## wp17110

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### I. Objectives and methodological contribution
- SDGs launched in September 2015 expand objectives from 8 goals and 18 targets to 17 goals and 169 targets and require significant additional financing.
- Prior estimate: Schmidt-Traub (2015) — average annual investment increase required in low-income countries (LICs) could reach up to $400 billion (or 50 percent of their GDP).
- New metric of fiscal space for LICs:
  - Safe debt defined by three criteria: (1) government solvency with a high probability; (2) accounting for macroeconomic and fiscal shocks and their correlation; and (3) feasibility of policy paths to return to safe debt levels after shocks.
  - LIC-specific features accounted for: (1) evolving financing mix; (2) financing constraints; and (3) exposure to terms of trade and exchange rate shocks.
  - Adapts stochastic frameworks to data-constrained LIC environments and allows for materialization of tail risks.
- Illustrative simulation findings:
  - Under benign conditions, fiscal space may be in the double digits but insufficient to meet SDG-related spending needs.
  - Accounting for uncertainty in commodity prices and exchange rates yields starker results.
  - A shift away from concessional borrowing can severely limit fiscal space, especially if real exchange rate appreciation reverses or financial conditions tighten.
  - Improving public investment efficiency and domestic revenue mobilization can narrow the spending gap but would require major efforts relative to recent trends.

### II. Stylized facts about LICs relevant for fiscal space
- Stylized fact 1: low public debt but increasing fiscal deficits
  - Post-debt relief public debt ratios declined to 23 percent of GDP by 2008.
  - Median real exchange rate appreciation vis-a-vis the U.S. dollar (average for 2005–14): 2 percent; mineral exporters 3⅓ percent; non-mineral exporters 1⅔ percent.
  - Since 2009 public debt began edging up driven by widening fiscal deficits from scaling up public investment, counter-cyclical policies, and later lower commodity prices and less-supportive global environment.
- Stylized fact 2: decreasing reliance on concessional financing
  - Share of concessional loans to total debt: around 65 percent in 2001, 40 percent by 2014.
  - Cumulative Eurobond issuance since 2007: US$41 billion (majority during 2010–14).
  - Real interest rates on non-concessional loans on average 230bps above those of concessional loans.
- Stylized fact 3: high macroeconomic volatility and relatively low financial depth
  - LICs experienced high volatility in terms of trade and real exchange rate; growth volatility was relatively lower than in advanced and emerging market economies.
  - Revenues fluctuated sharply, partly due to grant inflows and commodity price swings.
  - Under-developed domestic financial markets constrain funding options.
- Stylized fact 4: contingent liabilities as fiscal risk
  - Contingent liabilities may be explicit or implicit; data scarce—only six out of 28 countries in the sample disclose some (non-exhaustive) information.
  - For the sample, contingent liabilities have ranged between 0.7 and 14 percent of GDP, with highest costs from banking crises.

### III. Data, sample, and key quantitative highlights
- Sample and data sources:
  - Sample comprises 28 LICs for many figures; fragile and small states excluded.
  - Figures use IMF WEO, World Bank International Debt Statistics, Debt Sustainability Analysis Database, and IMF staff estimates.
- Selected key figures (preserved exactly):
  - Estimated incremental annual investment needs, average for 2015–30 (Billions, in 2013 USD): LICs 181; LMICs 473.
  - Post-debt relief public debt ratio among LICs: 23 percent of GDP by 2008.
  - Median real exchange rate appreciation vis-a-vis the U.S. dollar (average for 2005–14): 2 percent; mineral exporters 3⅓ percent; non-mineral exporters 1⅔ percent.
  - Share of concessional loans to total debt: around 65 percent in 2001, 40 percent by 2014.
  - Cumulative Eurobond issuance since 2007: US$41 billion.
  - Average real interest rate differential between non-concessional and concessional loans: 230bps.
  - Range of contingent liabilities in sample LICs: between 0.7 and 14 percent of GDP.
  - Sample size for many series and figures: 28 LICs.
  - Average annual residual SFA in sample: 3.2 percent of GDP.
  - Median annual residuals: 2¼ percent of GDP for mineral producers; 1¾ percent of GDP for non-mineral producers.
  - Historical min and max SFA values: -68.8 percent of GDP and 58.4 percent of GDP respectively.
  - SFA cap used in simulations: implicitly set at 3 percent of GDP.

