## Benchmarking Dynamically Stable Public Debt Trajectories for Low-Income Countries

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### Executive Summary — Overview
- Objective: Develop two complementary approaches for benchmarking the public debt trajectories of LICs to assess their dynamic stability.
- Operational definition: Dynamically stable public debt trajectories are assessed by comparing LICs’ public debt-to-GDP ratios over the past 20 years with historical experiences of countries with similar characteristics that are further along development and have not experienced public debt stress.
- Reference groups: Analysis focuses on reference LICs defined as the 25th, median, and 75th percentiles across LICs at different points in time (e.g., 1995, 2000, ..., 2023).
- LIC sample: 60 countries eligible to receive IMF and World Bank concessional financing as of end-2024, for which sufficient data are available.
- Historical pattern: LIC public debt-to-GDP ratios were high in the mid-1990s, declined in the 2000s after debt relief and growth, then rebounded from the mid-2010s due to infrastructure drives and COVID-19 financing; recent stabilization but elevated levels persist.
- Key figures (1995–2023, from Figure 1):
  - 75th percentile increased from 46 to 72 percent of GDP (26-percentage point increase).
  - Median and 25th percentile experienced increases of around 20 percentage points.
- Time window for benchmarking: past 20 years.

### Conceptual Framework
- Stylized government budget constraint (normalized by nominal GDP):
  - d_t = (1 + r_t / 1 + g_t) d_{t-1} − pb_t
  - Δd_t = (r_t − g_t) / (1 + g_t) d_{t-1} − pb_t
  - Debt-stabilizing primary balance: pb_t^0 = (r_t − g_t) / (1 + g_t) d_{t-1}
  - Long-run steady-state approximation: d̅ ≈ pb / (r − g)
- Jiang et al. (2022) closed-form steady-state (maximum sustainable debt):
  - d̅ = b̅ = [τ(b̅) − γ] / [r + ζ̃ − δ + λ − g]
  - Mapping: pb ≡ τ(b̅) − γ; r ≡ r + ζ̃ − δ + λ
- Operational conditions (based on Jiang, Sargent, Wang, Yang (2022) and Bohn tests):
  - If public debt-to-GDP is above its optimal value (medium-to-long term, five-to-ten year horizon): the Bohn test must be met — primary fiscal balance as a share of GDP should exhibit a statistically significant positive response to the public debt-to-GDP ratio (implying mean reversion).
  - If below optimal: observed upward trend must align with experiences of comparable countries ahead in convergence that have not experienced public debt stress (implying convergence from below).
- Rationale for benchmarking: Direct empirical evaluation is difficult for countries with short/unreliable time series and structural breaks; benchmarking against dynamically stable peers overcomes these difficulties.
- Alignment variable: Degree of economic development (per capita PPP GDP) used as key alignment variable.

### Empirical Approaches and Implementation
- Two complementary empirical approaches:
  - Historical comparison of reference LICs with present-day MACs aligned in development time (MACs’ per capita PPP GDP similar to reference LIC in 2005).
  - Synthetic Control Method (SCM) applied in a “development time” setting to construct a Synthetic Control Unit (SCU) resembling each reference LIC in the pre-2005 training period.
- Development-time alignment:
  - Base year chosen: 2005 (enables long-run analysis 2005–2023 and captures post-HIPC/MDRI period).
  - Construction of long-term per capita PPP GDP: back-spliced WDI per capita PPP GDP (constant 2021 international dollars) for 1990–2023 with Penn World Table 10.01 for 1970–1990; back-spliced using PWT growth rates.
- Donor pool selection:
  - Donor MACs excluded if they experienced public debt stress in the development time horizon (2005–2023); public debt stress identified using updated fiscal crises database (Badia, Arbelaez, and Xiang, 2022).
- SCM novel elements:
  - Move to development-time alignment to expand donor universe (include historical MAC data).
  - Control for key global variables to mitigate calendar-to-development year shifts.
  - Augmented Bohn test (ADL regressions) used to select SCM predictor variables relevant for LICs.

