## _wp16202

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---

### Introduction and core findings
- At end 2015, advanced economies reached levels of debt close to 106 percent of GDP.
- Public debt for advanced economies at end 2015 was above levels during the Great Depression and only slightly below the level registered in the aftermath of World War II.
- Developing economies experienced increases in public debt since the beginning of the Global Financial Crisis.
- Key puzzle and core finding:
  - Increases in public debt are not primarily the result of large primary deficits.
  - Focus is on episodes where debt to GDP increased by at least 10 percentage points of GDP (debt spike episodes).
  - Identified 179 debt spike episodes from a sample of 90 countries (including advanced and developing economies).
  - The main driver of public debt spikes is large stock-flow adjustments (SFAs), the residual term in a traditional debt decomposition exercise—not primary deficits, output, nor interest payments.

### Debt spike size, duration, and probability
- Sample and classification:
  - 179 debt spike episodes of multiyear debt accumulation greater than 10 percent of GDP.
  - Distribution: 80 episodes among advanced economies and 99 among developing countries.
  - The 179 episodes span 76 countries: 28 advanced economies, 26 emerging market economies, 22 low income economies.
- Representative median episode magnitudes:
  - Median advanced-economy episode: public debt increased by 25 percent of GDP; SFA increased by 20 percent of GDP.
  - Median developing-economy episode: public debt increased by 24 percent of GDP; SFA increased by 30 percent of GDP.
- Median episode duration:
  - Advanced economies: 6 years
  - Developing countries: 4 years
- Probability of entering a debt spike (10 percent of GDP threshold) based on inverse Kaplan–Meier:
  - After 10 years: about 50 percent
  - After 20 years: about 80 percent

### Debt decomposition and role of SFAs
- Debt decomposition components:
  - (i) lagged debt ratio times the differential between nominal effective interest rate and nominal GDP growth (cumulated);
  - (ii) cumulative primary deficit to GDP;
  - (iii) cumulative stock-flow adjustment (SFA) capturing valuation effects and below-the-line fiscal operations, errors, and omissions.
- Median subcomponent behavior (five years before, during, and five years after the episode):
  - Advanced-economy median episode:
    - SFA is the main driver during the debt spike; SFA reaches 20 percent of GDP at the median during the episode.
    - Lead-up: primary surpluses.
    - During episode: primary surpluses turn into mild primary deficits.
    - After episode: primary surpluses return, interest costs higher, SFA impact diminishes.
  - Developing-country median episode:
    - SFA explains bulk of increase during the episode with a sharp increase close to 30 percent of GDP.
    - Lead-up: small primary deficits offset by higher inflation and stronger growth.
    - After episode: debt falls somewhat with primary surpluses offset in part by higher interest costs; inflation helps reduce debt-to-GDP.

### What SFAs reflect and data limitations
- SFA accumulation may reflect:
  - Underreporting of fiscal deficits
  - Quasi-fiscal spending
  - Realization of contingent liabilities (e.g., bailouts)
  - Government debt-management strategies (financial asset accumulation)
- Data limitations:
  - Full decomposition of SFA is constrained outside advanced economies.
  - Eurostat is the primary credible source for detailed SFA subcomponents (2002–2014).

### EU evidence on SFA composition and liquidity
- Matched Eurostat sample (21 of 28 EU countries had a debt spike, 2002–2014):
  - Median debt increase during episodes: 27 percent of GDP
  - Median SFA during episodes: 12 percent of GDP
  - Net acquisition of financial assets accounted for about 9 percent of GDP (largest SFA component)
- Notable one-off outliers cited:
  - Greece in 2012: extensive restructuring of government debt
  - Ireland: large Other Adjustments related to consolidation of Irish Bank Resolution Corporation (IBRC)
  - Hungary 2011: pension transfers recorded as financial advance
  - Hungary, Poland, Romania (2008–2011): currency depreciation increased foreign-currency-denominated debt valuation
- Liquidity composition of net acquisition of financial assets:
  - Relatively liquid: currency and deposits; debt securities
  - Less liquid / harder to unwind: loans to non-government units; shares and other equity (privatization proceeds, equity injections); other account receivables (accruals); other financial assets (receivables in taxes/social contributions, EU reimbursements)
- Implication: accumulation of illiquid financial assets is a major contributor to SFA accumulation and constrains near-term debt reduction.