### IV. Methodology summary: debt limits, safe debt, stochastic simulations
- Conceptual distinctions:
  - Debt limit (ceiling): level above which debt becomes unsustainable (abstracting from liquidity) — proxied by IMF/World Bank DSF thresholds for LICs.
  - Safe debt: level that accommodates an increase in debt from shocks without breaching the debt limit.
  - Fiscal space = safe debt − current debt.
- Practical identification:
  - Use DSF thresholds (CPIA-based): 49 percent of GDP (low capacity), 62 percent of GDP (medium capacity), and 75 percent of GDP (high capacity).
  - Note: DSF last reviewed in 2012; thresholds subject to change.
- Debt dynamics and fiscal reaction:
  - Debt equation components preserved: d (debt-to-GDP), g (real growth), α_i^d, α_i^f, β_i^C, β_i^NC, r_it^d, r_it^f, r_it^C, r_it^NC, Δε (real exchange rate depreciation), and Stock-flow adjustments (SFA) as proxy for contingent liabilities.
  - Primary balance pb_it() = f(X, ε); fiscal reaction function estimated on a panel of 27 LICs.
  - Fiscal capacity ceiling on primary balance introduced to keep reaction function plausible.
- Stochastic approach:
  - Follows Celasun, Debrun, and Ostry (2007): combines fiscal policy shocks, budget sensitivity to macro/financial developments, and direct macro shocks to produce many debt trajectories over a six-year horizon.
  - Fan charts give probability of exceeding debt ceiling for a starting debt level.
  - Safe debt found iteratively so probability of exceeding ceiling under adverse shocks is below 5 percent (95 percent safety).
- Shock generation and tail risk:
  - Country-specific multivariate normal distributions calibrated around historical means; alternative Student’s t-distribution used to capture fatter tails (degrees of freedom v set to 4 for simulations).
  - Simulation draws N = 2000.
  - For multivariate t, smaller v increases tail fatness; special case v = 1 gives multivariate Cauchy.
  - Matlab sampling procedure described for converting normalized draws to real data.

### V. Empirical estimation of fiscal behavior and robustness
- Fiscal reaction function estimation:
  - Unbalanced panel of 27 LICs over 2003–13.
  - Baseline estimator: System GMM; baseline regressors include lagged primary balance, lagged gross public debt, TOT gap interacted with mineral/non-mineral dummies, external disbursements, debt relief dummy.
  - Baseline (Table 1 Specification (1)) notable coefficients and diagnostics (preserved exactly):
    - Lagged primary balance: 0.125 (0.048)***.
    - Lagged debt (LD): 0.009 (0.012).
    - TOT gap (mineral exporters): 0.094 (0.049)*.
    - TOT gap (non-mineral exporters): -0.021 (0.024).
    - External disbursements: -0.397 (0.238)*.
    - Debt relief dummy: 1.419 (0.71)**.
    - AR(2) test p-value: 0.377.
    - Hansen test p-value: 0.335.
    - Observations: 292; Countries: 27; Years per country (avge.): 10.81.
- Robustness checks (GLS, alternative specifications, sequential country omission) — key robust findings:
  - Persistence of primary balance confirmed.
  - Lagged debt term statistically insignificant under baseline GMM but small, positive and statistically significant under GLS.
  - Terms of trade gap significant for mineral exporters.
  - External disbursements coefficient negative and less than one in absolute value across specifications → reductions in external financing cannot be fully offset by increases in domestic funding.
  - No consistent evidence that fiscal policy is used as a countercyclical tool (output gap often insignificant under GMM).

### VI. Baseline results and sensitivity to macroeconomic uncertainty
- Simulation sample for results: 26 LICs (data availability).
- Debt ceilings used: CPIA-based DSF thresholds (49 percent, 62 percent, 75 percent of GDP by capacity).
- Baseline fiscal space estimates:
  - Median fiscal space up to 16 percent of GDP for full sample.
  - Space for mineral exporters more than 5 percentage points of GDP below other LICs.
  - Implied safety margins below debt ceilings range from 7 to 10 percent of GDP.
  - All results use 5 percent probability of breaching threshold (95 percent safety). Example sensitivity: assuming a 20 percent probability of breaching threshold, average fiscal space increases to 19 percent of GDP.
- Alternative and adverse scenarios:
  - Longer sample period (starting as early as 1996): dispersion of macro shocks higher → estimated fiscal space reduced by about a third; impact severe for mineral exporters.
  - Student’s t-distribution (fat tails): fiscal space up to 18 percent below baseline.
  - Persistent negative terms-of-trade gap of 15 percent: for mineral exporters fiscal space can turn negative (six major commodity producers experienced shocks at least as large about 20 percent of the time since 1970).