### Empirical Findings — Historical Comparison and SCM
- Broad outcome:
  - Historical comparison and SCM both indicate that the experiences of the 25th percentile, the median, and the legacy 75th percentile LICs are broadly in line with the majority of MACs at comparable levels of development that avoided public debt stress—interpreted as trajectories being dynamically stable over the last 20 years.
  - The recent 75th percentile LIC diverges from the confidence band around its dynamically stable benchmark under both approaches, signaling elevated divergence and a potential warning flag for country-specific debt sustainability analysis.
- SCM-specific implementation details:
  - Training sample: first 11 years after 2005 used as training sample.
  - Dependent variable: face value of overall public debt as a ratio to GDP.
  - Predictor selection informed by augmented Bohn ADL regressions (panel data for 53 LICs over 1970–2023).
  - Predictor list (selected controls from ADL Bohn regressions):
    - Public finance: PPG external debt (% overall debt); PPG external debt service (% Exports); PPG external debt (% Revenues); Public revenue (% GDP).
    - Macroeconomics: Real GDP growth; Exports (% GDP); REER depreciation; Natural resource rents (% GDP); Average US FFR; World GDP growth; PPP GDP per capita (log $).
    - Finance: Per capita net ODA (log $); FX reserves (months of imports); ST debt (% FX reserves).
  - Weighting: minimize absolute mean deviation between percentile values and LICs’ debt ratios; weight deviations twice as much in 2010–2023 to ensure representativeness over post-2010 debt build-up.
  - Treatment of 75th percentile: construct “legacy” 75th percentile closest neighbor (remains in top quartile until 2019) and “recent” 75th percentile closest neighbor (closest over last 20 years).
- Confidence bands for SCM:
  - SD_LIC = sd( d̂_LIC,t_start − d_LIC,t_start, ..., d̂_LIC,t0 − d_LIC,t0 )
  - Confidence band: +/- 1.96 ∙ SD_LIC around SCU public debt trajectory.
  - Narrower confidence band when synthetic benchmark closely tracks reference LIC during training.
- SCM results summary:
  - Reference 25th percentile, median, and legacy 75th percentile LICs closely track their SCUs.
  - Reference median LIC diverges for some time but realigns toward end of benchmark period.
  - Reference recent 75th percentile LIC diverges from its SCU confidence band — notable divergence uncovered by SCM.
  - SCM narrows confidence bands relative to historical comparison and uncovers divergent dynamics, notably for the recent 75th percentile LIC.

### Augmented Bohn Test (ADL) — Specification and Key Coefficients
- Baseline Bohn model: pb_t = β0 + β1 g̃_t + β2 ỹ_t + ρ d_{t−1} + ε_t; positive ρ sufficient for solvency under assumptions.
- Augmented ADL specification addresses non-stationarity and serial correlation; two lags included; indicators entered one at a time and standardized.
- Empirical associations (coefficient estimates with standard errors and sample sizes):
  - Public finance:
    - Exports-to-GDP Ratio: -0.007 (0.005); 1,217
    - Revenue-to-GDP Ratio: 0.039*** (0.004); 1,351
    - PPG External Debt Servicing (Share of Revenue): 0.002 (0.003); 1,348
    - PPG External Debt Servicing (Share of Exports): -0.009 (0.005); 1,348
    - PPG External Debt (Share of Total Debt): 0.000 (0.003); 1,345
  - Macro indicators:
    - Real GDP Growth: 0.007*** (0.001); 1,351
    - Risk-Free Rate (US FFR): -0.018 (0.006); 1,351
    - REER Depreciation: -0.406*** (0.069); 1,351
  - Financial characteristics:
    - Natural Resource Rents-to-GDP Ratio: -0.021** (0.005); 1,254
    - Net ODA per Capita (Log US$): 0.002 (0.009); 1,315
    - Reserves in Months of Imports: -0.033 (0.028); 1,084
    - Short-Term Debt-to-Reserves Ratio: 0.057 (0.021); 1,084
  - Institutional characteristics:
    - Control of Corruption: -0.02*** (0.003); 962
    - Political Stability & Absence of Violence: 0.008 (0.005); 967
    - Government Effectiveness: -0.012 (0.004); 960
    - Regulatory Quality: -0.006 (0.005); 960
    - Rule of Law: -0.006 (0.006); 968
    - Voice and Accountability: -0.011 (0.006); 968
- Main ADL findings:
  - Revenue-GDP share and real GDP growth: statistically significant positive association with reactiveness of primary balance to lagged debt.
  - Increases in US FFR and REER appreciation: dampen reactiveness.
  - Higher natural resource dependence: suppresses reactiveness.
  - Most institutional quality proxies not statistically significant except control of corruption (tends to lower reactiveness).

### Data, Sample, and Robustness
- Dataset: comprehensive in-house dataset of 60 LICs and 85 MACs over 1970–2023; sources include IMF WEO, Global Debt Database, Historical Public Debt Database, DSA vintages, World Bank WDI and WGI, UN Data, Penn World Table.
- Average PPP GDP per capita in 2005 for LIC percentiles:
  - 25th percentile: US$2,935
  - 50th percentile: US$2,275
  - 75th percentile: US$6,851
- SCM pre-benchmark goodness-of-fit (selected entries, percent differences LIC − Synth. Unit):
  - Overall Public Debt (% GDP): 25th: -0.4; 50th: 0.1; 75th: -0.5; Recent 75th: 0.4
  - Revenue (% GDP): 25th: -9.3; 50th: -3.0; 75th: -6.6; Recent 75th: 10.4
  - Short-Term Debt (% International Reserves): 25th: 8.7; 50th: -3.1; 75th: 246.9; Recent 75th: 34.8
  - Share of External in Overall Public Debt: 25th: 39.7; 50th: 35.5; 75th: 68.3; Recent 75th: 61.7
- Robustness checks:
  - Vary benchmarking start year t0 across {2014, 2015, 2016}: results do not qualitatively change.
  - Dropping predictor variables one-at-a-time: synthetic benchmarks broadly robust; some variation when dropping REER depreciation.

