## Annex 2. Baseline Regressions

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### Empirical objective and scope
- Estimate public debt overhang thresholds — defined as the level of public debt at which the marginal impact of additional debt accumulation on per capita GDP growth switches from positive to negative.
- Sample: 105 countries.
- Two-stage empirical approach:
  - Stage 1: Estimate debt overhang thresholds separately for each country using panel data and a Kalman Filter methodology to obtain time-varying estimates.
  - Stage 2: Examine the role of five sets of factors that could explain cross-country heterogeneity in estimated thresholds:
    - (i) a country’s track record in meeting its sovereign debt service obligations;
    - (ii) the quality of a country’s institutions and governance;
    - (iii) the composition and structure of the stock of public debt (in terms of currency, maturity, and creditor base);
    - (iv) the size of the domestic financial market;
    - (v) indicators of depth, access, and efficiency of a country’s domestic financial sector.

### Methodology
- Growth regressions relate per capita real GDP growth to public indebtedness and commonly used macroeconomic control variables.
- The public debt threshold is modeled as an unobservable, time-varying state variable estimated via a Kalman Filter.
- The marginal impact of public debt on per capita real GDP growth is allowed to vary depending on whether public debt is below or above the estimated threshold:
  - Public debt is interacted with an indicator based on whether it exceeds the threshold, permitting nonlinearities in the public debt–growth relationship.
- Approach follows literature noting lack of a universal public debt threshold and applies a Kalman Filter to derive country-specific, time-varying thresholds.

### Key empirical estimates and patterns
- Cross-country heterogeneity in debt overhang thresholds:
  - Range from around 20% of GDP to almost 2 10% of GDP.
  - Mean: 67%.
  - Median: 64%.
- Variation across country groups:
  - Mean threshold ranges from over 52% of GDP for fuel exporters to around 85% of GDP for high income countries.
- Time variation:
  - Estimated thresholds display relatively limited time-variation for individual countries and country groups.

### Drivers of cross-country heterogeneity (empirical findings)
- Payment track record:
  - Can be an important determinant of debt overhang thresholds, though its influence varies by country group.
- Governance and institutions:
  - Good governance (stronger law and order and improved bureaucratic quality) is consistently associated with higher thresholds.
- Debt composition and creditor base:
  - A greater share of non-resident public debt tends to lower the threshold.
  - A greater share of public debt held by official creditors tends to lower the threshold.
- Maturity structure and rollover risk:
  - A higher share of short-term external debt in total external debt is linked to a reduced public debt overhang threshold for some country groups.
- Financial sector size and development:
  - Size of the domestic financial sector is positively associated with the debt overhang threshold (banks/deposit-taking and nonbank financial corporations).
  - Capital market size — stock market capitalization plus outstanding stock of (public and private) debt securities issuances in percent of GDP — does not seem to have an impact on estimated thresholds (likely reflecting small sample size).
  - Financial development (overall FD and sub-indices FI and FM) robustly raises the debt overhang threshold, with notable variation across country groups.

### Contribution relative to existing literature
- Novelty:
  - Application of a Kalman Filter to a standard growth model to derive time-varying debt overhang thresholds separately for a large number of countries — methodology not previously used in this context.
- Comparison:
  - Builds on and expands prior work by using a larger sample and a broader set of potential explanatory factors for cross-country heterogeneity.

### Data issues and sample
- Panel dataset covers 105 countries over the period 1980–2022.
- Primary data sources include IMF WEO, World Bank WDI, Penn World Tables, IMF Sovereign Debt Investor Database (Arslanalp and Tsuda), IMF Historical Public Debt Database.
- Payment track record: debt in arrears/default from the Bank of Canada-Bank of England debt database; missing entries assumed to be zero arrears; historical track record defined as a 20-year rolling average of the annual share of debt in arrears.
- Governance and financial sector measures: ICRG political risk index; IMF Monetary and Financial Statistics; World Bank Global Financial Development; IMF Financial Development Index dataset (FD, FI, FM).
- Sample restricted to countries with at least forty consecutive years of data for first-stage estimation.

### Empirical methodology — state-space / Kalman filter (first stage)
- Measurement equation (variables preserved exactly):
  - g_{i,t} = α_{i,t} + β_{0} y_{i,t−1} + β_{1} ∆POPWA_{i,t−1} + β_{2} ∆HCI_{i,t−1} + β_{3} ∆KSTPC_{i,t−1} + β_{4} ∆OPEN_{i,t−1}
    + β_{5} ∆TOT_{i,t} + γ_{1} ∆d_{i,t−1} + γ_{2} * max(d_{i,t−1} − d_{i,t−1}^{*}, 0) + γ_{3} * min(d_{i,t−1} − d_{i,t−1}^{*}, 0) + DUM_{COVID} + ξ_{t}.
  - Variable definitions: g = growth of per capita GDP; y = log of per capita GDP; POPWA = log of population of working age; KSTPC = log of Capital stock per capita; HCI = log of Human Capital Index; OPEN = openness (exports plus imports in percent of GDP); TOT = log of terms of trade; d = public debt to GDP ratio; d* = debt overhang threshold in percent of GDP; DUM_{COVID} = dummy for years 2020, 2021, and 2022.
- State equations for d*:
  - Random walk (Equation (2a)): d_{i,t}^{*} = d_{i,t−1}^{*} + η_{t}, η_{t} ∼ N(0, γ_{0}). γ_{0} derived from variance of detrended public debt-to-GDP ratio (typically 40–70% of this variance).
  - Mean-reverting (Equation (2b)): d_{i,t}^{*} = ρ d_{i,t−1}^{*} + (1−ρ) d̄_{i}^{*} + η_{t}, η_{t} ∼ N(0, γ_{0}). ρ selected from [0.3, 1] over intervals of 0.1.
- Kalman filter details:
  - Initial values d_{i,0}^{*} from grid search from 20 percent of GDP to 1.5 times the maximum debt-to-GDP ratio for each country over 1980–2022; grid encompassed 100 starting points.
  - d̄_{i}^{*} computed in two steps: initial value of public debt-to-GDP ratio (percent); then average of thresholds estimated using the first step over 1980–2022.
- Limitations:
  - Potential missing endogenous variables (creditworthiness, borrowing costs, interest payments).
  - Potential reverse causality (low growth → higher debt → higher threshold).
  - Suggested remedies include instrumental variables and second-stage panel regressions.

