## _wp1628

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---

### I. Introduction and context
- Motivation
  - The global financial crisis and subsequent weakening of fiscal positions in advanced and emerging economies highlighted the importance of monitoring country’s vulnerability to fiscal distress.
  - Existing Early Warning Systems (EWS) literature uses predetermined sets of leading indicators and shows wide variation in variable lists and mixed results.
- Research objective
  - Revisit leading indicators of fiscal distress using an agnostic Extreme Bound Analysis (EBA) that ranks candidate indicators by robustness of association with fiscal distress.
- Main stated conclusions
  - Both fiscal and non-fiscal leading indicators are robustly associated with fiscal distress.
  - A vulnerability index based on robust indicators has performance comparable to the average performance of other EWS in the literature and better predictive power than the fiscal-only EWS of Baldacci et al. (2011).
  - The importance of both fiscal and non-fiscal indicators is robust to model specifications and sample compositions.
- Policy implication (stated)
  - Policymakers should not restrict attention to fiscal indicators only when assessing vulnerability to fiscal distress.

### II. Methodological approach and specification
- Core methodology: Extreme Bound Analysis (EBA) applied with a pooled logit EWS specification
  - Logit specification: log(P[Y=1|z,x]/P[Y=0|z,x]) = beta_z * z + sum beta_xj * x_j + epsilon.
  - For each candidate leading indicator z, estimate all combinations of k additional controls drawn from n−1 remaining variables.
  - Number of combinations per z: M = (n−1−k)! / k! (as described).
  - Weight coefficients by model relative likelihood L_zj:
    - omega_zj = L_zj / sum_i=1^M L_zi
    - Likelihood-weighted average coefficient beta_hat_z = sum_j=1^M omega_zj * beta_hat_zj
    - Likelihood-weighted average standard error computed similarly.
  - Robustness assessment: treat beta_hat_z as normal across regressions and compute the proportion of its distribution on one side of zero; indicator deemed robust if proportion exceeds chosen confidence level (e.g., 90 percent).
  - Forecasting horizon: 1 year (results qualitatively unchanged at 2 years).

- Implementation details
  - Baseline (pooled logit): k = 2 additional controls per regression.
  - Baseline combinations: 630 regressions per leading indicator → 23,410 regressions in total for 37 candidate indicators (baseline reported).
  - Robustness checks include: “narrow” fiscal distress, emerging economies subsample, k = 3 controls (7,140 regressions per indicator → 264,180 regressions in total), random effects logit, pooled probit, and alternative one-sided Christiano and Fitzgerald (2003) output gap.

### III. Data and definitions
- Sample
  - 29 advanced and 52 emerging economies (81 countries), period 1970–2015.
- Fiscal distress definition (expanded Baldacci et al. (2011) through 2015)
  - Episodes when government experiences extreme funding difficulties captured by four criteria:
    - (i) public debt default or restructuring;
    - (ii) sovereign bond yield pressure;
    - (iii) large IMF-supported program;
    - (iv) excessive inflation.
- Counts of fiscal distress episodes (including Baldacci et al. (2011) comparison in brackets)
  - Advanced Economies: Public debt default or restructuring: 1 (0); Bond Yield Pressures: 30 (29); Inflation Pressures: 5 (5); IMF program: 8 (6); Total: 41 (39).
  - Emerging Economies: Public debt default or restructuring: 54 (52); Bond Yield Pressures: 17 (15); Inflation Pressures: 6 (6); IMF program: 103 (79); Total: 160 (135).
- Overlap with other crises (sample through 2010)
  - Currency crises overlap with 26 percent of fiscal distress episodes.
  - Banking crises overlap with 24 percent of fiscal distress episodes.
- Candidate leading indicators
  - 37 variables covering fiscal, macro, monetary, external sectors; all variables measured in percentage points.
- Multicollinearity
  - Table 5 shows most variables are not highly correlated except some debt-related indicators.
  - Correlations of FX reserves (% of GDP) with robust fiscal indicators do not exceed 0.35 in absolute terms.

### IV. Estimation results — baseline and robustness checks
- Baseline EBA (pooled logit; k = 2 controls)
  - Total regressions: 23,410.
  - Main robust leading indicators (top-ranked by robustness; Coeff. / SEC(0) / robustness proportion / Obs.):
    - Output Gap: 0.296 / 0.069 / 1.000 / 3188
    - Current Account Balance (% of GDP): -0.046 / 0.014 / 1.000 / 3275
    - FX Reserves Growth: -0.010 / 0.003 / 0.998 / 3051
    - FX Reserves (% of GDP): -0.034 / 0.012 / 0.998 / 3103
    - Openness: (M+X)/ GDP: -0.006 / 0.003 / 0.970 / 3254
    - Primary Balance Gap (% of GDP): -0.029 / 0.017 / 0.958 / 688
    - Real GDP Growth: -0.039 / 0.023 / 0.957 / 3269
    - Overall Fiscal Balance (% of GDP): -0.052 / 0.031 / 0.953 / 2035
    - Primary Balance (% of GDP): -0.048 / 0.037 / 0.907 / 1874
    - Foreign Exchange Debt (% of GDP): 0.008 / 0.006 / 0.903 / 1124
  - Key interpretation points:
    - Both fiscal and non-fiscal variables are robust leading indicators.
    - Output gap consistently ranks at the top.
    - Debt-to-GDP ratio often does not differ pre-crisis but increases after crisis (more “ex post”); current account balance shows leading behavior.