### Conclusion and Implications
- Benchmarking approach and operational definition:
  - Two complementary approaches (historical comparison in development time; SCM in development time) provide tools to benchmark LIC public debt trajectories against dynamically stable peers further along development.
- Main empirical conclusions:
  - Most reference LICs analyzed (25th, median, legacy 75th percentiles) show trajectories broadly consistent with dynamically stable benchmarks over the last 20 years.
  - The recent 75th percentile LIC shows divergence from its dynamically stable benchmark and warrants further country-specific investigation.
- Interpretation framework for policy and DSA:
  - Conformity with benchmarks provides probabilistic evidence of convergence from below to optimal values or mean reversion from above when Bohn conditions hold.
  - Divergence signals should be incorporated into detailed, country-specific debt sustainability analysis.
- Suggestions for future research:
  - Explore the relationship between maximum reduction in public debt for synthetic controls and the maximum level of average debt reduction in debt restructurings.
  - Compare synthetic controls to countries in the sample period to assess performance of non-debt stress LICs in contemporary times.

*Source — IMF Working Paper (Executive Summary, Section III, Conclusion, Appendices and Tables as presented).*

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

### Executive Summary

### Overview
- Objective: Develop two complementary approaches for benchmarking the public debt trajectories of LICs to assess their dynamic stability.
- Operational definition: Dynamically stable public debt trajectories are assessed by comparing LICs’ public debt-to-GDP ratios over the past 20 years with historical experiences of countries with similar characteristics that are further along development and have not experienced public debt stress.
- Reference groups: Analysis focuses on reference LICs defined as the 25th, median, and 75th percentiles across LICs at different points in time (e.g., 1995, 2000, ..., 2023).
- LIC sample: LICs are defined as the 60 countries eligible to receive IMF and World Bank concessional financing as of end-2024, for which sufficient data are available (Appendix Table 1).
- Historical context: LIC public debt-to-GDP ratios were high in the mid-1990s, declined in the 2000s following debt relief and growth, then rebounded from the mid-2010s due to infrastructure drives and COVID-19 financing. Recent stabilization is observed but levels remain elevated.

Key statistics and observations from Figure 1 (1995-2023):
- 75th percentile increased from 46 to 72 percent of GDP, a 26-percentage point increase.
- Median and 25th percentile experienced increases of around 20 percentage points.
- Time window for benchmarking: past 20 years.

### Conceptual Framework
- Two operational conditions based on the Jiang, Sargent, Wang, Yang (2022) model:
  - If a LIC’s public debt-to-GDP ratio is above its optimal value (medium-to-long term, i.e., in the five-to-ten year horizon): the Bohn test must be met — primary fiscal balance as a share of GDP should exhibit a statistically significant positive response to the public debt-to-GDP ratio, implying mean reversion from above to the optimal value.
  - If a LIC’s public debt-to-GDP ratio is below its optimal value: the observed upward trend must be in line with experiences of comparable countries ahead in convergence that have not experienced public debt stress, implying convergence from below to the optimal value.
- Rationale: Direct empirical evaluation of operational conditions can be difficult for countries with short or unreliable time series and structural breaks; benchmarking against dynamically stable peers overcomes these difficulties.

Theoretical and empirical underpinnings:
- Bohn (1998, 2005) test and literature on intertemporal budget constraint and sustainability.
- Jiang et al. (2022) model provides a closed-form solution for the maximum sustainable (and optimal) public debt level as a function of macro variables and deeper parameters.
- The degree of economic development (per capita PPP GDP) is used as a key alignment variable, proxying institutional and fiscal policy characteristics correlated with per capita income.

### Empirical Analysis
- Two complementary empirical approaches:
  - Historical comparison of reference LICs with present-day MACs aligned in development time (per capita PPP GDP similar to reference LIC in 2005).
  - Synthetic Control Method (SCM) applied in a “development time” setting to construct a Synthetic Control Unit (SCU) that closely resembles each reference LIC in the pre-2005 training period.
- Extension of SCM: By moving to development-time alignment, the universe of candidate donor countries expands to include historical data for MACs; key global variables are controlled for to mitigate calendar-to-development year shifts.
- Augmented Bohn test: Used to determine empirically relevant country characteristics (public finance, macro, and debt-related) that drive the SCM specification; additional LIC-relevant indicators considered include institutional quality, revenue mobilization, real growth, resource dependence, access to development aid, reliance on short-term debt, and reserve coverage.
- Data issues addressed: Non-stationarity of relevant time series explicitly handled in regression specification.

Empirical findings:
- Both the historical comparison with MACs aligned by development time and the SCM results suggest that:
  - The experiences of the 25th percentile, the median, and the legacy 75th percentile LICs are broadly in line with the majority of MACs at comparable levels of development that have avoided public debt stress. This indicates these LICs’ public debt trajectories have been dynamically stable over the last 20 years.
  - The public debt trajectory of the recent 75th percentile LIC diverges from the confidence band around its dynamically stable benchmark under both approaches, signaling elevated divergence and a potential additional warning flag for country-specific debt sustainability analysis.
- Interpretation: Conformity with benchmarks provides probabilistic evidence of either convergence from below to optimal values or mean reversion from above when Bohn conditions hold; divergence signals warrant incorporation into detailed, country-specific debt sustainability assessments.