### VII. Financing mix, exchange rate, and interest rate shocks — simulated impacts
- Financing-mix substitutions:
  - Replacing half of concessional loans with non-concessional external financing results in a significant decline in fiscal space, particularly among non-mineral exporters where the drop is close to 25 percent.
  - Replacing external with domestic financing (keeping concessional share constant) has limited impact for non-mineral exporters and can increase fiscal space for mineral exporters.
  - Switch to external financing combined with real depreciation can shrink fiscal space to as low as 2 percent of GDP.
- Interest rate and exchange rate scenarios:
  - Assuming average annual real depreciation of 4 percent (with financing mix as given) reduces fiscal space up to 72 percent.
  - If relative costs of non-concessional sources increase from 100 bps to 350 bps (real exchange rate constant), fiscal space could plunge by more than 70 percent.
  - Under same increase in relative costs, fiscal space can turn negative if real exchange rate depreciates by 3 percent or more.
  - Generic-country simulation parameters: share domestic to foreign debt = 50 percent; CL to NCL in foreign financing mix = 40 percent.
- Key numeric parameters and thresholds preserved:
  - Interest differential shock example: increase from 100 bps to 350 bps.
  - Real depreciation examples: 3 percent and 4 percent average annual.

### VIII. Policy scenarios for expanding fiscal space
- Contextual benchmark: SDG incremental annual spending needs estimated around 30 percent of GDP.
- Public investment scaling-up:
  - Fiscal multipliers considered: 1.2 (higher efficiency) and 0.6 (lower efficiency).
  - Payoffs for higher efficiency are almost 80 percent larger than for lower efficiency.
  - Empirical suggestion: productivity of public capital in LICs is significantly higher than marginal costs of funds under normal financing conditions.
  - Caveats: results do not account for country-specific efficiency, absorption capacity, or crowding-out of private investment.
- Domestic revenue mobilization (DRM):
  - Revenues in non-mineral exporters increased by 2½ percent of GDP in 2010–15 relative to 2005–10.
  - Econometric evidence: primary balance increases by 0.2 percent of GDP for every one percentage point increase of revenues.
  - If recent trend continues over next five years, primary balance would improve by about ½ percent of GDP.
  - Scenario combining remaining additional revenue spent on high-efficiency public investment (multiplier 1.2) could increase fiscal space by as much as six percent of GDP.
  - Conclusion: maintaining DRM at recent trends will barely meet SDG-related spending needs in many countries — more ambitious DRM required.

### IX. Results under alternative fiscal-behavior assumptions
- Two alternatives:
  1. Fiscal policy responds to changes in debt (positive coefficient on lagged debt).
  2. Primary balance set at debt-stabilizing level as of 2014.
- Outcomes:
  - Debt-stabilizing assumption results in lowest primary deficits over forecast horizon — about 55 percent below baseline.
  - Improved fiscal performance under alternatives increases fiscal space:
    - About 20 percent higher for mineral exporters.
    - About 10 percent higher (about half of mineral exporters’ gain) for other LICs.

### X. Conclusions, policy implications, and caveats
- Main conclusions:
  - Fiscal policy in LICs driven more by access to financing than by cyclical considerations; exchange rates and terms of trade are major volatility sources.
  - Fiscal space varies widely with uncertainty; under benign scenarios fiscal space can be double digits but remains insufficient for SDG needs.
  - Severe historical shocks could lower fiscal space by about a third; large commodity price swings could wipe out fiscal space for mineral exporters.
  - Fiscal space could shrink by a factor of eight if financing mixes shift away from concessional loans while real exchange rates reverse recent appreciation.
- Policy implications:
  - Fiscal space assessments must account for endogenous fiscal responses, evolving financing mix, and exposure to terms-of-trade and exchange rate shocks including tail risks.
  - Policies to expand or protect fiscal space:
    - Improve public investment efficiency to raise growth dividends and tax potential.
    - Strengthen domestic revenue mobilization to increase budget predictability.
    - Carefully manage financing composition given higher cost/volatility of non-concessional and domestic financing.
    - Preserve concessional financing as a major funding source, especially if global financing conditions tighten.
- Caveats and research needs:
  - Debt limits are taken as given (DSF thresholds) and may not fully reflect solvency considerations, though they influence creditor behavior.
  - Framework does not account for assets (notably in resource-rich countries) and uses deterministic policy scenarios.
  - Integrating framework into a DSGE model proposed for future research.

