## _011212

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---

### Executive Summary — purpose and scope
- The DSF (Debt Sustainability Framework) is a standardized framework for conducting public and external debt sustainability analysis (DSA) in low-income countries (LICs).
- Introduced in 2005 and reviewed in 2006 and 2009, the DSF aims to:
  - Guide borrowing decisions of LICs to match financing needs with repayment ability;
  - Provide guidance for creditors‘ lending and grant allocation decisions;
  - Improve World Bank and IMF assessments and policy advice;
  - Help detect potential crises early so that preventive action can be taken.
- This paper provides a comprehensive review of the DSF to assess whether it remains adequate given evolving LIC circumstances, presents recent analytical work by IMF and World Bank staffs, and discusses possible framework improvements.

### Main analytical conclusions and recommended changes
- Staff analytical work broadly validates the indicative policy-dependent thresholds currently used in the framework.
- Recommended modest revisions:
  - Revise thresholds for debt service to revenue and for the PV of debt to the sum of exports and remittances.
  - Maintain all other thresholds at their current values.
- Strengthen the analysis of total public debt and fiscal vulnerabilities:
  - Focus on vulnerabilities most relevant to country teams.
  - Introduce benchmarks for total public debt to signal when deeper analysis is warranted.
- Where domestic public debt or private external debt vulnerabilities are significant, add an additional risk rating:
  - This additional risk rating would inform macroeconomic and structural policy dialogue.
  - It would provide an overall assessment of vulnerability complementing the existing external public debt assessment.
- Improve modeling of the investment-growth nexus:
  - Propose greater use of models developed by IMF and World Bank staffs to better capture debt-financed investment and growth linkages.
- Redesign stress tests to better reflect dynamic linkages between macroeconomic variables:
  - Introduce this refinement on an experimental basis.
- Simplify the DSA template to facilitate use by country authorities and reduce resource costs:
  - Propose a modular approach built around a baseline scenario and simple stress tests.
  - Propose producing full joint DSAs every three years, with lighter joint updates in intervening years.

### How the DSF operates (key features)
- Compares projections of external public debt over the next 20 years against indicative policy-dependent thresholds to assess the risk of debt distress.
- Vulnerability to external and policy shocks is explored via alternative scenarios and standardized bound tests.
- Indicative threshold for each debt burden indicator depends on policy and institutional capacity measured by the World Bank‘s CPIA index.
- Risk-of-debt-distress ratings (based on external public debt analysis): Low risk; Moderate risk; High risk; In debt distress.
- Public sector DSA assesses domestic debt risks and overall fiscal sustainability, but formal risk-of-debt-distress rating is guided solely by external public debt analysis.

### CPIA categories used in the DSF
- Weak policy (CPIA < 3.25)
- Medium policy (3.25 < CPIA < 3.75)
- Strong policy (CPIA > 3.75)

### Use and historical performance (key statistics)
- Since introduction, 367 DSAs have been produced for 73 different countries.
- Joint Fund-Bank DSAs have generally been produced annually for all IDA-only, PRGT-eligible countries; in some cases multiple DSAs per year; in other cases gap years.
- Since 2007, nearly all DSAs have contained both an external and a public sector DSA.
- 88 percent of DSAs have been published on the IMF or World Bank external website.
- An explicit risk-of-external-public-debt-distress rating has been assigned in all but 27 cases.
- Distributional observations:
  - Nearly all cases classified as “in debt distress” have been pre-HIPC completion point countries with poor CPIA ratings.
  - High-risk cases are evenly split between HIPCs and non-HIPCs with predominantly poor CPIA ratings.
  - Most low- or moderate-risk cases are post-HIPC completion point and non-HIPC countries with medium to strong CPIA ratings.
- Projection accuracy (limited evaluation):
  - DSAs produced in 2006 and 2007 projected external public debt to GDP in 2010 that were higher than actual in about half the cases and lower than actual in the other half.
  - In 60 percent of cases, the difference between the actual level of debt in 2010 and the level projected in the baseline scenario of the 2006 or 2007 DSA was 10 percentage points or less.
  - Large differences in HIPC cases mainly reflect uncertainty about the timing of debt relief; differences in non-HIPCs reflect larger-than-anticipated macroeconomic shocks related to the global financial crisis.

### IDA grant allocation and DSF use by lenders (selected figures)
- Since 2005, IDA has used DSA risk ratings to determine the share of grants and loans in its assistance to each LIC.
- Grant eligibility limited to IDA-only countries.
- Financing terms by risk rating:
  - Low risk: financing on standard IDA credit terms (40-year maturity, including a 10-year grace period, leading to a grant element of over 60 percent).
  - Moderate risk: 50 percent of financing on standard IDA credit terms and 50 percent on grant terms.
  - High risk or in debt distress: all assistance on grant terms.
- The grant portion of a country’s allocation is discounted by 20 percent.
- Nineteen countries at high risk of debt distress received their entire FY2011 allocation on grant terms.
- Of total IDA FY 2011 commitments of US$16.3 billion, 17 percent was provided on grant terms.

### Main issues flagged for improvement (overview)
- Improve analysis of total public debt and fiscal vulnerabilities as domestic debt has become more prominent.
- Reconsider thresholds (including potential formal treatment of workers’ remittances).
- Improve coverage of external debt to better account for private external debt where relevant.
- Better capture the investment-growth nexus to avoid overly conservative constraints on growth-enhancing borrowing.
- Redesign stress tests to reflect dynamic linkages rather than shocking variables one at a time.
- Simplify DSAs to enhance country ownership and reduce resource intensity.

---

### Improving analysis of total public debt and fiscal vulnerabilities — key facts and recommendations
- Structure of DSAs:
  - All LIC DSAs must include an external DSA and a public sector DSA.
  - External DSA covers external debt contracted by public and private sectors; public sector DSA covers external and domestic debt contracted by the public sector.
  - Risk of debt distress rating is based solely on external public debt analysis in the external DSA.
- Quantitative changes and facts:
  - Since 2005, the share of domestic public debt in total public debt increased from 19 percent to 29 percent on average across all LICs.
  - Domestic debt as a ratio to GDP has remained flat on average, but in 11 LICs the domestic debt-to-GDP ratio has more than doubled since 2006.
- Suggested improvements in DSA practice:
  - Explicitly discuss financing mix assumptions between domestic and external debt, and concessional versus nonconcessional debt.
  - Scrutinize assumptions about large fiscal adjustments given infrastructure and social needs and shallow tax bases.
  - Systematically assess realism of interest rate and growth assumptions and discuss domestic debt financing underlying interest rate assumptions.
  - Growth projections should attempt to capture the impact of public investment on growth, with model-based justification for significant accelerations.

### Costs and risks of domestic debt financing (selected statistics from 12 MTDSs)
- From analysis of 12 MTDSs prepared in 2010–11:
  - The median interest rate on domestic debt was 9 times higher than on external debt.
  - The sample median average time to maturity of the domestic debt portfolio was 2.5 years, compared to more than 13 years for external debt.
  - The share of domestic debt maturing within one year was much higher compared to external debt.
- Policy implications:
  - Short domestic maturities expose LICs to substantial refinancing and interest rate risks.
  - Developing domestic debt markets (longer maturities, broader creditor base) could lower risks but may increase costs depending on liquidity and inflation perceptions.
  - An MTDS complements the LIC DSA by outlining cost-risk tradeoffs.

### Strengthening contingent liabilities and coverage of public obligations
- Current framework includes one stress test: a 10-percent-of-GDP increase in debt-creating flows.
- Where information is available, DSAs should capture contingent liabilities from SOEs, PPPs, and financial sector weaknesses in a country-specific way.
- Stress tests should keep focus on likely risks but also analyze tail risks (low probability, high-impact events) as complementary analysis.
- DSAs should strive to incorporate all debt: central government, regional/local governments, central bank, public enterprises, and domestic arrears where material.

---

### Revisiting thresholds — re-estimation and main methodological points
- Thresholds originally calibrated using Kraay and Nehru (KN) and Staff 2004; staff re-estimated thresholds using a single, consistent methodology across indicators.
- Probit models relate probability of distress to debt burden, CPIA, and real GDP growth.
- Thresholds calculated for CPIA values: 3.25 (weak), 3.5 (medium), 3.75 (strong).
- Staff derived thresholds using three concepts of probability of debt distress:
  - Unconditional probability;
  - Probability at the median value of the debt burden indicator prior to distress;
  - Probability that minimizes type I and type II errors (preferred).
- Staff‘s preferred calibration produced implied probabilities of debt distress ranging from 13 to 15 percent depending on the indicator; alternative methods yielded 11 to 16 percent.
- Key recommended quantitative adjustment:
  - Lower debt service-to-revenue thresholds to 18, 20, and 22 percent (for weak, medium, and strong CPIA categories respectively) from current values of 25, 30, and 35 percent.
- Re-estimated thresholds for other indicators (PV of debt to GDP, debt service to exports, PV of debt to exports, PV of debt to revenue) broadly align with current DSF thresholds with some variation noted.
- Impact on risk ratings: applying proposed debt service-to-revenue thresholds would raise only 2 out of 66 countries from medium to high risk (analysis covers DSAs produced prior to June 2011).
- Judgment remains essential when interpreting breaches of thresholds.

### Including remittances in external debt thresholds
- Historical practice: remittances were taken into account by modifying denominators and lowering thresholds by 10 percent for countries with significant remittances.
- Staff re-estimated models including workers‘ remittances; smaller sample size due to limited remittance data.
- Main quantitative findings:
  - Threshold for PV of debt to the sum of GDP and remittances is approximately 10 percent lower than without remittances (on comparable sample).
  - Export-based thresholds with remittances are roughly 20 percent lower than their counterparts without remittances.
- Staff proposal for countries with large, reliable remittances:
  - Lower export-based thresholds by 20 percent relative to thresholds without remittances.
  - Retain current DSF threshold for PV of debt to the sum of GDP and remittances.
  - Continue to apply judgment informed by recent remittance developments.
- Implementation: staff will develop precise guidelines; retroactive application would lead to minimal changes in risk assessments.

### Use of country-specific information and operational guidance
- Current practice’s limitations: one-debt-variable-at-a-time approach and discrete CPIA cutoffs (3.25, 3.5, 3.75) create CPIA threshold effects.
- Country-specific growth should not be used to set thresholds (may impart pro-cyclical bias).
- Continuous CPIA scores would remove threshold effects but introduce operational complexity.
- Probability-based alternative would allow fully country-specific probabilities but staff does not advocate replacing current architecture now.
- Proposal: reinforce use of judgment and provide clearer guidance on minor/temporary breaches, combining debt measures, and use of probability-threshold analysis as a toolkit adjunct.