Methodological contributions:
- First: Application of historical comparisons and SCM in a novel “development time” setting to assess dynamic stability of LIC public debt trajectories.
- Second: Broader set of country characteristics incorporated in SCM choice variables, tailored to LIC contexts and informed by an augmented Bohn regression analysis.

### Conclusion
- The combined approaches provide empirical tools to benchmark LIC public debt trajectories against dynamically stable peers further along the development path and to assess the likelihood that observed trajectories are consistent with sustainability-relevant operational conditions.
- Empirical evidence indicates that most reference LICs analyzed (25th, median, legacy 75th percentiles) show trajectories broadly consistent with dynamically stable benchmarks; the recent 75th percentile LIC shows notable divergence and requires further country-specific investigation.

*IMF Working Papers — Benchmarking Dynamically Stable Public Debt Trajectories for Low-Income Countries. Source: Executive Summary of the provided PDF content.*

### Section III identifies alternative controls for constructing benchmarks of dynamically stable public debt trajectories

### Section III identifies alternative controls for constructing benchmarks of dynamically stable public debt trajectories

### Conceptual Framework
- Government budget constraint (stylized):
  - G_t + (1 + r_t) D_{t-1} = T_t + D_t  (II.1)
  - D_t = (1 + r_t) D_{t-1} − PB_t
  - Definitions:
    - T_t – Total tax revenue
    - G_t – Non-interest government expenditure
    - PB_t ≡ T_t − G_t – Primary fiscal balance
    - D_t – Overall public debt stock
    - r_t – Nominal interest rate
- Normalized by nominal GDP (lower case = ratio to GDP) yields:
  - d_t = (1 + r_t / 1 + g_t) d_{t-1} − pb_t  (II.2)
  - g_t – Nominal GDP growth
- Change in debt-to-GDP ratio:
  - Δd_t ≡ d_t − d_{t-1} = (r_t − g_t) / (1 + g_t) d_{t-1} − pb_t  (II.3)
- Debt-stabilizing primary balance (limit case Δd_t = 0):
  - pb_t^0 = (r_t − g_t) / (1 + g_t) d_{t-1}  (II.4)
- Long-run steady-state approximation:
  - d̅ ≈ pb / (r − g)  (II.5)
- Jiang et al. (2022) DGE model steady-state (closed-form maximum sustainable debt level):
  - d̅ = b̅ = [τ(b̅) − γ] / [r + ζ̃ − δ + λ − g]  (II.6)
  - Components explained:
    - Public finance channel: exogenous expenditure-to-GDP ratio (γ); optimal revenue-to-GDP ratio τ (capped by tax capacity τ̅)
    - Macro channel: stochastic nominal risk-free rate (r) and nominal GDP growth (g)
    - Debt channel: debt-surge probability (ζ̃), risk premium on sovereign debt (λ), convenience yield on debt (δ)
- Mapping to simpler steady-state form:
  - pb ≡ τ(b̅) − γ
  - r ≡ r + ζ̃ − δ + λ
- Model implication:
  - If public debt-to-GDP is below b̅, it converges to b̅ along a dynamically stable trajectory; if it exceeds b̅, optimal default occurs.
- Note on LICs:
  - For LICs, convenience yields are less important.

### Empirical Analysis — Data Description
- Dataset scope and sources:
  - Comprehensive in-house dataset of 60 LICs and 85 MACs over 1970-2023
  - Sources: IMF databases (WEO, Global Debt Database, Historical Public Debt Database, DSA vintages), World Bank WDI and WGI, UN Data, Penn World Table
  - Appendix I contains variable descriptions (not reproduced here)
- Development-time alignment and base year:
  - Align MACs to each reference LIC so MACs’ per capita PPP GDP matches LIC in base year t=0
  - Base year chosen: 2005
    - Reasoning: allows long-run analysis (2005-2023) and captures post-HIPC/MDRI period
  - Construction of long-term per capita PPP GDP series:
    - Back-spliced WDI per capita PPP GDP (constant 2021 international dollars) for 1990-2023 with Penn World Table 10.01 expenditure-side real GDP at chained PPPs for 1970-1990 (converted to per capita), back-spliced using PWT growth rates
- Donor pool selection:
  - Only MACs that have not experienced public debt stress in the near 20-year “development time horizon” (2005-2023) are used
  - Public debt stress identified using updated fiscal crises database (Badia, Arbelaez, and Xiang, 2022)
- Caveats of benchmarking LICs to MACs:
  - LICs: greater dependence on external financing, higher exposure to external shocks, weaker substitutability between domestic and external financing
  - MACs: greater exposure to investor sentiment shifts leading to liquidity squeezes and defaults
  - These opposing effects largely mitigate benchmarking biases