- Robustness checks (high-level outcomes)
  - “Narrow” fiscal distress (exclude episodes overlapping with banking/currency crises; sample through 2010)
    - Non-fiscal indicators remain robust; gross financing needs and interest costs become robust.
  - Emerging economies subsample (52 emerging economies, 1970–2015)
    - Results similar to total sample: 8 out of 10 robust indicators from total sample remain robust; unemployment rate emerges as additional robust variable.
  - Increase controls to 3 per regression (k = 3; 7,140 regressions per indicator; total 264,180)
    - 8 out of 10 baseline robust indicators remain robust.
  - Random effects logit
    - 8 out of 10 baseline robust indicators remain robust.
  - Pooled probit
    - Results practically unchanged (smaller coefficients reflecting probit scale).
  - Alternative one-sided Christiano-Fitzgerald output gap
    - Results unchanged: output gap robustness persists.

### V. Fiscal Distress Index construction and performance
- Index construction
  - Built from most robust leading indicators identified via EBA (Table 13) with pooled logit coefficients.
  - Index excludes primary balance gap (low observations), foreign exchange debt ratio (series end in 2012), and FX reserves to GDP ratio (because FX reserves growth is already controlled for).
- EBA-based pooled-logit coefficients (Table 13; number of observations: 1765; pseudo R^2: 0.537; AUROC: 0.815):
  - Output Gap: 0.4377*** [0.0860]
  - Current Account Balance (% of GDP): -0.0943*** [0.0196]
  - FX Reserves Growth: 0.0002 [0.0029]
  - Openness: (M+X)/ GDP: -0.0097*** [0.0035]
  - Real GDP Growth: -0.1312*** [0.0349]
  - Overall Fiscal Balance (% of GDP): -0.0030 [0.0407]
  - Primary Balance (% of GDP): -0.0078 [0.0439]
  - Intercept: -1.9855*** [0.3069]
  - Model fit statistics and error rates:
    - AUROC: 0.815
    - Type 1 error: 0.218
    - Type 2 error: 0.312
    - TME: 0.530

- Contribution analysis
  - Figure 8 reports change in log odds ratio for a shift from 75th to 25th percentile of each robust indicator.
  - Non-fiscal indicators have larger relative impacts than fiscal indicators.

- Dynamics
  - Fiscal distress index is lower for advanced economies than emerging economies and spikes around late 1990s and the global financial crisis.

- Performance metrics and thresholds
  - Total misclassification error TME(t) = Type1(t) + Type2(t), where Type1 = missed crises as share of all crises, Type2 = false alarms as share of all non-crisis periods.
  - In-sample TME minima:
    - EBA-based index: TME minimized at 0.52 when threshold = 0.7 (reported in main text summary).
    - Baldacci et al. (2011) index: TME minimum 0.73 at threshold = 0.38.
    - Reported TME reduction: TME reduced by 29 percent relative to Baldacci et al. (2011) in-sample.
  - In-sample threshold minimizing TME reported in figures:
    - Baseline model threshold reported as 0.07 (Figure 4) and 0.04 (Figure 5 in-sample minimization); figures present in-text thresholds used in different comparisons.

- Out-of-sample (fit 1970–2007; apply to 2008–2015)
  - Out-of-sample performance
    - Classification table for 2008–2015 (model classification using in-sample threshold) — preserved counts:
      - Crisis & Signal: 25
      - Crisis & No Signal: 11
      - No Crisis & Signal: 72
      - No Crisis & No Signal: 263
      - Row/Column totals (as presented): Yes total 36; No total 335; Total 371
    - Alternate figure text counts: 25 / 11 / 36 and 72 / 263 / 335 with overall totals reported as 323 / 44 / 367 in source—these multiple tabulations are preserved as presented.
    - Of 32 crises identified (alternate count in text), model predicts 25 correctly (78 percent).
    - False alarms: 118 out of 344 non-crisis years (34 percent) in the out-of-sample tabulation reported elsewhere in text.
  - Overall: in-sample outperforms out-of-sample, but out-of-sample TME is not much higher, suggesting reasonable predictive ability post–2007.

- Comparative performance with other EWS studies
  - Figure 7 places the model within the 1st and 3rd quartile of TME across EWS literature.
  - The model exhibits more Type2 errors (false alarms) slightly above average and Type1 errors slightly below average.
  - Authors note conservatism (more false alarms) may be appropriate because missed crises are costlier than false alarms.

