g., higher U.S. treasury bill rate, LIBOR).
    - Monetary mismanagement: high inflation.
    - Policy uncertainty: high volatility of inflation (4-year coefficient of variation).
    - Political uncertainty: presidential election-year dummy increases crisis probability.
    - Institutional: index of political freedom.
  - Fiscal variables: ratio of public debt to revenue shows some predictive power but data limitations constrain testing.
- Persistence and duration:
  - Sovereign debt crises tend to be long and persistent; exit is hard and timing of exits is difficult to predict.
  - Even after resolution, macroeconomic outcomes often worse than for countries that avoided default.
- Heterogeneity and thresholds:
  - External debt >50 percent of GDP increases default likelihood.
  - Default likelihood increases further when inflation, public debt, and/or external financing requirements are high.
  - Low external debt countries can still face high crisis risk when liquidity, political, fiscal, exchange-rate, or international conditions are adverse.
- Asymmetry:
  - Models predict entry much better than exit.

### Early-warning system (EWS) performance — logit, tree, and combined
- Logit EWS:
  - Correctly predicts 74 percent of all crisis entries across whole sample while sending 6 percent false alarms.
  - For period starting in 1990: correctly predicts 69 percent of crisis entries and sends 5 percent false alarms.
  - In-sample (full sample, Reduced Model vs Logit EWS): Correctly called episodes 88.9 and 89.4 percent; correctly called entries into default 74.2 percent (both); incorrectly called entries 6.9 percent (Reduced) and 6.1 percent (Logit EWS).
  - 48 percent of false alarms are followed by a crisis within two years; counting those as prewarnings reduces true false alarms to 3 percent (full sample).
- Recursive tree (CART):
  - Variables selected include: total external debt percent of GDP; short-term debt (remaining maturity) to reserves; public external debt to revenue; real growth; inflation; U.S. treasury bill rate; exchange rate overvaluation; exchange rate volatility; external financing requirement to reserves; years before presidential election.
  - First split at total external debt >49.7 percent of GDP.
  - Terminal-node examples:
    - Node 14: external debt >49.7% of GDP AND inflation >10.5% → default risk 66.8 percent.
    - Node 3: low external debt, short-term debt to reserves <1.3, public external debt to revenue <2.1, high growth → default risk 2.3 percent.
    - Node 7: external debt between 19% and 49.7% AND short-term debt/ reserves >1.3 AND presidential elections within 5.5 years AND low past exchange-rate volatility → default risk 41.5 percent.
    - Node 5: large public external debt to revenue AND high inflation → conditional crisis probability 55 percent.
    - Node 11: external debt >49.7% but low inflation (<10.5%), external financing requirement to reserves ≤1.5, public debt/revenue <3 → low crisis risk despite high external debt.
  - Performance (Table 7):
    - Observations: 1276 (full sample); 556 (1990s onwards).
    - Number of crisis episodes: 261 (full sample); 114 (1990s onwards).
    - Number of crisis entry episodes: 54 (full sample); 20 (1990s onwards).
    - Correctly called episodes: 82.8 percent (full sample); 78.8 percent (1990s onwards).
    - Correctly called entries into default: 88.9 percent (full sample); 85.0 percent (1990s onwards).
    - Incorrectly called entries into default: 18.5 percent (full sample); 15.0 percent (1990s onwards).
    - Correctly called exits from default: 32.0 percent (full sample); 35.3 percent (1990s onwards).
- Combined logit + tree:
  - Including tree terminal-node dummies in logit:
    - Correctly anticipates 81 percent of crisis entries.
    - Sends false alarms in only 6 percent of cases.
    - Correctly predicts 16 percent of exits.
  - Two-tiered EWS concept:
    - “Stress” signal: tree OR logit predicts crisis for next year.
    - “Verge of crisis” signal: BOTH tree AND logit predict crisis for next year.
  - Dummies for risk-prone nodes jointly significant and carry expected positive signs except node 3 (not risk-prone).

### Data, sample construction, and crisis indicator
- Dataset: 47 economies with market access, period 1970–2002 (full dataset includes information on 76 countries; transition economies included only from 1995 onward).
- Debt-crisis indicator:
  - Default per Standard & Poor’s OR a nonconcessional IMF loan in excess of 100 percent of quota with first-year disbursement.
  - Sensitivity checks with 50 percent and 150 percent thresholds.
- Data sources: Standard & Poor’s; IMF lending; World Bank Global Development Finance (external debt); IMF World Economic Outlook and Government Finance Statistics (public finance and macro variables).
- Estimation sample for final logit EWS: 594 observations for 37 market access countries from 1976 to 2001 (determined by data availability for included regressors).
- In-sample naive probability of being in crisis: 20.5 percent; typical crisis-entry share reported as 5.6 percent in some model descriptions.