### Determinants of SFA: regression findings and institutional correlates
- Regression results using 179 debt-spike episodes:
  - Realized contingent liabilities are a major driver of SFA accumulation (especially in developing countries).
  - Contingent liabilities from the financial sector have stronger impact on SFA than other contingent liabilities.
  - Currency depreciation is a major source of debt accumulation, especially where external debt share is higher.
  - Political conditions (forthcoming elections; fragmented coalition cabinets) are associated with higher average SFA during debt spikes; significance weakens when sample split into advanced vs developing countries.
  - Strong fiscal rules are associated with increased transparency and reduced SFA size.
- Institutional and governance correlations:
  - A one percent increase in PIE-X (Public Investment Management Efficiency) during implementation stage is associated with an 18.2 percent lower average SFA.
  - Comparable one percent increases in PIE-X during developing and planning stages are associated with 8.8 percent and 7.2 percent drops in SFA respectively.
  - A one-point gain in ICRG bureaucracy quality is associated with a 6.7 percent drop in SFA level.
- Institutional strength and probability of entering a debt spike:
  - Inverse-Kaplan–Meier estimates show that strong PIE-X/PIMA budget institutions are associated with a significantly lower probability of entering a debt spike.

### SFA and the non-declining debt path syndrome (probit results)
- Hypothesis: large SFAs (especially illiquid asset accumulation) increase probability of non-declining debt paths after debt spikes.
- Probit model (sample: 143 episodes with binary outcome; 65 episodes value 0; 78 episodes value 1):
  - Dependent variable = 1 if average drop in debt between years 3–5 after end of spike is less than 10 percent of GDP (non-declining path); = 0 if drop exceeds 10 percent of GDP (declining path).
  - Regressors include: debt level at end of episode; average SFA during episode; average primary balance during episode; average episode growth; average inflation.
- Selected coefficient estimates (reported specifications):
  - Debt level (end-of-episode): 1.181*** (standard error 0.0569); other specs show 1.017*** (0.0566), 1.011*** (0.0525), 1.016*** (0.0533).
  - Average SFA (during episode): 0.671*** (0.1), 0.782*** (0.0954), 0.613*** (0.183).
  - Average Primary Balance (during episode): -2.841*** (0.524), -2.776*** (0.537).
  - Average Episode Growth: -0.214 (0.576) (not statistically significant in reported spec).
  - Average Episode Inflation: 0.312 (0.32) (not statistically significant in reported spec).
  - Constant examples: 25.82*** (3.281), 24.15*** (2.935), 20.45*** (2.805), 20.71*** (2.832).
  - Observations: 178, 177 across specifications; reported pseudo R-squared values include 0.71, 0.77, 0.80, 0.807.
- Interpretation:
  - Higher average SFA during the episode and higher end-of-episode debt level significantly increase the probability of a non-declining debt path.
  - Higher primary surpluses during the episode significantly decrease that probability.
  - Average growth and inflation during the episode are not statistically correlated with the non-declining debt path in these regressions.

### Unforecasted SFAs, forecasting bias, and implications for DSAs
- Forecasting bias documented:
  - Median country underestimates debt by 1.5 percent of GDP each year, equivalent to 6 percent of GDP over a standard 4-year forecast period.
  - At the 75th percentile: underestimation can be 3 percent of GDP per year, or 12 percent of GDP in a 4-year forecast period.
  - SFAs are underestimated at the median by 1/2 percent of GDP per year.
- EU and WEO / SGP forecasting examples:
  - October 2015 Fiscal Monitor forecasts: debt declining by 2018 in 17 out of 23 European countries.
  - April 2015 SGP forecasts for 2018: 22 out of 25 countries would face declining debt ratios.
  - If historical SFA trends are applied instead:
    - Only 9 would have declining debt by 2018 in the WEO forecast when historical SFAs applied.
    - Only 16 would have declining debt by 2018 in the SGP forecast when historical SFAs applied.
- Implication: systematic underestimation of SFAs contributes materially to overoptimistic debt sustainability assessments.