### Baseline Stage 1 results (KF implementation and group averages)
- Baseline KF setup:
  - State equation: Equation (2a) (random walk).
  - Variance of state-equation error term set to 0.7 of the variance of the detrended public debt-to-GDP ratio for each country.
- Country grouping and aggregation:
  - Five groups: (i) fuel exporters (FEs), (ii) high-income countries (HICs), (iii) upper middle-income countries (UMICs), (iv) low middle-income countries (LMICs), (v) low-income countries (LICs).
  - Group debt thresholds obtained by averaging estimated thresholds for individual countries in each group.
- Sample-level descriptive results (numeric records preserved exactly):
  - No. of countries Mean Median Min Max Std
  - Fuel Exporters 13 52.55 2.22 1.5 102.2 2.3
  - High Income Countries 24 85.28 5.03 3.3 209.2 4.7
  - Upper Middle Income 10 79.57 9.63 5.3 121.4 2.8
  - Lower Middle Income 26 64.06 3.82 0.0 128.2 4.9
  - Low Income Countries 32 55.55 5.52 0.0 142.8 5.4
  - All 105 67.36 3.82 0.0 209.2 4.5
  - (Source: IMF Staff calculations — numeric values preserved as in source.)
- Key stage-1 patterns:
  - Group-average thresholds show limited time-variation within most groups.
  - Mean estimated thresholds across groups: over 52% of GDP (FEs) to around 85% of GDP (HICs).
  - Country-level estimates vary from a low of 20% of GDP to a high of almost 210% of GDP over 1980–2022.
  - γ_{2} and γ_{3} coefficients negative across groups, smallest magnitude in HICs (limited impact of public debt accumulation on growth in HICs).

### Baseline Stage 2 results (GLS regressions explaining cross-country heterogeneity)
- Second-stage approach:
  - Estimated debt overhang thresholds from stage 1 used as dependent variable in GLS panel regressions.
  - GLS corrects for heteroskedasticity across countries and serial correlation within countries, but not for cross-sectional dependence across countries.
- Summary of key empirical associations (preserved language):
  - Payment track record is associated with higher debt overhang thresholds, with impact size varying by country group.
  - Stronger law and order and improved bureaucratic quality are consistently associated with higher thresholds.
  - Greater share of non-resident public debt and of public debt held by official creditors are associated with a lower threshold.
  - Higher share of short-term external debt in total external debt linked to reduced threshold for some groups.
  - Size of domestic financial sector (banks and nonbank financial corporations) positively associated with threshold.
  - Capital market size (stock market capitalization plus debt securities issuances in percent of GDP) does not seem to have an impact (potentially reflecting small sample size).
  - Financial development (FD, FI, FM) raises the debt overhang threshold, with variation across country groups.
- Interpretation and caveats:
  - Stage-2 relationships should be interpreted as correlations, not causal effects, due to endogeneity and generated-regressor uncertainty.
  - Dependent variable in stage 2 embeds model-based assumptions and an error band of uncertainty.

### 1. Default Track Record and Institutional and Governance variables — core findings
- Whole sample:
  - Payment track record, law and order, corruption and bureaucratic quality are statistically associated with variation in debt overhang thresholds.
- Group-specific associations:
  - Default track record shows notable relationship for FEs and LMICs.
  - Law and order linked to debt thresholds for FEs and LICs.
  - Corruption linked to debt thresholds for LICs at the 10 percent level.
  - Political Risk Rating and Bureaucratic quality linked to debt thresholds, but with counter-intuitive sign for HICs (better governance associated with lower debt thresholds in HICs).
- Key coefficients and statistics (selected from Annex 2 Tables — numeric values preserved):
  - Annex 2 Table 1 (GLS: Payment Track Record - All Countries and Country Groups)
    - default_record: 0.100*** (All), 0.125*** (FEs), 4.234** (HICs), -0.158 (UMICs), 0.230*** (LMICs), -0.128*** (LICs)
    - Constant: 54.35*** (All); Observations: 3,757 (All); R-squared: 0.1100 (All); Number of Countries: 105
  - Annex 2 Table 2A (GLS: Payment Track Record and ICRG Governance Variables - All Countries)
    - default_record: 0.100*** (column 1)
    - Political_Risk_Rating: 0.155*** (column 3)
    - law_and_order: 1.734*** (column 4)
    - Corruption: 1.169*** (column 5)
    - Bureaucracy_Quality: 4.141*** (column 7)
    - Constant (column 1): 54.353***; Observations: 3,757; R-squared: 0.1100; Number of Countries: 105
  - Annex 2 Table 2B (GLS: Payment Track Record and ICRG Governance Variables - Country Groups)
    - default_record: 0.249*** (column 1), 0.225*** (column 2), 0.243*** (column 3), 0.145*** (column 4), 0.124*** (column 5), 0.108*** (column 6)
    - Political_Risk_Rating: 0.213*** (column 1), 0.244*** (column 2), 0.300*** (column 3)
    - law_and_order: 1.609*** (column 1), 1.627*** (column 2), 1.590*** (column 3)
    - Corruption: 0.541*** (column 1), 0.451** (column 2), 0.066 (column 3)
    - Bureaucracy_Quality: 4.354*** (column 1), 5.351*** (column 2), 7.217*** (column 3)
    - share_shortexternal: -0.0221* (column 1), -0.027* (column 2), -0.045*** (column 3)
    - share_nonresident_debt: -0.054*** (column 1), -0.046*** (column 2)
    - share_official_held_debt: -0.079*** (column 1), -0.034*** (column 2)
    - Constant (column 1): 30.96***; Observations: 2,604; R-squared: 0.4070; Number of Countries: 83
- Interpretation:
  - Institutional quality—particularly law and order and bureaucratic effectiveness—is consistently associated with a higher debt overhang threshold.
  - Strong sovereign debt repayment track record is important, with variation across groups.
  - Counter-intuitive HIC result likely reflects limited cross-country variation in governance among HICs.