---

### Introducing benchmarks for total public debt — main findings
- Empirical approach: probit model expanded to include domestic debt using sample period 1971–2007 and 155 countries (79 MICs at end-2007 in one description; another annex cites 123 countries with 81 LICs), with 99 public debt distress episodes observed.
- Indicative policy-dependent benchmarks (summary finding):
  - Public debt to GDP in excess of about 40 to 70 percent in PV terms, or 50 to 75 percent in nominal terms, signals heightened debt vulnerabilities, with actual benchmark varying by CPIA score.
- Baseline calibrated thresholds (selected results from Annex 2):
  - PV-term thresholds (minimizing type I and II errors): Weak (CPIA=3.25) 38 percent; Moderate (CPIA=3.5) 56 percent; Strong (CPIA=3.75) 74 percent.
  - Nominal-term thresholds (minimizing type I and II errors): Weak (CPIA=3.25) 49 percent; Moderate (CPIA=3.5) 62 percent; Strong (CPIA=3.75) 75 percent.
  - Using unconditional probability calibration yields somewhat higher nominal thresholds (e.g., Weak 60, Moderate 73, Strong 86 in one reported specification).
- Empirical regularities:
  - Higher total public debt or lower CPIA raises the risk of debt distress.
- Limitations and caveats:
  - Results sensitive to distress definition and episode length.
  - Domestic arrears data gaps may underestimate domestic debt stocks and overlook events.
  - Heterogeneity in public sector debt coverage complicates cross-country comparisons.
- Operational implications:
  - Benchmarks should trigger deeper discussion of total public debt when approached or exceeded during projection horizon.
  - Staff proposes supplementing external-based risk ratings with an additional overall risk rating where public sector DSA identifies significant domestic vulnerabilities; the additional rating would not substitute for external public debt risk rating but would inform policy dialogue.
  - If endorsed, staff to prepare detailed implementation guidance.

### External private debt and monitoring
- Private external debt in LICs has been broadly stable; in a sample of 70 LICs, only half report any private external debt in their most recent DSA.
- Suggested practice: add charts to DSAs to monitor private external debt accumulation and the path of total external debt where relevant and discuss risks where private external debt is significant.

---

### Better capturing the investment-growth nexus — tools and findings
- IMF and World Bank analytical tools:
  - IMF developed a dynamic general equilibrium model linking public investment and growth (piloted in Togo).
  - MAMS (Maquette for MDG Simulations): quantifies investment levels needed to meet MDGs and estimates growth impact; used in 16 LICs since 2008.
  - Spatial Approach model: geo-referenced analysis to prioritize and sequence infrastructure and capture synergies across projects (applied to Republic of Congo and DRC).
- Select findings from models (Togo case and others):
  - Togo: authorities’ investment plan worth 192 percent of GDP over 10 years; under favorable assumptions (rates of return 25 percent; efficiency similar to average Sub-Saharan African country; strong capacity to collect user fees and tax revenues), surge could be self-financing and increase output by more than 8 percent in the long run, but transition problems include total debt exceeding 55 percent of GDP and tax pressure increasing by 2 to 4 percent of GDP in the medium term.
  - MAMS: measures macro indicators and development outcomes; used to analyze financing options.
  - Spatial Approach (DRC): priority projects would raise real GDP growth by 0.7 percentage points on average during construction (2009–13) and by 0.2 percentage points after completion.
- Recommendation: where appropriate, DSAs should reference IMF/World Bank analytical work to anchor expected growth rates given planned public investments; staff to pilot and develop user-friendly apparatus for broader use.

---

### Redesigning stress tests — criticisms and proposed refinements
- Current stress tests: alternative scenarios and standardized bound tests calibrated to historical experience; criticized for shocking variables one at a time without feedback (no interaction among variables).
- Proposed VAR-based refinements (Annex 3):
  - Move from descriptive-statistics shocks to shocks generated by estimated VAR or panel VAR systems: X_t = μ + B(L) X_{t-1} + ε_t, ε_t ~ (0, Σ), with X_t = [g_t, π_t, i_t, b_t, p_t]'.
  - Advantages: captures dynamic interaction among variables and comovement of shocks via Σ; shocks have defined interpretation.
  - Practical approach: use panel VAR to estimate covariance matrix Σ for groups of similar countries, then impose Σ in country-specific VARs to retain country dynamics.
  - Use stochastic simulation (Monte Carlo, bootstrapping) to generate confidence intervals for debt projections and more realistic bound tests.
- Caveats:
  - Data limitations in many LICs (annual data, short histories) constrain country-specific VAR reliability.
  - VAR-based stochastic simulation unreliable for long projection horizons because VAR lacks exchange rate adjustments and endogenous fiscal policy rules.
- Implementation proposal: introduce methodological refinements experimentally, provide these as optional tools (not as determinant of risk rating), and retain simple standardized tests for cross-country comparability.

---

### Simplifying the DSA template — modular approach and frequency
- Rationale: current template resource-intensive and rarely produced by country authorities.
- Proposed modular approach:
  - Core module: simplified macroeconomic input sheet, a baseline scenario, and basic stress tests; require explicit assumptions about external/domestic public borrowing and public guarantees.
  - Optional modules: customized scenarios, additional stress tests, and more sophisticated analyses (e.g., VAR-based bound tests, investment-growth models).
- Frequency:
  - Full joint DSAs every three years; lighter joint updates in interim years (short write-up plus standard tables and charts) with risk ratings still assigned.
  - Full DSA when significant changes to global environment or authorities’ policies occur, especially if risk rating may change.
- Risk-based resourcing:
  - Depth of DSA to depend on extent of identified risks; countries with fiscal vulnerabilities or significant private external debt may need in-depth analysis.
- Projection horizon:
  - Staff view: retain 20-year horizon to capture returns on investment and long maturities/grace periods of concessional debt.

---

### Issues for Board/Director discussion (questions posed to Directors)
- Maintain indicative policy-dependent thresholds and revise thresholds for debt service to revenue and for the PV of debt to the sum of exports and remittances?
- Strengthen analysis of total public debt and fiscal vulnerabilities and introduce an additional complementary risk rating when domestic/public or private external debt vulnerabilities are significant?
- Systematically take country-specific information into account when assessing risk of debt distress?
- Support IMF and World Bank staff efforts to develop models/tools to strengthen investment-growth linkages in DSAs?
- Support optional inclusion of a new stress test reflecting dynamic linkages between macroeconomic variables?
- See merit in developing a simplified DSA template built around baseline scenario and simple stress tests to facilitate country authorities’ use?

---

### Annex highlights — empirical basis and selected quantitative results
- Annex 1 (External Public Debt Thresholds):
  - Re-estimated thresholds using probit models and consistent episode definitions.
  - Staff preferred calibration (minimizing type I and II errors) implied probabilities of debt distress 13–15 percent across indicators.
  - Re-estimated debt service-to-revenue thresholds proposed at 18, 20, and 22 percent (weak, medium, strong), down from current 25, 30, and 35 percent.
  - Sample medians and estimation coefficients reported for PV of debt-to-GDP, PV of debt-to-exports, PV of debt-to-revenue, debt service-to-exports, debt service-to-revenue (detailed tables in annexes).
- Annex 2 (Total Public Debt Benchmarks):
  - Sample period 1971–2007; thresholds derived from probit with total public debt as explanatory variable.
  - Total public debt benchmarks (minimizing type I and II errors) in PV terms: Weak 38 percent; Moderate 56 percent; Strong 74 percent.
  - Nominal-term benchmarks: Weak 49 percent; Moderate 62 percent; Strong 75 percent.
  - Unconditional probability of distress in sample: 14 percent overall; LICs 16 percent; MICs 11 percent.
  - "Tipping point" near 60 percent nominal debt-to-GDP observed in sample means before distress.
- Annex 3 (Developing More Realistic Bound Tests):
  - Proposes VAR and panel VAR frameworks to generate shocks that capture dynamic interactions and comovement, and to use stochastic simulation for confidence intervals.
  - Two-step estimation strategy: estimate covariance Σ from panel VAR for groups, then estimate country VARs imposing Σ.
  - Ghana illustration: VAR-based stochastic simulation shows baseline PV of debt-to-GDP rising by 5 percentage points over 2011–2015; most extreme bound test (non-debt flows shock) increases PV of debt by 9 percentage points by 2015; stochastic simulation gives 75th percentile of PV debt at 38.5 percent by 2015 (25 percent probability).
  - Caveats: VAR-based uncertainty estimates unreliable over long horizons and sensitive to model specification and sample period.

*Source: Executive Summary of IMF/World Bank review of the Debt Sustainability Framework for Low-Income Countries (DSA/DSF).*

### Executive Summary ......................................................................................................

### Executive Summary

### Purpose and scope
- The DSF (Debt Sustainability Framework) is a standardized framework for conducting public and external debt sustainability analysis (DSA) in low-income countries (LICs).
- Introduced in 2005 and reviewed in 2006 and 2009, the DSF aims to:
  - Guide borrowing decisions of LICs to match financing needs with repayment ability;
  - Provide guidance for creditors‘ lending and grant allocation decisions;
  - Improve World Bank and IMF assessments and policy advice;
  - Help detect potential crises early so that preventive action can be taken.
- This paper provides a comprehensive review of the DSF to assess whether it remains adequate given evolving LIC circumstances, presents recent analytical work by IMF and World Bank staffs, and discusses possible framework improvements.

### Main analytical conclusions and recommended changes
- Staff analytical work broadly validates the indicative policy-dependent thresholds currently used in the framework.
- Recommended modest revisions:
  - Revise thresholds for debt service to revenue and for the PV of debt to the sum of exports and remittances.
  - Maintain all other thresholds at their current values.
- Strengthen the analysis of total public debt and fiscal vulnerabilities:
  - Focus on vulnerabilities most relevant to country teams.
  - Introduce benchmarks for total public debt to signal when deeper analysis is warranted.
- Where domestic public debt or private external debt vulnerabilities are significant, add an additional risk rating:
  - This additional risk rating would inform macroeconomic and structural policy dialogue.
  - It would provide an overall assessment of vulnerability complementing the existing external public debt assessment.
- Improve modeling of the investment-growth nexus:
  - Propose greater use of models developed by IMF and World Bank staffs to better capture debt-financed investment and growth linkages.
- Redesign stress tests to better reflect dynamic linkages between macroeconomic variables:
  - Introduce this refinement on an experimental basis.
- Simplify the DSA template to facilitate use by country authorities and reduce resource costs:
  - Propose a modular approach built around a baseline scenario and simple stress tests.
  - Propose producing full joint DSAs every three years, with lighter joint updates in intervening years.

### How the DSF operates (key features)
- The DSF compares projections of external public debt over the next 20 years against indicative policy-dependent thresholds to assess the risk of debt distress.
- Vulnerability to external and policy shocks is explored via alternative scenarios and standardized bound tests.
- The indicative threshold for each debt burden indicator depends on a country‘s policy and institutional capacity, as measured by the World Bank‘s CPIA index.
- Risk-of-debt-distress ratings (based on external public debt analysis) are: Low risk; Moderate risk; High risk; In debt distress.
- The DSF also includes a public sector DSA assessing domestic debt risks and overall fiscal sustainability, but the formal risk-of-debt-distress rating is guided solely by the external public debt analysis.

### CPIA categories used in the DSF
- Weak policy (CPIA < 3.25)
- Medium policy (3.25 < CPIA < 3.75)
- Strong policy (CPIA > 3.75)
- [Document also presents a tabular depiction of indicative policy-dependent thresholds for public and publicly guaranteed external debt; the DSF assigns the four risk categories above based on comparisons to those thresholds.]