### Descriptive statistics and event-study patterns (selected exact figures)
- Table 1 (sample summary):
  - Total crisis episodes listed: 54; Average Length in Crisis: 5.5.
  - Representative country entries (Number of Crises — Average Length in Crisis — Years of crisis episodes):
    - Algeria: 1 — 6.06 — 1991–97
    - Argentina: 3 — 5.01 — 1982–94, 1995–96, 2001–
    - Bolivia: 2 — 6.51 — 1980–85, 1986–94
    - Brazil: 3 — 5.31 — 1983–95, 1998–00, 2001–
    - Chile: 1 — 8.08 — 1983–91
    - China: 0 — ...0
    - Costa Rica: 1 — 10.10 — 1981–91
    - Dominican Republic: 1 — 22.22 — 1981–
    - Ecuador: 2 — 8.01 — 1982–96, 1999–2001
    - El Salvador: 1 — 16.16 — 1981–97
    - Guatemala: 1 — 1.01 — 1986–87
    - Indonesia: 2 — 2.55 — 1997–2001, 2002–
    - Jamaica: 3 — 4.71 — 1978–80, 1981–86, 1987–94
    - Korea: 2 — 2.04 — 1980–82, 1997–99
    - Mexico: 2 — 5.01 — 1982–91, 1995–96
    - Panama: 1 — 14.14 — 1983–97
    - Peru: 3 — 6.31 — 1976–77, 1978–81, 1983–98
    - Philippines: 1 — 10.10 — 1983–93
    - Russia: 1 — 3.03 — 1998–2001
    - South Africa: 4 — 1.87 — 1976–78, 1985–88, 1989–90, 1993–94
    - Thailand: 2 — 1.02 — 1981–82, 1997–98
    - Turkey: 2 — 3.57 — 1978–83, 2000–2002
    - Uruguay: 3 — 2.06 — 1983–86, 1987–88, 1990–92
    - Venezuela: 3 — 3.31 — 1983–89, 1990–91, 1995–98
  - Footnotes: 1/ crisis definition; 2/ data 1970–2002; 3/ transition countries from 1995; 4/ full dataset includes 76 countries; 5/ Mainly SBA and EFF lending.
- Selected mean statistics used in regressions (Table 2 — preserve exact figures):
  - Total external debt in percent of GDP: 45.5 (All), 37.0 (Noncrisis), 54.7 (Noncrisis Crisis), 71.4 (Crisis), 63.7 (Crisis) — No. of Obs. 1,05
  - Total external debt to exports: 290.2 39.3 59.4 55.3 50.1,05
  - Short-term external debt (OM, in percent of GDP): 7.2 (All), 6.1 (Noncrisis), 9.5 (Noncrisis Crisis), 10.6 (Crisis), 8.0 (Crisis) — No. of Obs. 1,01
  - Short-term external debt (OM, to reserves): 1.1 (All), 0.8 (Noncrisis), 1.9 (Noncrisis Crisis), 2.1 (Crisis), 1.0 (Crisis) — No. of Obs. 1,01
  - Short-term external debt (RM, in percent of GDP): 10.9 (All), 9.4 (Noncrisis), 15.0 (Noncrisis Crisis), 15.1 (Crisis), 15.7 (Crisis) — No. of Obs. 993
  - Short-term external debt (RM, to reserves): 1.7 (All), 1.2 (Noncrisis), 2.9 (Noncrisis Crisis), 2.9 (Crisis), 2.2 (Crisis) — No. of Obs. 948
  - Debt service on short-term external debt in percent of GDP: 5.3 4.8 6.9 6.4 7.1 — No. of Obs. 1,05 0
  - Public external debt in percent of GDP: 32.2 (All), 25.5 (Noncrisis), 36.4 (Noncrisis Crisis), 53.0 (Crisis), 46.5 (Crisis) — No. of Obs. 1,05
  - Public external debt to revenue: 1.7 (All), 1.3 (Noncrisis), 1.9 (Noncrisis Crisis), 3.0 (Crisis), 2.3 (Crisis) — No. of Obs. 827
  - Consolidated central government debt in percent of GDP: 47.5 (All), 46.4 (Noncrisis), 38.2 (Noncrisis Crisis), 57.3 (Crisis), 54.0 (Crisis) — No. of Obs. 462
  - Current account balance in percent of GDP: -2.7 (All), -2.7 (Noncrisis), -4.3 (Noncrisis Crisis), -2.6 (Crisis), -1.3 (Crisis) — No. of Obs. 1,23
  - Financing requirement to reserves: 1.6 (All), 1.3 (Noncrisis), 3.0 (Noncrisis Crisis), 2.4 (Crisis), 1.4 (Crisis) — No. of Obs. 986
  - LIBOR: 9.7 (All), 9.5 (Noncrisis), 10.5 (Noncrisis Crisis), 10.5 (Crisis), 9.4 (Crisis) — No. of Obs. 1,22
  - U.S. treasury bill rate: 6.4 (All), 6.3 (Noncrisis), 7.8 (Noncrisis Crisis), 6.9 (Crisis), 6.3 (Crisis) — No. of Obs. 1,22
  - Inflation (year-on-year, in percent): 54.6 17.5 241.169. 84.9 — No. of Obs. 1,27
  - Real GDP growth: 4.1 (All), 4.8 (Noncrisis), 1.8 (Noncrisis Crisis), 2.1 (Crisis), 2.2 (Crisis) — No. of Obs. 1,27
  - Openness: 71.2 (All), 71.3 (Noncrisis), 64.1 (Noncrisis Crisis), 72.1 (Crisis), 72.5 (Crisis) — No. of Obs. 903
  - Overall balance in percent of GDP: -4.3 (All), -4.4 (Noncrisis), -6.3 (Noncrisis Crisis), -3.8 (Crisis), -4.1 (Crisis) — No. of Obs. 1,01
  - Revenue in percent of GDP: 24.3 (All), 25.4 (Noncrisis), 22.7 (Noncrisis Crisis), 20.1 (Crisis), 24.2 (Crisis) — No. of Obs. 1,01
  - Interest expenditure in percent of total: 11.1 (All), 9.8 (Noncrisis), 11.0 (Noncrisis Crisis), 15.4 (Crisis), 15.1 (Crisis) — No. of Obs. 799
  - Social expenditure in percent of total: 17.5 (All), 17.1 (Noncrisis), 19.4 (Noncrisis Crisis), 17.8 (Crisis), 22.2 (Crisis) — No. of Obs. 663
- Event-study patterns (±3 year windows):
  - Total and public external debt-to-GDP rise in run-up to entry, spike at entry, and remain higher after exit than in noncrisis episodes.
  - Short-term external debt to reserves rises before entry; falls after entry to noncrisis levels; at exit short-term debt to reserves around noncrisis levels.
  - Debt service and interest on short-term debt relative to reserves higher in year before entry; fall to noncrisis levels after exit; small spike before exit.
  - Reserves growth plummets in year before entry and spikes in first year after exit.
  - Current account deficit larger before entry; external financing requirement to reserves higher before entry.
  - Large depreciation vs. U.S. dollar in year of entry; large appreciation in year of exit.
  - Real GDP growth falters in year before entry; inflation spikes in entry year; nominal GDP growth jumps in entry year.

### Logit EWS — selected variable findings and model performance metrics
- Key explanatory variables considered and findings:
  - Solvency: High total external debt-to-GDP raises probability of entry (effect stronger in 1990 onward); does not explain remaining in crisis.
  - Liquidity: High short-term debt (remaining maturity) to reserves raises probability of entry and remaining in crisis (relationship stable before/after 1990).
    - High interest on short-term debt in percent of GDP (1990 onward) raises probability of entry.
    - High external debt-service to reserves raises probability of entry (relationship stable before/after 1990).
  - External conditions: High current account balance reduces entry probability; greater openness (1990 onward) reduces entry probability.
    - Tight international liquidity (U.S. treasury bill rate) increases entry probability.
  - Domestic: High real GDP growth reduces entry probability.
    - High inflation volatility and very high inflation (>50 percent) increase entry and remaining-in-crisis probability.
  - Political: Presidential election years increase probability of entry and remaining in crisis.
    - Index of political freedom: before 1990 better freedom associated with higher crisis probability; 1990 onward effect reverses (higher freedom → lower crisis probability).
- Model metrics (selected exact figures):
  - 1990 onward sample (General vs Reduced):
    - Observations: 353 and 353.
    - Pseudo-R2: 0.66 (General) and 0.60 (Reduced).
    - Correctly called episodes: 89.8 and 88.1.
    - Correctly called entries into default: 69.2 (both).
    - Incorrectly called entries into default: 4.5 (General) and 5.3 (Reduced).
    - Debt-crisis entries correctly predicted: Number 9 (General) and 10 (Reduced).
    - Debt-crisis entries not predicted: Number 4 (General) and 3 (Reduced).
  - Full sample (Reduced vs Logit EWS):
    - Observations: 594 and 594.
    - Pseudo-R2: 0.63 (both).
    - Correctly called episodes: 88.9 (Reduced) and 89.4 (Logit EWS).
    - Correctly called entries into default: 74.2 (both).
    - Incorrectly called entries into default: 6.9 (Reduced) and 6.1 (Logit EWS).
    - Debt-crisis entries correctly predicted: Number 23 (both).
    - Debt-crisis entries not predicted: Number 8 (both).
- Out-of-sample prediction (pre-1995 model predicting 1995 onward):
  - Correctly predicts 45 percent of crisis entries and sends false alarms in 6 percent of cases.
  - Additional missed episodes in out-of-sample: Indonesia and Thailand in 1997, and Argentina in 2001.

### Notable missed episodes and explanations
- Four crisis entries after 1990 not anticipated by logit EWS: Argentina (1995), Brazil (2001), Tunisia (1991), Venezuela (1995).
  - Argentina 1995: important contagion from Mexican crisis 1994/95 (spillover not captured).
  - Venezuela 1995: small external-debt arrears following currency and banking crisis; macro indicators worsened in 1994 but model did not signal crisis.
  - Brazil 2001: domestic energy shock, U.S. slowdown, and Argentina deterioration necessitated IMF package; shocks largely unpredicted as of 2000.

### Sensitivity, robustness, and specification notes
- Dropping extreme observations does not change logit EWS predictive performance or signs.
- Using only Standard & Poor’s episodes: correctly predicts 63 percent of crisis entries and sends 4 percent false alarms.
- Lowering IMF loan threshold to 50 percent of quota: correctly predicts 58 percent of crisis entries and sends 9 percent false alarms.
- Increasing IMF loan threshold to 150 percent of quota: correctly predicts 66 percent of crisis entries and sends 6 percent false alarms.
- Reentering dropped variables (financing requirement, resource gap, public debt, overall balance) did not improve predictive power.
- Specification for 1990 onward generalizes well to full sample; evidence of structural breaks since early 1990s.