### Empirical Analysis — Historical Comparison
- First-pass comparison:
  - Compare intertemporal values (debt trajectories) of 25th, 50th, and 75th percentiles of overall public debt-to-GDP across LICs with trajectories of present-day MACs that avoided public debt stress, starting when MACs were at a similar development stage as the reference LIC in 2005
- Quartile-stage proxying:
  - Stage of economic development for percentile groups proxied by median per capita PPP GDP in 2005 of LICs that are ranked in those quartiles at least half the time
- Key empirical observation:
  - Intertemporal experiences of 25th, median, and 75th percentile LICs over the last twenty years are broadly in line with MACs at similar development levels that avoided public debt stress
  - Post-2010 rapid public debt accumulation places these reference LICs near the top of the MAC interquartile range, sometimes exceeding it (notably for median and 75th percentile LICs), signaling a build-up of debt vulnerabilities
- Limitations:
  - Anchoring only on per capita PPP GDP in base year does not fully control for broader country characteristic differences or differing macro environments across calendar-year periods mapped to development time

### Empirical Analysis — Synthetic Control Method (SCM) Approach
- Methodological adaptation:
  - Use SCM to construct Synthetic Control Units (SCUs) that closely resemble reference LICs across macro characteristics over a training period
  - Novel application: combine SCM with “development time” and exclude MACs with public debt stress to create dynamically stable benchmarks
- Closest neighbor matching:
  - Identify countries whose public debt trajectories most closely resemble intertemporal patterns of 25th, 50th, and 75th percentiles across LICs at different points in time
  - Minimizes absolute mean deviation between percentile values and particular LICs’ debt ratios
  - Weight deviations twice as much in 2010-2023 to ensure representativeness over post-2010 debt build-up
- Treatment of 75th percentile:
  - Finding a single LIC that remains consistently in the top quartile over time is difficult
  - Construct both a “legacy” 75th percentile closest neighbor (remains in top quartile only until 2019) and a “recent” 75th percentile closest neighbor (closest over last 20 years)
- Training sample:
  - Use first 11 years after 2005 as the training sample
  - Dependent variable: face value of overall public debt as a ratio to GDP
- Predictor variable selection:
  - Informed by LIC-DSF debt burden indicators and augmented Bohn test regressions (ADL regressions estimated with panel data for 53 LICs over 1970-2023)
  - Empirical findings: revenue mobilization (revenue-GDP share), real GDP growth, average US Federal Funds Rate (FFR), changes in REER, and level of resource dependence are associated with changes in reactiveness of primary balance to lagged public debt
- Selected controls based on ADL Bohn regressions (Table 1)
  - Public Finance:
    - PPG external debt (% overall debt)
    - PPG external debt service (% Exports)
    - PPG external debt (% Revenues)
    - Public revenue (% GDP)
  - Macroeconomics:
    - Real GDP growth
    - Exports (% GDP)
    - REER depreciation
    - Natural resource rents (% GDP)
    - Average US FFR
    - World GDP growth
    - PPP GDP per capita (log $)
  - Finance:
    - Per capita net ODA (log $)
    - FX reserves (months of imports)
    - ST debt (% FX reserves)
- Practical SCM implementation:
  - Construct SCUs by weighting values in development time for MACs to match reference LICs in calendar time over the training period
  - Summary statistics in Appendix Table 4 show SCU countries resemble reference LICs significantly better than average MACs in donor pool
  - Goodness-of-fit varies across predictors depending on SCM-assigned weights and donor pool size
- Confidence bands around SCU trajectories:
  - Compute SD_LIC = sd( d̂_LIC,t_start − d_LIC,t_start, ..., d̂_LIC,t0 − d_LIC,t0 )  (III.1)
    - d_LIC,t – public debt-to-GDP ratio of the reference LIC
    - d̂_LIC,t – public debt-to-GDP ratio of the SCU for a reference LIC
  - Construct confidence bands of +/- 1.96 ∙ SD_LIC around SCU public debt trajectory
  - Interpretation: narrower confidence band when synthetic benchmark tracks reference LIC closely during training period
- SCM results summary:
  - Figure 3 compares reference LICs’ debt trajectories with SCUs (dynamically stable by construction), expressed in percentage point differences, with confidence bands
  - Reference 25th percentile, median, and legacy 75th percentile LICs closely track their SCUs
  - Reference median LIC diverges for some time but realigns toward the end of the benchmark period with its dynamically stable benchmark
  - Reference recent 75th percentile LIC diverges from the confidence band around its dynamically stable benchmark
  - Overall: SCUs trace reference LICs reasonably well over the training period; SCM narrows confidence bands vs. historical comparison and uncovers divergent dynamics (notably for the recent 75th percentile LIC)

*Italic: Source — IMF Working Paper Section III (authors’ estimates and equations as presented).*

### Conclusion

### Conclusion

### Benchmarking approach and operational definition
- Develop two complementary approaches for benchmarking public debt trajectories of LICs to assess their dynamic stability.
- Operational definition of dynamically stable public debt trajectories: compare the evolution of LICs’ public debt-to-GDP ratios over the past 20 years with historical experiences of other countries with similar characteristics that are further along the path of economic development and have not yet experienced public debt stress events.
- Novel technique: align data for a comparison group of MACs to that of each reference LIC so that their per capita PPP GDP is similar to that of the reference LIC in 2005.