### Policy-relevant implications and recommendations
- Improve forecasting of SFAs:
  - Address the typical downward bias in SFA forecasts to enhance the reliability of debt sustainability analyses.
  - Use stochastic methods to map uncertainty around public-debt trajectories.
  - Increase variance of idiosyncratic shocks in DSAs to account for exchange rate shock impacts (particularly in emerging markets).
- Use stress-testing and sensitivity analysis:
  - Greater use of sensitivity analysis in DSAs to account for potential existence and realization of SFAs.
  - Employ fiscal stress tests (particularly for financial-sector-related SFAs) instead of relying only on baseline forecasts.
- Strengthen fiscal transparency, monitoring, and institutions:
  - Fiscal transparency can reduce the magnitude of SFAs associated with debt increases.
  - Better monitoring of off-budget operations can limit use of SFA-related practices to circumvent fiscal rules.
  - Strengthen fiscal rules, public investment management, bureaucracy quality, and fiscal-council costing to reduce SFA accumulation and improve transparency.
- Monitor and limit contingent liabilities and balance-sheet risks:
  - Given the role of realized contingent liabilities from the private sector in driving SFAs and debt spikes, policies to limit and better account for contingent liabilities are important for fiscal risk management.
- Use diagnostic tools:
  - Employ tools (e.g., IMF Fiscal Transparency Evaluation) to identify potential SFA impacts related to quasi-fiscal spending and contingent liabilities.

### Robustness checks (Annex highlights)
- Annex 1.1 — 20 percent of GDP threshold:
  - Identified 107 episodes using 20 percent of GDP as threshold.
  - Key finding: after controlling for initial debt and average inflation, major drivers of SFA accumulation are size of realized contingent liabilities, currency depreciation, and the level/share of external debt.
- Annex 1.2 — Advanced vs Developing split:
  - Developing countries show larger coefficients across most factors (pre-existing debt level, currency depreciation, share of external debt).
  - Inflation appears to be the main factor in the case of advanced economies.
- Annex 1.3 — Contingent liabilities from financial sector:
  - Matched-sample evidence (limited N):
    - 20% threshold: Size of Realized Contingent Liabilities: 0.383*** N=51 [2.34]; financial: 0.639*** N=35 [3.30].
    - 10% threshold: Size of Realized Contingent Liabilities: 0.393*** N=39 [2.06]; financial: 0.618*** N=26 [2.60].
  - Interpretation: impact of contingent liabilities realized in the financial sector is roughly twice as high as in other cases within matched-sample evidence.
- Annex 2 — Kaplan–Meier and hazard methodology:
  - Defines survivor, hazard, and cumulative functions; notes limitations of non-parametric approach and presents Weibull baseline for proportional hazards modeling.

*Source: _wp16202 - References ········································· 31*

### References ······························································································· 31

### _wp16202 - References ·············································································· 31

### Introduction
- Long-term trends:
  - At end 2015, advanced economies reached levels of debt close to 106 percent of GDP.
  - Public debt for advanced economies at end 2015 was above levels during the Great Depression and only slightly below the level registered in the aftermath of World War II.
- Recent developments:
  - Developing economies experienced increases in public debt since the beginning of the Global Financial Crisis.
- Key puzzle and core finding:
  - Increases in public debt are not primarily the result of large primary deficits.
  - Focus: episodes where debt to GDP increased by at least 10 percentage points of GDP (debt spike episodes).
  - Identified 179 debt spike episodes from a sample of 90 countries (including advanced and developing economies).
  - Main driver of public debt spikes is large stock flow adjustments (SFAs), the residual term in a traditional debt decomposition exercise—not primary deficits, output, nor interest payments.
- Representative median episode magnitudes:
  - Median advanced-economy episode: public debt increased by 25 percent of GDP while SFA increased by 20 percent of GDP.
  - Median developing-economy episode: public debt increased by 24 percent of GDP while SFA increased by 30 percent of GDP.
- Additional empirical findings summarized:
  - For a reduced sample of 28 European Union countries with granular SFA data, the net acquisition of financial assets is the main component of SFA increases.
  - Regression analysis across a broader sample indicates that the cost of realized contingent liabilities from the private sector is a major driver of sizable SFA and public debt spikes.
  - Higher SFA accumulation during debt spikes is associated with a higher probability of non-declining debt paths in the aftermath of those episodes.
  - Forecasts of SFAs are typically downward biased, which can affect debt sustainability analyses.
- Structure of the paper (sections noted):
  - Section 2: literature review.
  - Section 3: data and criteria to select debt spike episodes.
  - Section 4: debt decomposition of the 179 episodes.
  - Section 5: drivers of SFAs using EU data and regression analysis.
  - Section 6: consequences of sizable and unforecasted SFAs for debt sustainability analysis.
  - Section 7: summary and conclusion.