### DSF use and historical performance (key statistics)
- Since introduction, 367 DSAs have been produced for 73 different countries.
- Joint Fund-Bank DSAs have generally been produced annually for all IDA-only, PRGT-eligible countries; in some cases multiple DSAs per year; in other cases gap years.
- Since 2007, nearly all DSAs have contained both an external and a public sector DSA.
- 88 percent of DSAs have been published on the IMF or World Bank external website.
- An explicit risk-of-external-public-debt-distress rating has been assigned in all but 27 cases (most of which date to early years of the framework).
- Distributional observations:
  - Nearly all cases classified as “in debt distress” have been pre-HIPC completion point countries with poor CPIA ratings.
  - High-risk cases are evenly split between HIPCs and non-HIPCs with predominantly poor CPIA ratings.
  - Most low- or moderate-risk cases are post-HIPC completion point and non-HIPC countries with medium to strong CPIA ratings.
- Projection accuracy (limited evaluation):
  - DSAs produced in 2006 and 2007 projected external public debt to GDP in 2010 that were higher than actual in about half the cases and lower than actual in the other half.
  - In 60 percent of cases, the difference between the actual level of debt in 2010 and the level projected in the baseline scenario of the 2006 or 2007 DSA was 10 percentage points or less.
  - Large differences in HIPC cases mainly reflect uncertainty about the timing of debt relief; differences in non-HIPCs reflect larger-than-anticipated macroeconomic shocks related to the global financial crisis.

### Issues highlighted for reconsideration (overview of paper organization)
- Section II: Reviews DSF performance to date and identifies improvement areas.
- Section III: Options for improving analysis of total public debt and fiscal vulnerabilities.
- Section IV: Reconsiders thresholds guiding risk-of-debt-distress assessment.
- Section V: Improving coverage of external debt.
- Section VI: Better capturing the investment-growth nexus in the DSF.
- Section VII: Options for redesigning stress tests.
- Section VIII: Options for simplifying the framework.
- Section IX: Issues for Board discussion.

*Source: Executive Summary of IMF/World Bank review of the Debt Sustainability Framework for Low-Income Countries (DSA/DSF).*

### 7.      Since the DSF was introduced, debt sustainability in LICs has been broadly

### _011212 - 7.      Since the DSF was introduced, debt sustainability in LICs has been broadly

### Overview and recent experience
- Since the DSF was introduced, debt sustainability in LICs has been broadly maintained.
- Only two non-HIPC LICs have experienced debt distress since 2005; both were already in debt distress at the time of their 2006 or 2007 DSA.
- An April 2010 IMF-IDA report concluded that, while the global financial crisis had a significant impact on LIC debt vulnerabilities, the crisis was not expected to result in systemic debt difficulties across LICs; this finding was corroborated by the lack of systemic evidence that debt vulnerabilities among LICs had intensified over the preceding 18 months.

### Use of the DSF by donors and lenders
- The DSF is used by a growing community of donors and lenders to inform financing decisions.
- Since 2005, IDA has used DSA risk ratings to determine the share of grants and loans in its assistance to each LIC.
- Regional development banks have geared lending practices to DSA risk assessments.
- The Paris Club relies on DSAs in the context of debt restructurings under the Evian Approach.
- OECD Working Group on Export Credit and Credit Guarantees members agreed in 2008 to take DSAs into account when providing official export credits to LICs.

### IDA Grant Allocation Framework (Box 2) — key features and FY2011 outcome
- Adopted during the IDA14 Replenishment agreement in mid-2005 to mitigate external debt distress risks revealed by the DSF.
- Eligibility limited to IDA-only countries; IBRD/IDA blend countries and “gap” countries are not eligible for grants regardless of external debt.
- Grant eligibility is determined by the country-specific risk of external debt distress from DSAs under the DSF.
- Financing terms by risk rating:
  - Low risk: financing on standard IDA credit terms (40-year maturity, including a 10-year grace period, leading to a grant element of over 60 percent).
  - Moderate risk: 50 percent of financing on standard IDA credit terms and 50 percent on grant terms.
  - High risk or in debt distress: all assistance on grant terms.
- The grant portion of a country’s allocation is discounted by 20 percent to mitigate equity and moral hazard concerns.
- Nineteen countries at high risk of debt distress received their entire FY2011 allocation on grant terms.
- Of total IDA FY 2011 commitments of US$16.3 billion, 17 percent was provided on grant terms.

### Main issues raised about the DSF and areas for improvement
- Improving analysis of total public debt and fiscal vulnerabilities:
  - Discussion of total public debt (external and domestic) has tended to be less rigorous than discussion of external public debt because the DSA risk rating is based exclusively on external public debt.
  - With domestic debt increasing in importance, public debt sustainability requires more attention.
- Reconsidering thresholds:
  - Policy-dependent thresholds for external public debt guide risk ratings; questions exist about their continued accuracy and whether thresholds should formally adapt to take into account workers’ remittances.
  - Questions whether thresholds for total public debt should be established and whether they should inform the risk rating.
- Improving coverage of external debt:
  - Historically focused on public external debt with less attention to private external debt; consideration warranted where private external debt is large and poses risks.
- Accounting for public investment’s impact on growth:
  - Criticisms that DSAs can be overly conservative and constrain borrowing for growth-enhancing investments.
  - The link between debt-financed investment and growth is integral to DSA quality; macroeconomic assumptions need careful treatment.
- Redesigning stress testing:
  - Current stress tests are often mechanistic, shocking variables one at a time without feedback.
  - Standardized tests facilitate cross-country comparison but may miss the most relevant shocks for a given country.
- Simplifying DSAs:
  - DSAs are time-consuming and data-intensive; few LICs use the current template.
  - Consider modular templates and simplification to enhance country ownership and use.

### Improving analysis of total public debt and fiscal vulnerabilities (Sections III–IV)
- Structure of DSAs:
  - All LIC DSAs must include an external DSA and a public sector DSA.
  - External DSA covers external debt contracted by public and private sectors; public sector DSA covers external and domestic debt contracted by the public sector.
  - Risk of debt distress rating is based solely on external public debt analysis in the external DSA.
- Changing context and implications:
  - External public debt remains the largest component of debt in most LICs, but domestic debt is becoming more prominent.
  - Domestic debt carries benefits (development of local financial markets, no exchange rate risk) and costs (crowding out private investment, incentives for financial repression).
  - Domestic debt tends to be more expensive and have shorter maturities compared to external debt.
- Key quantitative changes and facts:
  - Since the introduction of the DSF in 2005, the share of domestic public debt in total public debt has increased from 19 percent to 29 percent on average across all LICs, largely reflecting external debt relief under the HIPC Initiative.
  - Domestic debt as a ratio to GDP has remained flat on average, but in some countries domestic debt levels are substantial or growing rapidly.
  - In 11 LICs, the domestic debt-to-GDP ratio has more than doubled since 2006, albeit from low levels in some cases.
  - During the global financial crisis, LICs relied heavily on domestic sources to finance larger fiscal deficits; this trend is expected to continue as domestic financial markets develop.
- Suggested improvements in DSA practice:
  - Explicitly discuss financing mix assumptions between domestic and external debt, and concessional versus nonconcessional debt.
  - Scrutinize assumptions about large fiscal adjustments given infrastructure and social needs and shallow tax bases.
  - Systematically assess the realism of interest rate and growth assumptions, and explicitly discuss domestic debt financing underlying interest rate assumptions.
  - Growth projections should attempt to capture the impact of public investment on growth while being mindful of historical trends; significant accelerations should be justified, ideally using model-based analysis.

### Costs and risks of domestic debt financing (Box 3) — findings and implications
- Analysis of 12 LICs indicates the domestic debt portfolio is subject to substantial refinancing and interest rate risks because few countries issue long-term domestic debt.
- The World Bank and the IMF provide technical assistance to help LICs improve debt management via medium-term debt management strategies (MTDS).
- From the analysis of 12 MTDSs prepared in 2010–11:
  - The median interest rate on domestic debt was 9 times higher than on external debt.
  - The sample median average time to maturity of the domestic debt portfolio was 2.5 years, compared to more than 13 years for external debt.
  - The share of domestic debt maturing within one year was much higher compared to external debt.
  - Although most domestic debt was issued at fixed rates, the short maturity structure implies most interest rates would refix every year.
- Risks and policy implications:
  - Current domestic debt structures expose LICs to substantial refinancing risk; few LICs can issue domestic debt with maturities longer than 10 years.
  - Developing domestic debt markets by introducing longer maturities and expanding the creditor base could lower refinancing and interest rate risks but can increase costs depending on perceived liquidity and inflation risks.
  - An MTDS complements the LIC DSA by outlining cost-risk tradeoffs in meeting financing needs and payment obligations.

### Strengthening stress tests, contingent liabilities, and coverage of public obligations
- Strengthening contingent liabilities analysis:
  - Data on contingent liabilities in LICs is scarce; current framework includes one stress test—a 10-percent-of-GDP increase in debt-creating flows—that resembles a generic contingent liability shock.
  - Where information is available, a more country-specific approach should capture contingent liabilities from SOEs, PPPs, and financial sector weaknesses.
- Considering tail risks:
  - Stress tests are intended to capture the most likely risks; enhancing analysis of tail risks (low probability, high-impact events such as severe crises or climate-related risks) could complement the focus on likelier risks.
  - Tail risks should not inform the risk rating but merit attention given recent increases in debt levels in many advanced economies.
- Expanding coverage to all public sector obligations:
  - DSAs should strive to incorporate all debt, including debts of central government, regional/local governments, central bank, and public enterprises, as well as domestic arrears where material.
  - Given data and capacity constraints, initial focus should be on entities that pose the largest fiscal risk.
- Assessing public debt profile risks:
  - For more advanced LICs with higher market-term debt, both the level and profile matter—maturity, currency composition, and creditor base should inform vulnerability analysis.
  - Cost and risk indicators of domestic debt portfolios (as in Box 3) should be discussed.

_Italic: Source: Excerpt from the IMF staff paper contained in the supplied PDF content unit._

### 16.      Similar to the approach adopted for MACs, the depth and breadth of the

### 16.      Similar to the approach adopted for MACs, the depth and breadth of the

### IV. REVISITING THRESHOLDS — Major findings and methodology
- Thresholds for public and publicly guaranteed (PPG) external debt were originally calibrated using empirical analyses by Kraay and Nehru (KN) and IMF and World Bank staff (Staff 2004).
- Debt-distress probit models relate the probability of distress to: (i) a country‘s debt burden; (ii) quality of policies and institutions as measured by the CPIA index; and (iii) real GDP growth.
- Staff re-estimated thresholds using a single, consistent methodology across all debt-burden indicators to address technical issues including: controlling for middle-income countries in the sample, using debt service data on PPG external debt, and applying consistent definitions of distress and non-distress episodes.
- Thresholds were calculated for three CPIA values corresponding to policy performance categories: 3.25 (weak), 3.5 (medium), and 3.75 (strong).
- Staff derived thresholds using three concepts of the probability of debt distress:
  - (1) the unconditional probability of debt distress;
  - (2) the probability corresponding to the median value of the relevant debt burden indicator immediately prior to an outbreak of debt distress;
  - (3) the probability that minimizes the number of missed crises (type I errors) and false alarms (type II errors).  
- Staff‘s preferred calibration (minimizing type I and II errors) produced implied probabilities of debt distress ranging from 13 to 15 percent depending on the debt-burden indicator. Alternative methods yielded probabilities ranging from 11 to 16 percent. (Probabilities used in previous DSF work reflected different samples and definitions and cannot be directly compared.)