### 2. Composition of public debt — findings
- Whole sample:
  - Higher share of nonresident public debt tends to lower the debt overhang threshold.
  - Higher share of public debt held by official creditors tends to lower the debt overhang threshold.
  - No evidence that higher share of short-term external debt in total external debt, or higher share of foreign currency–denominated public debt, is associated with a lower threshold (contrary to some previous studies).
- By country group:
  - FEs: Higher share of public debt held by official creditors associated with a lower threshold.
  - HICs and LICs: Higher share of public debt held by nonresident creditors associated with a lower threshold.
  - LMICs: Higher shares of both official debt and nonresident debt associated with a lower threshold.
  - UMICs: No consistent evidence that composition of public debt or creditor base impacts the threshold.

### 3. Size of the financial sector — findings
- The size of the domestic financial sector is positively related to the debt overhang threshold.
- Positive relationship holds for:
  - Banks and other deposit-taking corporations.
  - Non-bank financial corporations separately.
- Financial sector holdings of loans and debt securities are particularly important.
- Capital market size does not appear to have any notable impact on the debt overhang threshold (sample: only 22 countries).

### 4. Financial Development Index — findings
- Financial development indicators cover depth, access, and efficiency beyond pure size.
- Whole sample:
  - Strong evidence that higher levels of financial development—both financial markets and financial institutions—are associated with a higher debt overhang threshold.
- By country group:
  - Financial development particularly strongly linked to higher debt thresholds for FEs, LMICs and LICs.
  - For FEs, LMICs and LICs: financial market development has a statistically significant positive impact on the threshold; development of financial institutions does not show the same effect.
  - For HICs and UMICs: no consistent evidence that financial development impacts the threshold.

### Robustness checks — procedures and impacts
- Robustness exercises:
  - Combining FGLS with panel-corrected standard errors (PCSEs) and Prais–Winsten to account for AR(1) serial correlation, heteroskedasticity, and cross-sectional dependence.
  - Re-estimating with smaller variance of the state-equation error term (0.4 rather than 0.7 times the variance of the detrended public debt-to-GDP ratio).
  - Re-specifying the state equation to mean-reverting (Equation 2b) instead of random walk.
- General outcome:
  - Main results broadly consistent with baseline findings, though some quantitative differences occur.
  - In most cases, R-squared and pseudo R-squared from baseline GLS regressions are higher than from robustness checks.
- Notable robustness-specific differences (selected):
  - Prais–Winsten PCSE: default track record weaker for full sample; share_shortexternal becomes more strongly linked to thresholds for full sample and LMICs; some unexpected sign changes for UMICs; financial development indicators largely similar to baseline.
  - Smaller state-equation variance: corruption index no longer clearly correlated for LICs; evidence less conclusive that financial development associates with higher thresholds for LICs.
  - Mean-reverting state equation: qualitative similarity overall; corruption index no longer linked to threshold; default track record pattern not clear for LMICs; share_official_held_debt association weaker for whole sample.

### Conclusions — synthesis and implications
- Contribution:
  - Empirically estimates country-specific public debt overhang thresholds using a Kalman Filter on a panel of 105 countries to provide time-varying estimates.
- Main empirical patterns:
  - Relatively limited time-variation in thresholds within most country groups.
  - Notable responses of estimated thresholds to crises such as the Global Financial Crisis and COVID-19.
  - Substantial heterogeneity across countries: mean thresholds from over 52% of GDP (FEs) to around 85% of GDP (HICs); country-level estimates range from 20% to almost 210% of GDP over 1980–2022.
- Factors explaining heterogeneity:
  - Sovereign debt repayment track record.
  - Governance and institutional quality.
  - Composition and structure of public debt (currency, maturity, creditor base).
  - Size and structure of domestic financial markets.
  - Overall level of financial sector development (markets and institutions).
- Key robust associations:
  - Institutional quality—particularly law and order and bureaucratic effectiveness—is consistently associated with a higher debt overhang threshold.
  - Strong default/repayment track record important, with variation across groups.
  - Certain structural debt characteristics (higher nonresident holdings or short-term external debt), domestic financial market size, and indicators of financial depth, access, and efficiency are linked to a country's debt overhang threshold.
- Policy relevance:
  - Results offer insights for policymakers aiming to expand public debt carrying capacity, highlighting the role of institutional strength and financial sector development.