### Literature Review
- Prior findings and gaps:
  - Campos, Jaimovich and Panizza (2006): dataset of debt spikes in 117 countries (24 high income, 59 middle income, and 34 low income countries) for 1972–2003; conclude debt spikes arise from stock-flow adjustments partly explained by contingent liabilities and balance sheet effects; these explain only 20 percent of intra-country variance of SFA.
  - Abbas et al. (2011): 60 episodes of debt increases between 1880–2007; key contributors during non-recessionary periods were both primary deficits and stock-flow adjustments.
  - Weber (2012): using data for 163 countries between 1980 and 2010, finds SFAs are a significant source of debt increases and play a minor role in debt decreases; fiscal transparency associated with smaller magnitude of SFA in debt increases.
  - Von Hagen and Wolff (2006): in EU sample, governments use SFA to circumvent EU fiscal rules; recommend improving fiscal transparency and monitoring to reduce off-budget operations.
- Contributions of the current paper:
  - Updated data to include the Global Financial Crisis.
  - Three innovations:
    - Deeper analysis of subcomponents of SFA using new databases; statistical examination of the role of major economic variables, contingent liabilities, and political factors in explaining average SFA contribution to debt spikes.
    - Demonstrates that higher SFA accumulation significantly increases the probability of non-declining debt paths after debt spike episodes.
    - Explores link between downward bias in debt forecasts and underestimation of SFAs, concluding that better SFA forecasting is needed to improve debt sustainability analysis.

### Selection of Episodes (Data and Methodology)
- Data sources:
  - Public debt: FAD Historical Public Debt Database and the IMF Fiscal Monitor.
  - Debt decomposition: Mauro et al. (2013) and the Fiscal Monitor.
- Episode identification criteria:
  - Identify years where public debt increased by more than 1 percent of GDP.
  - Define a debt spike episode when the overall change in debt over consecutive years is equal to or beyond 10 percent of GDP.
  - No fixed time limit for episode duration: episode continues as long as debt-to-GDP ratio increases by at least 1 percent per year.
  - Episode ends once the debt-to-GDP ratio changes by less than 1 percent for two consecutive years.
  - Final selection requires sufficient data to calculate the debt decomposition for the episode's duration.
  - Similar selection criteria used in Abbas et al. (2011) and Weber (2012).
- Sample and classification:
  - Total of 179 debt spike episodes of multiyear debt accumulation greater than 10 percent of GDP.
  - Distribution: 80 episodes among advanced economies and 99 among developing countries.
  - The 179 episodes span 76 countries: 28 advanced economies, 26 emerging market economies, 22 low income economies.

### Policy-relevant Implications and Recommendations (as emphasized in text)
- Improve forecasting of SFAs:
  - Address the typical downward bias in SFA forecasts to enhance the reliability of debt sustainability analyses.
- Strengthen fiscal transparency and monitoring:
  - Fiscal transparency can reduce the magnitude of SFAs associated with debt increases.
  - Better monitoring of off-budget operations can limit use of SFA-related practices to circumvent fiscal rules.
- Monitor contingent liabilities and balance-sheet risks:
  - Given the role of realized contingent liabilities from the private sector in driving SFAs and debt spikes, policies to limit and better account for contingent liabilities are important for fiscal risk management.

*Source: _wp16202 - References ·············································································· 31*

### Annex 3 provides a description of these episodes, by country and

### _wp16202 - Annex 3 provides a description of these episodes, by country and

### Debt spikes: size, duration, and probability
- Median debt spike size:
  - Advanced economies: 25 percent of GDP
  - Developing countries: 24 percent of GDP
- Median episode duration:
  - Advanced economies: 6 years
  - Developing countries: 4 years
- Probability of entering a debt spike (10 percent of GDP threshold) based on inverse Kaplan–Meier:
  - After 10 years: about 50 percent
  - After 20 years: about 80 percent