### B. Re-estimated thresholds and key quantitative adjustments
- Re-estimated thresholds are broadly in line with current DSF thresholds for most indicators; notable exception is debt service to revenue:
  - Staff proposes lowering debt service-to-revenue thresholds to 18, 20, and 22 percent (for weak, medium, and strong CPIA categories respectively) from current values of 25, 30, and 35 percent.
- Re-estimated thresholds:
  - PV of debt to GDP and debt service to exports: fairly close to current DSF thresholds.
  - PV of debt to exports: slightly higher than DSF thresholds.
  - PV of debt to revenue: slightly lower than DSF thresholds.
- Robustness: results across debt-burden indicators are robust to different measures of governance and macroeconomic shocks.
- Impact on risk ratings: Staff estimates that only 2 out of 66 countries would receive a higher risk rating (moving from medium to high) if the proposed debt service-to-revenue thresholds were applied. The analysis covered DSAs produced prior to June 2011.
- Sensitivity and judgment: re-estimated thresholds vary with definitional choices for distress episodes; therefore breaches of thresholds require judgment—marginal or temporary breaches do not necessarily imply significant vulnerability, while near breaches merit careful consideration.

### C. Including remittances in external debt thresholds — analysis and proposals
- Rationale: remittances can enhance a country‘s capacity to repay external debt and thus affect probability of debt distress.
- Historical treatment: after the last DSF review, remittances were taken into account by modifying denominators (GDP, exports, revenues) and lowering indicative thresholds by 10 percent for countries with significant remittances.
- Staff re-estimated econometric models explicitly including workers‘ remittances. Due to limited remittance data, the estimation sample size was reduced significantly; comparisons were made using a common (small) sample to avoid misleading inference.
- Main quantitative findings:
  - After controlling for sample size, the threshold for the PV of debt to the sum of GDP and remittances is approximately 10 percent lower than the corresponding threshold without remittances.
  - Export-based thresholds with remittances are roughly 20 percent lower than their counterparts without remittances.
- Staff proposal for countries with large, reliable remittances:
  - Export-based thresholds should be lowered by 20 percent compared to their counterparts without remittances.
  - The current DSF threshold for the PV of debt to the sum of GDP and remittances would remain unchanged (staff considers it appropriate).
  - Judgment remains essential when determining the impact of remittances on external risk ratings, informed by recent remittance developments and their prospects.
- Implementation and impact:
  - Staff will develop precise guidelines to account for remittances based on the newly estimated thresholds.
  - Retroactive application of proposed remittance-adjusted thresholds would lead to minimal changes in risk assessments.
  - Historical application: in 2010 and 2011, eight countries had risk assessments that used remittances; applying the proposed export-based remittance thresholds could reclassify one country from moderate to high risk.

### D. Use of country-specific information and operational guidance
- Current practice: DSF uses a one-debt-variable-at-a-time approach and fixes real GDP growth at the sample mean while using three discrete CPIA cutoffs (3.25, 3.5, 3.75). This yields a manageable set of thresholds but loses country-specific granularity and generates CPIA threshold effects when scores lie near cutoff boundaries.
- On using country-specific growth:
  - Staff finds little case for using country-specific recent growth rates to set thresholds because recent growth is not a robust predictor of future shocks and could impart pro-cyclical bias; country-specific growth already influences DSAs via debt dynamics.
- On using country-specific CPIA scores:
  - Using continuous CPIA scores would better reflect country-specific policy/institution quality and remove CPIA threshold effects, but would generate a large number of thresholds (five indicators × number of countries) and operational complexity.
  - Past Board discussions expressed concern about proposals that generated wider dispersion of thresholds; Directors preferred more manageable alternatives.
- Probability-based alternative:
  - Expressing thresholds in terms of the probability of debt distress would focus DSAs on the evolution of distress probability and allow fully country-specific assessments without CPIA threshold effects.
  - However, extensive econometric work has not produced a clearly superior probability-based approach; given the widespread adoption and understanding of the current architecture, staff does not advocate replacing it at this time.
- Strengthening judgment and guidance:
  - Staff proposes reinforcing and clarifying the use of judgment based on country-specific information when assessing debt-distress risk.
  - Examples of guidance: for minor or temporary breaches, consider whether a country‘s CPIA score is significantly higher than the cutoff used; undertake further analytical work on probability thresholds and combining debt measures to inform cases where the five indicators give conflicting signals.
  - If proven useful, probability-threshold analysis could be incorporated into the toolkit and reflected in the revised guidance note.

*Italic: Source — IMF staff chapter text (excerpts provided).*

### 33.      Introducing benchmarks for total public debt, in addition to existing thresholds

### 33.      Introducing benchmarks for total public debt, in addition to existing thresholds

### Rationale for introducing total public debt benchmarks
- Public sector DSAs have tended to focus on the projected path of public debt without always drawing firm conclusions about the risk of debt distress.
- External DSAs benefit from thresholds that anchor analysis by considering both the path and the level of debt, and by providing clear "danger zones" for broad audiences.
- The growing prominence of domestic public debt in some countries suggests total public debt benchmarks could strengthen public sector DSAs.

### Empirical approach and key results
- Sample and period:
  - Sample period: 1971–2007.
  - Sample size: 155 countries, of which 79 were classified as middle-income countries (MICs) at end-2007.
- Model:
  - The probit model underpinning thresholds for PPG external debt was expanded to include domestic debt.
  - Thresholds were calculated based on probabilities that minimize type I and type II errors.
- Definitions used in the analysis:
  - External debt distress signals: (i) PPG external arrears in excess of five percent of external PPG debt; (ii) a Paris Club restructuring; and (iii) IMF GRA financing disbursed in excess of 50 percent of quotas.
  - Domestic debt distress signals: instances of outright sovereign defaults (failure by the sovereign to meet a principal or interest payment on the due date, within a specified grace period), including restructurings; identified using Reinhart and Rogoff, Standard and Poor’s, Moody’s, and IMF staff reports. Data on domestic arrears was largely missing and not systematically included.
  - Debt distress episodes: non-overlapping periods in which either an external or domestic debt distress episode occurs. External debt distress episodes are defined as a period lasting three years or more in which at least one external distress signal is observed. Any instance of domestic default constitutes a domestic debt distress episode. A total of 99 public debt distress episodes are observed.
- Indicative policy-dependent benchmarks (summary finding):
  - Public debt to GDP in excess of about 40 to 70 percent in PV terms, or 50 to 75 percent in nominal terms, signals heightened debt vulnerabilities, with the actual benchmark varying according to the CPIA score.
- Empirical regularities:
  - The higher the level of total public debt, or the lower the quality of policies and institutions (CPIA), the higher the risk of debt distress.

### Limitations, caveats, and data issues
- Results are sensitive to the definition and length of debt distress and normal time episodes.
- Comprehensive data on domestic arrears still does not exist, implying domestic debt stocks could be underestimated and some debt distress events overlooked.
- Lack of homogeneity in public sector debt coverage across countries complicates cross-country comparisons.
- The probit did not perform significantly better when domestic debt was included as an explanatory variable, reflecting that domestic debt events often coincide with external debt events.
- Thresholds for public debt to revenue were estimated but results were not robust and therefore not presented.

### Operational implications for DSAs and risk ratings
- Use of benchmarks:
  - Benchmarks can define reference points to trigger deeper discussion of total public debt and determine when to conduct more detailed analysis.
  - When total public debt moves toward, or exceeds, the relevant benchmarks over the projection horizon, a detailed discussion of potential risks to debt sustainability is expected—even when external public debt indicators remain below their thresholds.
- Risk rating implications:
  - Currently, the DSA risk rating is determined by external public debt assessment only; the overall assessment of public sector debt vulnerability does not affect the risk rating.
  - Staff proposes that risk ratings derived from external DSAs could be supplemented where the public sector DSA identifies significant domestic vulnerabilities.
  - For the majority of LICs (where external public debt dominates), the external-based risk rating would continue to apply.
  - For LICs with total public debt moving toward or exceeding benchmarks, teams would be expected to conduct in-depth analysis of domestic vulnerabilities; if significant, an additional risk rating providing the overall assessment of debt vulnerability would be assigned.
  - The additional risk rating would not substitute for the external public debt risk rating; external assessments would continue to inform financing decisions of IDA, while the overall assessment would inform macroeconomic and structural policy dialogue.
- Next steps if the approach is endorsed:
  - If IDA and IMF Executive Boards agree, staff will develop detailed guidance for implementing the supplementary risk rating and analysis.

### Related considerations on external private debt and monitoring
- External DSAs nominally capture public and private external debt, but analysis has focused mostly on public external debt due to data limitations and public debt dominance in most LICs.
- Private external debt trends:
  - Private external debt has remained broadly stable across LICs, compared to a growing trend in MICs.
  - In a sample of 70 LICs, only half report any private external debt in their most recent DSA.
  - Some LICs already have substantial private external debt in relation to GDP.
- Suggested practice:
  - Adopt a country-specific approach: add charts to DSAs to monitor private external debt accumulation and the path of total external debt where relevant.
  - Where private external debt is significant, discuss its risks to overall external debt sustainability; if judged significant, reflect them in the additional overall assessment of debt vulnerability.

### Connection to the public investment–growth nexus (context for debt sustainability)
- Challenge:
  - LICs require much higher investment, particularly in infrastructure, to achieve accelerated and sustained growth; financing must be sustainable and efficient.
  - World Bank estimate for Sub-Saharan Africa infrastructure needs: around US$93 billion a year, equivalent to 15 percent of the region’s GDP, or 22 percent of GDP for the region’s low-income countries.
- Critique of DSF:
  - DSAs have been criticized for not adequately capturing the growth dividends from debt-financed public investment.
- Ongoing work:
  - IMF staff developed a dynamic general equilibrium model linking public investment and growth and analyzing debt sustainability implications; the model:
    - Incorporates private and public capital in a production function.
    - Accounts for inefficiencies in converting public investment into public capital, absorptive and capacity constraints.
    - Allows for concessional and nonconcessional borrowing and explicit fiscal policy reactions.
  - The framework was piloted in Togo (presented in the context of Togo’s 2011 Article IV consultation) where results favored a gradual investment path to reduce inefficiency losses and allow time for public financial management reforms.
  - IMF staff intends to pilot the framework in five more countries over the next year and to develop a user-friendly apparatus to facilitate broader use in DSAs.

*Source: 33. Introducing benchmarks for total public debt, in addition to existing thresholds (extracted from the provided IMF chapter content).*

### 51.      To inform lending operations and policies for economic and social development,

### _011212 - 51.      To inform lending operations and policies for economic and social development,

### World Bank analytical tools and their purpose
- World Bank staff has developed a broad set of analytical tools and instruments to inform lending operations and policies for economic and social development, touching upon the growth-investment nexus.
- The Bank’s analytical work takes a comprehensive approach to development, with growth and investment being key elements along with poverty alleviation and social inclusion.
- Tools highlighted:
  - Maquette for MDG Simulations (MAMS): quantifies investment levels needed to meet the MDGs and estimates their impact on growth (see Box 6).
  - Spatial Approach model: helps countries assess proposed infrastructure investment plans by identifying priorities and formulating adequate sequencing of projects.

