## Annex I. Definition of Variables and Data Sources (wpiea2024050-print-pdf)

## Source details

**Canonical URL:** [Annex I. Definition of Variables and Data Sources (wpiea2024050-print-pdf)](https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024050-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2024/english/wpiea2024050-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2024/english/wpiea2024050-print-pdf.pdf.json)

---

### Purpose and scope
- Provides formal definitions of the variables used in the analysis.
- Documents the data sources employed to construct the variables.
- Covers variable definitions and the provenance of data that underpin the working paper’s empirical analyses.
- Serves as the reference for variable construction used throughout the paper’s decompositions, impulse-response analysis, and regression work.
- Covers debt surge episodes for 183 countries over 1970–2021 to analyze drivers and consequences of debt surges, focusing on:
  - (i) how debt surges affect the probability of a financial crisis and
  - (ii) the probability that debt remains elevated ex-post.
- Uses public debt series from the WEO database; surge episodes restricted to debt increases of 10 percent of GDP or higher over the episode.

### Data coverage and episode counts
- Total identified debt surge episodes: 490 (1970–2021)
  - AEs: 93
  - EMs: 247
  - LICs: 150
- Sample used for debt decomposition (1990–2021): 343 episodes
  - AEs: 60
  - EMs: 171
  - LICs: 106
- Panel-VAR estimation samples:
  - AEs: 31 countries (annual data 1970–2021)
  - EMs: 82 countries (annual data 1970–2021)
  - LICs: 50 countries (annual data 1970–2021)

### Stylized facts and key statistics
- Median surge duration: 6–7 years.
- Median cumulative change in debt over surge duration: around 28-32 percent of GDP.
- Distribution tails:
  - 10 percent of episodes record 12–13 pp of GDP debt surge (lower tail).
  - 10 percent of episodes record debt accumulation of over 70 pp of GDP (upper tail).
- Table 1 summary statistics (1970–2021 / 1990–2021):
  - Mean debt accumulation (in pp): 50.6 (1970–2021), 38.5 (1990–2021)
  - Mean surge duration (in years): 8.1 (1970–2021), 6.6 (1990–2021)
  - SD debt accumulation: 107.1 (1970–2021), 45.2 (1990–2021)
  - SD duration: 6.7 (1970–2021), 5.9 (1990–2021)
  - 10% percentile debt accumulation: 13.7 (1970–2021), 12.9 (1990–2021)
  - 25% percentile debt accumulation: 18.9 (1970–2021), 16.7 (1990–2021)
  - Median debt accumulation: 32.3 (1970–2021), 28.4 (1990–2021)
  - 75% percentile debt accumulation: 51.6 (1970–2021), 42.8 (1990–2021)
  - 90% percentile debt accumulation: 90.6 (1970–2021), 69.1 (1990–2021)

### Drivers of debt surges (accounting and augmented decomposition)
- Main macro drivers quantified: real GDP growth, nominal interest expenses, primary balance, inflation, and Stock-Flow Adjustments (SFA).
- Fiscal policy (deficits) plays a larger role once the Augmented Decomposition (AD) strips out indirect effects of growth and inflation on primary balances.
- Across all surge-size brackets, fiscal policy explains a substantial part of debt accumulation; primary spending–driven expansions tend to matter more than discretionary revenue declines.
- For EMs and LICs, SFA are particularly important in large surge episodes.
- For LICs, SOE-related losses/liabilities and arrears are important contributors to large SFA.

### Role and composition of Stock-Flow Adjustments (SFA)
- Valuation effects (FX-related SFA) quantified by interacting changes in nominal exchange rate with share of FX debt using IMF Sovereign Debt Investor Base.
- For 222 episodes (1990–2021 with available FX-debt data), FX effects can explain as much as half of SFA in large episodes.
- High FX-debt shares and large depreciations contribute strongly to FX-driven SFA; large SFA tend to coincide with crises.
- Non-valuation SFA (other SFA) are often crisis-related costs:
  - Using contingent-liability data for top quartile surges, leading contributors include bank recapitalization, SOE contingent liabilities, and natural disasters.
  - For LICs (top 25th percentile reviewed via staff reports), about half of non-FX SFA originate from arrears, revisions in debt statistics, bank and SOE recapitalizations, off-budget transactions, and previously hidden/uncovered debt.
- Episodes without crises tend to have small SFA and a greater role for fiscal policy.

### Estimating fiscal policy’s role — Panel VAR approach
- Identification:
  - Panel VAR with country fixed effects and Cholesky decomposition; dependent variables include public debt, government primary spending and revenue, output, real effective exchange rate, inflation, and monetary policy variable.
  - Two lags included; baseline ordering places primary spending first, GDP growth second, government revenue third, inflation fourth, REER fifth, monetary policy sixth, and public debt last.
  - Robustness check: fiscal shocks constructed from WEO forecast errors (one-year-ahead forecasts) yield consistent results.
- Impulse-response findings (1% fiscal shocks measured in percent of GDP):
  - Debt-to-GDP responds significantly to fiscal shocks and peaks after two to three years.
  - Primary spending shocks have a larger impact on debt-to-GDP than revenue shocks.
  - Debt responses to a one percent hike in primary spending peak at 0.5 to one percentage points across country groups; responses to revenue cuts stay well below that level.
  - Instantaneous uptick in debt from primary spending shocks: roughly 0.25 percentage points in all country groups, peaking at one percentage point in AEs and barely exceeding 0.5 percentage points in EMs.
- Forecast error variance decomposition (after five years):
  - Baseline model explains approximately 30 to 55 percent of the variation in debt forecasts.
  - Fiscal policy accounts for 30 to 35 percent of the total variation in both AEs and EMs, and 25 percent in LICs.
  - Within fiscal policy, primary spending shocks explain the largest fraction, especially in AEs; in LICs, spending and revenue shocks explain an equal fraction.