### Drivers of debt spikes (decomposition results)
- Debt decomposition identifies three direct components of a change in debt-to-GDP:
  - (i) lagged debt ratio times the differential between nominal effective interest rate and nominal GDP growth (cumulated);
  - (ii) cumulative primary deficit to GDP;
  - (iii) cumulative stock-flow adjustment (SFA) capturing valuation effects and below-the-line fiscal operations, errors, and omissions.
- Further decomposition splits the interest-growth differential into contributions from nominal effective interest rate, GDP deflator inflation, and real GDP growth.
- Median subcomponent behavior (five years before, during, and five years after the episode) shows:
  - Advanced-economy median episode: SFA is the main driver during the debt spike; SFA reaches 20 percent of GDP at the median during the episode. Lead-up: primary surpluses; during episode: primary surpluses turn into mild primary deficits; after episode: primary surpluses return, interest costs higher, SFA impact diminishes.
  - Developing-country median episode: SFA explains bulk of increase during the episode with a sharp increase close to 30 percent of GDP. Lead-up: small primary deficits offset by higher inflation and stronger growth; after episode: debt falls somewhat with primary surpluses offset in part by higher interest costs; inflation helps reduce debt-to-GDP.

### Stock-Flow Adjustments (SFA): what they reflect
- SFA accumulation may reflect:
  - Underreporting of fiscal deficits
  - Quasi-fiscal spending
  - Realization of contingent liabilities (e.g., bailouts)
  - Government debt-management strategies (financial asset accumulation)
- Data limitations constrain full decomposition, especially outside advanced economies; Eurostat is the primary credible source for detailed SFA subcomponents (2002–2014).

### EU evidence on SFA composition and liquidity
- In matched Eurostat sample (21 of 28 EU countries had a debt spike, 2002–2014):
  - Median debt increase during episodes: 27 percent of GDP
  - Median SFA during episodes: 12 percent of GDP
  - Net acquisition of financial assets accounted for about 9 percent of GDP (largest SFA component)
- Notable one-off outliers:
  - Greece in 2012: extensive restructuring of government debt
  - Ireland: large Other Adjustments related to consolidation of Irish Bank Resolution Corporation (IBRC)
  - Hungary 2011: pension transfers recorded as financial advance
  - Hungary, Poland, Romania (2008–2011): currency depreciation increased foreign-currency-denominated debt valuation
- Liquidity of net acquisition of financial assets:
  - Liquid components: currency and deposits; debt securities
  - Illiquid components (harder to unwind): loans to non-government units, shares and other equity (privatization proceeds, equity injections), other account receivables (accruals), other financial assets (receivables in taxes/social contributions, EU reimbursements)
- Implication: accumulation of illiquid financial assets is a major contributor to SFA accumulation and constrains near-term debt reduction.

### Determinants of SFA (regression findings)
- Using 179 debt-spike episodes, regressions of average SFA during episodes on economic and political factors find:
  - Realized contingent liabilities are a major driver of SFA accumulation (especially in developing countries).
  - Contingent liabilities from the financial sector have stronger impact on SFA than other contingent liabilities.
  - Currency depreciation is a major source of debt accumulation, especially where external debt share is higher.
  - Political conditions (forthcoming elections; fragmented coalition cabinets) are associated with higher average SFA during debt spikes; significance weakens when sample split into advanced vs developing countries.
  - Strong fiscal rules are associated with increased transparency and reduced SFA size.
- Limited data prevents full regression inclusion of budget institutions; correlations show governance and public investment management quality lower SFA:
  - A one percent increase in PIE-X (Public Investment Management Efficiency) during implementation stage is associated with an 18.2 percent lower average SFA.
  - Comparable one percent increases in PIE-X during developing and planning stages are associated with 8.8 percent and 7.2 percent drops in SFA respectively.
  - A one-point gain in ICRG bureaucracy quality is associated with a 6.7 percent drop in SFA level.
- Institutional strength and probability of entering a debt spike:
  - Inverse-Kaplan–Meier estimates show that strong PIE-X/PIMA budget institutions are associated with a significantly lower probability of entering a debt spike.