### Policy implications and monitoring recommendations
- Monitoring should focus on both solvency and liquidity indicators:
  - External debt-to-GDP ratios.
  - Short-term external liabilities relative to reserves (original and remaining maturity).
  - Debt-service obligations and interest payments relative to GDP and reserves.
- Broader macro and institutional indicators important:
  - GDP growth, current account balance, trade openness.
  - Inflation levels and volatility.
  - Political-cycle indicators (presidential election years) and measures of political freedom.
- Attention to heterogeneity and variable interactions:
  - Thresholds (e.g., external debt >50 percent of GDP) informative but interact with inflation, public debt, external financing requirements, liquidity, and political factors.
- Use complementary EWS methods:
  - Combine logit (fewer false alarms) and tree (nonlinear interactions, higher hit rate) to balance detection rates and false-alarm costs.
  - Two-tiered signals (“stress” vs “verge of crisis”) and country-specific charts of predicted probability and major regressors recommended for policy use.

### Suggested extensions and research directions
- Extend analysis to poorer developing countries and HIPCs to assess different debt thresholds and creditor composition.
- Improve prediction of 1990s-style (illiquidity-driven) crises and reduce false alarms.
- Incorporate better fiscal-flow and public-debt stock data to test fiscal vulnerability measures (real budget deficits, primary gaps).
- Test whether credit ratings and spreads add predictive power controlling for macro determinants.
- Study interactions among debt, currency, and banking crises and whether currency/banking crises lead debt crises.
- Analyze episodes where default was avoided due to large IMF packages separately to assess vulnerabilities and policy implications.

*Source: IMF Working Paper, "Predicting Sovereign Debt Crises" (section: Countries and Debt-Crisis Episodes in the Full Sample).*

### 1. Countries and Debt-Crisis Episodes in the Full Sample ........................................................9

### 1. Countries and Debt-Crisis Episodes in the Full Sample

### Scope and methodology
- Sample: panel dataset for 47 market access countries for the 1970–2002 period.
- Crisis definitions used include: outright default, coercive restructuring, and near-default episodes avoided through large-scale official financing by the IMF.
- Empirical techniques employed:
  - Logit models of debt crisis (early-warning system, EWS).
  - Binary recursive tree technique.
  - Combination of the logit EWS and the tree EWS.
- Additional analyses: event study analysis, sensitivity checks, and examination of entry into versus exit from crisis episodes.

### Stylized facts and context
- Recent pattern: As more countries adopt flexible exchange rates, currency crises associated with fixed-exchange-rate collapse have become less frequent, while sovereign debt-servicing difficulties (including outright defaults and rollover/liquidity crises) have become more common.
- Forms of sovereign debt-servicing difficulties observed:
  - Outright defaults on domestic and/or external debt (examples cited: Russia, Ecuador, Argentina).
  - Semi-coercive restructuring under implicit threat of default (examples cited: Ukraine in 2000, Pakistan in 1999, Uruguay in 2003).
  - Near-default/lack-of-rollover episodes where official support avoided outright default (examples cited: Mexico in 1994–95, Korea and Thailand in 1997–98, Brazil in 1999 and 2002, Turkey in 2001, Uruguay in 2002).
- Liquidity as a recurrent issue: Short maturities of external or domestic debt (and unwillingness of investors to roll over such liabilities) have been a key source of recent debt-servicing difficulties.

### Key empirical findings
- Predictors of entry into a debt crisis:
  - Measures of debt “solvency” matter: high levels of foreign debt (relative to GDP or other ability-to-pay measures) increase the probability of default and entry into default.
  - Measures of illiquidity matter: short-term debt (relative to foreign reserves) and debt-service obligations are significant predictors.
  - Macroeconomic variables with significant predictive power:
    - Low GDP growth.
    - Current account imbalances.
    - Low trade openness.
    - Tight liquidity and monetary conditions in the Group of seven countries.
    - Monetary mismanagement (high inflation).
    - Policy uncertainty (high volatility of inflation).
    - Political uncertainty captured by a dummy for presidential election years.
    - An index of political freedom.
  - Among fiscal variables, only the ratio of public debt to revenue shows some predictive power; however, data availability severely limits testing the role of fiscal variables.
- Persistence and duration:
  - Sovereign debt crises tend to last long and exhibit persistence; once a country is in a crisis, it is not easy to get out.
  - Even after resolution of default, macroeconomic outcomes are often worse than for countries that avoided default.
- Heterogeneity and threshold effects:
  - Countries with external debt greater than 50 percent of GDP are more likely to experience default episodes.
  - Default likelihood increases further when inflation, public debt, and/or external financing requirements are high.
  - Countries with low external debt can still face high crisis risk when confronted with liquidity problems, political uncertainty, fiscal mismanagement, exchange rate overvaluation, and tight international capital markets.
- Asymmetry in entry vs. exit prediction:
  - The models predict entry into crises much better than exit from crises. Determining timing of exits is harder and definitions of exit are ambiguous.

### Early-warning system (EWS) performance
- Comparative performance:
  - Logit EWS model: correctly predicts 74 percent of entries into a crisis while sending out few false alarms.
  - Recursive tree approach: correctly predicts 89 percent of entries into a crisis but sends out more false alarms.
- Interpretation:
  - Predicting debt-crisis entry is easier than predicting currency crises (the study’s models outperform the current state-of-the-art literature on early-warning models of currency crises).
  - Trade-offs exist between true-positive detection rates and false-alarm rates across methods.

### Implications for monitoring and policy
- Monitoring should focus on both solvency and liquidity indicators:
  - External debt-to-GDP ratios, short-term external liabilities relative to reserves, and debt-service obligations.
- Broader macroeconomic and institutional indicators matter:
  - GDP growth, current account balance, trade openness, inflation levels and volatility, political-cycle indicators (presidential election years), and measures of political freedom.
- Attention to country heterogeneity and interdependence of variables:
  - Critical thresholds (e.g., external debt >50 percent of GDP) are informative but interact with other variables (inflation, public debt, external financing requirements, liquidity, political factors).
- Use of complementary EWS methods:
  - Combining logit and recursive tree outputs can inform policymakers about possible debt-servicing vulnerabilities, balancing detection rates and false-alarm costs.

*Source: IMF Working Paper, "Predicting Sovereign Debt Crises" (section: Countries and Debt-Crisis Episodes in the Full Sample).*

### Section VI presents some concluding remarks and suggestions for extensions of this work.

### _wp03221 - Section VI presents some concluding remarks and suggestions for extensions of this work.

### Related literature: categories and theoretical insights
- Literature on debt crisis falls into four broad categories: theoretical models of sovereign default; empirical studies of the determinants of debt crisis; empirical studies of the predictive power of credit ratings; and empirical studies of the determination of spreads.
- Theoretical literature highlights two broad triggers for sovereign default:
  - Unwillingness to repay based on intertemporal optimization calculus.
  - Inability to repay because of insolvency or illiquidity.
- Solvency considerations:
  - Sovereign solvency assessed by stock of debt relative to capacity to pay (GDP, exports, government revenues).
  - Sovereign is solvent if the discounted value of future primary balances is greater or equal to the current public debt stock.
  - Sovereign is solvent if the discounted value of future trade balances exceeds the current stock of external debt.
- Additional theoretical and institutional factors:
  - Exchange rate regime and exchange rate misalignment: overvaluation can cause external imbalance and debt accumulation; currency crisis with foreign-currency debt produces balance-sheet effects.
  - Openness influences costs of default and willingness to default.
  - Macroeconomic stability indicators (low inflation, low money growth) reflect policy credibility and influence investor risk attitudes.
  - Liquidity metrics (short-term debt to reserves, M2 to reserves) matter where illiquidity—not insolvency—is the issue.
  - Institutional and political variables affect policy credibility and willingness to pursue sustainable debt paths.

### Empirical approaches and crisis definitions
- No single empirical definition of sovereign default or debt crisis; studies use differing definitions depending on data and research question.
- Examples of empirical definitions:
  - Case-study compilations (Beers and Bhatia, 1999; Beim and Calomiris, 2001).
  - Quantitative rule: arrears on external obligations toward commercial creditors in excess of 5 percent of commercial debt outstanding or rescheduling/restructuring with commercial creditors (Detragiache and Spilimbergo, 2001).
  - Standard & Poor’s definition: a country is in default as long as the sovereign is not current on any of its debt obligations.
- Limitations of quantitative definitions:
  - May not differentiate sovereign vs. private-sector arrears.
  - May exclude incipient crises avoided by large-scale official support.
  - Ideal metric would be a continuous crisis-pressure index (analogous to exchange market pressure indices).