### Interpretation framework
- The comparison offers a probabilistic view of conformity of LICs’ public debt trajectories with one of two operational conditions:
  - If a LIC’s public debt-to-GDP ratio is above its optimal value in the medium to long term, then meeting the Bohn test would ensure eventual convergence from above to the optimal value.
  - If below its optimal value, the observed upward trend should be aligned with experiences of more advanced peers, implying consistency with convergence from below to the optimal value.

### Contributions to the literature
- First contribution: application of historical comparisons and the Synthetic Control Method (SCM) in a development time setting rather than calendar-year time, expanding the universe of candidate countries for the Synthetic Control Unit (SCU) by including historical data for MACs.
- Second contribution: consideration of a broader range of country characteristics related to the dynamic stability of public debt in the SCM application; expansion of indicators relevant in the LIC context beyond those typically used in the Bohn test literature for advanced and emerging economies.
- Methodological advancement: ADL regression specification to address issues of non-stationarity and serial correlation common in this literature.

### Main empirical findings
- Results from direct comparison and SCM:
  - Experiences of most LICs are broadly in line with those of the majority of MACs at similar levels of economic development that have avoided public debt stress.
  - This provides empirical evidence that the public debt trajectories of most LICs have broadly been dynamically stable over the last 20 years.
  - The public debt trajectory of the recent 75th percentile LIC, however, has diverged from the confidence band around its dynamically stable benchmark.
- Implication: cross-country comparison findings can be incorporated into detailed, country-specific debt sustainability analysis.

### Suggestions for future research
- Consider the relationship between the maximum reduction in public debt for synthetic controls as a potential measure for the maximum level of average debt reduction in debt restructurings.
- Compare synthetic controls to countries in the sample period to shed light on the performance of non-debt stress LICs in the contemporary time period.

### Data sample and peer selection (highlights)
- Analysis sample: 60 Low-Income Countries listed in Appendix I Table 1 (Countries 1–60 with ISO3 codes provided).
- Market Access Countries (MACs) used as peers are listed by LIC percentiles (25th, 50th, 75th) with base years chosen when MACs’ PPP GDP per capita was closest to the respective reference LIC percentile.
- The average PPP GDP per capita values in 2005 for LICs in the 25th, 50th, and 75th percentiles of the public debt-to-GDP ratio distribution are US$2,935, US$2,275, and US$6,851, respectively.

### Indicator definitions and data sources (selected)
- Face value (FV) of overall public debt: constructed using IDS series on PPG external public debt stocks, augmented with IMF credit and domestic debt from WEO.
- Nominal GDP in US$ and LCU: primary source is the 2024 October WEO; back-casted using growth rates from WDI, UNdata, and 2017 database.
- Public debt stress: identified using an updated version of the database of fiscal crises episodes compiled by Badia, Arbelaez, and Xiang (2022).
- PPP GDP per capita (constant US$): sourced from WDI for 1990-2022 and back-casted to 1970 using Penn World Table, version 10.01.
- Real GDP growth: October 2024 WEO; missing values imputed with WDI and UNdata.
- REER: IMF’s INS database; missing values imputed based on estimates of real exchange rates against the US dollar.
- Total natural resource rents as a share of GDP: World Bank WDI.
- Average US Federal Funds Rate: FRED.
- Net ODA per capita: WDI.
- International reserves: October 2024 WEO, with missing values imputed from WDI and IFS.
- Short-term debt as a share of total reserves: WDI.
- Overall public debt interest payments in US$: GGEI series from October 2024 WEO.
- CPIA index: World Bank’s CPIA database (“IDA resource allocation index (1=low to 6=high)”); missing early 1970s values fitted with a regression model.