### Annex 2 Table 3A. GLS: Adding Public Debt and Debtholder Composition Variables - All Countries (selected estimation notes and coefficients)
- Estimation setup and notes:
  - Models: (1) through (6) reported.
  - Standard errors in parentheses.
  - Significance: *** p<0.01, ** p<0.05, * p<0.1.
  - Observations: 386, 331, 236, 386, 331, 236 (for columns (1)–(6) respectively).
  - R-squared: 0.311, 0.347, 0.561, 0.359, 0.416, 0.669 (for columns (1)–(6) respectively).
  - Number of Countries: 121, 121, 121, 121, 121, 121 (for columns (1)–(6) respectively).
- Key estimated coefficients (Threshold variable) — numeric values preserved:
  - default_record:
    - (1): 0.0802*** (0.0298)
    - (2): 0.113*** (0.032)
    - (3): 0.166*** (0.046)
    - (4): 0.109*** (0.036)
    - (5): 0.144*** (0.041)
    - (6): 0.129** (0.059)
  - Political_Risk_Rating:
    - (1): 0.00105 (0.0266)
    - (2): 0.028 (0.039)
    - (3): 0.299*** (0.099)
  - law_and_order:
    - (1): 0.698** (0.306)
    - (2): 1.133*** (0.428)
    - (3): 3.636*** (0.807)
  - Corruption:
    - (1): 0.075 (0.360)
    - (2): 0.247 (0.499)
    - (3): 0.206 (0.743)
  - Government_Stability:
    - (1): -0.051 (0.081)
    - (2): -0.068 (0.128)
    - (3): -0.227 (0.226)
  - Bureaucracy_Quality:
    - (1): 0.862** (0.420)
    - (2): 1.296** (0.603)
    - (3): 8.523*** (1.717)
  - share_fc_debt:
    - (1): -0.00497 (0.00742)
    - (2): -0.009 (0.012)
    - (3): -0.020 (0.026)
    - (4): -0.011 (0.009)
    - (5): -0.014 (0.014)
    - (6): -0.000 (0.024)
  - share_shortexternal:
    - (1): 0.00614 (0.0189)
    - (2): -0.000 (0.025)
    - (3): -0.043 (0.057)
    - (4): -0.008 (0.023)
    - (5): -0.021 (0.032)
    - (6): -0.064 (0.055)
  - share_nonresident_debt:
    - (5): -0.008 (0.016)
    - (6): -0.009 (0.020)
  - share_official_held_debt:
    - (5): -0.049** (0.023)
    - (6): -0.050** (0.025)
- Constants (intercepts) — numeric values preserved:
  - Constant:
    - (1): 38.29*** (3.029)
    - (2): 35.445*** (3.645)
    - (3): 20.921*** (7.115)
    - (4): 33.477*** (3.568)
    - (5): 30.149*** (4.318)
    - (6): 16.745** (6.884)
- Summary implications:
  - default_record positive and statistically significant across specifications.
  - Institutional quality measures (law_and_order, Bureaucracy_Quality) show large positive and often highly significant coefficients.
  - Debtholder composition variables generally small; share_official_held_debt negative and significant in some specifications.
  - R-squared values increase substantially in specifications (3) and (6), up to 0.561 and 0.669.

*International Monetary Fund — Annex 2. Baseline Regressions*

### Annex 2. Baseline Regressions _______________________________________________________ 22

### Annex 2. Baseline Regressions

### Empirical objective and scope
- Estimate public debt overhang thresholds — defined as the level of public debt at which the marginal impact of additional debt accumulation on per capita GDP growth switches from positive to negative.
- Sample: 105 countries.
- Two-stage empirical approach:
  - Stage 1: Estimate debt overhang thresholds separately for each country using panel data and a Kalman Filter methodology to obtain time-varying estimates.
  - Stage 2: Examine the role of five sets of factors that could explain cross-country heterogeneity in estimated thresholds:
    - (i) a country’s track record in meeting its sovereign debt service obligations;
    - (ii) the quality of a country’s institutions and governance;
    - (iii) the composition and structure of the stock of public debt (in terms of currency, maturity, and creditor base);
    - (iv) the size of the domestic financial market;
    - (v) indicators of depth, access, and efficiency of a country’s domestic financial sector.

### Methodology
- Growth regressions relate per capita real GDP growth to public indebtedness and commonly used macroeconomic control variables.
- The public debt threshold is modeled as an unobservable, time-varying state variable estimated via a Kalman Filter.
- The marginal impact of public debt on per capita real GDP growth is allowed to vary depending on whether public debt is below or above the estimated threshold:
  - The public debt variable is interacted with an indicator variable based on whether it exceeds the threshold, permitting nonlinearities in the public debt–growth relationship.
- Approach follows literature noting lack of a universal public debt threshold (e.g., Pescatori, Sandri, and Simon, 2014), while applying a Kalman Filter to derive country-specific, time-varying thresholds.

### Key empirical estimates and patterns
- Estimated cross-country heterogeneity in debt overhang thresholds:
  - Range from around 20% of GDP to almost 2 10% of GDP.
  - Mean: 67%.
  - Median: 64%.
- Variation across country groups (fuel exporters; high income countries; upper middle-income countries; lower middle-income countries; and low-income countries):
  - Mean threshold ranges from over 52% of GDP for fuel exporters to around 85% of GDP for high income countries.
- Time variation:
  - Estimated thresholds display relatively limited time-variation for individual countries and country groups.

### Drivers of cross-country heterogeneity (empirical findings)
- Payment track record:
  - Can be an important determinant of debt overhang thresholds, though its influence varies by country group.
- Governance and institutions:
  - Good governance (stronger law and order and improved bureaucratic quality) is consistently associated with higher thresholds.
  - Suggests institutional strength enhances capacity to sustain public debt without adversely affecting economic growth.
- Debt composition and creditor base:
  - A greater share of non-resident public debt tends to lower the threshold.
  - A greater share of public debt held by official creditors tends to lower the threshold.
- Maturity structure and rollover risk:
  - A higher share of short-term external debt in total external debt is linked to a reduced public debt overhang threshold for some country groups.
- Financial sector size and development:
  - Size of the domestic financial sector is positively associated with the debt overhang threshold; this applies both to banks and deposit-taking financial institutions and to nonbank financial corporations.
  - Capital market size — measured by stock market capitalization and outstanding stock of (public and private) debt securities issuances in percent of GDP — does not seem to have an impact on estimated thresholds (likely reflecting small sample size).
  - Financial development (encompassing both financial markets and financial institutions) robustly raises the debt overhang threshold, with notable variation across country groups.

### Contribution relative to existing literature
- Novelty:
  - Application of a Kalman Filter to a standard growth model to derive time-varying debt overhang thresholds separately for a large number of countries across varying income and development levels — an empirical methodology not previously used in this context.
- Comparison:
  - Builds on and expands prior work that estimated thresholds for smaller sets or groups of countries (e.g., Gómez-Puig and Sosvilla-Rivero (2017); Ahlborn and Schweikert (2018); Gómez-Puig and Sosvilla-Rivero (2024)) by using a larger sample and a broader set of potential explanatory factors for cross-country heterogeneity.

