## ch3annex

## Source details

**Canonical URL:** [ch3annex](https://www.imf.org/-/media/files/publications/weo/2023/april/english/ch3annex.pdf)

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---

### 1. Duration — Debt decomposition methodology and caveats
- Debt decomposition isolates contributions to changes in public debt to GDP, with 푡 as the residual.  
- The residual can include: financial transactions where a government issues debt and uses proceeds to buy assets; changes in price due to market revaluation; exchange rate fluctuations; face value reductions.  
- When a face value reduction is involved, the residual can be decomposed as: 표푡 = −푓푣푟푡 + 표푡푓푣푟, where 푓푣푟푡 is reduction in the face value of debt in percentage of GDP.  
- Caveat: face value reductions may be recorded in primary balance as revenue, depending on whether a country’s statistics in the World Economic Outlook database are recorded according to IMF (2014).

### 1. Duration — Data and sample for decomposition results (Text Figure 3.2)
- Number of country-year observations during reduction episodes:  
  - 320 for 28 AEs from 1979 to 2021  
  - 810 for 83 EMs from 1991 to 2021  
  - 501 for 55 LICs from 1985 to 2021  
- Outliers excluded from calculations include the three largest positive and negative residuals (including Equatorial Guinea, Sudan, and Venezuela) and an outlier with effective interest rate higher than 100 percent.  
- Each bar in Text Figure 3.2 is an unweighted average of the decomposition of changes in debt ratios at the country-year level, averaged over the income-group and reduction episodes. Averages are over unbalanced observations.

### 1. Duration — Structural Vector Autoregressions (SVAR) — data and variables (Online Annex 3.3)
- VARs are estimated country by country on an annual sample of:  
  - 21 AEs (1981-2019)  
  - 37 EMs (1994-2019)5  
- Six variables included in the VAR results reported in the main text:  
  1) growth rate of real GDP (percent)  
  2) growth rate of real government revenues (percent)  
  3) change in primary balance to GDP ratio (percentage points)  
  4) change in the public debt to GDP ratio (percentage points)  
  5) change in effective interest rate (percentage points)  
  6) change in inflation (percentage points)  
- Figures 3.3.4 and 3.3.5 use a 7-variable VAR which uses revenues to GDP and expenditures to GDP separately and drops the primary balance to GDP ratio variable.  
- Indicators refer to general government coverage and were obtained from the World Economic Outlook database for 2002-2019, and from the Historical Public Finance Dataset (HPFD) for 1981-2011. A smooth linear interpolation was applied to link WEO series with HPFD over a 10-year period from 2002 to 2011 for all countries except ESP, SWE and NOR (WEO data available back to 1981).

### 1. Duration — Estimation and identification
- Identification is based on sign restrictions summarized in Table 3.1 in the main text. All sign restrictions are imposed on impact, except sign restrictions on GDP and debt to GDP in the case of the primary balance consolidation shocks, which are imposed one period ahead.  
- The reduced form VAR is estimated with two lags using Bayesian techniques with Minnesota priors, where hyperparameters are chosen to maximize marginal data density. Estimation uses the Empirical macro toolbox of Canova and Ferroni (2021).  
- Impulse responses are computed using inverse variance weights.  
- Contribution of shocks reported in Table 3.2 is computed by summing the absolute value of the contribution of all shocks in the historical decomposition of debt to GDP for years in which debt to GDP declined, and taking medians across countries and over time, separately for AE and EM samples.

### 1. Duration — Complementary VAR results and figures (Online Annex 3.3)
- Annex Figure 3.3.1: response of debt to GDP to a primary balance consolidation shock from a VAR without splitting the shock into successful and unsuccessful components.  
- Annex Figure 3.3.2: impulse response to successful and unsuccessful primary balance consolidation shocks for EMs (analogous to Figure 3.4 for AEs).  
- Annex Figure 3.3.3: implied impulse response in levels of GDP, primary balance to GDP and debt to GDP, based on first-difference estimates.  
- Annex Figures 3.3.4 and 3.3.5: VAR results replacing primary balance to GDP with revenue to GDP and expenditure to GDP separately.  
- Annex Figure 3.3.6: comparison of the contribution of revenues and expenditures to the impact response of primary balance.  
- Annex Figure 3.3.7 (outside VAR): unconditional probability of observing periods of primary balance to GDP improvements and debt ratio declines; bars reveal consolidations are as likely to be accompanied by debt ratio increases as by declines.