### SFA and the “non-declining debt path syndrome”
- Hypothesis: large SFAs (especially illiquid asset accumulation) increase probability of non-declining debt paths after debt spikes because such assets are hard to unload.
- Probit model setup:
  - Dependent variable = 1 if average drop in debt between years 3–5 after end of spike is less than 10 percent of GDP (non-declining path); = 0 if drop exceeds 10 percent of GDP (declining path).
  - Sample: 143 episodes with binary outcome (65 episodes value 0; 78 episodes value 1).
  - Regressors: debt level at end of episode; average SFA during episode; average primary balance during episode; average episode growth; average inflation.
- Probit results (selected coefficient estimates):
  - Debt level (end-of-episode): 1.181*** (standard error 0.0569) in one specification; other specs show 1.017***, 1.011***, 1.016*** with corresponding standard errors (0.0566), (0.0525), (0.0533).
  - Average SFA (during episode): 0.671*** (0.1), 0.782*** (0.0954), 0.613*** (0.183) in available specs.
  - Average Primary Balance (during episode): -2.841*** (0.524), -2.776*** (0.537) in reported specs.
  - Average Episode Growth (during episode): -0.214 (0.576) in one spec (not statistically significant).
  - Average Episode Inflation (during episode): 0.312 (0.32) in one spec (not statistically significant).
  - Constant terms reported (e.g., 25.82*** (3.281), 24.15*** (2.935), 20.45*** (2.805), 20.71*** (2.832)).
  - Observations: 178, 177 across specifications; R-squared (pseudo) values reported (e.g., 0.71, 0.77, 0.80, 0.807).
- Interpretation:
  - Higher average SFA during the episode and higher end-of-episode debt level significantly increase the probability of a non-declining debt path.
  - Higher primary surpluses during the episode significantly decrease that probability.
  - Average growth and inflation during the episode are not statistically correlated with the non-declining debt path in these regressions.

### Unforecasted SFAs and optimistic debt projections
- Forecasting bias in debt projections:
  - Median country underestimates debt by 1.5 percent of GDP each year, equivalent to 6 percent of GDP over a standard 4-year forecast period.
  - At the 75th percentile: underestimation can be 3 percent of GDP per year, or 12 percent of GDP in a 4-year forecast period.
  - SFAs are underestimated at the median by 1/2 percent of GDP per year.
- EU and WEO forecasting example:
  - October 2015 Fiscal Monitor forecasts: debt declining by 2018 in 17 out of 23 European countries.
  - April 2015 SGP forecasts for 2018: 22 out of 25 countries would face declining debt ratios.
  - If historical SFA trends are applied instead, outcomes change:
    - Only 9 would have declining debt by 2018 in the WEO forecast when historical SFAs applied.
    - Only 16 would have declining debt by 2018 in the SGP forecast when historical SFAs applied.
- Implication: systematic underestimation of SFAs contributes materially to overoptimistic debt sustainability assessments.

### Recommendations and tools to address SFA risk in forecasting and DSAs
- Improve forecasting and debt sustainability analysis by:
  - Greater use of sensitivity analysis in DSAs to account for potential existence and realization of SFAs.
  - Employ fiscal stress tests (particularly for financial-sector-related SFAs) instead of relying only on baseline forecasts.
  - Use stochastic methods to manage fiscal risks and map uncertainty around public-debt trajectories.
  - Increase variance of idiosyncratic shocks in DSAs to account for exchange rate shock impacts (particularly in emerging markets).
  - Use diagnostic tools (e.g., IMF Fiscal Transparency Evaluation) to identify potential SFA impacts related to quasi-fiscal spending and contingent liabilities.
- Institutional and governance improvements:
  - Strengthening fiscal rules, public investment management, bureaucracy quality, and fiscal-council costing can reduce SFA accumulation and improve transparency.

### Conclusions (from the chapter)
- Large debt spikes are typically driven by large stock-flow adjustments rather than primary deficits or declines in output.
- SFAs have been largely overlooked in debt sustainability analysis and fiscal-risk management, creating a blind spot.
- Large SFAs are often linked to accumulation of illiquid assets that cannot be easily sold to reduce debt, increasing the probability of non-declining debt paths after spikes.
- Debt forecasts exhibit a downward bias partly due to underestimation of SFAs; improving SFA forecasting via probabilistic methods, fiscal stress tests, and better transparency will improve understanding of debt vulnerabilities and fiscal-buffer building.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16202.pdf*

### ANNEX 1. Robustness Checks

### ANNEX 1. Robustness Checks

### Annex 1.1. Using a 20 percent of GDP threshold to identify debt spike episodes
- Sample: identified 107 episodes using 20 percent of GDP as the threshold of cumulative debt accumulation.
- Main descriptive result: Table 1.1.1 provides descriptive statistics for the selected episodes. (Table not reproduced here.)
- Regression replication: Table 1.1.2 replicates regression analysis on the average size of SFA using this 20 percent threshold sample.
- Key finding:
  - After controlling for underlying economic conditions like the initial level of debt and average inflation, the major drivers of SFA accumulation are:
    - the size of realized contingent liabilities,
    - currency depreciation,
    - the level/share of external debt.