*International Monetary Fund — Annex 2. Baseline Regressions*

### Annex 2  presents the baseline regression results.

### Annex 2  presents the baseline regression results

### Literature review: theoretical and empirical context
- Conventional theoretical channels by which public debt can reduce long-run output include:
  - lowering national savings, pushing up interest rates and reducing investment (Barro, 1990; Saint-Paul, 1992);
  - creating a debt overhang problem where a large share of output accrues to foreign lenders (Krugman, 1988);
  - expectations of future distortionary taxation (Barro, 1979) or of significant cuts in public spending;
  - expectations of emerging inflationary pressures due to fiscal dominance (Sargent and Wallace, 1981);
  - higher volatility of economic growth due to constrained scope for counter-cyclical fiscal policy (Aghion and Kharroubi, 2013);
  - higher uncertainty about future policy and prospects; and, in extreme cases, banking or currency crises.
- Countervailing arguments noted:
  - counter-cyclical fiscal stimuli could reduce permanent output costs by mitigating protracted recessions;
  - public debt can finance human development and infrastructure needs;
  - DeLong and Summers (2012) argue expansionary fiscal policy can be self-financing in a low-interest rate environment.
- Empirical literature:
  - Originated with Reinhart and Rogoff (2010) finding a negative relationship between high debt and growth in advanced economies; contested by Herdon, Ash, and Pollin (2013).
  - Subsequent work: studies controlling for covariates, endogeneity, extended samples, and tests for non-linearities (quadratics, splines, panel threshold regressions) produce mixed findings — some find inverse U-shaped relationships, others find complex or no universal threshold effects.
- Heterogeneity drivers examined in literature include:
  - institutional quality; maturity and currency composition of public debt; fiscal uncertainty; debt trajectory; production technologies; and macroeconomic and institutional frameworks.
- This paper expands the literature by estimating heterogeneous debt thresholds and exploring drivers with a larger set of explanatory variables.

### Data issues and sample
- Panel dataset:
  - covers 105 countries over the period 1980–2022.
- Primary data sources:
  - IMF’s World Economic Outlook (WEO) database, World Bank’s World Development Indicators, Penn World Tables, IMF’s Sovereign Debt Investor Database (Arslanalp and Tsuda), IMF’s Historical Public Debt Database.
- Debt composition and other variables:
  - sovereign debt by holder (Arslanalp and Tsuda); foreign currency debt (WEO); short-term external debt share (World Bank WDI).
- Payment track record:
  - debt in arrears/default from the Bank of Canada-Bank of England debt database; missing entries assumed to be zero arrears; historical track record defined as a 20-year rolling average of the annual share of debt in arrears.
- Governance and financial sector measures:
  - political risk index from International Country Risk Guide (ICRG); financial sector size from IMF Monetary and Financial Statistics and World Bank Global Financial Development; capital market size as stock market capitalization plus debt securities issuances (World Bank).
- Financial development:
  - IMF’s Financial Development Index dataset (overall index FD, sub-indices Financial Institutions FI and Financial Markets FM).
- Sample categorization:
  - World Bank income classifications combined with IMF WEO fuel exporter list.
- Data restriction:
  - sample restricted to countries with at least forty consecutive years of data for first-stage estimation.

### Empirical methodology — state-space / Kalman filter approach (first stage)
- Measurement equation (Equation (1)) specification (variables preserved as in source):
  - g_{i,t} = α_{i,t} + β_{0} y_{i,t−1} + β_{1} ∆POPWA_{i,t−1} + β_{2} ∆HCI_{i,t−1} + β_{3} ∆KSTPC_{i,t−1} + β_{4} ∆OPEN_{i,t−1}
    + β_{5} ∆TOT_{i,t} + γ_{1} ∆d_{i,t−1} + γ_{2} * max(d_{i,t−1} − d_{i,t−1}^{*}, 0) + γ_{3} * min(d_{i,t−1} − d_{i,t−1}^{*}, 0) + DUM_{COVID} + ξ_{t}.
  - Variable definitions preserved exactly: g = growth of per capita GDP; y = log of per capita GDP; POPWA = log of population of working age; KSTPC = log of Capital stock per capita; HCI = log of Human Capital Index; OPEN = openness (exports plus imports in percent of GDP); TOT = log of terms of trade; d = public debt to GDP ratio; d* = debt overhang threshold in percent of GDP; DUM_{COVID} = dummy for years 2020, 2021, and 2022.
- State equations for the unobserved threshold d*:
  - Random walk model (Equation (2a)):
    - d_{i,t}^{*} = d_{i,t−1}^{*} + η_{t}, with η_{t} ∼ N(0, γ_{0}).
    - γ_{0} is derived from the variance of the detrended public debt-to-GDP ratio for each country or country group (typically 40–70% of this variance).
  - Mean-reverting model (Equation (2b)):
    - d_{i,t}^{*} = ρ d_{i,t−1}^{*} + (1−ρ) d̄_{i}^{*} + η_{t}, with η_{t} ∼ N(0, γ_{0}).
    - ρ selected from the range [0.3, 1] over intervals of 0.1.
- Kalman filter estimation details:
  - initial values d_{i,0}^{*} taken from a grid search covering a dynamic range from 20 percent of GDP to 1.5 times the maximum value of the debt-to-GDP ratio (in percent) for each country over 1980–2022;
  - grid encompassed 100 starting points;
  - for some countries lower and upper limits imposed on grid search by authors’ judgment;
  - d̄_{i}^{*} computed in two steps: first taken as initial value of public debt-to-GDP ratio (percent); second computed as average of debt overhang thresholds estimated using the first step over 1980–2022.
- Estimation practice:
  - coefficients α, β, γ in the measurement equation estimated by running regressions for each country.
- Limitations noted:
  - potential missing endogenous variables in measurement equation (e.g., creditworthiness, borrowing costs, interest payments);
  - potential reverse causality (low growth → higher debt → higher threshold);
  - suggested remedies include instrumental variables and second-stage panel regressions.