### Robustness checks (VAR and fiscal-shock measures)
- VAR results robust to alternative orderings, inclusion of linear and country-specific time trends, oil-exporter dummy, and sample splits (starting in 1990s and 2000s).
- Alternative fiscal-shock measure using WEO forecast errors (available for 15 AEs, 78 EMs, 48 LICs from 1993–2016) confirms:
  - Debt-to-GDP responds substantially to both hikes in primary spending and cuts in revenue, especially in EMs.
  - Effects of revenue cuts are smaller than spending increases.
  - Responses generally peak after one to two years and revert.
- Alternative orderings considered:
  - Ordering 2 swaps primary spending and revenue: (1) Revenue (2) GDP (3) Primary spending (4) Inflation (5) REER (6) Monetary variable (7) Debt — debt responses to revenue shocks smaller but results robust.
  - Ordering 3: (1) GDP (2) Inflation (3) Primary spending (4) Revenue (5) REER (6) Monetary variable (7) Debt — very minor changes.
  - Ordering 4: (1) GDP (2) Inflation (3) REER (4) Monetary variable (5) Primary spending (6) Revenue (7) Debt — no significant changes.

### Consequences: debt surges and financial crises (panel random-effect logit)
- Empirical setup:
  - Panel logit with random effects (annual data 1986–2021) for 15 AEs, 82 EMs, 50 LICs.
  - Binary outcome: financial crisis if banking crisis, currency crisis, or sovereign default (Laeven and Valencia).
  - Main regressors: debt accumulation, fiscal policy shocks, currency depreciation; each interacted with debt-surge dummy and lagged up to three years.
- Main regression results (marginal effects and interpretation):
  - The first lag of debt accumulation during debt surges is significant and positive: accumulating one percentage point more debt as a share of GDP over the past three years raises the crisis probability by 2.4 percentage points (evaluated at sample means).
  - Estimated marginal effect: "2.9 percent, implying that financial crises are markedly more likely to emerge subsequently to a debt surge episode."
  - Revenue shocks and spending shocks during debt surges increase crisis probability:
    - If revenue has been decreased or primary spending increased by one percent of GDP during the previous three years, the probability of the surge ending in a crisis is higher by 20 to 40 basis points (evaluated at sample means).
  - Currency depreciation cross-terms with debt surge dummy are insignificant for crisis occurrences.
- Additional marginal effects (evaluated at sample means):
  - A one percentage point stronger depreciation of the nominal exchange rate translates into a 0.63 higher probability of a financial crisis.
  - A one percentage point higher stock of reserves as a share of GDP reduces the probability by an average of 0.93 percentage points.
- Offsetting rising debt: on average, to keep a debt surge from ending in a crisis, a one percentage point increase of debt accumulation at sample means needs to be outweighed by:
  - an average increase of growth by 3.5 percentage points, or
  - reserves by 2.5 percentage points of GDP.
- Predicted probability that a debt surge results in financial crisis:
  - Overall: 11–21 percent
  - LICs: 21 percent
  - AEs: 11 percent
  - EMs (median predicted probability): 17 percent
- Interpretation:
  - Debt accumulation is a dominant factor driving crisis probabilities during surge episodes.
  - Marginal effects are fairly equal across country groups, but unconditional predicted probabilities differ substantially across regions.

### Post-surge debt trajectories (ex-post debt paths)
- Predicted probabilities that debt remains high after a surge:
  - AEs: 75 percent probability of sustaining high debt levels ex-post.
  - EMs: 57 percent probability of sustaining high debt levels ex-post.
  - LICs: 2 percent probability of sustaining high debt levels ex-post (downward corrections almost certain).
- Empirical strategy:
  - Binary outcome Y_i ∈ {0,1}: equals one if debt surge episode i results in an elevated debt level ex-post.
  - Ex-post change of debt computed as change between peak level in last year of episode and average across years three to five after the surge; a debt level is defined as staying elevated if it does not decline by more than seven percentage points (alternative thresholds used for robustness).
  - Cross-sectional logit model estimated with episodic data for 12 AEs, 55 EMs, and 20 LICs over 1970–2014.
  - Explanatory vector S_i includes: debt accumulation, peak debt level, duration, fiscal policy shocks, FX component of SFA, other SFA, IMF financial market depth index.
  - Fiscal shocks taken from baseline panel VAR to address endogeneity.
- Ex-post empirical results (marginal effects at sample means):
  - A one percent hike of primary spending during a debt surge increases the probability of debt staying high afterwards by roughly 30 to 50 basis points (largest effect for AEs).
  - Revenue cuts do not significantly affect ex-post debt paths.
  - A one percentage point increase of other SFA reduces the probability of debt staying elevated by 2.5 percentage points (when other SFA and debt accumulation are not too large).
  - If other SFA and debt accumulation exceed 36 percentage points, debt is likely to stay high ex-post.
  - Debt surges more strongly driven by exchange rate fluctuations are, on average, by eight to nine percentage points more likely to see a downward correction of debt afterwards if they last no longer than six years; repeated depreciations with sustained external imbalances increase the probability of debt staying high.

### Interpretation of mechanisms
- Primary-spending driven debt surges:
  - Tend to lower near-term crisis probabilities relative to revenue cuts (near-term gains).
  - Tend to increase longer-term probability of permanently higher debt levels because spending increases are unlikely to be reversed (longer-term costs).
- FX-driven surges:
  - Short-lived depreciations often reverse, allowing debt correction.
  - Repeated or sustained depreciations, combined with external imbalances, lead to persistently high debt.
- Other SFA (e.g., contingent liabilities such as bank or SOE recapitalizations):
  - Small-scale other SFA can be unloaded after a one-time surge.
  - Large-scale other SFA combined with large debt accumulation makes debt reduction difficult.