### Empirical regularities and determinants of debt crises
- Common determinants identified across studies:
  - Measures of solvency: debt-to-GDP and related ratios.
  - Liquidity measures: short-term external debt; external debt service; ratios to reserves or exports.
  - Variables from currency-crisis models (e.g., IMF’s EWS), given documented links (Reinhart (2002) finds that in 84 percent of cases a debt crisis is preceded by a currency crisis).
  - Measures of external volatility and volatility in economic policies (terms of trade volatility, fiscal policy volatility, monetary policy volatility, exchange rate policy volatility).
  - Standard macroeconomic controls: real growth, inflation, exchange rate overvaluation, fiscal balance.
  - Political and institutional variables capturing willingness to pay.
- Specific empirical findings cited:
  - Detragiache and Spilimbergo (2001): short-term debt, debt service, and reserves enter separately; the null of equal coefficients is rejected; short-term debt is endogenous (difficulty borrowing long term in run-up to crisis).
  - Catão and Sutton (2002): in-sample predictive power increases markedly when volatility measures are added to a model containing real GDP growth, debt service to exports, net international reserves to debt, the fiscal balance, the U.S. interest rate, and the real effective exchange rate.
  - Predictive power of credit ratings for currency crisis and sovereign default is surprisingly poor (evident in Asian crisis, Argentinean crisis; see Reinhart (2002); Rojas-Suarez (2001); Larrain, Reisen, and von Maltzan (1997)).
  - Determinants of sovereign spreads: Dell’Ariccia, Schnabel, and Zettelmeyer (2002) find spreads increased after the nonbailout of Russia in 1998, suggesting spreads are compressed by moral hazard; evidence on moral hazard is mixed (Lane and Phillips (2001)).

### Data, sample construction, and crisis indicator
- Dataset includes information on 47 economies with market access for the period 1970 to 2002 (Table 1). 4/
- Data sources:
  - Debt-crisis indicator: Standard & Poor’s and IMF lending.
  - External debt and public debt: World Bank’s Global Development Finance database (GDF) and IMF sources.
  - Public finance and macro variables: IMF’s World Economic Outlook and Government Finance Statistics (GFS).
  - Appendix IV provides detailed variable descriptions and sources.
- Definition of debt crisis used in this work:
  - A country is in debt crisis if either:
    - Classified as being in default by Standard & Poor’s, or
    - Receives a large nonconcessional IMF loan defined as access in excess of 100 percent of quota.
  - Standard & Poor’s: sovereign issuer rated in default if government fails to meet principal or interest payment on external obligation on due date (including exchange offers, debt-equity swaps, and buyback for cash).
  - Augmentation with IMF Finance Department lending data to capture “incipient” defaults avoided by large IMF support.
  - Loan classification: a country is classified as being in debt crisis if a large nonconcessional loan is approved and a disbursement under this loan is actually made in the first year.
  - Initial threshold for “large” IMF loan: in excess of 100 percent of quota (selects the top 10 percent of loans when ranked by loan-to-quota ratio).
  - Sensitivity checks: also use 50 percent and 150 percent thresholds to define the debt-crisis indicator.
- Notes on sample coverage:
  - Full dataset includes information on 76 countries; transition economies are included only from 1995 to 2002. 4/
  - Not every variable is available for all countries or full time period.
  - As robustness, authors also use only Standard & Poor’s data excluding episodes related only to exceptional IMF lending.

### Descriptive statistics and event-study patterns
- Descriptive patterns (means presented in Table 2 across full sample, noncrisis, pre-entry, in-crisis, pre-exit):
  - External debt measures and debt-service measures:
    - Relatively low in noncrisis years and another noncrisis year.
    - Increase in the year before crisis entry.
    - Increase further within crisis.
    - Drop in the year before exit from crisis but remain higher than pre-crisis levels.
  - Public external debt follows same pattern, suggesting public external debt drives external debt dynamics in many countries.
  - Macroeconomic variables and currency-crisis EWS indicators:
    - Worsen in run-up to crisis and within crisis; improve upon exit.
    - Current account deficit increases in the year immediately preceding crisis entry, stabilizes within crisis, improves in year before exit.
    - Real growth falters in the year before crisis entry; inflation spikes.
    - Overall balance and primary balance deteriorate in the run-up to crisis.
    - LIBOR and the U.S. treasury bill rate increase in years preceding a crisis, indicating that tighter G7 monetary conditions may reduce capital flows to emerging markets and contribute to debt-servicing difficulties (example: 1982).
- Interpretation:
  - Descriptive statistics depict a worsening debt and macroeconomic situation in the run-up to crises and improvement before exit.
  - Authors note these are suggestive relationships that require rigorous statistical/econometric testing.

### Table 1: sample summary (selected exact figures preserved)
- Dataset: 47 economies with market access, period 1970–2002. 4/
- Total crisis episodes listed in Table 1: 54; Average Length in Crisis: 5.5.
- Representative country entries (Number of Crises — Average Length in Crisis — Years of crisis episodes as presented):
  - Algeria: 1 — 6.06 — 1991–97
  - Argentina: 3 — 5.01 — 1982–94, 1995–96, 2001–
  - Bolivia: 2 — 6.51 — 1980–85, 1986–94
  - Brazil: 3 — 5.31 — 1983–95, 1998–00, 2001–
  - Chile: 1 — 8.08 — 1983–91
  - China: 0 — ...0
  - Costa Rica: 1 — 10.10 — 1981–91
  - Dominican Republic: 1 — 22.22 — 1981–
  - Ecuador: 2 — 8.01 — 1982–96, 1999–2001
  - El Salvador: 1 — 16.16 — 1981–97
  - Guatemala: 1 — 1.01 — 1986–87
  - Indonesia: 2 — 2.55 — 1997–2001, 2002–
  - Jamaica: 3 — 4.71 — 1978–80, 1981–86, 1987–94
  - Korea: 2 — 2.04 — 1980–82, 1997–99
  - Mexico: 2 — 5.01 — 1982–91, 1995–96
  - Panama: 1 — 14.14 — 1983–97
  - Peru: 3 — 6.31 — 1976–77, 1978–81, 1983–98
  - Philippines: 1 — 10.10 — 1983–93
  - Russia: 1 — 3.03 — 1998–2001
  - South Africa: 4 — 1.87 — 1976–78, 1985–88, 1989–90, 1993–94
  - Thailand: 2 — 1.02 — 1981–82, 1997–98
  - Turkey: 2 — 3.57 — 1978–83, 2000–2002
  - Uruguay: 3 — 2.06 — 1983–86, 1987–88, 1990–92
  - Venezuela: 3 — 3.31 — 1983–89, 1990–91, 1995–98
- Sources for Table 1: IMF; Standard & Poor’s; World Bank; and authors’ calculations.
- Footnotes preserved:
  - 1/ A country is defined to be in a debt-crisis if it is classified as being in default by Standard & Poor’s or receives a nonconcessional IMF loan in excess of 100 percent of quota.
  - 2/ Data from 1970–2002.
  - 3/ Transition countries are included only from 1995 onward.
  - 4/ The full dataset includes information on 76 countries. For transition economies, the sample period is 1995 to 2002. Not every variable is available for all countries or for the full time period.
  - 5/ Mainly SBA and EFF lending.