*Source: wp17110 (excerpt).*

### References ________________________________________________________________35

### wp17110 - References ________________________________________________________________35

### I. Introduction: objectives and methodological contribution
- The Sustainable Development Goals (SDGs) launched in September 2015 set ambitious objectives for 2030 and are broader than the Millennium Development Goals (MDGs), expanding from 8 goals and 18 targets to 17 goals and 169 targets.
- Significant additional financing will be required for developing countries to meet the SDGs; Schmidt-Traub (2015) estimated that the average annual investment increase required in low-income countries (LICs) could reach up to $400 billion (or 50 percent of their GDP).
- The paper develops a new metric of fiscal space in LICs that:
  - Defines a safe debt level based on three criteria: (1) government solvency with a high probability; (2) accounting for macroeconomic and fiscal shocks and their correlation; and (3) feasibility of policy paths to return to safe debt levels after shocks.
  - Accounts for LIC-specific features: (1) evolving financing mix; (2) financing constraints; and (3) exposure to terms of trade and exchange rate shocks.
  - Adapts stochastic frameworks to data-constrained LIC environments and allows for the materialization of tail risks.
- Illustrative simulations indicate:
  - Under benign conditions, fiscal space in LICs may be in the double digits, but insufficient to meet SDG-related spending needs.
  - Accounting for uncertainty in commodity prices and exchange rates yields starker results.
  - A shift away from concessional borrowing can severely limit fiscal space, especially if real exchange rate appreciation reverses or financial conditions tighten.
  - Improving public investment efficiency and domestic revenue mobilization can narrow the spending gap but would require major efforts relative to recent trends.

### II. Stylized facts about LICs relevant for fiscal space assessment
- Stylized fact 1: low public debt but increasing fiscal deficits
  - Post-debt relief, public debt ratios declined among LICs to 23 percent of GDP by 2008.
  - Favorable macro conditions included largely negative interest-growth differentials and median real exchange rate appreciation vis-a-vis the U.S. dollar of 2 percent (3⅓ percent for mineral exporters and 1⅔ percent for non-mineral exporters).
  - Since 2009, public debt began edging up driven by widening fiscal deficits due to scaling up of public investment, counter-cyclical policies post-global financial crisis, and later by lower commodity prices and a less-supportive global environment.
- Stylized fact 2: decreasing reliance on concessional financing
  - The share of concessional loans to total debt declined from around 65 percent in 2001 to 40 percent by 2014.
  - Cumulative Eurobond issuance since 2007 reached US$41 billion, with the majority issued during 2010–14.
  - Real interest rates on non-concessional loans are on average 230bps above those of concessional loans.
- Stylized fact 3: high macroeconomic volatility and relatively low financial depth
  - Over the last decade, LICs experienced high macroeconomic volatility in some dimensions: particularly volatile terms of trade and real exchange rate; growth volatility was relatively lower than in advanced and emerging market economies.
  - Revenues have fluctuated sharply, partly due to grant inflows and commodity price swings.
  - Under-developed domestic financial markets constrain funding options; growth outlooks are clouded, especially for mineral exporters.
- Stylized fact 4: contingent liabilities as a source of fiscal risks
  - Contingent liabilities can be explicit (contractual) or implicit (political pressures to assume costs of defaults/arrears from SOEs, banking crises, sub-national entities, strategic private enterprises, and natural disaster recovery).
  - Data on contingent liabilities is scarce; only six out of 28 countries in the sample disclose some (non-exhaustive) information on contingent liabilities.
  - For the sample of LICs, contingent liabilities have ranged between 0.7 and 14 percent of GDP in the recent past, with the highest costs stemming from banking crises.