### Complementarity of IMF and World Bank models
- Different analytical tools are needed to reflect heterogeneity of country-specific circumstances regarding growth and investment.
- IMF model focus:
  - Produces macroeconomic frameworks for DSAs that explicitly incorporate public investment and growth linkages.
  - Incorporates fiscal reaction functions and produces trajectories for growth, the real exchange rate, and debt stocks that can be compared to DSF thresholds.
- MAMS focus:
  - Links across different sectoral investments and examines implications for growth and development outcomes.
- Spatial Approach focus:
  - Estimates rates of return of groups of investment projects from a micro-sectoral perspective.
- Joint use:
  - Available tools offer complementary views on the investment-growth nexus and could be used jointly.
  - Where appropriate, future DSAs will include specific references to analytical work by IMF and World Bank staff to anchor expected growth rates, taking into account planned public investments.

### Regional projects and positive externalities
- Macroeconomic frameworks underpinning DSAs are country-specific and may not reflect growth impact from large regional infrastructure projects.
- Spatial Approach can estimate economic return from synergies between cross-country investment projects.
- Other models could be expanded to explicitly account for positive externalities, allowing comprehensive analysis of expected costs (debt accumulation) and benefits (higher growth path) and alternative financing options.

### Box 6 — Modeling the Links Between Public Investment and Economic Growth (select findings)
- IMF model application to Togo (Article IV consultation; Appendix III):
  - Authorities’ investment plan worth 192 percent of GDP over 10 years.
  - Under good structural conditions (rates of return of 25 percent; efficiency similar to average Sub-Saharan African country; high capacity to collect user fees and tax revenues):
    - Surge could be self-financing and could increase output by more than 8 percent in the long run.
    - Transition problems: total debt exceeding 55 percent of GDP and required tax pressure increasing by 2 to 4 percent of GDP in the medium term.
  - Nonconcessional borrowing could smooth adjustment but strategy would be risky due to high cost of borrowing; small changes in rates of return or investment efficiency can lead to unsustainable debt dynamics.
  - Model suggested a gradual investment path is preferable to reduce inefficiency losses due to capacity constraints and allow time for public financial management reforms.
  - Judgment is critical when applying the model; careful choice of parameters and scenarios required.
- MAMS:
  - Country studies carried out in 16 LICs since 2008, mainly in Sub-Saharan Africa.
  - MAMS is a dynamic computable general equilibrium model including fiscal spending across sectors and financing options (taxation, domestic and foreign borrowing, and foreign aid).
  - Measures economic performance via macroeconomic indicators (GDP, budget, balance of payments) and other indicators (poverty or MDG targets).
- Spatial Approach:
  - Applied to Republic of Congo and Democratic Republic of Congo (DRC).
  - Geo-references data on productive sectors and infrastructure networks to evaluate returns associated with existing and proposed investment packages and synergy effects of spatially coordinated bundles of infrastructure.
  - DRC case findings:
    - Priority public infrastructure projects would raise real GDP growth by 0.7 percentage points on average during construction phase 2009–13 (mainly via domestic demand).
    - By 0.2 percentage points following completion, reflecting gains in total factor productivity associated with improved public infrastructure.
    - Higher growth projections incorporated in baseline scenario of DRC’s annual LIC DSAs since 2009.
    - Large variation in economic rates of return across investments, including cross-border investments, underscoring importance of project screening.

### Redesigning stress tests — current design and criticisms
- Purpose:
  - DSF features stress tests to assess impact of shocks that could significantly deteriorate debt outlook.
  - Baseline scenario based on explicit macroeconomic assumptions deemed most likely, considering authorities’ intended policies.
  - Stress tests: alternative scenarios (permanent changes to key assumptions) and bound tests (temporary adverse deviations calibrated to match country’s historical experience).
  - Standardized stress tests facilitate cross-country comparisons and ensure consistency; country teams encouraged to design customized scenarios.
- Calibration and historical performance:
  - Bound tests originally calibrated to yield roughly a 25 percent probability of shock occurrence at a 10-year horizon based on stochastic simulations for a representative PRGT-eligible country.
  - Comparison of actual levels of debt in 2010 to projections from 2006–2007 LIC DSAs: in only 7 out of 60 cases did actual 2010 debt exceed the level projected by the most extreme stress test.
  - Unexpectedly high 2010 debt mostly reflects larger-than-anticipated macroeconomic shocks related to the global financial crisis.
- Criticisms:
  - Too standardized and lacking interaction between key variables.
  - Example: bound test simulating a one-time 30 percent permanent depreciation of the domestic currency has no impact on exports or the current account balance.
  - Persistence of shocks constrained to be same across countries despite dynamic adjustments depending on country-specific attributes (e.g., exchange rate regime).

### Proposed methodological refinements for stress tests
- Consider estimating country-specific dynamic interaction between key variables and covariance between shocks using vector autoregressive (VAR) models (Annex 3).
  - VARs have been used to assess public debt sustainability in advanced and emerging market countries.
  - Limitations for LICs:
    - Lack of adequate data (quarterly balance of payments and national accounts not available in most LICs; annual data available going back to 1970 in 50 of the 72 LICs).
    - Estimates sensitive to model specification and sample period; may be misleading with frequent structural shifts.
- Panel data approach:
  - Pool observations across countries to increase degrees of freedom and maintain cross-country comparability; reduces resource intensity.
  - More granular approach: estimate VARs for different groups of countries based on economic characteristics (exchange-rate regime, dependence on a specific commodity export).
  - Country teams could still use alternative model specifications tailored to capture country-specific attributes.
- Implementation proposal:
  - Introduce methodological refinements on an experimental basis to enable users to become familiar with new techniques.
  - Innovations would provide a broader menu of options to enrich analysis but would not have a formal role in determining risk rating.
  - Innovations would not be incorporated into the standard template to maintain simplification objective.

### Simplifying the DSA template
- Rationale:
  - Producing a DSA is resource-intensive due to template complexity and extensive data input requirements.
  - Time to produce a DSA can range from a few weeks to well over a month, depending on country and staff experience.
  - Few country authorities can produce their own DSAs despite workshops.
- Evolution and tradeoffs:
  - Template has undergone changes (e.g., unification of external and public sector DSAs; additional tools to incorporate remittances), increasing complexity.
  - Introducing new features could enhance analysis but risks further complexity.
- Modular approach under consideration:
  - (i) Introduce a core module: simplified macroeconomic framework input sheet, a baseline scenario, and basic stress tests.
    - Redesigned input sheet would require explicit assumptions about external and domestic public borrowing and private external borrowing, and differentiate between borrowing and guaranteeing by the public sector to narrow scope for inconsistencies and unexplained debt dynamics.
  - (ii) Group customized scenarios and additional stress tests in optional modules.
- Benefits:
  - Core DSF module would be more intuitive and ensure consistency of macroeconomic framework with underlying economic and financing assumptions.
  - Output limited to a set of standard tables and charts.
  - IMF and World Bank staffs could continue to use modules as needed, preserving sophistication and accuracy.
- Frequency of DSAs:
  - Staff proposes full joint DSAs every three years, with lighter joint updates in interim years to reduce resource intensity through streamlined written analysis while maintaining in-depth look when warranted.
    - Lighter joint updates would consist of a short write-up and the same set of standard tables and charts included in a full DSA. Risk ratings would still be assigned.
  - Full DSA expected whenever significant changes to global environment or authorities’ policy stance occur, particularly if changes entail a change in risk rating.
- Risk-based approach:
  - Depth of DSA would depend on extent of identified risks.
  - Countries with public debt and fiscal vulnerabilities or significant external private debt may need additional resources for in-depth analysis.
  - In countries where scaling up public investment is envisaged, country teams may use one of the IMF/Bank models to evaluate investment impact on growth.
  - In countries where public investment is relatively small, a model-based approach would not be recommended.
- Note on projection horizon:
  - Some have argued that DSF’s 20-year projection horizon should be shortened; staff’s view is that a long projection horizon is necessary to capture returns on investment and long maturities and grace periods associated with concessional debt.

### Issues for discussion (questions posed to Directors)
- Do Directors agree to maintain the indicative policy-dependent thresholds defined in terms of the various debt burden indicators and to introduce revisions to the thresholds for debt service to revenue and for the PV of debt to the sum of exports and remittances?
- Do Directors agree with the need for strengthening the analysis of total public debt and fiscal vulnerabilities in DSAs? Do they agree to introduce an additional risk rating, which would complement the assessment of external public debt, in cases where there are significant vulnerabilities related to domestic public debt or private external debt?
- Do Directors agree that country-specific information should be more systematically taken into account when assessing the risk of debt distress?
- Do Directors support ongoing efforts by IMF and World Bank staffs to develop models and tools that will strengthen the treatment of investment-growth linkages in DSAs?
- Do Directors support the inclusion, on an optional basis, of a new stress test reflecting dynamic linkages between macroeconomic variables?
- Do Directors see merit in developing a simplified DSA template, built around a baseline scenario and simple stress tests, to facilitate its use by country authorities?

*Source: _011212 - 51.      To inform lending operations and policies for economic and social development,*

### Annex 1. External Public Debt Thresholds

### Annex 1. External Public Debt Thresholds

### Overview and empirical basis
- The DSF thresholds for public and publicly guaranteed (PPG) external debt are based on studies by Kraay and Nehru (KN) and IMF and IDA Staff (Staff 2004).
- The calibration of thresholds comprises three main steps:
  - (i) Identification of debt distress and non-distress episodes on the basis of ‘signals’ of external debt servicing difficulties such as arrears, Paris Club reschedulings, and IMF GRA financing.
  - (ii) Estimation of a parsimonious econometric model (probit) to explain the incidence (probability) of debt distress. The probit model takes the following form:
    - (debt distress) = Φ(burdendebt * β1 + governance * β2 + shock * β3 + other * β4)
    - Presented in the source as:
      - (other* shock * governance* burdendebt *distress)debt (P 4321 ββββ ++++ Φ = )
    - Where:
      - “debt distress” is a binary variable (1 = distress, 0 = no distress).
      - Φ is the cumulative distribution function (CDF) of the standard normal distribution.
      - “debt burden” is a measure of indebtedness (PV of debt or debt service) scaled by a measure of repayment capacity (GDP, exports, or government revenue).
      - “governance” is the World Bank‘s CPIA index.
      - “shock” is proxied by real GDP growth.
      - “other explanatory variables” in Staff 2004 included GDP per capita and a dummy variable for Africa.
    - For debt distress episodes, explanatory variables are lagged one period.
  - (iii) Calibration of indicative debt burden thresholds by fixing values for the probability of debt distress, governance, and macroeconomic shock in the probit (equation (1)), and solving for the debt burden. The DSF set the probability of debt distress between 18–22 percent, depending on the debt burden indicator. The calibration is expressed as:
    - Threshold(debt) = Φ^{-1}(P(distress)) - β̂2 * governancê - β̂3 * shock̂ - β̂4 * other̂ all divided by β̂1
    - Presented in the source as:
      - (1 432 -1 ˆ other* ˆ shock * ˆ governance* ˆ distress)P(debt Threshold β βββ −−− Φ = )