### VI. Conclusions, policy implications, and limitations
- Key conclusions
  - Both fiscal and non-fiscal leading indicators are robust predictors of fiscal distress, consistent with multiple-equilibrium theories and cross-sector spillovers.
  - A vulnerability index incorporating robust fiscal and non-fiscal indicators improves performance relative to a fiscal-only EWS (Baldacci et al. (2011)), reducing TME by 29 percent in-sample.
  - Non-fiscal indicators (external and real sector) can matter more than traditional fiscal indicators as early signals.
- Policy implications
  - Policymakers should monitor selected non-fiscal leading indicators — Output Gap, Current Account Balance, FX Reserves dynamics, Openness — alongside fiscal indicators to assess vulnerability to fiscal distress.
  - A conservative EWS that tolerates more false alarms may be appropriate given higher costs of missed crises.
- Limitations and areas for future work
  - Estimation sample constrained by shortest time series required for logit, reducing sample size and precision.
  - Pooled advanced and emerging samples impose common indicator effects; separate advanced-only analysis is challenging due to few advanced-economy fiscal distress events.
  - Identifying “narrow” fiscal distress events is difficult because of frequent twin or multiple crises and spillovers.

*Source: _wp1628 (IMF PDF content provided).*

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

### _wp1628 - References

### I. Introduction and context
- The global financial crisis and subsequent weakening of fiscal positions in advanced and emerging economies highlighted the importance of monitoring country’s vulnerability to fiscal distress.
- Existing Early Warning Systems (EWS) literature:
  - Uses a predetermined set of leading indicators, typically based on economic reasoning.
  - Shows wide variation in the list of variables across studies, often driven by researchers' preference for parsimonious models with a large number of significant leading indicators.
  - Produces mixed results with no agreement on the most robust leading indicators of fiscal distress.

### Methodological approach
- The paper revisits leading indicators of fiscal distress using the Extreme Bound Analysis (EBA).
- Key features of the EBA approach as applied:
  - Takes an agnostic approach with respect to leading indicators; does not require the researcher to predetermine the set of explanatory variables.
  - “Allows the data to speak” by ranking possible leading indicators based on the “robustness” of their association with fiscal distress.
  - EBA has precedents in growth theory (Sala-i-Martín, 1997) and has been applied to financial crises (Ho, 2010); this paper is, to the authors' knowledge, the first application to fiscal distress.

### Main conclusions (as stated)
- Both fiscal and non-fiscal leading indicators are robustly associated with fiscal distress.
  - This contrasts with traditional measures of fiscal stress based solely on fiscal leading indicators (Baldacci et al., 2011).
- A vulnerability index based on these robust indicators:
  - Has a performance comparable to the average performance of other EWS (for fiscal, currency, banking, and other types of crises) in the literature.
  - Has better predictive power than the EWS of Baldacci et al. (2011), which is based only on fiscal leading indicators.
- The result on the importance of both fiscal and non-fiscal leading indicators is robust to various model specifications and sample compositions.

### Policy implications
- Policymakers should not restrict attention to fiscal indicators only when assessing a country’s vulnerability to fiscal distress.

### Document structure (as provided)
- The remainder of the paper is structured as follows: Section II surveys the related literature.

### Tables and Figures (listing from the source)
- Tables (with page references as given):
  - 1. Definition of Fiscal Distress (page 19)
  - 2. Fiscal Distress Episodes (page 19)
  - 3. List of Leading Indicators of Fiscal Distress (page 20)
  - 4. Descriptive Statistics (page 21)
  - 5. Correlation Matrix (page 22)
  - 6. EBA results: Baseline Specification (page 24)
  - 7. Robustness Check 1: ‘Narrow’ Fiscal Distress Episodes (page 25)
  - 8. Robustness Check 2: Emerging Economies (page 26)
  - 9. Robustness Check 3: Number of Control Variables (page 27)
  - 10. Robustness Check 4: Random Effects Logit Model (page 28)
  - 11. Robustness Check 5: Pooled Probit Model (page 29)
  - 12. Robustness check 6: Using New Measure of Output Gap (page 30)
  - 13. Early Warning System Based on Most Robust Leading Indicators (page 31)
- Figures (with page references as given):
  - 1 Banking Currency and Fiscal Crises (page 32)
  - 2 Event Study Analysis (page 32)
  - 3 Fiscal Distress Index Based on Robust Leading Indicators (page 33)
  - 4 In-sample Performance: EBA-based Fiscal Distress Index versus Baldacci et al. (2011) Index (page 34)
  - 5 In-sample Versus Out-of-sample Performance of the EBA-based Fiscal Distress Index (page 35)
  - 6 Classification Table for Out-of-sample Predictions of the EBA-based Fiscal Distress Indicator (page 36)
  - 7 Comparison with Other Studies (page 36)
  - 8 Economic Significance of Robust Leading Indicators (page 37)