### Robustness of crisis-probability and ex-post path results
- Coefficient significance and magnitude are robust across alternative specifications (fixed effects, alternative lags).
- Fixed effects regression does not change main results.
- Lag-length checks (two and four lags) support findings; higher-order lags of primary spending have larger long-run impacts on crisis probability.
- Ex-post results robust to alternative decline thresholds (ten and 15 percentage points) and alternative adjustment windows after a surge (four to seven years).

### Variables and data sources (selected)
- Panel VAR variables (Annex Table AI.1):
  - Public Debt: Total General Government Gross Debt (in percent of GDP) — Arslanalp and Tsuda (2014)
  - Government Primary Spending: General government expenditure: primary expenditure (in percent of GDP) — IMF WEO
  - Government Revenue: General government revenue (in percent of GDP) — IMF WEO
  - Output: Real GDP (constant $) — IMF WEO
  - Real Effective Exchange Rate: Real Effective Exchange Rate (in natural logarithm) — IMF WEO
  - Inflation: Year-on-year change of the consumer price index (in percent) — IMF WEO
  - Monetary Policy: Central Bank Policy Rate used for Advanced economies and Broad Money (in percent of GDP) used for Emerging markets and Low-Income countries — BIS and World Bank WDI
  - Oil Price: Crude Oil (petroleum), simple average of three spot prices (US$ per barrel) — IMF GAS
- Crisis prediction variables (Annex Table AI.2) — examples:
  - FinancialCrisis: Dummy from Laeven and Valencia (2016)
  - DebtSurge: Own definition based on IMF WEO
  - DebtAccumulation: Year-on-year change of the debt-to-GDP ratio (in percentage points) — IMF WEO
  - RevenueShock / PrimarySpendingShock: shocks retrieved from a panel VAR — Own calculations based on IMF WEO
  - Reserves: Foreign currency reserves (in percent of GDP) — IMF WEO
  - ExternalDebt: External government debt (in percent of total government debt) — IMF Sovereign Debt Investor Base
- Ex-post debt path variables (Annex Table AI.3) — examples:
  - ExPostDebtPath: Dummy based on a seven percentage point threshold — Own definition based on IMF WEO
  - FXEffect and OtherSFA: computed using IMF WEO, IMF Sovereign Debt Investor Base, and standard debt decomposition
  - FinancialMarketDepth: IMF Financial Market Depth Index

### FX effect in debt decomposition
- FX effect proxy provides percentage point change in debt-to-GDP due to FX depreciation.
- Other SFA defined as: “other SFAs” = Residuals – FX effect.
- FX effect computed using end-of-year bilateral USD/LC exchange rates and share of FX debt to total debt at the previous year of debt surge.
- Data sources for FX effect inputs:
  - Bilateral USD/LC exchange rates.
  - Share of FX debt from IMF Sovereign Debt Investor Base for EMDE (2023) (“ExtendedDataset_Currency”).
  - For missing AEs, the share of external debt is alternatively used.

### Augmented Decomposition (AD) — methodology and findings (Annex II)
- AD follows Mauro and Zilinsky (2016) and expands the standard accounting identity that decomposes change in debt-to-GDP into components (real interest rate, direct growth effect, indirect growth effect via primary balance, fiscal measures, initial primary balance).
- AD captures how economic growth affects the primary surplus (tax income rises with growth), isolating fiscal measures (policy) from growth’s embedded effects.
- Empirical findings:
  - AD shows higher fiscal policy and growth contributions compared to the standard decomposition (SD) across country groups and almost all percentiles.
  - Removing growth’s embedded positive effect on debt-to-GDP from the primary balance makes the negative effect of fiscal slippages on debt tend to be higher in AD.
  - By country group:
    - AEs: AD reflects a pronounced effect from fiscal policy vs. SD; growth contribution remains marginal.
    - EMs: AD shows more accentuated fiscal policy impact, especially within the [0.5, 0.75] debt surge quartile.
    - LICs: AD consistently reveals a more considerable fiscal policy effect across quartiles compared to SD; growth displays significant effects in AD predominantly in the [0.5, 0.75] and >0.75 brackets.

### Key policy-relevant findings and implications
- Fiscal policy (especially primary spending increases) is a major contributor to debt surges and to the variance in debt forecasts; sizable spending-driven fiscal consolidation is often required to reduce debt.
- Stock-Flow Adjustments matter substantially for EMs and LICs; avoid exchange rate misalignment, strengthen fiscal risks monitoring, and enhance contingent-liability management and resolution frameworks to limit SFA-driven debt accumulation.
- Crisis-related non-valuation SFA (bank recapitalization, SOE liabilities, arrears, hidden/off-budget debt) can lock in higher debt paths—necessitating careful monitoring of fiscal risks and strengthened governance of SOEs and financial sectors.
- LICs’ post-surge debt dynamics typically involve downward corrections, creating an imperative for concessional external assistance to preserve development and social spending while restoring debt sustainability.
- Allow exchange rate flexibility supported by prudent fiscal and monetary policy to avoid large external imbalances.
- Quantitative role of fiscal policy: fiscal policy estimated to explain 30 to 35 percent of the variation in both AEs and EMs, and 25 percent in LICs.

*Source: wpiea2024050-print-pdf — Annex I. Definition of Variables and Data Sources (extracts as provided in the source content).*

### Annex I. Definition of Variables and Data Sources ......................................................................

### Annex I. Definition of Variables and Data Sources

### Purpose
- Provides formal definitions of the variables used in the analysis.
- Documents the data sources employed to construct the variables.

### Scope
- Covers variable definitions and the provenance of data that underpin the working paper’s empirical analyses.
- Serves as the reference for variable construction used throughout the paper’s decompositions, impulse-response analysis, and regression work.