### Annex 1.2. Results dividing the sample into advanced and developing countries
- Sample split: regressions run separately for advanced and developing economies.
- Key comparative findings:
  - Developing countries show larger coefficients (than in the main text) across most factors:
    - pre-existing level of debt,
    - currency depreciation,
    - the share of external debt.
  - Inflation appears to be the main factor in the case of advanced economies.
- Table 1.2.1 presents regression results comparing Advanced vs. Developing Economies (table not reproduced here).

### Annex 1.3. Are Contingent Liabilities from the Financial Sector Different?
- Data limitation: Lack of detailed data on realized contingent liabilities and affected sectors; matching to Bova et al. (2016) dataset yields about 53 matched cases.
- Correlations observed:
  - Some correlation between contingent liabilities realized in the financial sector and large SFA episodes.
  - Relationship appears much stronger for contingent liabilities realized in the legal sector, but that result is attributed to the presence of two sizable outliers.
- Simple regression results (Table 1.3.1):
  - 20% Threshold block:
    - Size of Realized Contingent Liabilities: 0.383*** N=51 [2.34]
    - Size of Realized Contingent Liabilities (financial): 0.639*** N=35 [3.30]
  - 10% Threshold block:
    - Size of Realized Contingent Liabilities: 0.393*** N=39 [2.06]
    - Size of Realized Contingent Liabilities (financial): 0.618*** N=26 [2.60]
  - T-statistics are in brackets. Significance notation: *** p<0.01, ** p<0.05, * p<0.1.
- Interpretive summary:
  - Simple regressions indicate that the impact of contingent liabilities realized in the financial sector is roughly twice as high as that in other cases (within the matched-sample evidence).

### ANNEX 2. The Kaplan-Meier Survival Estimation Technique
- Definition:
  - T is the discrete random variable measuring the time span between periods in which countries fail to maintain public debt under control and thus experience a debt spike episode.
  - Observations of T in the sample are a series (t1, t2, ... tn) corresponding to each observed non-increasing debt-to-GDP year in the sample.
- Data construction: example provided illustrating country-year dummy indicators, duration variable T, and failure variable (debt spike episode).
- Distribution and functions:
  - Cumulative distribution: F(t) = Pr(T < t)
  - Survivor function: S(t) = Pr(T ≥ t) = 1 − F(t)
  - Hazard function: h(t) = Pr(T = t | T ≥ t)
- Non-parametric hazard estimation:
  - Discrete hazard estimator: ĥ(t) = dt / nt where dt is the number of failures at t and nt is the surviving population at t before the change.
  - Cumulative hazard function: Ĥ(t) = Σ ĥ(j) for j = 1 to t
  - Kaplan-Meier survivor function: Ŝ(t) = ∏ (1 − d j / n j ) over j = 1..t (product of one minus the existing risk until period t)
- Limitations of non-parametric approach: does not account for covariates that may influence the probability of ending a period of non-increasing debt.
- Proportional hazards model:
  - Hazard specified as h(X,t) = h0(t) g(X) where h0(t) is baseline hazard (duration dependence) and g(X) is a function of covariates (regressors rescale conditional probability but not duration).
- Parametric baseline — Weibull specification:
  - h0(t) = p t^(p−1), p to be estimated.
  - Interpretation of p:
    - p = 1 → exponential model (no dependency on duration).
    - p > 1 → positive dependency on duration.
    - p < 1 → negative dependency on duration.
  - Estimating p allows testing duration dependency of non-increasing debt episodes.
- Footnote on episode identification:
  - As defined above, a debt spike episode is identified when there is an annual change of at least 1 percent of GDP and the cumulative multiannual debt spike is equal or greater than 10 percent of GDP.

### ANNEX 3. Description of Debt Spike Episodes
- Annex contains description and listings of debt spike episodes and figures (not reproduced here).
- Includes visualization heading: "EU debt spike episodes 2002-2014" (figure/table not reproduced here).

*Source: _wp16202 - ANNEX 1. Robustness Checks*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16202.pdf_