### 1. Duration — Fiscal consolidations and debt ratios — simplified arithmetic framing
- Simplifying assumptions: maturity of entire stock of debt fixed to one year; inflation and nominal rates do not change. Framing aims to show qualitative features rather than precise quantification.  
- Definitions and relations:  
  - 훥푙푛퐷푡 = 푟푡 − 푃퐵푡 / 퐷푡−1  
  - 훥푙푛푌푡 = −푚푦 훥푃퐵푡 / 푌푡−1  (where 푚푦 < 0)  
  - Combined: 훥ln(퐷푡/푌푡) = 푟푡 − 푃퐵푡−1 / 퐷푡−1 + 훥푃퐵푡 / 푌푡−1 (푚푦 − 푌푡−1 / 퐷푡−1)  
- Condition for consolidation (훥푃퐵푡 / 푌푡−1) to reduce the debt ratio (assuming constant inflation and effective interest rate):  
  - 푚푦 퐷푡−1 / 푌푡−1 < 1  
- Two takeaways:  
  - The size of the multiplier is a key determinant of whether consolidations reduce debt ratios (consistent with Figure 3.4).  
  - Higher debt ratios tend to mitigate the impact of consolidations in reducing debt ratios, all else equal.  
  - This is reconciled with evidence that the multiplier declines with the level of debt to GDP (Ilzetzki and others (2013); Kirchner and others (2012)), which helps explain why consolidations can be more likely successful when crowding out effects are high (one indicator of high crowding out is the level of Debt to GDP itself).

### 1. Duration — Notes on figures and scaling
- Primary balance shock is scaled to 1 percentage point of GDP on impact on average. Displayed impulse responses are inverse variance weighted means across countries from a Bayesian vector autoregression estimated country by country at annual frequency. X-axis denotes horizon in years. Shaded areas represent the 16th–84th percentile range of the posterior distribution. Sample consists of 21 advanced economies from 1981 to 2019 and 37 emerging market economies from 1991 to 2019.

---

### 2. Emerging Market Economies — Data and sample
- Country-level economic indicators (GDP, general government debt, inflation, exchange rates) are obtained from the WEO database.  
- Narrative fiscal consolidation episodes are identified from contemporaneous policy documents and sources including IMF Article IV Staff Reports, European Commission Assessment of Stability Programmes, OECD Economic Surveys, and country budget documents.  
- Jamaica is removed because of repeated restructuring events since the mid-1970s and their impact on the debt ratio.  
- Final datasets:  
  - 17 AEs between 1978 and 2019.  
  - 13 EMs between 1989 and 2019.  
  - 706 restructuring events spanning 111 EMs and LICs between 1987 and 2021.  
- Restructuring events duration: roughly 80 percent of restructuring events last for a single year (or less); average duration is about 1.4 years.  
- Outcomes (changes in the debt ratio) are winsorized at the 1 percent level.  
- The estimation sample only includes country-year pairs for which at least 5 leads of the outcome variable are available (consistency across horizons).

### 2. Emerging Market Economies — Identification of fiscal consolidations and restructuring
- Fiscal consolidations are identified using a narrative approach based on policymakers’ intentions and contemporaneous documents; episodes are included only if measures were motivated primarily by deficit reduction.  
- Restructuring definition: a sovereign debt restructuring is a debt distressed exchange—an exchange of outstanding sovereign debt instruments under debt distress for new debt instruments and/or cash through a formal renegotiation process, typically involving an NPV loss for creditors.  
- Types of restructuring considered:  
  - Face value reduction (principal/nominal debt reduction).  
  - Debt rescheduling / reprofiling (maturity extension, sometimes with coupon rate reduction).  
- Timing taxonomy:  
  - Preemptive restructurings: implemented with no missed payments or only short delays during renegotiation (no unilateral default).  
  - Post-default restructurings: payments missed unilaterally ahead of negotiations (unilateral default).  
- Coverage of restructuring dataset:  
  - Private external debt restructurings.  
  - Official (bilateral) external debt restructurings (Paris Club and China).  
  - Domestic debt restructurings (1950–2021).  
- Main sources: Asonuma and Trebesch (2016); Horn and all (2022); Paris Club database; IMF (2021); complemented by granular sources (Asonuma, Niepelt and Ranciere (2023), Asonuma and Wright (2022), Cheng and all (2018), Cruces and Trebesch (2013)).