*Source: _wp1628 - References*

### Section III describes the empirical methodology and data. Section IV presents the estimation

### _wp1628 - Section III describes the empirical methodology and data. Section IV presents the estimation

### Related literature: theories and empirical evidence
- Theoretical framing
  - Distinction between underlying vulnerabilities (necessary but not sufficient) and crisis triggers (external/domestic shocks).
  - Early literature emphasizes fiscal and monetary fundamentals (Krugman (1979); Detragiache and Spilimbergo (2001)).
  - Later literature emphasizes self-fulfilling expectations and non-fiscal fundamentals via multiple-equilibrium models (Obstfeld, 1984; Calvo, 1988; Alesina et al., 1989; Cole and Kehoe, 1994; Jeanne, 1997; Masson, 1999).
  - Main takeaway: no a priori reason to restrict leading indicators of fiscal distress to fiscal fundamentals.
- Empirical evidence on early warning indicators (EWS)
  - Two broad empirical approaches: non-parametric (signals approach) and parametric (multivariate logit, probit).
  - Non-fparametric “signals” approach: focuses on bivariate thresholds; cannot directly determine statistical significance; applied in fiscal context by Reinhart (2002), Hemming et al. (2003), Baldacci et al. (2011), Berti et al. (2012), de Cos et al. (2014).
  - Parametric EWS: tests significance while accounting for correlation; requires long time series; applied by Marashaden (1997), Peter (2002), Manasse et al. (2003), Kraay and Nehru (2006), Gourinchas and Obstfeld (2012).
  - Common characteristic: researcher pre-selects candidate indicators, often with hindsight (“publication bias”).
- Gap addressed
  - Extreme Bound Methodology (EBA) and Bayesian equivalents let the data speak by examining all combinations of explanatory variables; prior EBA/Bayesian model averaging studies exist for other crises but not for fiscal distress (closest: Chakrabarti and Zeaiter (2014) on external debt arrears).

### Empirical methodology and data
- Methodology: Extreme Bound Analysis (EBA) applied with pooled logit early warning specification
  - Logit specification: log(P[Y=1|z,x]/P[Y=0|z,x]) = beta_z * z + sum beta_xj * x_j + epsilon.
  - For each candidate leading indicator z, estimate all combinations of k additional controls drawn from n-1 remaining variables:
    - Number of combinations per z: M = (n−1−k)! / k!  (as described in the text).
  - Procedure per indicator z:
    - Estimate each of the M regressions and store coefficient estimates beta_hat_zj.
    - Weight coefficients by model relative likelihood L_zj so unlikely models receive less weight:
      - omega_zj = L_zj / sum_i=1^M L_zi
    - Compute likelihood-weighted average coefficient beta_hat_z = sum_j=1^M omega_zj * beta_hat_zj.
    - Compute likelihood-weighted average standard error similarly.
    - Assess robustness: assume beta_hat_z ~ normal across regressions; compute proportion of its distribution on one side of zero; indicator deemed robust if this proportion exceeds a chosen confidence level (e.g., 90 percent).
  - Forecasting horizon used in estimation: 1 year (results qualitatively unchanged at 2 years).
- Data
  - Sample: 29 advanced and 52 emerging economies (81 countries in total), period 1970–2015.
  - Fiscal distress definition (based on Baldacci et al. (2011), expanded through 2015): episodes when government experiences extreme funding difficulties captured by four criteria: (i) debt default or restructuring; (ii) sovereign bond yield pressure; (iii) large IMF-supported program; (iv) excessive inflation.
  - Overlap with other crises: currency crises overlap with 26 percent of fiscal distress episodes; banking crises overlap with 24 percent (sample spanning through 2010).
  - Leading indicators: 37 variables used in the literature covering fiscal, macro, monetary, external sectors; all variables measured in percentage points.
  - Multicollinearity: Table 5 shows most variables are not highly correlated except some debt-related indicators (correlations between FX reserves (% of GDP) and robust fiscal indicators do not exceed 0.35 in absolute terms).

### Estimation results (baseline and robustness checks)
- Baseline EBA (pooled logit)
  - Combinations used: 2 additional controls per regression → 630 regressions per leading indicator → 23,410 regressions in total.
  - Main findings
    - Both fiscal and non-fiscal variables are robust leading indicators of fiscal distress.
    - Non-fiscal robust indicators include output gap (overheating), high current account deficit, low FX reserves/GDP ratio, slowdown in FX reserves growth, and higher openness.
    - Fiscal robust indicators include foreign exchange debt to GDP ratio, primary fiscal balance gap, primary and overall fiscal balance to GDP ratios.
    - Output gap consistently ranks at the top of robustness lists.
    - Debt-to-GDP ratio often does not differ pre-crisis but increases after crisis → debt-to-GDP is more an “ex post” indicator; current account balance shows leading behavior.
  - Implication: limiting leading indicators to fiscal variables risks omitting important external and macro indicators.
- Robustness checks
  - “Narrow” fiscal distress (exclude episodes overlapping with banking/currency crises)
    - Sample restricted through 2010 (data availability).
    - Non-fiscal indicators remain robust.
    - Gross financing needs and interest costs become robust as well.
  - Emerging economies subsample
    - Table 8: subsample results very similar to total sample; 8 out of 10 robust indicators from total sample remain robust.
    - Additional robust variable: unemployment rate (consistent with output gap result).
  - Increase number of controls: 3 controls per regression
    - Number of regressions per leading indicator: 7,140 → total 264,180 regressions.
    - Main results unchanged: 8 out of 10 baseline robust indicators remain robust.
  - Random effects logit and pooled probit
    - Random effects logit: 8 out of 10 baseline robust indicators remain robust.
    - Pooled probit: results practically unchanged (fat tails in logit do not drive results).
  - Alternative output gap filter
    - One-sided Christiano and Fitzgerald (2003) filter used to address potential end-of-sample bias from two-sided HP filter.
    - Results unchanged: output gap robustness persists.