*Source: wpiea2024050-print-pdf - Annex I. Definition of Variables and Data Sources*

### ANNEX TABLES

### ANNEX TABLES

### Scope and objectives
- Covers debt surge episodes for 183 countries over 1970–2021 to analyze drivers and consequences of debt surges, focusing on: (i) how debt surges affect the probability of a financial crisis and (ii) the probability that debt remains elevated ex-post.
- Uses public debt series from the WEO database; surge episodes restricted to debt increases of 10 percent of GDP or higher over the episode.

### Data coverage and episode counts
- Total identified debt surge episodes: 490 (1970–2021)
  - AEs: 93
  - EMs: 247
  - LICs: 150
- Sample used for debt decomposition (due to data availability): 343 episodes (1990–2021)
  - AEs: 60
  - EMs: 171
  - LICs: 106
- Panel-VAR estimation samples:
  - AEs: 31 countries (annual data 1970–2021)
  - EMs: 82 countries (annual data 1970–2021)
  - LICs: 50 countries (annual data 1970–2021)

### Stylized facts (selected statistics)
- Median surge duration: 6–7 years.
- Median cumulative change in debt over surge duration: around 28-32 percent of GDP.
- Distribution tails:
  - 10 percent of episodes record 12–13 pp of GDP debt surge (lower tail).
  - 10 percent of episodes record debt accumulation of over 70 pp of GDP (upper tail).
- Table 1 summary statistics (1970–2021 / 1990–2021):
  - Mean debt accumulation (in pp): 50.6 (1970–2021), 38.5 (1990–2021)
  - Mean surge duration (in years): 8.1 (1970–2021), 6.6 (1990–2021)
  - SD debt accumulation: 107.1 (1970–2021), 45.2 (1990–2021)
  - SD duration: 6.7 (1970–2021), 5.9 (1990–2021)
  - 10% percentile debt accumulation: 13.7 (1970–2021), 12.9 (1990–2021)
  - 25% percentile debt accumulation: 18.9 (1970–2021), 16.7 (1990–2021)
  - Median debt accumulation: 32.3 (1970–2021), 28.4 (1990–2021)
  - 75% percentile debt accumulation: 51.6 (1970–2021), 42.8 (1990–2021)
  - 90% percentile debt accumulation: 90.6 (1970–2021), 69.1 (1990–2021)

### Drivers of debt surges (accounting and augmented decomposition)
- Main macro drivers quantified: real GDP growth, nominal interest expenses, primary balance, inflation, and Stock-Flow Adjustments (SFA).
- Fiscal policy (deficits) plays a larger role once the Augmented Decomposition (AD) strips out indirect effects of growth and inflation on primary balances.
- Across all surge-size brackets, fiscal policy explains a substantial part of debt accumulation; primary spending–driven expansions tend to matter more than discretionary revenue declines.
- For EMs and LICs, SFA are particularly important in large surge episodes.
- For LICs, SOE-related losses/liabilities and arrears are important contributors to large SFA.

### Role of Stock-Flow Adjustments (SFA)
- Valuation effects (FX-related SFA) quantified by interacting changes in nominal exchange rate with share of FX debt using IMF Sovereign Debt Investor Base.
- For 222 episodes (1990–2021 with available FX-debt data), FX effects can explain as much as half of SFA in large episodes.
- High FX-debt shares and large depreciations contribute strongly to FX-driven SFA; large SFA tend to coincide with crises.
- Non-valuation SFA (other SFA) are often crisis-related costs:
  - Using contingent-liability data (Bova et al., 2016) for top quartile surges, leading contributors include bank recapitalization, SOE contingent liabilities, and natural disasters.
  - For LICs (top 25th percentile reviewed via staff reports), about half of non-FX SFA originate from arrears, revisions in debt statistics, bank and SOE recapitalizations, off-budget transactions, and previously hidden/uncovered debt.
- Episodes without crises tend to have small SFA and a greater role for fiscal policy.

### Estimating fiscal policy’s role in debt surges (panel VAR approach)
- Identification:
  - Panel VAR with country fixed effects and Cholesky decomposition; dependent variables include public debt, government primary spending and revenue, output, real effective exchange rate, inflation, and monetary policy variable.
  - Two lags included; ordering places primary spending first, GDP growth second, government revenue third, inflation fourth, REER fifth, monetary policy sixth, and public debt last.
  - Robustness check: fiscal shocks constructed from WEO forecast errors (one-year-ahead forecasts) yield consistent results.
- Impulse-response findings (1% fiscal shocks measured in percent of GDP):
  - Debt-to-GDP responds significantly to fiscal shocks and peaks after two to three years.
  - Primary spending shocks have a larger impact on debt-to-GDP than revenue shocks.
  - Debt responses to a one percent hike in primary spending peak at 0.5 to one percentage points across country groups; responses to revenue cuts stay well below that level.
  - Instantaneous uptick in debt from primary spending shocks: roughly 0.25 percentage points in all country groups, peaking at one percentage point in AEs and barely exceeding 0.5 percentage points in EMs.
- Forecast error variance decomposition (after five years):
  - Baseline model explains approximately 30 to 55 percent of the variation in debt forecasts.
  - Fiscal policy accounts for 30 to 35 percent of the total variation in both AEs and EMs, and 25 percent in LICs.
  - Within fiscal policy, primary spending shocks explain the largest fraction, especially in AEs; in LICs, spending and revenue shocks explain an equal fraction.

### Robustness checks
- VAR results robust to alternative orderings, inclusion of linear and country-specific time trends, oil-exporter dummy, and sample splits (starting in 1990s and 2000s).
- Alternative fiscal-shock measure using WEO forecast errors (available for 15 AEs, 78 EMs, 48 LICs from 1993–2016) confirms:
  - Debt-to-GDP responds substantially to both hikes in primary spending and cuts in revenue, especially in EMs.
  - Effects of revenue cuts are smaller than spending increases.
  - Responses generally peak after one to two years and revert.