### 2. Emerging Market Economies — Estimation approach: Local projections and AIPW
- Estimator: Augmented Inverse Probability Weighted (AIPW) estimator of Jorda and Taylor (2016).  
- Two-step calculation of average treatment effects (ATE):  
  1. Treatment model (probit) estimates the probability that a country consolidates each year. Predictors include:  
     - 2 lags of GDP growth (Δ GDP t-1, Δ GDP t-2).  
     - 2 lags of the treatment dummy (Treatment t-1).  
     - Global output gap (controls for global economic conditions).  
     - Nominal exchange and inflation rates (controls for changes in the real value of debt).  
     - Initial level of the debt ratio.  
     - Dummy indicating whether the country is undergoing a debt restructuring event.  
  2. Outcome model estimated via local projections:  
     - Δ_h y_c,t = y_c,t+h − y_c,t−1 indicates changes in the debt ratio over horizons h ∈ {0,1,2,3,4,5}.  
     - Regression includes lags of the outcome, lags of the treatment, interactions between treatment and controls (X_c,t), country fixed effects (α_c^h) and year fixed effects (α_t^h).  
     - The specification interacts all control variables with the treatment to allow heterogeneous impacts.  
- ATE formula (as used in the chapter) preserves inverse-probability reweighting plus a bias-adjustment term.  
- Observations with estimated propensity p̂_c,t outside (10^−4,1−10^−4) are excluded to avoid outliers.  
- The estimator is “doubly robust”: consistency if either the treatment or outcome model is correctly specified.

### 2. Emerging Market Economies — Estimating impacts of different restructuring types
- Treatment dummy for restructuring indicates the start year of a restructuring event.  
- Effects of subtypes (e.g., restructurings joint with fiscal consolidation; HIPC & MDRI; with face value reduction) are calculated by restricting the sample to events satisfying those characteristics.  
- To address selection bias for face-value reductions (FVR), a probit predicts the probability of an FVR based on information available before negotiations:  
  - Explanatory variables: debt/GDP, GDP growth, global output gap, inflation, nominal exchange rates, whether the restructuring involves official creditors, HIPC/MDRI eligibility, whether the country is undergoing sequential restructuring events.  
  - An event is classified as likely to involve an FVR if the estimated probability exceeds the median of its distribution.

### 2. Emerging Market Economies — First-stage (treatment) estimation results and diagnostics
- Probit estimation results (Online Annex Table 3.5.1) indicate:  
  - Both fiscal consolidation and restructuring are more likely when GDP growth is lower and global conditions are less favorable.  
  - Lagged treatment (t-1) is highly positive and significant (treatment persistence / sequencing).  
- Selected numeric diagnostics and statistics reported:  
  - Number Observations: 560, 271, 2677 (columns shown in table).  
  - Pseudo R2: 0.354, 0.090, 0.076.  
  - AUROC (area under the receiver operating curve): 0.8706, 0.7597, 0.7141.  
  - Balancing test (Imai and Ratkovic (2014)) p-values: 0.9955, 0.4248, 0.0709.  
- Table coefficients shown (as reported): -0.097***, -0.057, -0.121* (with standard errors in parentheses as in the source).  
- Despite high AUROC values, the distribution of propensity scores exhibits significant overlap between treated and control observations (Online Annex Figure 3.5.1).