### Fiscal Distress Index and its performance
- Construction
  - Fiscal distress index built from most robust leading indicators identified via EBA (see Table 13).
  - Note: index excludes primary balance gap (low observations), foreign exchange debt ratio (series end in 2012), and FX reserves to GDP ratio (because FX reserves growth is already controlled for).
- Contribution analysis
  - Figure 8: impact of change from 75th to 25th percentile in robust indicators on log odds ratio shows non-fiscal indicators have a larger relative impact than fiscal indicators.
- Dynamics
  - Figure 3: fiscal distress index shows lower levels for advanced economies versus emerging economies and spikes around late 1990s and the global financial crisis.
- Performance metric
  - Total misclassification error (TME(t)) = Type1(t) + Type2(t)
    - Type1 = missed crises as share of all crises.
    - Type2 = false alarms as share of all non-crisis periods.
  - Choice of threshold t trades off Type1 and Type2; TME minimized over t.
- In-sample results
  - TME is minimized at 0.52 when threshold = 0.7 for the EBA-based index.
  - Baldacci et al. (2011) index: TME minimum 0.73 at threshold = 0.38.
  - TME reduced by 29 percent relative to Baldacci et al. (2011).
- Out-of-sample results (1970–2007 fit; apply to 2008–2015)
  - In-sample outperforms out-of-sample, but out-of-sample TME is not much higher suggesting reasonable predictive ability post–2007.
  - Classification table (out-of-sample 2008–2015): of 32 crises identified, model predicts 25 correctly (78 percent).
  - False alarms: 118 out of 344 non-crisis years (34 percent).
- Comparison with other EWS studies
  - Figure 7: the model lies within the 1st and 3rd quartile of TME across EWS literature.
  - Model issues more Type2 errors (false alarms) slightly above average and Type1 errors slightly below average.
  - The model is conservative (more false alarms), which may be preferable as missed crises are costlier than false alarms.

### Conclusions and policy implications
- Key conclusions
  - Both fiscal and non-fiscal leading indicators are robust predictors of fiscal distress, consistent with theories emphasizing multiple equilibria and cross-sector spillovers.
  - A vulnerability index based on robust fiscal and non-fiscal indicators improves performance relative to a fiscal-only EWS (Baldacci et al. (2011)), reducing TME by 29 percent in-sample.
  - Non-fiscal indicators (external and real sector) can matter more than traditional fiscal indicators as early signals.
- Policy implications
  - Policymakers should monitor selected non-fiscal leading indicators (output gap, current account balance, FX reserves dynamics, openness) alongside fiscal indicators to assess vulnerability to fiscal distress.
  - A conservative EWS that tolerates more false alarms may be appropriate given higher costs of missed crises.
- Limitations and areas for future work
  - Estimation sample constrained by shortest time series required for logit, reducing sample size and precision.
  - Pooled advanced and emerging samples force common indicator effects; separate advanced-only analysis is challenging due to few advanced-economy fiscal distress events.
  - Identifying “narrow” fiscal distress events is difficult because of frequent twin or multiple crises and spillovers.

*Source: _wp1628 - Section III describes the empirical methodology and data. Section IV presents the estimation*

### REFERENCES

### _wp1628 - REFERENCES

### Literature and conceptual foundations
- Key topics covered by cited works:
  - Early warning systems and regime-switching approaches (Abiad, 2003; Berg, Borensztein, and Pattillo, 2005; Comelli, 2013).
  - Fiscal stress and fiscal distress measurement (Baldacci et al., 2011; Berti, Salto, and Lequien, 2012).
  - Sovereign default, debt sustainability, and debt crises models (Calvo, 1988; Cole and Kehoe, 1996; Kraay and Nehru, 2006; Manasse, Roubini, and Schimmelpfennig, 2003; Reinhart, 2002).
  - Currency and balance-of-payments crises, contagion, and speculative attacks (Eichengreen, Rose, and Wyplosz, 1995; Krugman, 1979; Kaminsky and Reinhart, 1999).
  - Methods and robustness concerns: sensitivity analysis, publication bias, and many-regressions critique (Leamer, 1985; Rothstein, Sutton, and Borenstein, 2006; Sala-i-Martin, 1997).
- Methodological references cited include IMF, BIS, ECB, NBER, World Bank, and academic journals covering logit/probit, OLS, binary tree, EBA, and event-study techniques.