### Key empirical findings
- Countries with higher debt burdens are more likely to experience a debt distress episode.
- Countries with strong policies can sustain a higher debt burden than those with weak policies; this result is robust to alternative model specifications and a broader set of explanatory variables.
- The KN study finds that the basic model has good out-of-sample predictive power.
- The DSF calibrated thresholds for five debt burden indicators:
  - PV of debt to GDP
  - PV of debt to exports
  - PV of debt to revenue
  - Debt service to exports
  - Debt service to revenue
- The calibration approach:
  - PV of debt indicator thresholds mainly followed econometric results reported in Staff 2004.
  - Debt service indicator thresholds used estimates from KN.
  - Specific debt burden thresholds were calibrated for CPIA scores associated with:
    - strong performers: 3.75
    - medium performers: 3.5
    - weak performers: 3.25
  - Probabilities ranging from 18–22 percent, depending on the debt burden indicator, were used to calibrate thresholds.
  - The probabilities were essentially based on the median PV of debt-to-GDP ratio in LICs immediately preceding an outbreak of debt distress in the Staff 2004 sample and were fairly close to the unconditional probability (frequency) of debt distress episodes found in the KN study.
- The unconditional probability of debt distress reported:
  - 25 percent in KN‘s sample
  - roughly 36 percent in Staff 2004

### Differences between KN and Staff 2004 methodologies
- Sample coverage:
  - Staff 2004 focuses on LICs.
  - KN uses data for both LICs and MICs.
- Distress signal definitions:
  - Staff 2004 considers only arrears on PPG external debt to official creditors as a signal of debt distress.
  - KN relies on three distress signals: arrears on PPG external debt to all creditors (official and private), Paris Club reschedulings, and IMF GRA financing on a commitment basis.
- Episode definitions:
  - Staff 2004 defines a non-distress episode as at least three consecutive years with no signal of debt distress; all other individual years are distress episodes.
  - KN characterizes a debt distress episode as a period of three years or longer with at least one distress signal, and defines a non-distress episode as a non-overlapping five-year period showing no distress signal.
- As a consequence, the studies identify episodes differently and thus the underlying events for the calibrated probabilities (18–22 percent) are not uniform across debt burden indicators.

### Limitations and areas for improvement
- Non-uniform definition of debt distress and non-distress episodes across thresholds: PV of debt thresholds were calibrated using Staff 2004 while debt service thresholds used KN, so the probabilities (18–22 percent) refer to different types of events and direct comparisons can be misleading.
- The technical analysis underlying the DSF thresholds could be improved in at least three main areas (only the first area is explicitly detailed in the source excerpt above; additional areas are noted but not enumerated in the provided text).

*Source: Annex 1. External Public Debt Thresholds*

### 2004. The median PV of debt-to-GDP ratio observed in LICs immediately prior to an outbreak of debt distress is

### _011212 - 2004. The median PV of debt-to-GDP ratio observed in LICs immediately prior to an outbreak of debt distress is

### Background and motivation
- Staff 2004: The median PV of debt-to-GDP ratio observed in LICs immediately prior to an outbreak of debt distress is 43 percent, and such a figure implies a probability of debt distress of 20 percent for a country with average CPIA score.
- Motivation for Staff 2011 re-estimation:
  - Address inconsistencies across KN, Staff 2004, and the DSF: heterogenous episode definitions, inclusion of MICs without controls, and use of total external debt service rather than PPG external debt service.
  - Produce thresholds calibrated on a consistent methodology applicable to LICs.

### Data, episode definitions, and core indicators
- Sample and coverage:
  - Sample of 130 countries, of which 61 are LICs.
  - Identified 105 debt distress episodes and 654 non-distress episodes.
  - Database covers LICs and MICs over 1970–2007.
- Distress signals (at least one signals a distress episode):
  - Accumulation of arrears on PPG external debt in excess of five percent of the PPG external debt stock outstanding.
  - A rescheduling of obligations due to Paris Club creditors (adjusted so HIPC completion is not treated as distress).
  - Disbursement by the IMF of GRA resources exceeding 50 percent of IMF quota.
- Episode duration rules:
  - Debt distress episode: period lasting three or more years with at least one distress signal; must not be preceded by another episode ending in any of the three previous years.
  - Non-distress episode: non-overlapping three-year period during which none of the distress signals is observed.
- Debt burden measures and calculation:
  - PV of debt taken from World Bank‘s Debt Reporting System: PV calculated by discounting stream of debt service denominated in original currencies using time-varying currency-specific commercial interest reference rates (CIRRs), as in KN.
  - Staff uses debt service data from WDI adjusted for accumulation of arrears to estimate service on a due basis.
- CPIA: World Bank CPIA used to measure quality of policy and institutions.

### Key statistics and empirical findings
- Median values (year prior to outbreak for distress; first year for non-distress):
  - Median PV of debt-to-GDP ratio: 30 percent in debt distress episodes and 17 percent in non-distress episodes.
- Sample composition and effects:
  - Compared to KN and Staff 2004, the redefinition (three-year non-distress, three-year distress) decreases unconditional frequency of distress episodes relative to previous studies.
  - LICs and MICs exhibit different debt levels between distress and non-distress episodes, motivating control for country group in regressions.
- Probit model results:
  - Basic specification includes a debt burden, CPIA score, and real GDP growth; interactive dummy variables allow debt burden coefficient to vary between LICs and MICs.
  - Estimated probability of debt distress increases with level of debt and decreases with CPIA and real GDP growth.
  - Interactive dummies significant in regressions including PV of debt-to-exports and debt service-to-revenue ratios, enabling LIC-specific threshold calibration.

### Staff 2011 estimations and calibration of debt thresholds
- Estimation approach:
  - Probit model estimated on developing countries (LICs and MICs) over 1970–2007, with consistent episode definitions, controls for MIC presence, and use of debt service on PPG external debt.
- Calibration of indicative debt burden thresholds fixes:
  - (i) a probability of experiencing a debt distress episode;
  - (ii) a CPIA score (3.25, 3.5, and 3.75 for weak, medium, strong performers); and
  - (iii) a real GDP growth rate set to its sample average for LICs.
- Three probability bases for thresholds:
  - (i) Unconditional probability of debt distress (frequency in sample).
  - (ii) Probability associated with the median debt burden indicator (evaluating probit at median debt burden and median CPIA and growth).
  - (iii) Probability that minimizes combined type I and type II errors (preferred approach): minimizes missed crises and false alarms in in-sample forecasting.
- Example: For PV of debt-to-GDP, the probability minimizing type I and II errors in the basic specification is 13.5 percent; this probability increases to 19.5 percent and 24.2 percent when non-distress episodes are defined as four and five years, respectively.

### Robustness checks and alternative specifications
- Alternative samples and proxies tested:
  - Excluding the 1970s: most estimated coefficients and calibrated thresholds similar to basic specifications.
  - Alternative governance and shock proxies: sub-CPIA macroeconomic/debt-management index, ICRG index, deviation of real GDP growth from three-year historical average, growth rate of export receipts—coefficients remain significant and calibrated thresholds broadly similar, with some exceptions (e.g., PV of debt-to-exports).
  - Longer non-distress definitions (four and five years): lead to higher calibration probabilities and higher estimated coefficients for debt burden indicators.
- Results: Basic specifications robust in point estimates and statistical significance; numerical threshold values similar across alternative regressions with noted exceptions.

### Remittances
- Testing remittances in denominators:
  - Probit re-estimated with denominators = GDP + gross remittances and exports + gross remittances.
  - Data limitations: sample for PV of debt-to-GDP including remittances is 315 observations vs. 740 excluding remittances; comparisons made using consistent small samples.
- Findings:
  - Adding remittances raises estimated coefficients on debt burdens and lowers the corresponding calibrated thresholds relative to regressions excluding remittances (on comparable samples).
  - Interpretation: A country can carry higher debt only if remittances are sufficiently large to offset the lower threshold implied when remittances are included.

### Probability thresholds vs. debt-burden thresholds (methodological implications)
- CPIA threshold effects:
  - Calibrating thresholds at fixed CPIA scores (3.25, 3.5, 3.75) generates discrete jumps in debt burden thresholds for small CPIA differences (example: CPIA 3.24 → PV debt-to-exports threshold 100 percent; CPIA 3.26 → threshold 150 percent).
  - Conversely, countries with substantially different CPIA scores can share identical thresholds (example: CPIA 3.74 and 3.26 can face same thresholds), causing potential over- or under-estimation of external debt distress risk.
- Probability-threshold approach:
  - Use equation (1) directly to produce country-specific probabilities of debt distress consistent with actual CPIA and other covariates, avoiding fixed-variable calibration and CPIA threshold effects.
  - Allows evaluation of the evolution of the probability of debt distress over time relative to a probability cutoff.
  - Enables richer specifications that can include multiple debt burden indicators and other risk variables (e.g., rate of debt accumulation, exchange rate misalignment, trade openness), potentially incorporating additional risk into baseline analysis rather than as separate stress tests.

*Source: IMF staff chapter text (Staff 2004 and Staff 2011 estimations and discussion).*

### 7.5 percent.

### 7.5 percent.

### PV of M&LT PPG external debt (methodology)
- Computed using time-varying currency-specific commercial interest reference rates (CIRRs).