### Appendix II — Augmented Bohn Test (overview and findings)
- Baseline Bohn model (AIII.1): pb_t = β0 + β1 g̃_t + β2 ỹ_t + ρ d_{t−1} + ε_t; a positive ρ is sufficient for solvency under reasonable assumptions.
- Limitations of baseline Bohn test for LICs: LICs often on convergence paths with potentially negative interest rate–growth differentials and structural differences in fiscal responsiveness.
- Augmented specification (AIII.2): pb_t = β0 + β1 g̃_t + β2 ỹ_t + ρ d_{t−1} + γ I_{t−1} + δ d_{t−1} I_{t−1} + ε_t, where I_{t−1} are economic indicators determining maximum sustainable public debt-to-GDP ratio and dynamically stable trajectories.
  - In this augmented test, responsiveness of the primary balance to lagged debt is ρ + δ I_{i,t−1}.
  - Statistically significant δ implies the economic indicator I affects the responsiveness of the primary balance to lagged public debt.
- Estimation approach:
  - Panel estimation for 53 LICs over 1970-2023 due to limited per-country observations (ranging from 8 to 24 years).
  - Output and government expenditure gaps (ỹ_{i,t} and g̃_{i,t}) obtained using Hodrick–Prescott filter with smoothing parameter of 100.
  - Serial correlation detected in AIII.2 residuals via Breusch-Godfrey test at the 5 percent level; addressed by estimating an Autoregressive Distributed Lag (ADL) specification (AIII.3) with two lags.
  - Re-running Breusch-Godfrey on AIII.3 shows the null of no serial correlation cannot be rejected.
  - For each indicator I, regression estimated one at a time (levels and interaction with lagged debt), indicators standardized by their standard deviation; standard errors heteroskedasticity-robust and clustered at country level.
- Empirical results from augmented Bohn / ADL:
  - Revenue mobilization (revenue-GDP share), real GDP growth, average US FFR (global risk-free rate), changes in REER, and level of resource dependence are associated with changes in the reactiveness of the primary balance to lagged public debt-to-GDP.
  - Revenue-GDP share: statistically significant positive association with reactiveness of the primary balance to lagged debt.
  - Real GDP growth: positively related to reactiveness.
  - Increases in the US FFR and appreciation of REER: dampen reactiveness.
  - Higher reliance on natural resource rents: suppresses reactiveness.
  - Most proxies for institutional quality not statistically significant, except control of corruption, which tends to lower reactiveness of the primary balance to lagged debt levels.

*Source: Conclusion and relevant appendices of the IMF working paper.*

### Appendix II Table 1. Effect of Institutional Features on Debt Sustainability

### Appendix II Table 1. Effect of Institutional Features on Debt Sustainability

### ADL Specification — Coefficient Estimates and Sample Sizes
- Public Finance
  - Exports-to-GDP Ratio: -0.007 (0.005); 1,217
  - Revenue-to-GDP Ratio: 0.039*** (0.004); 1,351
  - PPG External Debt Servicing (Share of Revenue): 0.002 (0.003); 1,348
  - PPG External Debt Servicing (Share of Exports): -0.009 (0.005); 1,348
  - PPG External Debt (Share of Total Debt): 0.000 (0.003); 1,345
- Macro Indicators
  - Real GDP Growth: 0.007*** (0.001); 1,351
  - Risk-Free Rate (US Federal Funds Rate): -0.018 (0.006); 1,351
  - Real Effective Exchange Rate Depreciation: -0.406*** (0.069); 1,351
- Financial Characteristics
  - Natural Resource Rents-to-GDP Ratio: -0.021** (0.005); 1,254
  - Net ODA Received Per Capita (Log of Current US$): 0.002 (0.009); 1,315
  - Reserves in Months of Imports: -0.033 (0.028); 1,084
  - Short-Term Debt-to-Reserves Ratio: 0.057 (0.021); 1,084
- Institutional Characteristics
  - Control of Corruption: -0.02*** (0.003); 962
  - Political Stability & Absence of Violence: 0.008 (0.005); 967
  - Government Effectiveness: -0.012 (0.004); 960
  - Regulatory Quality: -0.006 (0.005); 960
  - Rule of Law: -0.006 (0.006); 968
  - Voice and Accountability: -0.011 (0.006); 968

### Notes on Inference and Significance
- Standard errors are heteroskedasticity-robust and clustered at the country level.
- Statistical significance is indicated by ***, **, and * at the 1%, 5%, and 10% confidence levels, respectively.

### Appendix III — Synthetic Control Method (Overview)
- Setup and indexing
  - Define a reference LIC and a year t0; consider T years from t_start to t_end composed of T0 pre-benchmark periods and T1 benchmark periods.
  - For each MAC j find t_j = argmin_t |y_t_j − y_t_start_LIC|.
  - Use the subsequent T periods of development time for each MAC.
- Synthetic benchmark construction
  - Observe outcome d_i,t (debt-ratio) and k predictors X_i,t for each MAC in donor pool.
  - Construct synthetic benchmark:
    - d̂_LIC,t = ∑_{j=1}^J ω_j d_j,t
    - where ω_j are time-invariant weights chosen to best resemble pre-benchmark predictor values and debt-to-GDP ratios.
  - Weight selection:
    - ω = argmin_ω ( (∑_{h=1}^{k+1} ν_h (X_h,LIC − ω_1 X_h,MAC1 − … − ω_J X_h,MACJ)^2 )^{1/2} )
    - Choose ν to minimize the mean squared prediction error of the synthetic control benchmark with respect to public debt-to-GDP.
- Rationale
  - This procedure sidesteps direct estimation of dynamically stable public debt levels, which can be volatile for LICs with noisy data.
  - Compare LICs’ debt trajectories to observed experience of similar MACs that did not face public debt stress events over a similar duration.