### Definition of fiscal distress (Table 1 / Table 2)
- Fiscal distress events and criteria (Source: Baldacci et al., 2011):
  - Public debt default or restructuring: Failure to service debt as payments come due, as well as distressed debt exchanges. (S&P definition applies.)
  - Sovereign bond yield pressure: Sovereign spreads greater than 1,000 basis points or 2 s.d. from the country average.
  - Large IMF-supported program: Access to 100 percent of quota or more.
  - Inflation pressures / implicit/internal public debt default: Inflation greater than 35 percent per annum (Advanced Economies) and inflation greater than 500 percent per annum (Emerging Economies).
- Counts of fiscal distress episodes (including comparison to original Baldacci et al. (2011) dataset in brackets):
  - Advanced Economies: Public debt default or restructuring: 1 (0); Bond Yield Pressures: 30 (29); Inflation Pressures: 5 (5); IMF program: 8 (6); Total: 41 (39).
  - Emerging Economies: Public debt default or restructuring: 54 (52); Bond Yield Pressures: 17 (15); Inflation Pressures: 6 (6); IMF program: 103 (79); Total: 160 (135).

### Leading indicators of fiscal distress (Table 3)
- Leading indicators (source and grouping preserved as in table), examples include:
  - Average Maturity — Baldacci et al. (2011) — Public Sector: Liquidity Pressure Indicators — Signals — "Average Maturity of remaining debt (in years)".
  - Gross Financing Need — Baldacci et al. (2011) — Public Sector: Debt Burden — Signals — "Gross financing needs (short-term debt plus the overall balance), percent of GDP".
  - Interest-Growth Differential — Baldacci et al. (2011) — Public Sector: Debt Tolerance Indicators — Signals — "Difference between average effective interest rate and GDP growth in percent".
  - Primary Balance (% of GDP) — Baldacci et al. (2011) — Public Sector: Liquidity Pressure Indicators — Signals — "Revenue-Expenditure+Interest Expenditure, percent of GDP".
  - Short Term Debt (% of FX Reserves), Short Term Debt (% of total), FX Reserves (% of GDP), Real Exchange Rate Undervaluation, Domestic Credit Gap, Real Interest Rate, Short Term External Debt (% of GDP), Debt (% of GDP), External Debt (% of GDP), FDI (% of GDP), FX Reserves Growth, Interest Expenditure (% of total Expenditure), LIBOR, Nominal GDP Growth, Openness: (M+X)/GDP, Overall Fiscal Balance (% of GDP), Real GDP Growth, Unemployment Rate, US TBill Rate, Output Gap, Average Effective Interest Rate, Foreign Exchange Debt (% of GDP), FX Reserve Coverage, Primary Balance Gap (% of GDP), Amortisation of Total Public Debt (% of GDP).
- Estimation methods associated with indicators include EBA and OLS, OLS/Probit/Logit (FE), Logit, Probit, Binary Tree, Signals, and combinations thereof as listed.

### Descriptive statistics (Table 4) — selected variables preserved exactly
- Debt (% of GDP): Obs. 3,073; Mean 52.54; Median 45.3; St. Dev. 34.11; 10th percentile 6.6; 90th percentile 95.2
- Output Gap: Obs. 3,188; Mean -0.1; Median -0.1; St. Dev. 2.0; 10th percentile -1.5; 90th percentile 1.3
- Openness: (M+X)/ GDP: Obs. 3,254; Mean 71.26; Median 60.0; St. Dev. 53.22; 10th percentile 6.1; 90th percentile 123.0
- CPI Inflation: Obs. 2,804; Mean 28.36; Median 6.2; St. Dev. 224.0; 10th percentile 1.4; 90th percentile 26.1
- FX Reserve Coverage: Obs. 1,581; Mean 1.7; Median 0.7; St. Dev. 11.2; 10th percentile 0.1; 90th percentile 2.9
- Amortisation of Total Public Debt (% of GDP ): Obs. 2,030; Mean 10.0; Median 4.2; St. Dev. 19.9; 10th percentile 0.6; 90th percentile 19.4
- Real Interest Rate: Obs. 1,387; Mean -1.2; Median 1.4; St. Dev. 52.9; 10th percentile -4.9; 90th percentile 6.9
- Domestic Credit Gap: Obs. 2,588; Mean -48.1; Median -1.4; St. Dev. 1754.8; 10th percentile -94.0; 90th percentile 26.3
- FX Reserves (% of GDP): Obs. 3,103; Mean 12.3; Median 7.5; St. Dev. 15.0; 10th percentile 1.9; 90th percentile 25.9
- Interest-Growth Differential: Obs. 2,154; Mean -15.7; Median -4.1; St. Dev. 108.6; 10th percentile -24.7; 90th percentile 3.0
- Primary Balance (% of GDP): Obs. 1,874; Mean 0.7; Median 0.3; St. Dev. 3.9; 10th percentile -3.4; 90th percentile 5.3
- Short Term Debt (% of total): Obs. 2,107; Mean 17.9; Median 13.8; St. Dev. 17.5; 10th percentile 0.0; 90th percentile 41.3
- Short Term Debt (% of FX Reserves): Obs. 1,984; Mean 654; Median 50.0; St. Dev. 51.6; 10th percentile 3.2; 90th percentile 328.2 (note: values preserved exactly as in source)
- GDP per Capita: Obs. 3,291; Mean 9.3; Median 9.7; St. Dev. 4.2; 10th percentile 0.0; 90th percentile 13.3
- Average Effective Interest Rate: Obs. 1,951; Mean 17.5; Median 0.2; St. Dev. 75.1; 10th percentile 0.0; 90th percentile 14.4
- Gross Financing Need: Obs. 735; Mean 11.4; Median 8.8; St. Dev. 11.3; 10th percentile 1.3; 90th percentile 26.6
- Average Maturity: Obs. 733; Mean 7.2; Median 6.2; St. Dev. 4.2; 10th percentile 3.0; 90th percentile 13.3
- Foreign Exchange Debt (% of GDP): Obs. 1,124; Mean 15.4; Median 4.4; St. Dev. 22.6; 10th percentile 0.0; 90th percentile 41.5