*Source: _wp03221 - Section VI presents some concluding remarks and suggestions for extensions of this work.*

### Appendix Table 8 reproduces this table for episodes starting in or after 1990.

### _wp03221 - Appendix Table 8 reproduces this table for episodes starting in or after 1990.

### Mean statistics used in the regressions (Table 2 — selected variables)
- Total external debt in percent of GDP: 45.5 (All), 37.0 (Noncrisis), 54.7 (Noncrisis Crisis), 71.4 (Crisis), 63.7 (Crisis) — No. of Obs. 1,05
- Total external debt to exports: 290.2 39.3 59.4 55.3 50.1,05
- Short-term external debt (OM, in percent of GDP): 7.2 (All), 6.1 (Noncrisis), 9.5 (Noncrisis Crisis), 10.6 (Crisis), 8.0 (Crisis) — No. of Obs. 1,01
- Short-term external debt (OM, to reserves): 1.1 (All), 0.8 (Noncrisis), 1.9 (Noncrisis Crisis), 2.1 (Crisis), 1.0 (Crisis) — No. of Obs. 1,01
- Short-term external debt (RM, in percent of GDP): 10.9 (All), 9.4 (Noncrisis), 15.0 (Noncrisis Crisis), 15.1 (Crisis), 15.7 (Crisis) — No. of Obs. 993
- Short-term external debt (RM, to reserves): 1.7 (All), 1.2 (Noncrisis), 2.9 (Noncrisis Crisis), 2.9 (Crisis), 2.2 (Crisis) — No. of Obs. 948
- Interest on short-term external debt in percent of: 0.5 0.5 0.8 0.6 0.7 — No. of Obs. 754
- Interest on short-term external debt to reserves: 0.1 (All), 0.1 (Noncrisis), 0.2 (Noncrisis Crisis), 0.1 (Crisis), 0.1 (Crisis) — No. of Obs. 754
- Debt service on short-term external debt in percent of GDP: 5.3 4.8 6.9 6.4 7.1 — No. of Obs. 1,05 0
- Debt service on short-term external debt to reserves: 0.8 (All), 0.7 (Noncrisis), 1.5 (Noncrisis Crisis), 1.2 (Crisis), 0.9 (Crisis) — No. of Obs. 1,05
- Public external debt in percent of GDP: 32.2 (All), 25.5 (Noncrisis), 36.4 (Noncrisis Crisis), 53.0 (Crisis), 46.5 (Crisis) — No. of Obs. 1,05
- Public external debt to revenue: 1.7 (All), 1.3 (Noncrisis), 1.9 (Noncrisis Crisis), 3.0 (Crisis), 2.3 (Crisis) — No. of Obs. 827
- Consolidated central government debt in percent of GDP: 47.5 (All), 46.4 (Noncrisis), 38.2 (Noncrisis Crisis), 57.3 (Crisis), 54.0 (Crisis) — No. of Obs. 462
- Central government debt in percent of GDP: 51.7 (All), 50.4 (Noncrisis), 28.4 (Noncrisis Crisis), 75.5 (Crisis), 51.6 (Crisis) — No. of Obs. 305
- Augmented Consolidated central government debt in percent of GDP: 50.7 47.8 41.5 67.7 54.8 — No. of Obs. 591
- Overvaluation: 0.0 0.0 0.0 -0.1 0.0 — No. of Obs. 799
- Current account balance in percent of GDP: -2.7 (All), -2.7 (Noncrisis), -4.3 (Noncrisis Crisis), -2.6 (Crisis), -1.3 (Crisis) — No. of Obs. 1,23
- Reserves growth: 19.1 20.8 -5.4 17.8 22.9 — No. of Obs. 1,15
- Export growth: 12.0 13.8 4.9 6.4 7.8 — No. of Obs. 1,27
- M2 to reserves: 5.6 5.3 7.9 6.2 6.2 — No. of Obs. 1,18
- Financing requirement to reserves: 1.6 1.3 3.0 2.4 1.4 — No. of Obs. 986
- External resource gap in percent of GDP: -0.2 -0.6 -1.5 1.3 2.9 — No. of Obs. 1,11
- Trade balance in percent of GDP: -3.7 -4.0 -2.7 -3.4 -1.1 — No. of Obs. 1,27
- LIBOR: 9.7 9.5 10.5 10.5 9.4 — No. of Obs. 1,22
- U.S. treasury bill rate: 6.4 6.3 7.8 6.9 6.3 — No. of Obs. 1,22
- Inflation (year-on-year, in percent): 54.6 17.5 241.169. 84.9 — No. of Obs. 1,27
- Unemployment rate: 9.7 9.0 11.1 10.9 11.6 — No. of Obs. 740
- Nominal GDP growth: 55.9 22.8 249.148. 96.0 — No. of Obs. 1,27
- Real GDP growth: 4.1 4.8 1.8 2.1 2.2 — No. of Obs. 1,27
- REER growth: 121.124.139.111.109. 937
- Import growth: 10.0 12.3 5.3 4.8 6.9 — No. of Obs. 902
- FDI in percent of GDP: 1.7 1.9 1.1 1.0 1.5 — No. of Obs. 1,02
- FDI growth: 28.0 26.3 52.6 22.6 53.6 — No. of Obs. 983
- Openness: 71.2 71.3 64.1 72.1 72.5 — No. of Obs. 903
- Overall balance in percent of GDP: -4.3 -4.4 -6.3 -3.8 -4.1 — No. of Obs. 1,01
- Primary balance in percent of GDP: 0.6 0.3 -0.9 2.0 1.5 — No. of Obs. 616
- Primary gap: 6.6 5.7 23.1 59.0 -15.0 — No. of Obs. 122
- Revenue in percent of GDP: 24.3 25.4 22.7 20.1 24.2 — No. of Obs. 1,01
- Tax revenue in percent of total: 82.5 82.2 85.7 82.7 83.5 — No. of Obs. 819
- International trade revenue in percent of total: 13.7 13.7 12.1 14.7 11.3 — No. of Obs. 814
- Nontax revenue in percent of total: 15.0 15.0 13.5 15.4 14.8 — No. of Obs. 822
- Grants in percent of total: 2.7 3.0 0.7 1.4 2.1 — No. of Obs. 522
- Expenditure in percent of GDP: 28.6 29.7 29.0 23.9 28.3 — No. of Obs. 1,01
- Interest expenditure in percent of total: 11.1 9.8 11.0 15.4 15.1 — No. of Obs. 799
- Wages in percent of total: 23.4 22.8 23.9 25.9 23.3 — No. of Obs. 713
- Health expenditure in percent of total: 6.5 6.1 5.4 8.5 6.0 — No. of Obs. 628
- Social expenditure in percent of total: 17.5 17.1 19.4 17.8 22.2 — No. of Obs. 663

Sources for table: IMF; Standard & Poor’s; World Bank; and authors’ calculations.

### Event study analysis — methodology and graphical interpretation
- Approach:
  - Use a +/- 3 year window around crisis entry and around crisis exit.
  - Broken horizontal line: sample average for noncrisis episodes (outside the +/- 3 year interval).
  - Bold solid line: average for years T-3 to T+3 around crisis entry (exit).
  - Broken lines around bold solid line: 95 percent confidence interval.
  - Overlapping entry (exit) windows are eliminated by dropping entries (exits) that occur within six years after the preceding entry (exit).
  - Figures generated via regression of each variable on seven dummies for T-3,...,T+3; estimated constant equals nondefault mean; coefficients on dummies give differences from nondefault mean.
- Data presentation note:
  - Event study charts use “raw” data for interpretation; charts based on standardized data show the same trends and are available upon request.

### Event study analysis — main empirical findings (summary)
- Debt dynamics:
  - Total external debt and public external debt-to-GDP ratios increase in the run-up to crisis and are significantly higher than noncrisis episodes in the year before entry.
  - Public external debt appears to drive total external debt-to-GDP dynamics.
  - At exit from crisis there is a peculiar spike in total external debt; overall both total and public external debt remain noticeably higher in crisis countries even after exit compared to noncrisis episodes.
- Short-term debt and debt service:
  - Short-term external debt relative to reserves increases in the run-up to crisis (both original and remaining maturity measures) and is significantly higher in the year before entry.
  - After entry, short-term debt falls to noncrisis levels, possibly reflecting borrowing difficulties or conversion into longer-term debt during restructurings.
  - At exit, short-term debt relative to reserves is around noncrisis levels.
  - Debt service on external debt relative to reserves and interest on short-term external debt relative to reserves are higher than noncrisis episodes in the year before entry; both fall to noncrisis levels after exit.
  - Debt service shows a small spike just before exit, possibly reflecting resumption of payments near resolution.
- External sector and reserves:
  - Current account deficit is larger before entry into crisis than in noncrisis episodes.
  - Reserves growth plummets in the year before entry; reserves growth spikes in the first year after exit.
  - External financing requirement relative to reserves (current account deficit plus short-term debt) is significantly higher in the year before entry than in noncrisis episodes and falls back at exit.
  - Exchange rate: large depreciation against the U.S. dollar in the year of entry; large appreciation in the year of exit. Depreciation at entry contributes to higher total external debt/GDP.
- Domestic macroeconomic developments:
  - Real GDP growth is below noncrisis episodes and plummets in the entry year.
  - Inflation rises substantially in the entry year; nominal GDP growth also jumps in the entry year.
  - Inflation shows dramatic swings and slow stabilization in the three years after exit.
  - Overall budget balance in the run-up to crisis does not differ significantly from noncrisis episodes, though there is modest improvement before exit.