### Baseline Stage 1 results (KF implementation and group averages)
- Baseline KF setup:
  - state equation used: Equation (2a) (random walk);
  - variance of the error term of the state equation set to 0.7 of the variance of the detrended public debt-to-GDP ratio for each individual country.
- Country grouping and aggregation:
  - five groups: (i) fuel exporters (FEs), (ii) high-income countries (HICs), (iii) upper middle-income countries (UMICs), (iv) low middle-income countries (LMICs), and (v) low-income countries (LICs).
  - group debt thresholds obtained by averaging estimated debt overhang thresholds for individual countries in each group.
- Sample-level descriptive results (Table 1 reproduced as numeric records exactly as shown):
  - No. of countries Mean Median Min Max Std
  - Fuel Exporters 13 52.55 2.22 1.5 102.2 2.3
  - High Income Countries 24 85.28 5.03 3.3 209.2 4.7
  - Upper Middle Income 10 79.57 9.63 5.3 121.4 2.8
  - Lower Middle Income 26 64.06 3.82 0.0 128.2 4.9
  - Low Income Countries 32 55.55 5.52 0.0 142.8 5.4
  - All 105 67.36 3.82 0.0 209.2 4.5
  - (Source: IMF Staff calculations — numeric values preserved as in source.)
- Key patterns and statistics from stage 1:
  - time-variation of group-average debt overhang thresholds is relatively limited within most groups;
  - mean estimated thresholds across groups range from over 52% of GDP for fuel exporters to around 85% of GDP for high-income countries;
  - country-level estimates vary from a low of 20% of GDP to a high of almost 210% of GDP over 1980–2022;
  - γ_{2} and γ_{3} coefficients: negative across all groups, with smallest magnitude in the high-income group (implying limited impact of public debt accumulation on economic growth in HICs).
- Growth effects relative to thresholds (figures summarized):
  - Figure 3: mean regression coefficients for γ_{2} and γ_{3} are negative across groups; the negative effect of debt above threshold decreases with income level.
  - Figure 4.A: average per capita GDP growth computed separately for periods when public debt exceeded threshold and when below threshold; HICs show smaller differences in growth across these regimes.
  - Figure 4.B: experiment varying thresholds by ±10% shows higher debt levels associated with more pronounced economic slowdown across groups except HICs; fuel-exporting and LIC groups show greatest vulnerability.

### Baseline Stage 2 results (GLS regressions explaining cross-country heterogeneity)
- Second-stage approach:
  - estimated debt overhang thresholds (from stage 1) used as dependent variable in GLS panel regressions;
  - GLS corrects for heteroskedasticity across countries and for serial correlation within countries, but not for cross-sectional dependence across countries;
  - full empirical second-stage results presented in Annex 2 (this Annex 2 contains the baseline regression results).
- Summary of key empirical associations (preserved language):
  - payment track record is associated with higher debt overhang thresholds, with impact size varying by country group;
  - stronger law and order and improved bureaucratic quality are consistently associated with higher thresholds;
  - a greater share of non-resident public debt and of public debt held by official creditors are associated with a lower threshold;
  - a higher share of short-term external debt in total external debt is linked to a reduced public debt overhang threshold for some country groups;
  - the size of the domestic financial sector (both banks/deposit-taking institutions and nonbank financial corporations) is positively associated with the debt overhang threshold;
  - capital market size (stock market capitalization plus debt securities issuances in percent of GDP) does not seem to have an impact on estimated thresholds (potentially reflecting small sample size);
  - financial development (overall FD and sub-indices FI and FM) raises the debt overhang threshold, with notable variation across country groups.
- Interpretation and caveats:
  - second-stage relationships should be interpreted as correlations, not causal effects, due to endogeneity and generated-regressor uncertainty;
  - the dependent variable in stage 2 embeds model-based assumptions and an error band of uncertainty, complicating inference.

*Source: IMF Staff calculations and analysis as presented in Annex 2 of the working paper "Explaining Cross-Country Heterogeneity in Debt Overhang Thresholds."*

### 1. Default Track Record and Institutional and Governance variables (Figure 5 and Annex 2 Tables 1,

### 1. Default Track Record and Institutional and Governance variables (Figure 5 and Annex 2 Tables 1, 2A and 2B)

### Default track record and governance — core findings
- For the whole sample, payment track record, law and order, corruption and bureaucratic quality are statistically associated with variation in debt overhang thresholds.
- The default track record shows a notable relationship for FEs and LMICs.
- Law and order is linked to debt thresholds for FEs and LICs.
- Corruption is linked to debt thresholds for LICs, although only at the 10 percent level of statistical significance, even though corruption seems highly relevant for the sample as a whole.
- Political Risk Rating and Bureaucratic quality are linked to debt thresholds, but with a counter-intuitive sign for HICs:
  - Better governance is associated with lower debt thresholds in high-income countries, which is surprising and may reflect limited variation in governance scores among high-income countries.