### Correlation structure (Table 5) — selected pairwise correlations preserved exactly
- Debt (% of GDP) correlations:
  - with Output Gap: -0.173
  - with CPI Inflation: 0.249
  - with FX Reserve Coverage: -0.272
  - with Amortisation of Total Public Debt (% of GDP ): -0.421
  - with Real Interest Rate: 0.353
  - with Current Account Balance (% of GDP): -0.451
  - with Interest-Growth Differential: 0.556
  - with Primary Balance (% of GDP): 0.652
  - with Short Term Debt (% of total): -0.665
  - with Short Term External Debt (% of GDP): -0.595
- Debt Service due (% of GDP) correlations (selected):
  - with External Debt (% of GDP): 0.742
  - with Debt (% of GDP): 0.444
  - with Gross Financing Need: 0.629
  - with Interest Expenditure (% of total Expenditure): 0.561
- Notation: full correlation matrix spans multiple pages; values above are preserved exactly as presented.

### EBA (Extreme Bounds Analysis) baseline and robustness results (Tables 6–12)
- Baseline EBA results (Table 6) — pooled logit, sample: 29 advanced and 52 emerging economies, period 1970–2015. Top-ranked indicators by robustness (Coeff. / SEC(0) / Obs.):
  - Output Gap: 0.296 / 0.069 / 1.000 / 3188
  - Current Account Balance (% of GDP): -0.046 / 0.014 / 1.000 / 3275
  - FX Reserves Growth: -0.010 / 0.003 / 0.998 / 3051
  - FX Reserves (% of GDP): -0.034 / 0.012 / 0.998 / 3103
  - Openness: (M+X)/ GDP: -0.006 / 0.003 / 0.970 / 3254
  - Primary Balance Gap (% of GDP): -0.029 / 0.017 / 0.958 / 688
  - Real GDP Growth: -0.039 / 0.023 / 0.957 / 3269
  - Overall Fiscal Balance (% of GDP): -0.052 / 0.031 / 0.953 / 2035
  - Primary Balance (% of GDP): -0.048 / 0.037 / 0.907 / 1874
  - Foreign Exchange Debt (% of GDP): 0.008 / 0.006 / 0.903 / 1124
  - (Full table lists many additional indicators with coefficients, SEC(0) and Obs.)
- Robustness Check 1: “Narrow” fiscal distress episodes (Table 7) — sample 29 advanced and 52 emerging economies, period 1970–2010. Top indicators:
  - Output Gap: 0.194 / 0.076 / 0.995 / 2955
  - FX Reserves Growth: -0.011 / 0.006 / 0.979 / 2736
  - CPI Inflation: 0.025 / 0.012 / 0.978 / 2576
  - FX Reserves (% of GDP): -0.049 / 0.024 / 0.977 / 2788
  - Primary Balance Gap (% of GDP): -0.105 / 0.057 / 0.968 / 453
  - Gross Financing Need: 0.032 / 0.017 / 0.965 / 502
- Robustness Check 2: Emerging Economies (Table 8) — sample covers 52 emerging economies, 1970–2015. Top indicators:
  - Output Gap: 0.259 / 0.070 / 1.000 / 3188
  - FX Reserves Growth: -0.012 / 0.004 / 0.999 / 3051
  - FX Reserves (% of GDP): -0.040 / 0.013 / 0.999 / 3103
  - Current Account Balance (% of GDP): -0.033 / 0.014 / 0.989 / 3275
  - Real GDP Growth: -0.050 / 0.023 / 0.987 / 3269
- Robustness Check 3: Number of Control Variables (Table 9) — pooled logit with 3 additional controls per specification. Top indicators:
  - Output Gap: 0.333 / 0.083 / 1.000 / 3188
  - Current Account Balance (% of GDP): -0.054 / 0.017 / 0.999 / 3275
  - FX Reserves (% of GDP): -0.038 / 0.014 / 0.996 / 3103
  - FX Reserves Growth: -0.011 / 0.004 / 0.993 / 3051
- Robustness Check 4: Random Effects Logit Model (Table 10) — top indicators:
  - Output Gap: 0.302 / 0.071 / 1.000 / 3188
  - Current Account Balance (% of GDP): -0.054 / 0.016 / 1.000 / 3275
  - FX Reserves Growth: -0.010 / 0.003 / 0.998 / 3051
  - FX Reserves (% of GDP): -0.035 / 0.013 / 0.997 / 3103
- Robustness Check 5: Pooled Probit Model (Table 11) — top indicators with smaller coefficients reflecting probit scale:
  - Output Gap: 0.138 / 0.034 / 1.000 / 3188
  - Current Account Balance (% of GDP): -0.025 / 0.007 / 1.000 / 3275
  - FX Reserves (% of GDP): -0.016 / 0.005 / 0.998 / 3103
  - FX Reserves Growth: -0.003 / 0.001 / 0.995 / 3051
- Robustness Check 6: Using New Measure of Output Gap (Table 12) — one-sided Christiano-Fitzgerald filter:
  - Output Gap: 0.074 / 0.018 / 1.000 / 3188
  - Current Account Balance (% of GDP): -0.025 / 0.007 / 1.000 / 3275
  - FX Reserves (% of GDP): -0.016 / 0.005 / 0.998 / 3103
  - FX Reserves Growth: -0.003 / 0.001 / 0.995 / 3051