### Appendix III — Implementation Details
- The SCM constructs a synthetic MAC reproducing predictor values of public debt-to-GDP over the pre-benchmark period.
- Appendix Table 4 (referenced) compares pre-benchmark characteristics of LICs with their synthetic benchmarks and averages of shifted MACs.
- Predictors are sorted by SCM-assigned weight for the 25th percentile LIC; ordering differs for 50th and 75th percentiles and is unrelated to predictor weights for those percentiles.
- Findings from implementation
  - Synthetic benchmarks typically provide a better fit in predictor variables than the average of sample MACs.
  - LIC-specific synthetic benchmarks closely resemble LICs over the pre-benchmark period in debt-to-GDP and key predictor variables.
  - Goodness-of-fit varies across LICs depending on predictor weights.

### Appendix III Table 1 — Pre-Benchmark Differences (Selected entries, percent unless otherwise noted)
- Overall Public Debt (% GDP)
  - 25th Percentile LIC: Δ(LIC − Synth. Unit) = -0.4; Δ(LIC − All MACs1/) = -9.2
  - 50th Percentile LIC: Δ(LIC − Synth. Unit) = 0.1; Δ(LIC − All MACs1/) = -9.7
  - 75th Percentile LIC: Δ(LIC − Synth. Unit) = -0.5; Δ(LIC − All MACs1/) = 13.4
  - Recent 75th Percentile LIC: Δ(LIC − Synth. Unit) = 0.4; Δ(LIC − All MACs1/) = 1.5
- Revenue (% GDP)
  - 25th: -9.3; -11.4
  - 50th: -3.0; 0.6
  - 75th: -6.6; -9.7
  - Recent 75th: 10.4; 6.5
- Net ODA per Capita (log USD)
  - 25th: 0.4; 0.3
  - 50th: 0.9; 1.2
  - 75th: 0.9; 1.0
  - Recent 75th: 2.6; 2.3
- Natural Resource Rents (% GDP)
  - 25th: -7.9; -11.7
  - 50th: -18.6; -8.3
  - 75th: 13.4; 4.3
  - Recent 75th: -2.4; -10.2
- International Reserve Coverage (months of imports)
  - 25th: -0.8; -0.5
  - 50th: -0.3; -0.8
  - 75th: -1.4; -1.2
  - Recent 75th: -2.4; -1.9
- External Debt Servicing (% Exports)
  - 25th: 1.6; -2.3
  - 50th: -3.3; -5.1
  - 75th: 2.1; 5.7
  - Recent 75th: -6.1; -5.5
- US Federal Funds Rate (percentage points)
  - 25th: -2.3; -2.0
  - 50th: -1.2; -0.8
  - 75th: -0.7; -0.9
  - Recent 75th: -2.7; -2.6
- Short-Term Debt (% International Reserves)
  - 25th: 8.7; -5.8
  - 50th: -3.1; -4.0
  - 75th: 246.9; 245.8
  - Recent 75th: 34.8; 37.7
- Share of External in Overall Public Debt
  - 25th: 39.7; 17.1
  - 50th: 35.5; 47.8
  - 75th: 68.3; 62.9
  - Recent 75th: 61.7; 43
- Real GDP growth (percentage points)
  - 25th: -3.4; -1.8
  - 50th: -6.6; -4.6
  - 75th: -2.1; -4.5
  - Recent 75th: -3.4; -3.3
- PPP GDP Per Capita
  - 25th: -0.2; -0.1
  - 50th: -0.4; -0.3
  - 75th: -0.2; -0.4
  - Recent 75th: -0.1; -0.2
- Exports (% GDP)
  - 25th: -14.2; -12.2
  - 50th: 5.9; 14.4
  - 75th: 7.5; -0.4
  - Recent 75th: 143.7; 138.5
- External Debt Servicing (% Revenues excluding Grants)
  - 25th: 3.9; 1.8
  - 50th: -4.7; -6.6
  - 75th: 10.3; 14.4
  - Recent 75th: 1.1; 2.8
- REER Depreciation (+ = Appreciation)
  - 25th: 2.3; 1.1
  - 50th: 0.0; 0.5
  - 75th: 1.1; -0.5
  - Recent 75th: -1.5; -0.7
- World Growth
  - 25th: -0.3; -0.2
  - 50th: -0.2; -0.2
  - 75th: -0.1; -0.1
  - Recent 75th: -0.2; -0.3
- Notes: Predictors are sorted in descending order of the weight ω_h assigned to them in the SCM for the 25th percentile LIC. The ordering is not necessarily the same for the 50th and 75th percentile LICs.
- 1/ Universe of MACs with per capita PPP GDP similar to that of the reference LIC in 2005.

### Appendix III — Robustness Checks
- Vary benchmarking start year t0 across {2014, 2015, 2016}; results do not qualitatively change.
- Re-run analysis dropping predictor variables one-at-a-time; synthetic benchmarks broadly robust to dropping single predictors.
  - Some variation noted when dropping REER depreciation (see Appendix Figure 1).

*IMF WORKING PAPERS Benchmarking Dynamically Stable Public Debt Trajectories for Low-Income Countries — INTERNATIONAL MONETARY FUND*

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026075-source-pdf.pdf_