### Key coefficients and statistics (selected from Annex 2 Tables)
- Annex 2 Table 1 (GLS: Payment Track Record - All Countries and Country Groups)
  - default_record: 0.100*** (All), 0.125*** (FEs), 4.234** (HICs), -0.158 (UMICs), 0.230*** (LMICs), -0.128*** (LICs)
  - Constant: 54.35*** (All); Observations: 3,757 (All); R-squared: 0.1100 (All); Number of Countries: 105
- Annex 2 Table 2A (GLS: Payment Track Record and ICRG Governance Variables - All Countries)
  - default_record: 0.100*** (column 1)
  - Political_Risk_Rating: 0.155*** (column 3)
  - law_and_order: 1.734*** (column 4)
  - Corruption: 1.169*** (column 5)
  - Bureaucracy_Quality: 4.141*** (column 7)
  - Constant (column 1): 54.353***; Observations: 3,757; R-squared: 0.1100; Number of Countries: 105
- Annex 2 Table 2B (GLS: Payment Track Record and ICRG Governance Variables - Country Groups)
  - default_record: 0.249*** (column 1), 0.225*** (column 2), 0.243*** (column 3), 0.145*** (column 4), 0.124*** (column 5), 0.108*** (column 6)
  - Political_Risk_Rating: 0.213*** (column 1), 0.244*** (column 2), 0.300*** (column 3)
  - law_and_order: 1.609*** (column 1), 1.627*** (column 2), 1.590*** (column 3)
  - Corruption: 0.541*** (column 1), 0.451** (column 2), 0.066 (column 3)
  - Bureaucracy_Quality: 4.354*** (column 1), 5.351*** (column 2), 7.217*** (column 3)
  - share_shortexternal: -0.0221* (column 1), -0.027* (column 2), -0.045*** (column 3)
  - share_nonresident_debt: -0.054*** (column 1), -0.046*** (column 2)
  - share_official_held_debt: -0.079*** (column 1), -0.034*** (column 2)
  - Constant (column 1): 30.96***; Observations: 2,604; R-squared: 0.4070; Number of Countries: 83

### Interpretation
- Institutional quality—particularly law and order and bureaucratic effectiveness—is consistently associated with a higher debt overhang threshold.
- A strong sovereign debt repayment track record is important, but its role varies across country groups.
- The counter-intuitive negative association between governance and thresholds in HICs may reflect limited cross-country variation in governance among HICs, complicating identification.

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### 2. Composition of public debt — findings (Figure 6 and Annex 2 Tables 3A–3F)
- Whole sample:
  - A higher share of nonresident public debt tends to lower the debt overhang threshold.
  - A higher share of public debt held by official creditors tends to lower the debt overhang threshold.
  - No evidence that a higher share of short-term external debt in total external debt, or a higher share of foreign currency-denominated public debt, is associated with a lower debt overhang threshold (contrary to some previous studies).
- By country group:
  - FEs: Higher share of public debt held by official creditors associated with a lower debt overhang threshold.
  - HICs and LICs: Higher share of public debt held by nonresident creditors associated with a lower debt overhang threshold.
  - LMICs: Higher shares of both official debt and nonresident debt associated with a lower debt overhang threshold.
  - UMICs: No consistent evidence that composition of public debt or creditor base impacts the debt overhang threshold.

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### 3. Size of the financial sector — findings (Figure 7 and Annex 2 Table 4)
- The size of the domestic financial sector is positively related to the debt overhang threshold.
- This positive relationship holds for:
  - Banks and other deposit-taking corporations.
  - Non-bank financial corporations separately.
- Financial sector holdings of loans and debt securities are particularly important.
- The size of the capital market does not appear to have any notable impact on the debt overhang threshold (possibly due to small sample size: only 22 countries).

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### 4. Financial Development Index — findings (Figure 8 and Annex 2 Tables 5A–5F)
- Financial development indicators cover depth, access, and efficiency beyond pure size.
- Whole sample:
  - Strong evidence that higher levels of financial development—both financial markets and financial institutions—are associated with a higher debt overhang threshold.
- By country group:
  - Financial development is particularly strongly linked to higher debt thresholds for FEs, LMICs and LICs.
  - For FEs, LMICs and LICs: financial market development has a statistically significant positive impact on the debt overhang threshold; development of financial institutions does not show the same effect.
  - For HICs and UMICs: no consistent evidence that financial development impacts the debt overhang threshold.

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### Robustness checks — procedures and impacts
- Robustness exercises:
  - Combining feasible generalized least squares (FGLS) with panel-corrected standard errors (PCSEs) and Prais–Winsten to account for AR(1) serial correlation, heteroskedasticity, and cross-sectional dependence.
  - Re-estimating the model with a smaller variance of the state-equation error term (set to 0.4 rather than 0.7 times the variance of the detrended public debt-to-GDP ratio).
  - Re-specifying the state equation to follow a mean-reverting process (Equation 2b) instead of a random walk.
- General outcome:
  - Main results remain broadly consistent with baseline findings, though some quantitative differences occur.
  - In most (but not all) cases, R-squared and pseudo R-squared from baseline GLS regressions are higher than those from robustness checks.
- Specific differences under robustness specifications:
  - Prais–Winsten PCSE:
    - Default track record shows a weaker relationship for the full sample and no clear pattern for HICs and LMICs.
    - Bureaucratic quality follows expected pattern for FEs but shows no clear relationship for HICs.
    - For the full sample, share of short-term external debt in total external debt becomes more strongly linked to debt overhang thresholds.
    - For LMICs, higher share of short-term external debt appears to lower the debt overhang threshold.
    - For UMICs, higher share of foreign currency–denominated debt associated with a lower threshold; unexpectedly, greater share of public debt held by nonresidents associated with a higher threshold.
    - Financial sector size results similar to baseline except: assets of nonbank financial corporations no longer display clear correlation; higher financial sector holdings of equities and other assets associated with a lower debt overhang threshold.
    - Financial development indicators yield very similar conclusions to baseline.
  - Smaller state-equation variance:
    - Corruption index no longer displays a clear correlation for LICs, though it remains strong for whole sample.
    - For LICs, evidence less conclusive that overall financial development and development of financial markets associate with a lower debt overhang threshold.
  - Mean-reverting state equation:
    - Results qualitatively similar overall.
    - Corruption index no longer appears linked to the debt threshold.
    - Default track record variable no longer shows clear pattern for LMICs.
    - For whole sample, no longer consistent evidence that higher share of public debt held by official creditors is associated with a lower debt overhang threshold.
    - Financial sector size results very similar to baseline.
    - Financial development indicators no longer show clear relationship for all individual country groups, except LMICs.