### Consequences: debt surges and financial crises (panel random-effect logit)
- Empirical setup:
  - Panel logit with random effects (annual data 1986–2021) for 15 AEs, 82 EMs, 50 LICs.
  - Binary outcome: financial crisis if banking crisis, currency crisis, or sovereign default (Laeven and Valencia).
  - Main regressors: debt accumulation, fiscal policy shocks, currency depreciation; each interacted with debt-surge dummy and lagged up to three years.
- Main regression results (marginal effects and interpretation):
  - The first lag of debt accumulation during debt surges is significant and positive: accumulating one percentage point more debt as a share of GDP over the past three years raises the crisis probability by 2.4 percentage points (evaluated at sample means).
  - Revenue shocks and spending shocks during debt surges increase crisis probability:
    - If revenue has been decreased or primary spending increased by one percent of GDP during the previous three years, the probability of the surge ending in a crisis is higher by 20 to 40 basis points (evaluated at sample means).
  - Currency depreciation cross-terms with debt surge dummy are insignificant for crisis occurrences, indicating exchange rate movements’ impact on crises is not particularly linked to debt surges (though exchange rate fluctuations are highly significant predictors of currency crises in general).
- Predicted probabilities by country group (median predictive probabilities):
  - AEs: 11.0 percent
  - EMs: 17.0 percent
  - LICs: 20.8 percent
  - Overall median predictive probability range reported: 11–21 percent; LICs at the high end with 21 percent.
- Interpretation:
  - Debt accumulation is a dominant factor driving crisis probabilities during surge episodes, implying substantial macroeconomic adjustments are required to offset rising debt’s effect on crisis risk.
  - Marginal effects are fairly equal across country groups, but unconditional predicted probabilities differ substantially across regions.

### Post-surge debt trajectories (ex-post debt paths)
- Predicted probabilities that debt remains high after a surge:
  - AEs: 75 percent probability of sustaining high debt levels ex-post.
  - EMs: 57 percent probability of sustaining high debt levels ex-post.
  - LICs: 2 percent probability of sustaining high debt levels ex-post; LICs almost certainly see downward corrections, reducing vulnerability to new shocks but underscoring need for sustained post-crisis external assistance at concessional terms to meet development and social needs.

### Key policy-relevant findings and implications (derived from analysis)
- Fiscal policy (especially primary spending increases) is a major contributor to debt surges and to the variance in debt forecasts; sizable spending-driven fiscal consolidation is often required to reduce debt.
- Stock-Flow Adjustments matter substantially for EMs and LICs; avoiding exchange rate misalignment, strengthening fiscal risks monitoring, and enhancing contingent-liability management and resolution frameworks are important to limit SFA-driven debt accumulation.
- Crisis-related non-valuation SFA (bank recapitalization, SOE liabilities, arrears, hidden/off-budget debt) can lock in higher debt paths—necessitating careful monitoring of fiscal risks and strengthened governance of SOEs and financial sectors.
- LICs’ post-surge debt dynamics typically involve downward corrections, creating an imperative for concessional external assistance to preserve development and social spending while restoring debt sustainability.
- Macroeconomic stabilization to limit debt accumulation (including prudent spending controls and revenue mobilization) helps reduce the probability that debt surges culminate in financial crises.

*IMF Working Paper — ANNEX TABLES (extracts as provided in the source content)*

### 2.9 percent, implying that financial crises are markedly more likely to emerge subsequently to a debt surge

### wpiea2024050-print-pdf - 2.9 percent, implying that financial crises are markedly more likely to emerge subsequently to a debt surge

### Marginal effects on crisis probability and key statistics
- Estimated marginal effect: "2.9 percent, implying that financial crises are markedly more likely to emerge subsequently to a debt surge episode."
- Evaluated at sample means:
  - A one percentage point stronger depreciation of the nominal exchange rate translates into a 0.63 higher probability of a financial crisis.
  - A one percentage point higher stock of reserves as a share of GDP reduces the probability by an average of 0.93 percentage points.
- Offsetting rising debt: on average, to keep a debt surge from ending in a crisis, a one percentage point increase of debt accumulation at sample means needs to be outweighed by:
  - an average increase of growth by 3.5 percentage points, or
  - reserves by 2.5 percentage points of GDP.
- Predicted probability that a debt surge results in financial crisis:
  - 11–21 percent overall,
  - 21 percent for LICs,
  - 11 percent for AEs,
  - median predicted probability for EMs: 17 percent.

### Robustness of crisis-probability results
- Coefficient significance and magnitude are robust across alternative specifications in Table 2 (including different control variables).
- Fixed effects regression (despite Hausman test favoring random effects) does not change results (see Table AIII.1).
- Lag-length checks (two and four lags: Tables AIII.2 and AIII.3) support the findings and reveal time-varying effects of primary spending:
  - Higher-order lags of primary spending make a substantially larger impact on the probability of a debt surge resulting in a crisis than lower-order lags or revenue coefficients.
  - Revenues increase crisis probability more immediately; primary spending shocks increase crisis probability over a longer term.

### Ex-post debt paths — empirical strategy
- Binary outcome variable Y_i ∈ {0,1}: equals one if debt surge episode i results in an elevated debt level ex-post, and zero otherwise.
- Ex-post change of debt computed as change between peak level in last year of episode and average across years three to five after the surge; a debt level is defined as staying elevated if it does not decline by more than seven percentage points (alternative thresholds used for robustness).
- Cross-sectional logit model estimated with annual episodic data for 12 AEs, 55 EMs, and 20 LICs over 1970–2014.
- Explanatory vector S_i includes: debt accumulation, peak debt level, duration, fiscal policy shocks, FX component of SFA, other SFA, IMF financial market depth index.
- To address endogeneity of fiscal policy, fiscal shocks are taken from baseline panel VAR to construct an exogenous shock to the primary balance.