### III. Data and sample notes (as summarized)
- The sample comprises 28 LICs for many of the figures and analyses; fragile and small states were excluded from the LIC sample due to data constraints.
- Figures referenced use sources including IMF, World Economic Outlook; World Bank's International Debt Statistics; Debt Sustainability Analysis Database; and IMF staff estimates.

### IV. Key quantitative highlights (preserve reported figures exactly)
- Estimated incremental annual investment needs, average for 2015–30 (Billions, in 2013 USD): LICs 181; LMICs 473; Private, commercial financing and Public financing are components shown in Figure 1.
- Post-debt relief public debt ratio among LICs: 23 percent of GDP by 2008.
- Median real exchange rate appreciation vis-a-vis the U.S. dollar (average for 2005–14): 2 percent; mineral exporters 3⅓ percent; non-mineral exporters 1⅔ percent.
- Share of concessional loans to total debt: around 65 percent in 2001, 40 percent by 2014.
- Cumulative Eurobond issuance since 2007: US$41 billion.
- Average real interest rate differential between non-concessional and concessional loans: 230bps.
- Range of contingent liabilities in sample LICs: between 0.7 and 14 percent of GDP.
- Sample size for many series and figures: 28 LICs.

### V. Policy-relevant implications highlighted
- Fiscal space assessments for LICs must incorporate:
  - The endogenous response of fiscal policy to macro shocks.
  - The evolving financing mix and potential move away from concessional financing.
  - Exposure to terms-of-trade and exchange rate shocks and materialization of tail risks.
- Policy actions that can expand fiscal space or mitigate constraints include:
  - Improving public investment efficiency to raise growth dividends and tax collection potential.
  - Domestic revenue mobilization to increase predictability of budgetary resources.
  - Careful management of financing composition given higher costs and volatility of non-concessional and domestic financing.
- Even with improvements in efficiency and revenue mobilization, major efforts relative to recent trends are required to close the gap between fiscal space and SDG-related spending needs.

*Source: wp17110 - References ________________________________________________________________35 (excerpt)*

### Appendix I.

### Appendix I.

### Financial depth and contingent liabilities (figures)
- Figure 10: Financial Depth, 2015 (Ratio of M2 to GDP, percent). Source: IMF, World Economic Outlook. AE: advanced economies, EM: emerging market economies, LIC: low-income countries. The sample for LICs comprises 28 countries.
- Figure 11: Main Sources of Contingent Liabilities in Low-income Countries.
- Figure 12: Materialization of Contingent Liabilities: Some Examples (Percent of GDP). Source: IMF staff reports, MEFMI (2013); and Laeven and Valencia (2012).
  - Numeric entries shown in the figure: 0.9; 1.2; 4.5; 5.3; 12.0; 3.0; 0.6; 1.2; 1.4; 3.7; 4.2; 6.0; 10.0; 11.8; 13.6; 03691215 (preserved verbatim as in source).
  - Specific materializations listed with associated values and cases:
    - Loan guarantees for SOEs (Malawi, 2012-14).
    - Agri. loan guarantees (Honduras, 2003).
    - Transfers/loan guarantees to SOEs (Gambia, 2014).
    - Ebola-related outlays (Liberia, 2015-2016) — note: 3.2 percent of GDP for 2015 and 2.1 percent of GDP for 2016. The amount covers only the cost that the government acknowledges.
    - Guarantees on private infra. project (Guinea, 2015).
    - Transfers to SOEs (Burkina Faso, 2013).
    - Transfers to SOE (Gambia, 2014).
    - Natural disaster response (Mauritania, 2012).
    - Resolution of banking crisis (Zambia, 1995-1998).
    - Resolution of banking crisis (Kazakhstan, 2008).
    - Resolution of banking crisis (Mongolia, 2008).
    - Resolution of banking crisis (Bolivia, 1994).
    - Resolution of banking crisis (Vietnam, 1997).
    - Resolution of banking crisis (Nigeria, 2011).
    - Resolution of banking crisis (Nicaragua, 2000).
  - Implicit vs. explicit distinctions are indicated in the figure.