### 2. Emerging Market Economies — Impact of restructuring: main results and horizons
- Long-horizon impact (up to 10 years, Annex Figure 3.5.2):  
  - ATEs fluctuate between -8 and -10 percentage points decrease in the debt ratio over long horizons.  
  - Most of the impact of debt restructuring occurs in the first 5 years, and effects are long lasting on average.  
- Figure specifications:  
  - Online Annex Figure 3.5.2 plots the average treatment effect of restructuring on debt to GDP and on GDP growth using AIPW estimation with 90 percent confidence intervals.  
  - X-axis denotes years since the restructuring event starts; sample covers 111 emerging market and developing economies from 1987 to 2021.

### 2. Emerging Market Economies — Additional methodological notes
- Fixed effects are included only in the outcome model; the treatment model (propensity score) uses a simpler specification to avoid estimating a large number of incidental parameters in a probit model.  
- Winsorization at the 1 percent level is applied to avoid outliers in the outcome variable (changes in the debt ratio).  
- Sample consistency across horizons requires y_c,t+h to be observed for all h ∈ {0,1,2,3,4,5}.

### 2. Emerging Market Economies — Case studies and illustrations
- Online Annex Figure 3.7.1 presents case studies on restructurings with durable debt reductions (time series plotted in percent of GDP, with grey shaded areas denoting the duration of restructuring events).  
- Notes in the case studies:  
  - “Residuals” includes other debt-creating flows.  
  - Cumulative debt service relief corresponds to that provided at only domestic debt restructuring in 2013; domestic debt restructuring in 2010 is not available.  
  - A non-Paris Club bilateral (Venezuela) debt restructuring occurred in 2015 (noted in the figure caption).

---

### 1. Economic and FiscalConditions, Seychelles — Public debt and indicators
- Public debt (figure label present; no numeric values provided in the source excerpt).  
- Associated series indicated: Primary balance (percent, right scale); Real GDP growth (percent, right scale); Cumulative debt service relief (percent, right scale).

### 1. Economic and FiscalConditions, Seychelles — Fiscal indicators and macroeconomic links
- Primary balance (percent, right scale) — presented as an accompanying series to public debt.  
- Real GDP growth (percent, right scale) — presented as an accompanying series to public debt.  
- Cumulative debt service relief (percent, right scale) — presented as an accompanying series to public debt.

*Source: ch3annex - 1. Duration; 2. Emerging Market Economies; 1. Economic and FiscalConditions, Seychelles, International Monetary Fund | April 2023*

### 1. Duration

### 1. Duration

### Debt decomposition methodology and caveats
- The debt decomposition isolates contributions to changes in public debt to GDP, with 푡 as the residual.  
- The residual can include: financial transactions where a government issues debt and uses proceeds to buy assets; changes in price due to market revaluation; exchange rate fluctuations; face value reductions.  
- When a face value reduction is involved, the residual can be decomposed as: 표푡 = −푓푣푟푡 + 표푡푓푣푟, where 푓푣푟푡 is reduction in the face value of debt in percentage of GDP.  
- Caveat: face value reductions may be recorded in primary balance as revenue, depending on whether a country’s statistics in the World Economic Outlook database are recorded according to IMF (2014).

### Data and sample for decomposition results (Text Figure 3.2)
- Number of country-year observations during reduction episodes:  
  - 320 for 28 AEs from 1979 to 2021  
  - 810 for 83 EMs from 1991 to 2021  
  - 501 for 55 LICs from 1985 to 2021  
- Outliers excluded from calculations include the three largest positive and negative residuals (including Equatorial Guinea, Sudan, and Venezuela) and an outlier with effective interest rate higher than 100 percent.  
- Each bar in Text Figure 3.2 is an unweighted average of the decomposition of changes in debt ratios at the country-year level, averaged over the income-group and reduction episodes. Averages are over unbalanced observations.