### Ex-post debt paths — empirical results
- Main predictors of debt staying elevated ex-post:
  - Higher peak debt level increases probability of debt staying elevated.
  - Surge driven by primary spending hikes increases probability of debt staying elevated.
- Non-linearities:
  - FX-driven debt surges and large-scale debt surges driven by other SFA are more likely to keep debt elevated when:
    - They last longer than 6 years, or
    - They are associated with debt accumulation of more than 36 percentage points.
- Marginal effects (evaluated at sample means):
  - A one percent hike of primary spending during a debt surge increases the probability of debt staying high afterwards by roughly 30 to 50 basis points (largest effect for AEs).
  - Revenue cuts do not significantly affect ex-post debt paths.
  - A one percentage point increase of other SFA reduces the probability of debt staying elevated by 2.5 percentage points (when other SFA and debt accumulation are not too large).
  - If other SFA and debt accumulation exceed 36 percentage points, debt is likely to stay high ex-post.
  - Debt surges more strongly driven by exchange rate fluctuations are, on average, by eight to nine percentage points more likely to see a downward correction of debt afterwards if they last no longer than six years; repeated depreciations with sustained external imbalances increase the probability of debt staying high.
- Country-group differences in predicted probabilities of stable ex-post debt trajectories:
  - AEs: 75 percent sustain high debt levels afterwards.
  - EMs: 57 percent sustain high debt levels afterwards.
  - LICs: 2 percent sustain high debt levels afterwards (downward corrections almost certain).

### Interpretation and mechanisms
- Primary-spending driven debt surges:
  - Tend to lower near-term crisis probabilities relative to revenue cuts (near-term gains).
  - Tend to increase longer-term probability of permanently higher debt levels because spending increases are unlikely to be reversed (longer-term costs).
- FX-driven surges:
  - Short-lived depreciations often reverse, allowing debt correction.
  - Repeated or sustained depreciations, combined with external imbalances, lead to persistently high debt.
- Other SFA (e.g., realization of contingent liabilities such as bank or SOE recapitalizations):
  - Small-scale other SFA can be unloaded after a one-time surge.
  - Large-scale other SFA combined with large debt accumulation makes debt reduction difficult, possibly due to higher interest bills and limited ability to offset via primary balance.

### Robustness of ex-post debt-path results
- Results robust to alternative thresholds for declining debt path (ten and 15 percentage points) and alternative adjustment windows after a surge (four to seven years) (Tables AIII.4 to AIII.6).

### Conclusions and policy implications
- Drivers of debt surges:
  - Fiscal policy and stock-flow adjustments (SFA) are major contributors.
  - Valuation effects explain more than half of SFA, highlighting the need to avoid large external imbalances and to manage creditor and currency composition prudently.
  - Non-valuation related SFA mainly reflect materialization of fiscal risks from banks or SOEs, arrears and off-budget transactions for LICs; when large, they are sticky and raise probability of debt staying high.
- Policy priorities suggested by findings:
  - Strengthen fiscal risk management to minimize direct (higher debt levels) and indirect (higher probability of debt staying high) costs.
  - Enhance financial sector regulation and supervision and develop crisis resolution frameworks.
  - Broaden debt reporting to include SOE debt and implement SOE oversight frameworks to monitor and prevent loss-making operations.
  - Emphasize expenditure-based consolidations: primary spending is the dominant fiscal driver of debt surges, implying a greater role for expenditure-based consolidations to prevent debt growth.
  - Support LICs with sustained post-crisis external assistance at concessional terms to enable necessary debt reduction while meeting development and social needs.
  - Allow exchange rate flexibility supported by prudent fiscal and monetary policy to avoid large external imbalances.
- Quantitative role of fiscal policy:
  - Fiscal policy estimated to explain 30 to 35 percent of the variation in both AEs and EMs, and 25 percent in LICs.

*Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024050-print-pdf.pdf*

### Annex I.  Definition of Variables and Data Sources

### Annex I.  Definition of Variables and Data Sources

### Definition of Debt Surges
- Identification approach follows IMF (2023a) using a two-step process to break the debt-to-GDP time series into episodes.
- Turning points are determined using the Harding and Pagan (2002) business cycle dating methodology.
- Criteria for turning points:
  - Minimum gap of 2 years between successive peaks and troughs.
  - Minimum duration of 4 years for a complete cycle.
- The time series is segmented into non-overlapping periods characterized by either debt surges or reductions.
- A subset of periods is categorized as stable with a minimum duration of 3 years.
- Stability is defined by one of two conditions:
  - The cumulative change in the debt-to-GDP ratio falls between 2 and 10 percentage points, or
  - It is less than 10 percentage points relative to the country-specific standard deviation.

### FX Effect in Debt Decomposition
- A proxy for the “FX effect” on debt surges is constructed to give the percentage point change in debt-to-GDP due to FX depreciation.
- Other SFA is defined as “other SFAs” = Residuals – FX effect.
- The FX effect is computed using end-of-year bilateral USD/LC exchange rates and the share of FX debt to total debt at the previous year of debt surge.
  - Exchange rate variables: end-of-year exchange rate (LC/$) at the previous year of start of debt surge and at the end year of debt surge.
  - Debt share variables: debt-to-GDP ratio at the previous year of debt surge and share of FX debt to total debt at the previous year of debt surge.
  - The start year and end year of a debt surge are denoted as 푎푎푑푑 푡푡=1 and 푎푎, respectively (as in the source).
- Data sources for FX effect inputs:
  - Bilateral USD/LC exchange rates (used).
  - Share of FX debt from IMF Sovereign Debt Investor Base for EMDE (2023) (“ExtendedDataset_Currency”).
  - For missing Advanced Economies (AEs), the share of external debt is alternatively used.