### Materialization of contingent liabilities — selected country examples (Box 1)
- Called loan guarantees
  - Guinea: Guarantees issued during 2014 and 2015 to local and foreign banks to implement large-scale infrastructure projects (equivalent to 15.2 percent of GDP, 85 percent of which benefited from the guarantees). Starting in 2015, the guarantees were called and the Central Bank began settling the associated obligations.
- Transfers to state-owned enterprises (SOEs)
  - The Gambia: Three SOEs encountered financial difficulties in 2014. The SOEs called on loan guarantees that amounted to 4.5 percent of GDP (direct transfers added another 0.6 percent of GDP).
  - Burkina Faso: In 2013, the two largest SOEs received net government transfers equivalent to 3 percent of GDP. The transfers (implicit and explicit subsidies) covered losses from the gap between domestic retail oil prices and international oil prices, as well as from fixed electricity tariffs.
- Banking crisis resolution
  - Nigeria: During 2009–11 a severe banking crisis involving more than 40 percent of the banking sector assets substantially raised public debt by as much as 11.8 percent of GDP (Laeven and Valencia 2012; IMF 2013b).
- Other events
  - Mauritania: Authorities expanded subsidized food shops in response to the 2011–12 drought and rising food prices, ultimately covering a larger than anticipated cost of 1.2 percent of non-oil GDP in 2012 due to delayed donor disbursements and a more severe-than-expected drought impact.
  - Cote d’Ivoire: Insufficient traffic on a bridge relative to PPP contract assumptions triggered an implicit guarantee of 0.07 percent of GDP in 2015. Cote d’Ivoire’s 2015 PPP portfolio included 114 projects for a total amount of about 75 percent of GDP, mostly in transportation, energy, animal and fishing, and tourism sectors, which could give rise to further fiscal risks.

### Methodology: assessing fiscal space via debt limits and safe debt
- Conceptual framework
  - Distinguishes between a debt limit (ceiling) and safe debt.
    - Debt limit: level above which debt becomes unsustainable, abstracting from liquidity risks (the point beyond which debt would rise indefinitely because the primary surplus would never be enough).
    - Safe debt: level that would accommodate an increase in debt (resulting from a shock) without breaching the debt limit.
  - Fiscal space is the difference between safe debt and current debt levels.
- Practical identification of debt limit
  - Use public debt thresholds defined in the IMF/World Bank Debt Sustainability Framework (DSF) for LICs as proxies for debt limits.
  - DSF thresholds capture risk of debt distress while accounting for institutional capacity via the World Bank's CPIA index.
  - Notes on alternatives and existing rules:
    - Two currency unions (WAEMU and CEMAC) have a convergence criteria of public debt not exceeding 70 percent of GDP.
    - Four other LICs have a rule stipulating that public debt should not exceed 60 percent of GDP.
- Drivers of debt dynamics to be examined
  - Volatility of terms of trade and real exchange rates.
  - Changing financing mix.
  - Financing constraints.
  - Contingent liabilities.
  - Standard interest-growth differential.
- Controlling for endogenous fiscal policy response
  - Primary balance pb_it captures the response of fiscal policy to shocks: pb_it() = f(X, ε), where X includes macroeconomic variables driving fiscal behavior and ε represents fiscal policy shocks (expenditure slippages or revenue shortfalls).
  - Fiscal reaction function estimated using a panel of 27 LICs.
  - A fiscal capacity ceiling on the primary balance is introduced to keep the fiscal reaction function plausible in light of past experience.
- Debt dynamics equation and components (as presented)
  - The framework is guided by a standard debt equation based on the evolution of the existing stock of debt, contemporaneous fiscal behavior, and other components (used as a proxy for contingent liabilities).
  - Notation preserved from source: d is the debt-to-GDP ratio; g is the real growth rate; α_i^d and α_i^f are ratios of domestic and foreign to total debt; β_i^C and β_i^NC are ratios of concessional and non-concessional to foreign debt; r_it^d, r_it^f, r_it^C, and r_it^NC are the real interest rates on domestic, foreign, concessional and non-concessional loans respectively; Δε is the real exchange rate depreciation. Stock-flow adjustments (SFA) are used as a proxy for unexplained components (contingent liabilities).
- Stochastic forecasting approach
  - Follows Celasun, Debrun, and Ostry (2007): debt is forecast via a stochastic approach incorporating three sources of risk:
    - Fiscal policy shocks (ε in the primary balance equation).
    - Budget sensitivity to macroeconomic (growth, terms of trade) and financial developments (foreign loan disbursements).
    - Direct impact of macroeconomic shocks (growth, exchange rate, interest rates) on debt dynamics.
  - A large number of debt trajectories over a six-year horizon are derived by combining shocks with fiscal policy behavior and contingent liabilities (as in the debt equation).
  - Resulting fan charts give the probability of exceeding the debt ceiling for a starting debt level.
  - Safe debt is calculated iteratively by adjusting the starting point until the probability of exceeding the ceiling in the event of adverse shocks is below 5 percent.
- Additional methodological notes
  - Given the dearth of data on contingent liabilities, SFAs are used as a proxy (see Appendix II for definitions and assumptions in the source).
  - The Debt Sustainability Framework (DSF) was last reviewed in 2012 and work on the next review is ongoing, so these thresholds are subject to change.