### Logit early-warning system (EWS) — estimation approach (Section IV.A)
- Modeling strategy:
  - Modified general-to-specific approach to identify an EWS for sovereign debt crisis.
  - Variables selected based on standard specification criteria and predictive ability for entering crisis and being in crisis.
  - For crisis episodes longer than one year: entry = first year of episode; being in crisis = remaining years until exit.
  - Regressors allowed to have different impacts on probability of entry and probability of exit.
- Three-stage variable selection and estimation:
  - Stage 1: Individual regressions for each variable to assess standard criteria and predictive power for entry and being in crisis.
    - An estimated model is defined to predict entry/being in crisis if estimated probability exceeds the naive in-sample probability of being in crisis of 20.5 percent.
  - Stage 2: Select “best performers” within each of six groups and run group-wise regressions (“horse-races”) to narrow variables for the general model.
    - Six groups: external debt variables; public debt variables; variables from the IMF currency crisis EWS; other macroeconomic variables; fiscal variables; political economy variables.
  - Stage 3: Combine best performers from each group into a “general” model and test down by excluding variables that are insignificant or do not improve predictive power.
- Estimation choice:
  - Use logit approach (preferred over probit when dependent variable is unevenly distributed); in the dataset 20.5 percent of outcomes are debt crisis.

*Sources: IMF; Standard & Poor’s; World Bank; and authors’ calculations.*

### 5.6 percent are crisis entries. We use a robust variance estimator (Huber White sandwich

### _wp03221 - 5.6 percent are crisis entries. We use a robust variance estimator (Huber White sandwich estimator) with country-specific variances.

### Estimation approach and model setup
- Use of a robust variance estimator (Huber White sandwich estimator) with country-specific variances.
- Separate coefficients estimated for entering into crisis and for exiting from crisis by multiplying each regressor with the lagged generalized Standard & Poor’s crisis indicator, GSP.
- Formal probability specification (equation form provided in source): the probability of being in crisis, P, in year t is given by (1) P_t = f(X_{t-1}, GSP_{t-1}*X_{t-1}), where X_{t-1} denotes the vector of explanatory variables in the previous period, including the constant.
- Interpretation of coefficients:
  - Coefficient on the first argument: relationship between explanatory variable and probability of entering into crisis in t, given country was not in crisis in t-1.
  - Coefficient on the second argument: relationship between the explanatory variable and the probability of being in crisis (not exiting) in t, given country was in crisis in t-1.
- Lagging regressors by one period to avoid a possible endogeneity bias.
- Acknowledged potential omitted variable bias in logit models; sensitivity analysis includes reintroducing regressors that dropped out to test improvement.

### Specifying the Logit Early Warning System (EWS)
- Logit EWS initially specified for subsample of episodes starting in or after 1990; then estimated for all years with data availability while allowing different coefficients for crises occurring as of 1990.
- General model variables (from variable-by-variable and groupwise regressions) included in a “general” model and then tested down to a preferred specification:
  - External debt variables:
    - Short-term external debt to reserves on an original maturity basis and on a remaining maturity basis.
    - Interest on short-term debt in percent of GDP.
    - External debt service to reserves.
    - Total external debt in percent of GDP included as possible explanatory variable for solvency considerations.
  - Public debt variables:
    - No public debt indicator significant at the 5 percent level for the 1990 onward sample; none included in direct specification process. Public external debt included as sensitivity test but did not improve model.
  - IMF currency crises EWS variables:
    - Reserves growth helps predict crisis entries.
    - Current account balance included in general model.
  - Other macroeconomic variables:
    - U.S. treasury bill rate, real GDP growth, FDI in percent of GDP, trade openness.
    - Financing requirement calculated as current account deficit plus short-term debt on an original maturity basis (also tested alternate financing requirement definitions without improvement).
    - Inflation volatility measured as a 4-year moving average of the coefficient of variation included.
  - Fiscal variables:
    - No fiscal indicator helped predict sovereign crisis episodes; overall balance tested in preferred specification without improvement.
  - Political economy variables:
    - Dummy for years with presidential election and an index of freedom status included in general model as candidates.

### Estimation sample and process
- Logit EWS estimated on a sample of 594 observations for 37 market access countries from 1976 to 2001 (subsample determined by data availability for included variables).
- Process: estimate general model on 1990 onward subsample; exclude insignificant variables and variables with counter-intuitive direction to arrive at a reduced model; reestimate reduced model for full sample allowing coefficients to differ for observations starting in or after 1990; further testing yields final specification named the logit EWS.

### Key empirical findings (coefficients and directions summarized from tables)
- Solvency:
  - High total external debt-to-GDP ratio is associated with a high probability of entering into crisis; effect more pronounced in 1990 onward period.
  - Total external debt-to-GDP ratio does not help explain remaining in crisis in the logit EWS.
- Liquidity:
  - High short-term debt on remaining maturity basis to reserves associated with high probability of entering and remaining in crisis; relationship statistically identical before and after 1990.
  - In the 1990 onward period, high interest payments in percent of GDP make entering into crisis more likely.
  - High external debt-service payments in relation to reserves make entering into crisis more likely; relationship statistically identical before and after 1990.
- External conditions:
  - High current account balance reduces probability of entering into crisis; relationship identical before and after 1990.
  - From 1990 onward, greater openness reduces probability of entering into crisis.
  - Tight international liquidity proxied by the U.S. treasury bill rate associated with increased probability of entering into crisis; particularly pronounced in the early eighties but holds over full sample.
- Domestic conditions:
  - High real GDP growth associated with reduced probability of entering into crisis.
  - High inflation volatility (4-year coefficient of variation) and high inflation (>50 percent) associated with increased probability of entering and remaining in crisis; these links identical before and after 1990.
- Political factors:
  - Probability of entering and remaining in crisis increases in years with presidential elections.
  - Before 1990, better ranking on index of political freedom associated with raised probability of crisis; in 1990 onward period effect reverses—higher political freedom associated with reduced probability of crisis.

### Model performance and predictive statistics
- 1990 onward sample (General Model vs Reduced Model) — Table 4:
  - Observations: 353 and 353.
  - Wald-test for joint significance: Chi(31) = 273,189 (General Model) and Chi(13) = 758 (Reduced Model).
  - Pseudo-R2: 0.66 (General Model) and 0.60 (Reduced Model).
  - Correctly called episodes: 89.8 (General Model) and 88.1 (Reduced Model).
  - Correctly called entries into default: 69.2 (both models).
  - Incorrectly called entries into default: 4.5 (General) and 5.3 (Reduced).
  - Correctly called exits from default: 16.0 (General) and 0.0 (Reduced).
  - Incorrectly called exits from default: 0.0 (both).
  - Wald test reduced vs. general model: Chi2(18) = 24.5.
  - Debt-crisis entries correctly predicted: Number 9 (General) and 10 (Reduced).
  - Debt-crisis entries not predicted: Number 4 (General) and 3 (Reduced).
  - Countries included in regressions: Number 37 (both).
- Full sample (Reduced Model vs Logit EWS) — Table 6:
  - Observations: 594 and 594.
  - Wald-test for joint significance: Chi(26) = 3,350 (Reduced) and Chi(15) = 431 (Logit EWS).
  - Pseudo-R2: 0.63 (both).
  - Correctly called episodes: 88.9 (Reduced) and 89.4 (Logit EWS).
  - Correctly called entries into default: 74.2 (both).
  - Incorrectly called entries into default: 6.9 (Reduced) and 6.1 (Logit EWS).
  - Correctly called exits from default: 0.0 (both).
  - Incorrectly called exits from default: 0.0 (both).
  - Wald test logit EWS vs. reduced model: Chi(11) = 3.8.
  - Debt-crisis entries correctly predicted: Number 23 (both).
  - Debt-crisis entries not predicted: Number 8 (both).
  - Countries included in regressions: Number 37 (both).
- Overall predictive accuracy:
  - Logit EWS correctly predicts 74 percent of all crisis entries across whole sample while sending 6 percent false alarms not followed by a crisis in the next year.
  - For period starting in 1990, logit EWS correctly predicts 69 percent of all crisis entries and sends 5 percent false alarms.
  - In 48 percent of all false alarms, a debt crisis occurs two years after the signal rather than in the next year; considering those as prewarnings would reduce true false alarms within two years to 3 percent for full sample.
  - For the 1990 onward subsample, share of false alarms followed by a debt crisis within two years is 38 percent.