### Variables — Panel VAR (Annex Table AI.1)
- Public Debt: Total General Government Gross Debt (in percent of GDP) — Arslanalp and Tsuda (2014)
- Government Primary Spending: General government expenditure: primary expenditure (in percent of GDP) — IMF WEO
- Government Revenue: General government revenue (in percent of GDP) — IMF WEO
- Output: Real GDP (constant $) — IMF WEO
- Real Effective Exchange Rate: Real Effective Exchange Rate (in natural logarithm) — IMF WEO
- Inflation: Year-on-year change of the consumer price index (in percent) — IMF WEO
- Monetary Policy: Central Bank Policy Rate used for Advanced economies and Broad Money (in percent of GDP) used for Emerging markets and Low-Income countries — Bank of International Settlements (BIS) and World Bank WDI
- Oil Price: Crude Oil (petroleum), simple average of three spot prices (US$ per barrel) — IMF GAS

Notes:
- Fiscal variables are measured in natural logarithms of real per-capita US dollar aggregates, where the GDP deflator is used for the conversion into real terms.
- To ensure the model’s stability, first differences are taken of GDP and the monetary policy variable.

### List of Variables — Crisis Prediction (Annex Table AI.2)
- FinancialCrisis: Dummy equal to one if a country is in a banking, currency, or sovereign debt crisis in a year, and zero otherwise — Laeven and Valencia (2016)
- DebtSurge: Dummy equal to one if a country is in a debt surge episode in a year, and a financial crisis breaks out in some year later than the start year during this debt surge episode, and zero otherwise — Own definition based on IMF WEO
- DebtAccumulation: Year-on-year change of the debt-to-GDP ratio (in percentage points) — IMF WEO
- RevenueShock: Minus one times shock to the revenue-to-GDP ratio retrieved from a panel VAR (in natural logarithm) — Own calculation based on IMF WEO
- PrimarySpendingShock: Shock to the primary-spending-to-GDP ratio retrieved from a panel VAR (in natural logarithm) — Own calculation based on IMF WEO
- FXDepreciation: Year-on-year change of the nominal exchange rate vis-à-vis the US dollar (in percent) — IMF WEO
- PrimaryBalanceShock: Shock to the primary balance constructed based on fiscal shocks retrieved from a panel VAR and sample average revenue- and primary-spending-to-GDP ratios (in percent of GDP) — Own calculation based on IMF WEO
- Reserves: Foreign currency reserves (in percent of GDP) — IMF WEO
- BankCredit: Total credit to the private sector provided by domestic banks (in percent of GDP) — World Bank WDI
- ExternalDebt: External government debt (in percent of total government debt) — IMF Sovereign Debt Investor Base
- Growth: Year-on-year change of GDP in constant 2015 US dollar (in percent) — World Bank WDI
- Inflation: Year-on-year change of the consumer price index (in percent) — IMF WEO
- RealInterestRate: Average real lending interest rate — World Bank WDI
- CurrentAccount: Current account balance (in percent of GDP) — IMF WEO
- GDPpc: GDP per capita in constant 2015 US dollar — World Bank WDI

### List of Variables — Ex-post Debt Path Prediction (Annex Table AI.3)
- ExPostDebtPath: Dummy equal to one if a country’s debt-to-GDP ratio drops by more than seven percentage points between the last year of a debt surge episode and the average of years three to five afterwards, and zero otherwise — Own definition based on IMF WEO
- DebtAccumulation: Change of the debt-to-GDP ratio between the year prior to and the last year of a debt surge episode (in percentage points) — Own calculation based on IMF WEO
- DebtPeak: Debt in the last year of a debt surge episode (in percent of GDP) — IMF WEO
- Duration: Number of years of a debt surge episode — Own calculation based on IMF WEO
- FinancialMarketDepth: Average IMF Financial Market Depth Index during a debt surge episode (between zero and one) — Own calculation based on IMF Index of Financial Development
- RevenueShock: Minus one times average of shocks to the revenue-to-GDP ratio retrieved from a panel VAR during a debt surge episode (in natural logarithm) — Own calculation based on IMF WEO
- PrimarySpendingShock: Average of shocks to the primary-spending-to-GDP ratio retrieved from a panel VAR during a debt surge episode (in natural logarithm) — Own calculation based on IMF WEO
- FXEffect: Part of SFA driven by FX fluctuations computed based on standard debt decomposition SFA, the share of external debt, and nominal exchange rate depreciation during a debt surge episode (in percentage points) — Own calculation based on IMF WEO, IMF Sovereign Debt Investor Base, and standard debt decomposition
- OtherSFA: Residual part of SFA during a debt surge episode (in percentage points) — Own calculation based on IMF WEO, IMF Sovereign Debt Investor Base, and standard debt decomposition
- PrimaryBalanceAfter: Average of shocks to the primary balance constructed based on fiscal shocks retrieved from a panel VAR and sample average revenue- and primary-spending-to-GDP ratios during the five years after a debt surge episode (in percent of GDP) — Own calculation based on IMF WEO
- GrowthAfter: Annualized average change of GDP in constant 2015 US dollar during the five years after a debt surge episode (in percent) — Own calculation based on World Bank WDI
- InflationAfter: Annualized average change of the consumer price index during the five years after a debt surge episode (in percent) — Own calculation based on IMF WEO
- RestructuringAfter: Dummy equal to one if a country is in a debt restructuring during the five years after a debt surge episode, and zero otherwise — Own calculation based on Laeven and Valencia (2016)
- FXDepreciationAfter: Change of the nominal exchange rate vis-à-vis the US dollar between the last year of and the fifth year after a debt surge episode (in percent) — Own calculation based on IMF WEO