### Summary statistics: Debt distress vs non-distress (Table A2)
- Observations and sample medians for debt burden indicator, governance, and real GDP growth are reported by group.
- All countries
  - Non-distress: Observations 65; Frequency of debt distress (non-distress group) — debt burden indicator sample median 43.5; Governance 5.0
  - Distress: Observations 105; Frequency of debt distress 13.8%; Debt burden indicator sample median 3.0; Governance 1.6
- LICs
  - Non-distress: Observations 31; Debt burden indicator sample median 73.3; Governance 4.8
  - Distress: Observations 57; Frequency of debt distress 15.2%; Debt burden indicator sample median 2.9; Governance 2.8
- MICs
  - Non-distress: Observations 33; Debt burden indicator sample median 73.6; Governance 5.2
  - Distress: Observations 48; Frequency of debt distress 12.5%; Debt burden indicator sample median 3.2; Governance 0.2
- PV of debt-to-GDP (sample medians)
  - All countries: Non-distress Observations 64; 17.1; 3.5; 4.9
  - All countries: Distress Observations 100; 13.5%; 29.9; 3.0; 1.6
  - LICs: Non-distress 30; 17.3; 3.3; 4.8
  - LICs: Distress 52; 14.5%; 31.9; 2.9; 2.7
  - MICs: Non-distress 33; 17.0; 3.6; 5.2
  - MICs: Distress 48; 12.6%; 27.4; 3.2; 0.2
- PV of debt-to-exports (sample medians)
  - All countries: Non-distress 64; 61.9; 3.5; 5.0
  - All countries: Distress 101; 13.6%; 119.1; 3.0; 1.7
  - LICs: Non-distress 31; 63.3; 3.3; 4.8
  - LICs: Distress 53; 14.6%; 111.0; 2.9; 2.9
  - MICs: Non-distress 33; 59.9; 3.6; 5.2
  - MICs: Distress 48; 12.6%; 119.7; 3.2; 0.2
- PV of debt-to-revenue (sample medians)
  - All countries: Non-distress 48; 86.4; 3.5; 4.9
  - All countries: Distress 71; 12.7%; 159.1; 3.2; 1.7
  - LICs: Non-distress 21; 89.6; 3.4; 4.8
  - LICs: Distress 34; 13.8%; 171.4; 3.0; 2.7
  - MICs: Non-distress 27; 83.8; 3.7; 4.9
  - MICs: Distress 37; 11.9%; 153.2; 3.4; 0.5
- Debt service-to-revenue (sample medians)
  - All countries: Non-distress 47; 8.1; 3.5; 4.9
  - All countries: Distress 65; 12.0%; 23.2; 3.2; 1.7
  - LICs: Non-distress 20; 9.1; 3.4; 4.8
  - LICs: Distress 30; 12.6%; 20.7; 3.1; 2.7
  - MICs: Non-distress 26; 9.1; 5.4; 3.7; 5.1
  - MICs: Distress 35; 11.5%; 26.5; 3.2; 0.5
- Debt service-to-exports (sample medians)
  - All countries: Non-distress 57; 6.9; 3.5; 4.9
  - All countries: Distress 83; 12.6%; 19.8; 3.1; 1.6
  - LICs: Non-distress 26; 7.5; 3.3; 4.8
  - LICs: Distress 41; 13.3%; 15.4; 3.0; 2.8
  - MICs: Non-distress 30; 9.1; 10.6; 3.7; 5.1
  - MICs: Distress 42; 12.0%; 24.3; 3.2; 0.5
- Note: "1/ Sample median for the debt burden indicator, governance, and real GDP growth."

### Distributional evidence (Figures A2 and A3)
- Figure A2: Relative frequency distribution of the PV of debt-to-exports ratio presented for:
  - All non-distress episodes; All distress episodes
  - Non-distress and distress episodes stratified by performance: strong performers, medium performers, weak performers
  - Histogram bins: 0-25, 25-50, 50-75, 75-100, 100-125, 125-150, 150-175, 175-200, 200-225, 225-250, 250-275, 275-300, 300-325, 325-350, 350-375, 375-400, 400-425, 425-900
  - Vertical axis range shown: 0.0% to 30.0%
- Figure A3: Relative frequency distribution of the debt service-to-exports ratio presented for:
  - All non-distress episodes; All distress episodes
  - Non-distress and distress episodes stratified by performance: strong performers, medium performers, weak performers
  - Histogram bins: 0-2.5, 2.5-5, 5-7.5, 7.5-10, 10-12.5, 12.5-15, 15-17.5, 17.5-20, 20-22.5, 22.5-25, 25-27.5, 27.5-30, 30-32.5, 32.5-35, 35-37.5, 37.5-40, 40-42.5, 42.5-90
  - Vertical axis range shown: 0.0% to 30.0%

### Estimation results and threshold calibration (Table A3 — Basic specifications)
- Reestimation results (coefficients and significance)
  - Debt burden indicator: 1.912***; 0.305***; 0.319***; 4.877***; 3.398***
  - Governance: -0.603***; -0.583***; -0.421***; -0.365***; -0.448***
  - Shock: Real GDP growth: -6.136***; -5.693***; -7.447***; -7.386***; -5.550***
  - Interaction dummy (for MIC debt burden): 0.232; 0.197**; 0.0511; -1.730**; -0.105
  - Constant: 0.562*; 0.576*; 0.0433; -0.434; -0.00442
  - Number of observations: 740; 743; 557; 543; 659
  - Pseudo R-square: 0.188; 0.181; 0.175; 0.224; 0.186
- Implied Thresholds (unconditional probability)
  - Probability used to calibrate thresholds: 14%, 15%, 14%, 13%, 13%
  - Weak (CPIA=3.25): 30 30 10 0 16 32 00 17 02 5 16 15 16 (as listed in table)
  - Medium (CPIA=3.5): 40 38 15 02 10 25 02 03 30 17 20 19 (as listed)
  - Strong (CPIA=3.75): 50 46 20 02 58 30 02 36 35 19 25 23 (as listed)
- Implied Thresholds (median debt burden indicator) and (minimizing type I and II errors) also reported with probabilities used to calibrate thresholds 15%, 11%, 12%, 16%, 12% and 14%, 13%, 15%, 15%, 14% respectively, with corresponding weak/medium/strong thresholds listed in the table.

### Robustness checks and alternative specifications (Table A4)
- Samples and coefficients reported for alternative definitions (4-year non-distress, 5-year non-distress, basic specification, macroeconomic shock, governance, definition of non-distress etc.)
- PV of debt-to-GDP (coefficients and implied thresholds)
  - Debt burden indicator coefficients across specifications: 1.912***; 2.131***; 1.993***; 1.686***; 1.924***; 1.511***; 2.505***; 2.915***
  - Governance coefficients: -0.603***; -0.650***; -0.614***; -0.414***; -0.0244***; -0.587***; -0.624***; -0.623***
  - Macroeconomic shock coefficients: -6.136***; -6.159***; -0.00881**; -6.780***; -6.751***; -6.705***; -5.301***; -6.417***
  - Number of observations: 740; 607; 662; 740; 740; 500; 556; 438
  - Pseudo R-square: 0.188; 0.185; 0.166; 0.174; 0.173; 0.195; 0.204; 0.228
  - Probability used to calibrate thresholds: 13.5%; 13.5%; 13.5%; 13.5%; 13.5%; 13.5%; 19.5%; 24.2%
  - Implied thresholds (Weak/Moderate/Strong): Weak (CPIA=3.25) 28 30 28 26 25 28 27 26; Moderate (CPIA=3.5) 36 38 35 32 32 37 34 31; Strong (CPIA=3.75) 44 45 43 38 38 47 40 36
- PV of debt-to-exports, PV of debt-to-revenue, debt service-to-revenue, debt service-to-exports: coefficients, observations, pseudo R-squares, probabilities used to calibrate thresholds, and implied thresholds provided across robustness checks (values reproduced exactly in the table).

### Thresholds with remittances (Table A5)
- Estimation results with remittances included (full and small samples)
  - Debt burden indicator: 1.912*** (full sample); 1.463**; 1.567*** (small sample variants)
  - PV of debt-to-GDP and PV of debt-to-exports and Debt service-to-exports coefficients and governance, shock, interaction reported for full and small samples
  - Number of observations: 740; 315; 315; 743; 318; 318; 659; 307; 307
  - Pseudo R-square: 0.188; 0.159; 0.160; 0.181; 0.170; 0.176; 0.186; 0.220; 0.231
- Implied Thresholds (unconditional probability) with and without remittances
  - Weak (CPIA=3.25): With remittances — PV of debt-to-exports 30 33 30 (-9% in small sample); Debt service-to-exports 16 31 54 12? (table entries show changes and percent changes)
  - Medium (CPIA=3.5) and Strong (CPIA=3.75): thresholds reported for full and small samples with percent changes (e.g., Medium 38 45 41 -8%; Strong 46 57 52 -8%)
- Note: Table entries present "% Change in small sample" alongside thresholds; exact values appear in the table.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/np/pp/eng/2012/_011212.pdf*

### Annex 2. Total Public Debt Benchmarks

### Annex 2. Total Public Debt Benchmarks

### A. Introduction
- Motivation:
  - Growing importance of domestic debt in LICs, especially post external debt relief and with developing domestic financial markets.
  - Past decision not to derive thresholds for total public debt due to empirical and conceptual challenges, notably absence of reliable and comprehensive historical data on domestic debt stocks and debt service.
- Key conceptual issues noted:
  - Domestic debt differs from external debt: indirect default via seigniorage or financial repression; uses beyond budget financing (monetary policy, exchange rate management, financial market development).
  - Coverage of domestic debt differs across countries; residency of holders may be unknown leading to domestically-issued debt ambiguity.
- Previous staff guidance:
  - Post-April 2006 DSF review: integrate domestic debt more systematically in DSAs by scrutinizing pace of domestic debt accumulation and assessing vulnerabilities, rather than incorporating domestic debt into existing thresholds.
- New impetus:
  - Availability of improved domestic debt data spanning several decades enabled IMF staff to derive thresholds for total public debt.
- Relevant prior work mentioned:
  - Reinhart and Rogoff (2009); IMF Fiscal Affairs Department historical public debt database covering 174 countries spanning 130 years; Reinhart and Rogoff domestic debt data for 70 countries over a hundred years.

### B. Data Sources
- Sample coverage:
  - 123 countries total, of which 81 are classified as low income (LICs). A country‘s income classification can change within the sample period.
  - Sample period: 1971–2007.
- Data sources (period 1971–2007 unless noted):
  - Governance indicator: CPIA Index — World Bank.
  - Nominal GDP — World Development Indicators (WDI); UN COMTRADE; World Economic Outlook (WEO).
  - Real GDP growth — WDI; UN COMTRADE; WEO.
  - Domestic revenue — WDI, Government Financial Statistics (GFS), UN COMTRADE, WEO.
  - Public Debt-to-GDP ratio — FAD's Historical Public Debt Database (HPDD).
  - Domestic debt (share of total public debt) — Abbas et al.
  - Domestic debt distress events — Reinhart and Rogoff: Variety of Crisis Database; Standard and Poor's; Moody's; and IMF staff reports.

### C. Methodology
- Empirical approach:
  - Probit model to explain incidence of debt distress (following Annex 1 external debt threshold approach).
  - Explanatory variables:
    - Measure of indebtedness: stock of total public debt (nominal or present value), scaled by GDP.
    - Governance: World Bank's CPIA index.
    - Macroeconomic shocks: real GDP growth.
    - Interaction dummy to differentiate LICs and MICs.
  - Present value (PV) of total public debt calculated as nominal domestic debt + PV of external debt (domestic debt assumed non-concessional ⇒ nominal = PV).
  - Thresholds derived only for stock indicators (lack of reliable domestic debt service data prevents PV of domestic debt).
- Definition of distress signals:
  - External debt distress signals:
    - (i) PPG external arrears in excess of five percent of external PPG debt;
    - (ii) existence of a Paris Club rescheduling, with adjustment for HIPC countries;
    - (iii) IMF GRA financing disbursed in excess of 50 percent of quota.
  - Domestic debt distress signals:
    - Instances of outright sovereign defaults: failure to meet principal or interest on due date as prescribed under original loan terms; restructurings (currency conversion to less-equivalent value, rescheduling at less favorable terms, discounting) constitute domestic distress signals.
    - Domestic arrears to suppliers excluded due to unavailability of reliable data.
- Episode definitions:
  - Normal time episodes: non-overlapping periods of three consecutive years with no public debt distress signal (external nor domestic).
  - Debt distress episodes: non-overlapping periods in which either an external or domestic debt distress episode occurs.
    - External distress episodes: periods lasting three years or more in which at least one external distress signal is observed.
    - Domestic distress episodes: any instance of domestic default constitutes a domestic distress episode.
  - Additional rule: a debt distress episode cannot be preceded by another such episode ending in any of the three previous years.