### Structural Vector Autoregressions (SVAR) — data and variables (Online Annex 3.3)
- VARs are estimated country by country on an annual sample of:  
  - 21 AEs (1981-2019)  
  - 37 EMs (1994-2019)5  
- Six variables included in the VAR results reported in the main text:  
  1) growth rate of real GDP (percent)  
  2) growth rate of real government revenues (percent)  
  3) change in primary balance to GDP ratio (percentage points)  
  4) change in the public debt to GDP ratio (percentage points)  
  5) change in effective interest rate (percentage points)  
  6) change in inflation (percentage points)  
- Figures 3.3.4 and 3.3.5 use a 7-variable VAR which uses revenues to GDP and expenditures to GDP separately and drops the primary balance to GDP ratio variable.  
- Indicators refer to general government coverage and were obtained from the World Economic Outlook database for 2002-2019, and from the Historical Public Finance Dataset (HPFD) for 1981-2011. A smooth linear interpolation was applied to link WEO series with HPFD over a 10-year period from 2002 to 2011 for all countries except ESP, SWE and NOR (WEO data available back to 1981).

### Estimation and identification
- Identification is based on sign restrictions summarized in Table 3.1 in the main text. All sign restrictions are imposed on impact, except sign restrictions on GDP and debt to GDP in the case of the primary balance consolidation shocks, which are imposed one period ahead.  
- The reduced form VAR is estimated with two lags using Bayesian techniques with Minnesota priors, where hyperparameters are chosen to maximize marginal data density. Estimation uses the Empirical macro toolbox of Canova and Ferroni (2021).  
- Impulse responses are computed using inverse variance weights.  
- Contribution of shocks reported in Table 3.2 is computed by summing the absolute value of the contribution of all shocks in the historical decomposition of debt to GDP for years in which debt to GDP declined, and taking medians across countries and over time, separately for AE and EM samples.

### Complementary VAR results and figures (Online Annex 3.3)
- Annex Figure 3.3.1: response of debt to GDP to a primary balance consolidation shock from a VAR without splitting the shock into successful and unsuccessful components.  
- Annex Figure 3.3.2: impulse response to successful and unsuccessful primary balance consolidation shocks for EMs (analogous to Figure 3.4 for AEs).  
- Annex Figure 3.3.3: implied impulse response in levels of GDP, primary balance to GDP and debt to GDP, based on first-difference estimates.  
- Annex Figures 3.3.4 and 3.3.5: VAR results replacing primary balance to GDP with revenue to GDP and expenditure to GDP separately.  
- Annex Figure 3.3.6: comparison of the contribution of revenues and expenditures to the impact response of primary balance.  
- Annex Figure 3.3.7 (outside VAR): unconditional probability of observing periods of primary balance to GDP improvements and debt ratio declines; bars reveal consolidations are as likely to be accompanied by debt ratio increases as by declines.

### Fiscal consolidations and debt ratios — simplified arithmetic framing
- Simplifying assumptions: maturity of entire stock of debt fixed to one year; inflation and nominal rates do not change. Framing aims to show qualitative features rather than precise quantification.  
- Definitions and relations:  
  - 훥푙푛퐷푡 = 푟푡 − 푃퐵푡 / 퐷푡−1  
  - 훥푙푛푌푡 = −푚푦 훥푃퐵푡 / 푌푡−1  (where 푚푦 < 0)  
  - Combined: 훥ln(퐷푡/푌푡) = 푟푡 − 푃퐵푡−1 / 퐷푡−1 + 훥푃퐵푡 / 푌푡−1 (푚푦 − 푌푡−1 / 퐷푡−1)  
- Condition for consolidation (훥푃퐵푡 / 푌푡−1) to reduce the debt ratio (assuming constant inflation and effective interest rate):  
  - 푚푦 퐷푡−1 / 푌푡−1 < 1  
- Two takeaways:  
  - The size of the multiplier is a key determinant of whether consolidations reduce debt ratios (consistent with Figure 3.4).  
  - Higher debt ratios tend to mitigate the impact of consolidations in reducing debt ratios, all else equal.  
  - This is reconciled with evidence that the multiplier declines with the level of debt to GDP (Ilzetzki and others (2013); Kirchner and others (2012)), which helps explain why consolidations can be more likely successful when crowding out effects are high (one indicator of high crowding out is the level of Debt to GDP itself).

### Notes on figures and scaling
- Primary balance shock is scaled to 1 percentage point of GDP on impact on average. Displayed impulse responses are inverse variance weighted means across countries from a Bayesian vector autoregression estimated country by country at annual frequency. X-axis denotes horizon in years. Shaded areas represent the 16th–84th percentile range of the posterior distribution. Sample consists of 21 advanced economies from 1981 to 2019 and 37 emerging market economies from 1991 to 2019.