### Annex II — Augmented Decomposition (AD)
- The augmented decomposition (AD) follows Mauro and Zilinsky (2016) and expands the standard accounting identity that decomposes change in debt-to-GDP into three components.
- Standard identity (symbols as in source):
  - 푑푑푡 − 푑푑푡−1 = �(퐷퐷푡 1+퐷퐷푡)푑푑푡−1 − �(퐷퐷푡 1+퐷퐷푡)푑푑푡−1 − 푝푝푡
  - where d is debt-to-GDP ratio, r is the real interest rate, g is the real growth rate, and p is the primary surplus.
- Rationale for augmentation:
  - The standard breakdown does not fully capture how economic growth affects the primary surplus (tax income rises with growth, improving the primary surplus).
  - Assume revenues move with nominal GDP and primary expenditures grow with the GDP deflator; a neutral policy stance implies primary surplus proportionate to GDP evolves as:
    - 푝푝푡 = 푝푝푡−1 + �(퐷퐷푡 1+퐷퐷푡)�푒푒푡−1 + 푚푚푡
    - where e is the ratio of primary expenditures to GDP and m is the effect of policy measures (residual).
- Summing the identity between year 0 and year N yields a decomposition where:
  - First item: contribution of the real interest rate.
  - Second item: direct growth effect.
  - Third item: contribution of the “indirect” effect of growth (via erosion of primary expenditure-to-GDP ratio).
  - Fourth item: effect of fiscal measures (sum of ∑∑ ∆푚푚푡푖).
  - Last term: initial primary balance effect (−N푝푝0).
- Empirical findings (Annex Figure AII.1 summary):
  - AD shows higher fiscal policy and growth contributions compared to the standard decomposition (SD) across country groups and almost all percentiles.
  - Capturing growth’s effect on primary balance and counting it as growth raises AD’s growth contribution relative to SD.
  - Removing growth’s embedded positive effect on debt-to-GDP from the primary balance makes the negative effect of fiscal slippages on debt (remaining fiscal policy measure ∑∑ ∆푚푚푡푖) tend to be higher in AD.
  - By country group:
    - Advanced Economies (AEs): AD reflects a pronounced effect from fiscal policy vs. SD; growth contribution remains marginal, with AD marginally higher.
    - Emerging Markets (EMs): AD shows more accentuated fiscal policy impact, especially within the [0.5, 0.75] debt surge quartile.
    - Low-Income Countries (LICs): AD consistently reveals a more considerable fiscal policy effect across quartiles compared to SD; growth displays significant effects in AD predominantly in the [0.5, 0.75] and >0.75 brackets.
- Conclusion: AD disentangles growth and fiscal policy effects, offering a more nuanced picture while both methods identify fiscal policy as a key driver of debt surges.

### Annex III — Estimating Fiscal Policy Shocks and Consequences of Debt Surges (summary of figures and robustness)
- Panel VAR impulse responses:
  - Impulse responses depicted for a 1% fiscal shock (negative one percent shock to revenue, positive one percent shock to primary spending) for AEs, EMs, and LICs (Annex Figures AIII.1–AIII.6).
  - Figures show estimated impulse responses with 95-percent confidence intervals.
- Forecast Error Variance Decompositions:
  - Debt-to-GDP decomposition to various shocks over five years for AEs, EMs, and LICs (Annex Figures AIII.7–AIII.9).
  - Red bars refer to fiscal shocks; blue bars refer to macroeconomic and monetary shocks.
- Local projections:
  - Impulse responses of debt-to-GDP to a positive one percent shock to revenue and a negative one percent shock to primary spending using WEO forecast errors (Annex Figure AIII.10). Responses measured in percentage points; 95-percent confidence intervals shown.
- Distribution of fiscal shocks:
  - Panel VAR and WEO forecast error distributions presented (Annex Figures AIII.11–AIII.12); fiscal shocks measured in percent on x-axis.
- Robustness checks:
  - Three alternative orderings to the Cholesky decomposition were considered.
  - Ordering 2 swaps primary spending and revenue; new ordering: (1) Revenue (2) GDP (3) Primary spending (4) Inflation (5) REER (6) Monetary variable (7) Debt.
  - Results are robust to this change; the only significant difference is that debt responses to revenue shocks are smaller under the alternative ordering compared to the baseline, albeit being insignificant shortly after the impulse.

*Source: Annex I. Definition of Variables and Data Sources (document content provided).*

### Annex Figure AIII.13. Alternative Ordering 2

### Annex Figure AIII.13. Alternative Ordering 2

### Description of alternative ordering experiments
- Under ordering 3 the authors place the two most exogenous macroeconomic variables, i.e., GDP and inflation, before fiscal policy while maintaining the ordering of spending before revenue. The ordering is: (1) GDP (2) Inflation (3) Primary spending (4) Revenue (5) REER (6) Monetary variable (7) Debt.
- Under ordering 4 the authors place all macro variables before fiscal policy to check sensitivity if fiscal policy is considered highly endogenous. The ordering is: (1) GDP (2) Inflation (3) REER (4) Monetary variable (5) Primary spending (6) Revenue (7) Debt.

### Key findings from the alternative orderings
- Debt responses show very minor changes under ordering 3.
- As under ordering 3, no significant changes are found under ordering 4.

### Annex regression and robustness items (titles and specifications preserved)
- Annex Table AIII .1. Debt Surges and Financial Crises — Random-effect logit regression (fixed effects)
- Annex Table AIII .2 . Debt Surges and Financial Crises — Random-effect logit regression (2 lags)
- Annex Table AIII .3. Debt Surges and Financial Crises — Random-effect logit regression (4 lags)
- Annex Table AIII .4 . Debt Surges and Ex-post Debt Paths — Logit regression (10 percentage point threshold)
- Annex Table AIII .5 . Debt Surges and Ex-post Debt Paths — Logit regression (15 percentage point threshold)
- Annex Table AIII .6 . Debt Surges and Ex-post Debt Paths — Logit regression (4–7-year time window)

### Other explicit numeric and bibliographic items present in the unit
- Working Paper No. WP/2024/050
- Page markers appearing in the unit: 41, 42, 43, 44, 45, 46, 47, 48, 49, 50
- Thresholds and windows mentioned: 10 percentage point threshold; 15 percentage point threshold; 4–7-year time window

*Source: Authors’ calculations.*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024050-print-pdf.pdf_