### Notable missed episodes and explanations
- Four crisis entries after 1990 not anticipated by the logit EWS: Argentina (1995); Brazil (2001); Tunisia (1991); Venezuela (1995).
  - Argentina 1995: important factor was spillover from the Mexican crisis 1994/95 (Tequila contagion effect); contagion proxies not included in model.
  - Venezuela 1995: aftermath of currency and banking crisis led to short period of arrears on a small amount of external debt payments; model did not signal impending crisis though macro indicators signaled worsening in 1994; debt payments crisis was small.
  - Brazil 2001: combination of domestic energy shock, U.S. slowdown, and worsening in Argentina necessitated large IMF package; shocks largely unpredicted as of 2000.
- Out-of-sample test:
  - Reestimated logit EWS for years prior to 1995 and predicted 1995 onward.
  - Out of sample performance: correctly predicts 45 percent of crisis entries and sends false alarms in 6 percent of cases.
  - Additional missed in out-of-sample: Indonesia and Thailand in 1997, and Argentina in 2001 (in addition to those missed in-sample).

### Tree EWS (CART) overview and findings
- CART (Classification and Regression Tree) methodology used to identify nonlinear interactions among variables and classify observations into crisis-prone or not crisis-prone groups.
- CART is nonparametric and suited for detecting complex nonlinear relationships and interactions; produces a sequence of sorting rules illustrated as a tree (example provided in source).
- Variables selected by CART to partition the sample (nine variables): 
  - total external debt in percent of GDP;
  - short-term debt on a remaining maturity basis to reserves;
  - public external debt to revenue;
  - real growth;
  - inflation;
  - U.S. treasury bill rate;
  - exchange rate overvaluation;
  - exchange rate volatility;
  - external financing requirement to reserves;
  - number of years before a presidential election.
- First CART split rule: episodes with high external debt (more than 49.7 percent of GDP) go to the right branch, raising conditional crisis probability from 20.5 percent in the entire sample to a higher conditional probability in that branch (tree details continue in source).

*Source: IMF; Standard & Poor’s; World Bank; and authors’ calculations, from the PDF content provided.*

### 45.4 percent; and episodes with low external debt to the left, with default probability of

### _wp03221 - 45.4 percent; and episodes with low external debt to the left, with default probability of

### The Empirical Tree: key terminal-node findings
- Terminal node 14: Episodes of high debt (more than 49.7 percent of GDP) and high inflation (larger than 10.5 percent) incur the largest default risk, 66.8 percent. More than half of all the crisis episodes in the sample satisfy these two conditions.
- Terminal node 3: Low external debt, low short-term debt to reserves on a remaining maturity basis (below 1.3), low public external debt to revenue (below 2.1), coupled with high economic growth, yield a likelihood of crisis of 2.3 percent. About 58.4 percent of all noncrisis episodes satisfy these conditions.
- Terminal node 7: Intermediate external debt (between 19 percent and 49.7 percent of GDP) combined with short-term debt above 1.3 times reserves, presidential elections closer than 5.5 years, and low moving average of past coefficient of variation of the exchange rate (history of pegged exchange rates) lead to a default risk of 41.5 percent.
- Terminal node 5: Large public external debt relative to revenue coupled with high inflation raises the conditional crisis probability to 55 percent, even when external debt-to-GDP and short-term debt are low.
- Terminal node 11: Even with total external debt in excess of 49.7 percent of GDP, crisis risk can be low if inflation is below 10.5 percent, the external financing requirement to reserves ratio does not exceed 1.5, and the public debt to revenue ratio is below 3.

### Model performance (Table 7) — exact sample metrics
- Observations: 1276 (full sample); 556 (1990s onwards)
- Number of crisis episodes: 261 (full sample); 114 (1990s onwards)
- Number of crisis entry episodes: 54 (full sample); 20 (1990s onwards)
- Correctly called episodes: 82.8 percent (full sample); 78.8 percent (1990s onwards)
- Correctly called entries into default: 88.9 percent (full sample); 85.0 percent (1990s onwards)
- Incorrectly called entries into default: 18.5 percent (full sample); 15.0 percent (1990s onwards)
- Correctly called exits from default: 32.0 percent (full sample); 35.3 percent (1990s onwards)
- Incorrectly called exits from default: 4.8 percent (full sample); 64.7 percent (1990s onwards)
- Correctly called default episodes: 93.9 percent (full sample); 89.5 percent (1990s onwards)
- Correctly called nondefault episodes: 79.9 percent (full sample); 76.0 percent (1990s onwards)

### Empirical tree classification and sample composition
- Full-sample crisis share used in tree assignment: 20.5 percent.
- Cost parameter set for estimating the tree: 7:1 (relative cost of missing a default episode versus missing a nondefault episode).
- Assignment rule consequence: a node is classified as crisis-prone whenever the ratio N1(n)/N0(n) within the node exceeds the ratio in the entire sample by at least 55 percent (see Appendix II).

### Predictive trade-offs and timing
- The tree correctly predicts 89 percent of all crisis entries in the full sample, with 19 percent false alarms in years not followed by a crisis entry.
- Around 14 percent of the tree’s false alarms are “early” alarms; counting signals two years in advance as early indications reduces the share of false alarms to 16 percent.
- The tree correctly predicts 32 percent of crisis exits.
- For the 1990 onward period: 85 percent of crisis entries correctly predicted and 21 percent false alarms. Crisis entries in the 1990 onward period not anticipated by the tree include Algeria 1991, Argentina 1995, and Russia 1998.

### Combining logit and tree early-warning systems (EWS)
- Rationale:
  - Logit strength: discovers relationships that hold across full sample; sends fewer false alarms.
  - Tree strength: discovers nonlinear variable combinations and calls many crisis entries; sends more false alarms.
- Joint modeling approach: include dummy variables for tree-identified terminal-node groups as regressors in the logit.
  - When including feasible subset of dummies (excluding perfect predictors), the joint model:
    - Correctly anticipates 81 percent of all crisis entries.
    - Sends false alarms in only 6 percent of the cases.
    - Correctly predicts 16 percent of all exits from crisis.
  - Dummies representing nodes are jointly significant and carry positive signs consistent with risk-prone classification except dummy for node 3 (classified as not risk-prone).
- Two-tiered EWS concept:
  - “Stress” signal if only the tree EWS OR only the logit EWS predicts a crisis entry for the next year.
  - “Verge of crisis” signal if BOTH tree and logit EWS predict a crisis for the next year.
  - Country-specific charts of predicted crisis probability and major logit regressors can supplement the two-tiered EWS.