*Source: ch3annex - 1. Duration, International Monetary Fund | April 2023*

### 2. Emerging Market Economies

### 2. Emerging Market Economies

### Data and sample
- Country-level economic indicators (GDP, general government debt, inflation, exchange rates) are obtained from the WEO database.
- Narrative fiscal consolidation episodes are identified from contemporaneous policy documents and sources including IMF Article IV Staff Reports, European Commission Assessment of Stability Programmes, OECD Economic Surveys, and country budget documents.
- Jamaica is removed because of repeated restructuring events since the mid-1970s and their impact on the debt ratio.
- Final datasets:
  - 17 AEs between 1978 and 2019.
  - 13 EMs between 1989 and 2019.
  - 706 restructuring events spanning 111 EMs and LICs between 1987 and 2021.
- Restructuring events duration: roughly 80 percent of restructuring events last for a single year (or less); average duration is about 1.4 years.
- Outcomes (changes in the debt ratio) are winsorized at the 1 percent level.
- The estimation sample only includes country-year pairs for which at least 5 leads of the outcome variable are available (consistency across horizons).

### Identification of fiscal consolidations and restructuring
- Fiscal consolidations are identified using a narrative approach based on policymakers’ intentions and contemporaneous documents; episodes are included only if measures were motivated primarily by deficit reduction.
- Restructuring definition: a sovereign debt restructuring is a debt distressed exchange—an exchange of outstanding sovereign debt instruments under debt distress for new debt instruments and/or cash through a formal renegotiation process, typically involving an NPV loss for creditors.
- Types of restructuring considered:
  - Face value reduction (principal/nominal debt reduction).
  - Debt rescheduling / reprofiling (maturity extension, sometimes with coupon rate reduction).
- Timing taxonomy:
  - Preemptive restructurings: implemented with no missed payments or only short delays during renegotiation (no unilateral default).
  - Post-default restructurings: payments missed unilaterally ahead of negotiations (unilateral default).
- Coverage of restructuring dataset:
  - Private external debt restructurings.
  - Official (bilateral) external debt restructurings (Paris Club and China).
  - Domestic debt restructurings (1950–2021).
- Main sources: Asonuma and Trebesch (2016); Horn and all (2022); Paris Club database; IMF (2021); complemented by granular sources (Asonuma, Niepelt and Ranciere (2023), Asonuma and Wright (2022), Cheng and all (2018), Cruces and Trebesch (2013)).

### Estimation approach: Local projections and AIPW
- Estimator: Augmented Inverse Probability Weighted (AIPW) estimator of Jorda and Taylor (2016).
- Two-step calculation of average treatment effects (ATE):
  1. Treatment model (probit) estimates the probability that a country consolidates each year. Predictors include:
     - 2 lags of GDP growth (Δ GDP t-1, Δ GDP t-2).
     - 2 lags of the treatment dummy (Treatment t-1).
     - Global output gap (controls for global economic conditions).
     - Nominal exchange and inflation rates (controls for changes in the real value of debt).
     - Initial level of the debt ratio.
     - Dummy indicating whether the country is undergoing a debt restructuring event.
  2. Outcome model estimated via local projections:
     - Δ_h y_c,t = y_c,t+h − y_c,t−1 indicates changes in the debt ratio over horizons h ∈ {0,1,2,3,4,5}.
     - Regression includes lags of the outcome, lags of the treatment, interactions between treatment and controls (X_c,t), country fixed effects (α_c^h) and year fixed effects (α_t^h).
     - The specification interacts all control variables with the treatment to allow heterogeneous impacts.
- ATE formula (as used in the chapter) preserves inverse-probability reweighting plus a bias-adjustment term.
- Observations with estimated propensity p̂_c,t outside (10^−4,1−10^−4) are excluded to avoid outliers.
- The estimator is “doubly robust”: consistency if either the treatment or outcome model is correctly specified.