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### Conclusions (Section VI) — synthesis and implications
- Contribution:
  - Empirically estimates country-specific public debt overhang thresholds (point beyond which additional public debt accumulation begins to have a negative marginal effect on per capita real GDP growth) using a Kalman Filter on a panel of 105 countries to provide time-varying estimates.
- Main empirical patterns:
  - Relatively limited time-variation in thresholds within most country groups, reflecting slow movement of structural drivers (e.g., institutional quality, financial market deepening).
  - Notable responses of estimated thresholds to crises such as the Global Financial Crisis (GFC) and COVID-19.
  - Substantial heterogeneity across countries:
    - Mean threshold ranges from over 52% of GDP for fuel exporters to around 85% of GDP for high income countries.
    - Country-level estimates vary from a low of 20% of GDP to a high of almost 210% of GDP over the sample period.
- Factors assessed for explaining heterogeneity:
  - Sovereign debt repayment track record.
  - Governance and institutional quality.
  - Composition and structure of public debt (currency, maturity, creditor base).
  - Size and structure of domestic financial markets.
  - Overall level of financial sector development (markets and institutions).
- Key robust associations:
  - Institutional quality—particularly law and order and bureaucratic effectiveness—is consistently associated with a higher debt overhang threshold.
  - Strong default/repayment track record important, with variation across groups.
  - Certain structural debt characteristics (higher nonresident holdings or short-term external debt), domestic financial market size, and indicators of financial depth, access, and efficiency are linked to a country's debt overhang threshold.
- Policy relevance:
  - Results offer insights for policymakers aiming to expand public debt carrying capacity, highlighting the role of institutional strength and financial sector development.

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*IMF Working Papers — Explaining Cross-Country Heterogeneity in Debt Overhang Thresholds (figures and Annex 2 tables as presented in the source content).*

### Annex 2 Table 3A.  GLS: Adding Public Debt and Debtholder Composition Variables - All Countries

### Annex 2 Table 3A.  GLS: Adding Public Debt and Debtholder Composition Variables - All Countries

### Estimation setup and notes
- Models: (1) through (6) reported.
- Standard errors in parentheses.
- Significance: *** p<0.01, ** p<0.05, * p<0.1.
- Observations: 386, 331, 236, 386, 331, 236 (for columns (1)–(6) respectively).
- R-squared: 0.311, 0.347, 0.561, 0.359, 0.416, 0.669 (for columns (1)–(6) respectively).
- Number of Countries: 121, 121, 121, 121, 121, 121 (for columns (1)–(6) respectively).

### Key estimated coefficients (Threshold variable)
- default_record:
  - (1): 0.0802*** (0.0298)
  - (2): 0.113*** (0.032)
  - (3): 0.166*** (0.046)
  - (4): 0.109*** (0.036)
  - (5): 0.144*** (0.041)
  - (6): 0.129** (0.059)

- Political_Risk_Rating:
  - (1): 0.00105 (0.0266)
  - (2): 0.028 (0.039)
  - (3): 0.299*** (0.099)

- law_and_order:
  - (1): 0.698** (0.306)
  - (2): 1.133*** (0.428)
  - (3): 3.636*** (0.807)

- Corruption:
  - (1): 0.075 (0.360)
  - (2): 0.247 (0.499)
  - (3): 0.206 (0.743)

- Government_Stability:
  - (1): -0.051 (0.081)
  - (2): -0.068 (0.128)
  - (3): -0.227 (0.226)

- Bureaucracy_Quality:
  - (1): 0.862** (0.420)
  - (2): 1.296** (0.603)
  - (3): 8.523*** (1.717)

- share_fc_debt:
  - (1): -0.00497 (0.00742)
  - (2): -0.009 (0.012)
  - (3): -0.020 (0.026)
  - (4): -0.011 (0.009)
  - (5): -0.014 (0.014)
  - (6): -0.000 (0.024)

- share_shortexternal:
  - (1): 0.00614 (0.0189)
  - (2): -0.000 (0.025)
  - (3): -0.043 (0.057)
  - (4): -0.008 (0.023)
  - (5): -0.021 (0.032)
  - (6): -0.064 (0.055)

- share_nonresident_debt:
  - (5): -0.008 (0.016)
  - (6): -0.009 (0.020)

- share_official_held_debt:
  - (5): -0.049** (0.023)
  - (6): -0.050** (0.025)

### Constants (intercepts)
- Constant:
  - (1): 38.29*** (3.029)
  - (2): 35.445*** (3.645)
  - (3): 20.921*** (7.115)
  - (4): 33.477*** (3.568)
  - (5): 30.149*** (4.318)
  - (6): 16.745** (6.884)

### Summary implications from coefficients
- A positive and statistically significant association between default_record and the estimated threshold is present across all specifications, with coefficients ranging from 0.0802*** to 0.166*** in columns (1)–(3) and 0.109*** to 0.144*** in (4)–(5), and 0.129** in (6).
- Institutional quality measures show heterogeneous effects:
  - law_and_order and Bureaucracy_Quality display large positive and often highly significant coefficients in several specifications (e.g., law_and_order up to 3.636***; Bureaucracy_Quality up to 8.523***).
  - Political_Risk_Rating is significant in column (3) (0.299***).
- Debtholder composition variables (share_fc_debt, share_shortexternal, share_nonresident_debt, share_official_held_debt) are generally small in magnitude; notable is share_official_held_debt which is negative and significant in columns (5) and (6) (-0.049** and -0.050**).
- R-squared values rise substantially in specifications (3) and (6), indicating improved explanatory power when certain controls or interactions are included (R-squared up to 0.561 and 0.669).

*Source: Annex 2 Table 3A, IMF Working Paper "Explaining Cross-Country Heterogeneity in Debt Overhang Thresholds" (tables and notes reproduced exactly as in the source).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026051-source-pdf.pdf_