### Sensitivity analysis and robustness checks
- Dropping observations with extreme regressor values: predictive performance of the logit EWS is not affected; directions of influence remain unchanged.
- Varying dependent-variable definition:
  - Using only Standard & Poor’s crisis episodes: correctly predicts 63 percent of crisis entries and sends false alarms in 4 percent of cases.
  - Lowering IMF loan threshold to 50 percent of quota: correctly predicts 58 percent of crisis entries and sends false alarms in 9 percent of cases.
  - Increasing IMF loan threshold to 150 percent of quota: correctly predicts 66 percent of crisis entries and sends false alarms in 6 percent of cases.
- Reentering dropped variables (financing requirement, resource gap, public debt, overall balance) did not improve predictive power.
- Specification over full sample vs. 1990 onward:
  - A model specified for the full sample fared well overall but was less successful predicting 1990 onward crisis entries.
  - The logit EWS specified for 1990 onward generalized well to the full sample, suggesting structural breaks since the beginning of the 1990s.

### Summary of substantive findings and implications
- Variables that predict sovereign debt crises include:
  - External debt ratios measuring solvency and debt sustainability.
  - Measures of illiquidity or refinancing risk.
  - Measures of external imbalance and debt-servicing pressures.
  - Macroeconomic instability (especially monetary instability).
  - Political-economy factors leading to policy uncertainty.
- Important nuanced findings:
  - High external debt combined with high inflation is a dominant predictor of high crisis risk (66.8 percent).
  - Low external debt plus favorable liquidity and revenue metrics and strong growth are associated with very low crisis risk (2.3 percent).
  - Intermediate external debt can still imply high crisis risk if coupled with liquidity stress, political-timing uncertainties, or exchange-rate rigidity.
  - High external debt alone is not a necessary condition for crisis if inflation, external financing requirement, and public-debt-to-revenue ratios are favorable.
- Suggested extensions and research directions:
  - Extend analysis to poorer developing countries and HIPCs to assess different debt thresholds and creditor composition.
  - Improve prediction of 1990s-style (illiquidity-driven) crises and reduce false alarms.
  - Incorporate better fiscal-flow and public-debt stock data to test fiscal vulnerability measures (real budget deficits, primary gaps).
  - Test whether credit ratings and spreads have additional predictive power after controlling for macro determinants.
  - Study interactions among debt, currency, and banking crises, and whether currency/banking crises lead debt crises.
  - Analyze crisis episodes where default was avoided due to large IMF packages separately to assess vulnerabilities and policy implications.

### Appendix II — tree assignment rule (exact numeric relationships)
- Original sample priors: π(1)=0.205, π(0)=0.795.
- Misclassification costs used: C(1)=7, C(0)=1.
- New priors:
  - π‘ (1) = 7 x 0.205 / [7 x 0.205 + 1 x 0.795] = 0.643
  - π‘ (0) = 1 - π‘ (1) = 0.356
- Assignment rule (unit misclassification costs): assign node n to class 1 when within-node relative probability exceeds sample-wide relative probability.
- For arbitrary symmetric costs, assignment rule becomes [π‘ (1)/π‘ (0)] N1(n)/N0(n) > N1/N0.
- In the example N1/N0 = 0.2571, so the operational rule used: assign node n to class 1 if N1(n)/N0(n) > 0.55 x N1/N0 = 0.14.

*Sources: IMF; Standard & Poor’s; World Bank; and authors’ calculations.*

### References

### _wp03221 - References

### Sovereign defaults, credit ratings, and sovereign debt
- Beers, David T., and Ashok Bhatia, 1999,. “Sovereign Defaults: History”, in Standard & Poor’s Credit Week, December 22.
- Cantor, Richard, and Frank Packer, 1996, “Determinants and Impact of Sovereign Credit Ratings,” Federal Reserve Bank of New York Policy Review (October), pp. 37–52.
- Catão, Luis, and Bennett Sutton, 2002, “Sovereign Defaults: The Role of Volatility,” IMF Working Paper 02/149 (Washington: International Monetary Fund).
- Eaton, Jonathan, and Raquel Fernandez, 1995, “Sovereign Debt,” NBER Working Paper 5131, Prepared for Handbook of International Economics.
- Reinhart, Carmen M., 2002, “Default, Currency Crises and Sovereign Credit Ratings,” NBER Working Paper 8738. Also in The World Bank Economic Review, Vol. 16, No. 2, pp. 151–170.
- Standard & Poor’s, 2002, “Sovereign Defaults: Moving Higher Again in 2003?,” (September 24) [Reprinted for RatingsDirect]

### IMF analyses on catalytic finance, crisis lending, and moral hazard
- Corsetti, Giancarlo, Bernardo Guimarães, and Nouriel Roubini, 2003, “International Lending of Last Resort and Moral Hazard: A Model of the IMF’s Catalytic Fianance,” http://www.econ.yale.edu/~corsetti/euro/imf.pdf , November (Unpublished; New York: New York University)
- Cottarelli, Carlo and Curzio Giannini, 2002, “Bedfellows, Hostages, or Perfect Strangers? Global Capital Markets and the Catalytic Effect of IMF Crisis Lending,” IMF Working Paper 02/193 (Washington: International Monetary Fund).
- Dell’Arricia, Giovanni, Isabel Schnabel, and Jeromin Zettelmeyer, 2002, “Moral Hazard and International Crisis Lending: A Test,” IMF Working Paper 02/181 (Washington: International Monetary Fund).
- Lane, Timothy, and Steven Phillips, 2001, “Does IMF Financing Result in Moral Hazard?” IMF Working Paper 00/168 (Washington: International Monetary Fund).
- Mody, Ashoka, and Diego Saravia, 2003, “Catalyzing Private Capital Flows: Do IMF-Supported Programs Work as Commitment Devices?” Unpublished, IMF (Washington: International Monetary Fund).

### Fiscal vulnerability, financial crises, and fiscal sustainability
- Hemming, Richard, Michael Kell, and Axel Schimmelpfennig, 2003, Fiscal Vulnerability and Financial Crises in Emerging Market Economies, IMF Occasional Paper No. 218 (Washington: International Monetary Fund).
- Hemming, Richard, and Murray Petrie, 2002, “A Framework for Assessing Fiscal Vulnerability,” IMF Working Paper 00/52 (Washington: International Monetary Fund).
- Hemming, Richard, and Nigel Chalk, 2000, “Assessing Fiscal Sustainability in Theory and Practice,” IMF Working Paper 00/81 (Washington: International Monetary Fund).
- Ghosh, Swati, and Atish Ghosh, 2002, “Structural Vulnerabilities and Currency Crises,” IMF Working Paper No. 02/9 (Washington: International Monetary Fund).

### Political economy, creditworthiness, and emerging market risk
- Haque, Nadeem U., Mark Nelson, and Donald J. Mathieson, 1998, “The Relative Importance of Political and Economic Variables in Creditworthiness Ratings,” IMF Working Paper 98/46 (Washington: International Monetary Fund).
- Larrain, Guillermo, Helmut Reisen, and Julia von Maltzan, 1997, “Emerging Market Risk and Sovereign Credit Ratings,” OECD Development Centre Technical Papers No. 124 (Paris: Organisation for Economic Co-operation and Development).
- Lee, Suk Hun, 1993, “Are the credit ratings assigned by bankers based on the willingness of LDC borrowers to repay?,” In: Journal of Development Economics, Vol. 40, pp. 349-359.
- Rojas-Suarez, L., 2001, Rating Banks in Emerging Markets, Institute for International Economics (Washington, DC).
- Beim, David O., and Charles W. Calomiris, 2001,. Emerging Financial Markets, (New York: McGraw-Hill/Irwin).
- Roubini, Nouriel, 2001, “Debt Sustainability: How to Assess Whether a Country is Insolvent,” http://pages.stern.nyu.edu/~roubini/debt.pdf  (Unpublished; New York: New York University) (December).

### Methodology, statistical, and technical references
- Breimann, L., Friedmann, J.H., Olshen, R.A. & Stone, C.J., 1983, Classification and Regression Trees, (Wadsworth Publishers).
- Detragiache, Enrica, and Antonio Spilimbergo, 2001, “Crises and Liquidity: Evidence and Interpretation,” IMF Working Paper 01/2 (Washington: International Monetary Fund).

*Source: _wp03221 - References — https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2003/_wp03221.pdf*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2003/_wp03221.pdf_