### D. Results
- Sample statistics:
  - Total public debt distress episodes observed: 99 over sample period.
  - Episode composition:
    - About 90 percent of all episodes are due solely to external events.
    - About 3 percent are due solely to domestic events.
    - 7 percent are due to a combination of both.
  - Unconditional probability of debt distress (entire sample): 14 percent.
  - Frequency of distress:
    - LICs: 16 percent.
    - MICs: 11 percent.
  - Sample means (debt burden indicators measured in the year immediately preceding distress):
    - Nominal debt-to-GDP ratio: around 60 percent in the year before distress (described as a "tipping point").
- Estimation results and implied policy-dependent thresholds (Table A8 summary):
  - Baseline estimation coefficients (PV to GDP / Nominal to GDP):
    - Debt burden indicator: 0.807** / 1.008***.
    - Governance: -0.586*** / -0.526***.
    - Shock: Real GDP growth: -6.508*** / -6.150***.
    - Interaction dummy (for MIC debt burden): 0.0597 / 0.0214.
    - Constant: 0.701* / 0.336.
    - Number of observations: 497 / 597.
    - Pseudo R-square: 0.138 / 0.154.
  - Threshold calibration approaches and calibrated thresholds:
    - Using unconditional probability:
      - Probability used to calibrate thresholds: 14% (PV), 15% (Nominal).
      - Implied Thresholds (PV to GDP): Weak (CPIA=3.25) 49, Moderate (CPIA=3.5) 68, Strong (CPIA=3.75) 86.
      - Implied Thresholds (Nominal to GDP): Weak (CPIA=3.25) 60, Moderate (CPIA=3.5) 73, Strong (CPIA=3.75) 86.
    - Using median debt burden indicator:
      - Probability used to calibrate thresholds: 12% (PV), 14% (Nominal).
      - Implied Thresholds (PV to GDP): Weak (CPIA=3.25) 37, Moderate (CPIA=3.5) 55, Strong (CPIA=3.75) 73.
      - Implied Thresholds (Nominal to GDP): Weak (CPIA=3.25) 56, Moderate (CPIA=3.5) 69, Strong (CPIA=3.75) 82.
    - Minimizing type I and II errors:
      - Probability used to calibrate thresholds: 12% (PV), 13% (Nominal).
      - Implied Thresholds (PV to GDP): Weak (CPIA=3.25) 38, Moderate (CPIA=3.5) 56, Strong (CPIA=3.75) 74.
      - Implied Thresholds (Nominal to GDP): Weak (CPIA=3.25) 49, Moderate (CPIA=3.5) 62, Strong (CPIA=3.75) 75.
  - Interpretation:
    - Policy-dependent thresholds (nominal terms) for weak, medium, and strong performers: 49, 62, and 75 percent (note: these appear in the text as calibrated results; see table specifics above).
    - PV-term thresholds for weak, medium, and strong performers: 38, 56, and 74 percent.
    - Nominal threshold for medium performers aligns with the "tipping point" near 60 percent nominal debt-to-GDP.
  - Robustness checks (Table A9 overview):
    - Alternative specifications tested:
      - Alternative macroeconomic shocks: deviation of real GDP growth to its three-year trend; export growth.
      - Alternative governance measures: International Country Risk Guide (ICRG) index; sub-CPIA index related to macroeconomic and debt management.
      - Alternative sample period excluding the 1970s.
    - Coefficients generally remain significant with expected signs across robustness checks.
    - Calibrated thresholds remain broadly in line with baseline results.
    - Selected robustness implied thresholds (PV to GDP; probability used 12% across checks):
      - Weak (CPIA=3.25): 38, 30, 24, 33, 31, 38 (across specifications).
      - Moderate (CPIA=3.5): 56, 50, 50, 48, 46, 65.
      - Strong (CPIA=3.75): 74, 71, 77, 63, 60, 91.
    - Selected robustness implied thresholds (Nominal to GDP; probability used 13% across checks):
      - Weak (CPIA=3.25): 49, 41, 39, 44, 44, 42.
      - Moderate (CPIA=3.5): 62, 56, 57, 54, 53, 57.
      - Strong (CPIA=3.75): 75, 71, 74, 63, 63, 73.
- Overall conclusions:
  - Addition of domestic debt does not increase explanatory power of the model substantially, reflecting that most debt distress episodes are due to external events.
  - Nevertheless, calibrated policy-dependent thresholds for total public debt (nominal and PV terms) provide indicative benchmarks that are broadly consistent with external-debt-based thresholds and the observed nominal "tipping point" near 60 percent.

*Source: Annex 2. Total Public Debt Benchmarks (1971–2007 data and estimation results).*

### Annex 3. Developing More Realistic Bound Tests

### Annex 3. Developing More Realistic Bound Tests

### Overview
- Purpose: Outline an empirical methodology to make bound tests more realistic by incorporating dynamic interaction between key variables and comovement between shocks into the framework.
- Core idea: Move from descriptive-statistics-based shocks calculated over a fixed historical period to shocks generated by estimated dynamic models (VAR and panel VAR), and use stochastic simulation to generate confidence intervals for debt projections.

### Status Quo: current bound-test framework
- Forcing variables (annual, ten-year historical-period descriptive statistics) modeled as:
  - (1a) g_t = μ_g + ε_gt,   ε_gt ~ (0, σ_g^2)
  - (1b) π_t = μ_π + ε_πt,   ε_πt ~ (0, σ_π^2)
  - (1c) i_t = μ_i + ε_it,   ε_it ~ (0, σ_i^2)
  - (1d) p_t = μ_p + ε_pt,   ε_pt ~ (0, σ_p^2)
  - (1e) b_t = μ_b + ε_bt,   ε_bt ~ (0, σ_b^2)
  - Definitions: g_t = real GDP growth; π_t = inflation rate (GDP deflator in U.S. dollar terms); i_t = nominal interest rate (average implicit interest rate on external debt); p_t = non-debt incurring capital inflows as percent of GDP; b_t = non-interest current account balance as percent of GDP.
- Debt accumulation equation:
  - (2) d_t = (1+i_t)/[(1+g_t)(1+π_t)] d_{t-1} - b_t - p_t
  - d_t = external debt as percent of GDP.
- Calibration and simulation features:
  - Magnitude and persistence of shocks calibrated using stochastic simulation.
  - Standard deviations of outcomes calculated over historical period on a country-by-country basis.
  - Practical appeal: relatively simple to implement and transparent.

- Shortcoming highlighted:
  - Dynamic interaction between variables and comovement between shocks are rather arbitrary in the current framework—shocks persist for two periods and are introduced separately then combined.

### Incorporating more realistic shocks: VAR-based approach
- VAR representation for five-variable system:
  - (3) X_t = μ + B(L) X_{t-1} + ε_t,   ε_t ~ (0, Σ)
  - X_t = [g_t, π_t, i_t, b_t, p_t]'; B(L) = 5-by-5 matrix of polynomial lag operators; Σ = 5-by-5 symmetric covariance matrix of reduced-form residuals.
- Advantages:
  - Captures dynamic interaction among all five variables via B(L).
  - Captures comovement between shocks via Σ.
  - Shocks generated by VAR have a well-defined interpretation, making bound tests more realistic.
- Estimation considerations:
  - Country-specific VARs require sufficient data; parameter estimates may be unreliable where data are limited.
  - Panel (pooled cross-section/time series) VARs can increase degrees of freedom and produce more reliable parameter estimates but impose common comovement structure across countries.

- Two-step estimation strategy proposed:
  - Step 1: Estimate covariance matrix Σ using a panel VAR model for a group of similar countries.
  - Step 2: Estimate a standard VAR for each country with the same covariance structure Σ imposed.
  - Benefit: dynamics and volatility of shocks vary across countries while comovement between shocks is common.

### Illustration: Ghana case study (VAR application)
- Model: VAR estimated using annual data over 1971–2010 for Ghana.
- Use: Shocks applied to the five reduced-form residuals generate dynamic responses of forcing variables; equation (2) generates a dynamic profile for d_t.
- Comparative finding (qualitative): Largest shock from the VAR is quite similar to the non-debt creating flows shock over the medium term (2011–15) but closer to the combination shock and the GDP deflator shock over the longer term.
- Confidence-intervals and stochastic-simulation results for Ghana (projection period 2011–2015):
  - Baseline scenario: PV of debt-to-GDP ratio projected to increase by 5 percentage points over the five-year period.
  - Most extreme bound test (non-debt flows shock): PV of debt increases by 9 percentage points by 2015.
  - Stochastic simulations indicate there is a 25 percent probability that the PV of debt would increase to 38.5 percent of GDP by 2015 (the 75th percentile), implying that the most extreme bound test has a likelihood of much less than 25 percent.

- Caveats noted for VAR + stochastic simulation approach:
  - VAR-based stochastic simulation does not yield reliable uncertainty estimates over projection periods beyond a few years because the VAR lacks an exchange rate adjustment mechanism and endogenous fiscal policy rules that respond to shocks.
  - Confidence intervals can be sensitive to model specification and the sample period; structural shifts (e.g., fiscal/monetary policy, exchange rate regime) can make intervals misleading.

### Further enhancements and methodological extensions
- Model extensions:
  - Incorporate exogenous variables (world commodity prices, output growth, interest rates).
  - Include variables omitted from simplified debt-accumulation equation: capital grants, net portfolio equity flows, changes in international reserves, exceptional financing.
  - Tailor models to country-specific risk drivers (e.g., world oil price uncertainty for oil-dependent countries).
- Simulation and distributional considerations:
  - Monte Carlo simulations typically draw from a normal distribution; can be generalized to other probability distributions.
  - Bootstrapping methods can allow for skewness and excess kurtosis (fat tails) in residuals.
- Addressing data limitations:
  - Pooling parameter estimates across countries via panel VAR:
    - (4) X_{it} = μ_i + B(L) X_{it-1} + ε_{it},   ε_{it} ~ (0, Σ)
    - X_{it} = vector of variables for country i; identification over time (t) and across country dimension (i = 1 to n) increases degrees of freedom.
    - Typical fixed-effect panel: μ_i allowed to vary across countries to allow for differences in conditional means.
  - Panel VAR approach can generate more reliable uncertainty estimates for countries with limited data, at the cost of some country specificity unless mitigated by hybrid estimation strategies (e.g., common Σ with country-specific dynamics).

### Practical recommendations (methodological)
- Adopt VAR-based bound tests where data permit to capture dynamic interactions and shock comovement.
- Use panel VARs to estimate covariance structure Σ when country data are limited, then impose Σ in country-specific VARs to retain country-specific dynamics.
- Apply stochastic simulation to VAR models to generate probability distributions and confidence intervals for debt indicators, while treating long-horizon uncertainty estimates cautiously.
- Consider non-normal simulation techniques (alternative distributions, bootstrap) to account for skewness and fat tails in residuals.
- Expand the set of variables and exogenous drivers in the VAR to reflect country-specific risk exposures (e.g., commodity prices, capital flows, exceptional financing).

*Source: Annex 3. Developing More Realistic Bound Tests*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/np/pp/eng/2012/_011212.pdf_