*Source: wp17110 - Appendix I.*

### Appendix III.

### Appendix III.

### Generation of shocks
- Ideally estimate unrestricted VAR for each country; not feasible due to data limits in LICs (quarterly data rarely available; annual series short).
- Panel VAR unsuitable because it imposes same coefficients across countries, failing to capture heterogeneity.
- Adopted alternative: calibrate country-specific multivariate normal distributions around historical means and sample country-specific shocks from these distributions.
  - Disadvantage: cannot account for persistence.
  - Benefit: can include a large set of variables since correlations between every pair of variables are mutually independent.
- Note: “VAR shocks are drawn only from the unexplained part of each variable, hence the variance of the shocks themselves is smaller in the VAR than that in the multivariate distribution.” (footnote)

### Tail risks
- LICs exposed to fat tails and asymmetric shocks.
- Alternative simulations use a Student’s t-distribution to account for fatter tails and infrequent extreme deviations (see Appendix III comparison between Student’s t and multivariate normal).

### Policy scenarios and flexibility of framework
- Framework allows scenario analysis by changing assumptions on αd, αf, βC, and βNC to explore shifting financing mix toward non-concessional loans.
- Trade-offs in public investment decisions can be analyzed by modifying growth distribution assumptions.
- Section V applies these features.

### Fiscal behavior (estimation approach)
- Estimated fiscal reaction function for an unbalanced panel of 27 LICs over 2003–13.
- Baseline specification (system GMM) includes:
  - Dependent variable: general government primary balance (percent of GDP).
  - Regressors: lagged gross public debt ratio, lagged primary balance, terms-of-trade gap interacted with mineral and non-mineral exporter dummies, external disbursements (proxy for financing constraints), dummy for years when countries received debt relief, and other controls in alternative specifications.
- Findings from Table 1 (Specification (1) Baseline):
  - Lagged primary balance: 0.125 (0.048)***
  - Lagged debt (LD): 0.009 (0.012)
  - TOT gap (mineral exporters): 0.094 (0.049)*
  - TOT gap (non-mineral exporters): -0.021 (0.024)
  - External disbursements: -0.397 (0.238)*
  - Debt relief dummy: 1.419 (0.71)**
  - AR(2) test p-value: 0.377
  - Hansen test p-value: 0.335
  - Observations: 292; Countries: 27; Years per country (avge.): 10.81
  - Notes: Robust standard errors in parentheses. Symbols ***, ** and * denote statistical significance at 1 percent, 5 percent, and 10 percent levels respectively.

### Fiscal behavior (interpretation and contrasts)
- Persistence and sensitivity:
  - Primary balance tends to be persistent; sensitivity to terms of trade significant only for mineral exporters.
- Financing constraints:
  - External disbursements coefficient negative and less than one in absolute value in all specifications → reductions in external financing cannot be fully offset by increases in domestic funding.
- Aid receipts:
  - Grants found to be a significant determinant of the primary balance with a positive sign (in specifications where included).
- Response to debt increases:
  - Coefficient on lagged debt ratio statistically insignificant in most specifications → fiscal policy in LICs does not appear to react to public debt developments in a stabilizing fashion (contrast with advanced and emerging markets).
  - Controlling for HIPC makes the debt coefficient significant and similar in magnitude to other studies (Table 1, column 4).
- Stabilization role:
  - No evidence LICs use fiscal policy as countercyclical tool (insignificant output gap coefficient).
  - Terms-of-trade booms/busts more relevant for fiscal behavior in mineral exporters.
- Non-linearity:
  - No evidence of non-linear response of fiscal policy to debt (spline term insignificant for levels of debt ranging from 40 to 60 percent of GDP in unreported estimates).