### Early Warning System specification and performance (Table 13 and Figures)
- EBA-based fiscal distress early warning model using most robust leading indicators (Table 13, pooled logit):
  - Coefficients (with standard errors in brackets, significance indicated):
    - Output Gap: 0.4377*** [0.0860]
    - Current Account Balance (% of GDP): -0.0943*** [0.0196]
    - FX Reserves Growth: 0.0002 [0.0029]
    - Openness: (M+X)/ GDP: -0.0097*** [0.0035]
    - Real GDP Growth: -0.1312*** [0.0349]
    - Overall Fiscal Balance (% of GDP): -0.0030 [0.0407]
    - Primary Balance (% of GDP): -0.0078 [0.0439]
  - Intercept: -1.9855*** [0.3069]
  - Number of observations: 1765
  - Pseudo R^2: 0.537
  - AUROC: 0.815
  - Type 1 error: 0.218
  - Type 2 error: 0.312
  - TME: 0.530
- Fiscal Distress Index (Figure 3):
  - Constructed from predicted values of the logit model using robust indicators: (i) Output Gap; (ii) Current Account Balance (% of GDP); (iii) FX Reserves Growth; (iv) Openness: (M+X)/GDP; (v) Real GDP Growth; (vi) Overall Fiscal Balance (% of GDP); (vii) Primary Balance (% of GDP).
  - Number of observations for the pooled-logit model in Table 13: 1765.
  - Confidence bands: 90 percent.
- In-sample performance (Figure 4):
  - The threshold minimizing TME is reported as 0.07 for the baseline model based on robust leading indicators.
- In-sample vs out-of-sample performance (Figure 5):
  - In-sample years: 1970–2007; Out-of-sample years: 2008–2015.
  - Threshold minimizing in-sample TME: 0.04 (vertical line).
- Out-of-sample classification table (Figure 6) for years 2008–2015 (model classification using in-sample threshold):
  - Crisis / Signal matrix (preserved counts):
    - Yes (Crisis) & Yes (Signal): 25
    - Yes (Crisis) & No (Signal): 11
    - No (Crisis) & Yes (Signal): 72
    - No (Crisis) & No (Signal): 263
    - Row/Column totals: Yes total 36; No total 335; Total 371 (table reproduced as counts: Yes/No/Total rows and columns align with source)
  - Alternate formatted counts in figure text:
    - Yes/Yes/Total: 25 / 11 / 36
    - No/Yes/Total: 72 / 263 / 335
    - Overall totals: 323 / 44 / 367 (note: figures in source present multiple tabulations; counts above are preserved exactly as listed in the figure and caption)
- Comparative performance (Figure 7):
  - Reports in-sample total misclassification error (TME), Type 1 and Type 2 errors of 8 Early Warning Systems from literature — values represented by minimum, 25th percentile, mean, 75th percentile and maximum (visual summary in source).
- Economic significance of robust leading indicators (Figure 8):
  - Presents difference in logarithm of odds ratio for 75th vs 25th percentile of each component indicator. The indicators plotted (in order shown) include:
    - Real GDP Growth, Current Account Balance (% of GDP), Output Gap, Openness: (M+X)/ GDP, Primary Balance (% of GDP), Overall Fiscal Balance (% of GDP), FX Reserves Growth.
  - Visual scale ranges from 0 to 0.6 (per figure), indicating relative economic impact magnitudes.

*Source: _wp1628 - REFERENCES (IMF PDF content provided).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1628.pdf_