### Estimating impacts of different restructuring types
- Treatment dummy for restructuring indicates the start year of a restructuring event.
- Effects of subtypes (e.g., restructurings joint with fiscal consolidation; HIPC & MDRI; with face value reduction) are calculated by restricting the sample to events satisfying those characteristics.
- To address selection bias for face-value reductions (FVR), a probit predicts the probability of an FVR based on information available before negotiations:
  - Explanatory variables: debt/GDP, GDP growth, global output gap, inflation, nominal exchange rates, whether the restructuring involves official creditors, HIPC/MDRI eligibility, whether the country is undergoing sequential restructuring events.
  - An event is classified as likely to involve an FVR if the estimated probability exceeds the median of its distribution.

### First-stage (treatment) estimation results and diagnostics
- Probit estimation results (Online Annex Table 3.5.1) indicate:
  - Both fiscal consolidation and restructuring are more likely when GDP growth is lower and global conditions are less favorable.
  - Lagged treatment (t-1) is highly positive and significant (treatment persistence / sequencing).
- Selected numeric diagnostics and statistics reported:
  - Number Observations: 560, 271, 2677 (columns shown in table).
  - Pseudo R2: 0.354, 0.090, 0.076.
  - AUROC (area under the receiver operating curve): 0.8706, 0.7597, 0.7141.
  - Balancing test (Imai and Ratkovic (2014)) p-values: 0.9955, 0.4248, 0.0709.
- Table coefficients shown (as reported):
  - Example coefficients: -0.097***, -0.057, -0.121* (with standard errors in parentheses as in the source).
- Despite high AUROC values, the distribution of propensity scores exhibits significant overlap between treated and control observations (Online Annex Figure 3.5.1).

### Impact of restructuring: main results and horizons
- Long-horizon impact (up to 10 years, Annex Figure 3.5.2):
  - ATEs fluctuate between -8 and -10 percentage points decrease in the debt ratio over long horizons.
  - Most of the impact of debt restructuring occurs in the first 5 years, and effects are long lasting on average.
- Figure specifications:
  - Online Annex Figure 3.5.2 plots the average treatment effect of restructuring on debt to GDP and on GDP growth using AIPW estimation with 90 percent confidence intervals.
  - X-axis denotes years since the restructuring event starts; sample covers 111 emerging market and developing economies from 1987 to 2021.

### Additional methodological notes
- Fixed effects are included only in the outcome model; the treatment model (propensity score) uses a simpler specification to avoid estimating a large number of incidental parameters in a probit model.
- Winsorization at the 1 percent level is applied to avoid outliers in the outcome variable (changes in the debt ratio).
- Sample consistency across horizons requires y_c,t+h to be observed for all h ∈ {0,1,2,3,4,5}.

### Case studies and illustrations
- Online Annex Figure 3.7.1 presents case studies on restructurings with durable debt reductions (time series plotted in percent of GDP, with grey shaded areas denoting the duration of restructuring events).
- Notes in the case studies:
  - “Residuals” includes other debt-creating flows.
  - Cumulative debt service relief corresponds to that provided at only domestic debt restructuring in 2013; domestic debt restructuring in 2010 is not available.
  - A non-Paris Club bilateral (Venezuela) debt restructuring occurred in 2015 (noted in the figure caption).

*Source: ch3annex - 2. Emerging Market Economies (PDF chapter content provided).*

### 1. Economic and FiscalConditions, Seychelles

### 1. Economic and FiscalConditions, Seychelles

### Public debt
- Public debt (figure label present; no numeric values provided in the source excerpt).
- Associated series indicated: Primary balance (percent, right scale); Real GDP growth (percent, right scale); Cumulative debt service relief (percent, right scale).

### Fiscal indicators and macroeconomic links
- Primary balance (percent, right scale) — presented as an accompanying series to public debt.
- Real GDP growth (percent, right scale) — presented as an accompanying series to public debt.
- Cumulative debt service relief (percent, right scale) — presented as an accompanying series to public debt.

*Source: ch3annex - 1. Economic and FiscalConditions, Seychelles (PDF).*

---


_Source: https://www.imf.org/-/media/files/publications/weo/2023/april/english/ch3annex.pdf_