### Results — Baseline and macroeconomic uncertainty
- Sample: 26 LICs for which data are available (simulations use country-specific models; debt ceilings from CPIA-based debt thresholds in LIC DSF: 49 percent of GDP for low capacity countries; 62 percent of GDP for medium capacity countries; and 75 percent of GDP for high capacity countries).
- Baseline estimates:
  - Fiscal space in LICs estimated to be in the double digits, with the median value reaching up to 16 percent of GDP for the full sample.
  - Space for mineral exporters is more than 5 percentage points of GDP below other LICs (dark blue bar in Figure 14).
  - Implied safety margins below debt ceilings range from 7 to 10 percent of GDP.
  - All results in this section are based on a 5 percent probability of breaching the debt threshold.
    - Example sensitivity: assuming a 20 percent probability of breaching the threshold, the average fiscal space increases to 19 percent of GDP.
- Alternative simulations and impacts:
  - Longer sample period (starting as early as 1996 for many countries):
    - Dispersion of macro shocks higher than baseline → estimated fiscal space reduced by about a third.
    - Impact particularly severe for mineral exporters.
  - Stochastic simulations based on tail events (Student’s t-distribution):
    - Fiscal space is up to 18 percent below the baseline.
    - Student’s t allows for higher kurtosis so more macro variance comes from infrequent extreme deviations.
  - Persistent terms-of-trade shocks:
    - Assume persistently negative average terms-of-trade gap of 15 percent.
    - Six major commodity producers in sample experienced shocks at least as large for about 20 percent of the time since 1970.
    - Implication: for mineral exporters fiscal space can turn negative under this persistent shock assumption.

### Results — Fiscal behavior alternatives
- Two alternative fiscal-behavior assumptions:
  1. Fiscal policy responds to changes in debt (introduce positive coefficient for lagged debt).
  2. Primary balance set at level that stabilizes debt as of 2014 (debt-stabilizing assumption).
- Comparisons:
  - Debt-stabilizing assumption results in the lowest primary deficits over the forecast horizon — about 55 percent below the baseline.
  - Improved fiscal performance under these alternatives increases fiscal space:
    - About 20 percent higher for mineral exporters.
    - About half of that increase for the rest of LICs.

### Financing mix and exchange rate considerations
- Increasing reliance on non-concessional external and domestic financing may raise the interest burden.
- Reversal of real exchange rate appreciation could significantly increase debt service depending on the financing mix.

*Source: IMF’s staff calculations.*

### conclusion is that access to new sources of funding may ease the financing constraints faced

### wp17110 - conclusion is that access to new sources of funding may ease the financing constraints faced

### Financing mix and fiscal space
- Substituting half of concessional loans with non-concessional external financing results in a significant decline in fiscal space, particularly among non-mineral exporters where the drop is close to 25 percent.
- Replacing external with domestic financing (while keeping the share of concessional loans constant) has limited impact on fiscal space for non-mineral exporters and can increase fiscal space for mineral exporters.
- A switch to external financing combined with real depreciation can amplify losses in fiscal space, potentially shrinking fiscal space to a meager 2 percent of GDP.

### Interest rates, exchange rates, and fiscal space
- Assuming an average annual real depreciation of 4 percent (with the financing mix as given) reduces fiscal space up to 72 percent.
- If the relative costs of non-concessional sources increase from 100 bps to 350 bps (with real exchange rate constant), fiscal space could plunge by more than 70 percent.
- Under the same increase in relative costs, fiscal space can turn negative if the real exchange rate depreciates by 3 percent or more.
- The simulations take a generic-country case where the share of domestic to foreign debt is 50 percent, and the ratio of concessional loans (CL) to non-concessional loans (NCL) in the foreign financing mix is 40 percent.
- The analysis highlights conflicting forces: domestic interest rates tend to be higher than external ones, but exchange rate volatility can make external non-concessional loans costlier.

### Policy scenarios illustrating potential to expand fiscal space
- Context: Incremental annual spending needs to achieve the SDGs are estimated at around 30 percent of GDP.
- Scaling-up of public investment:
  - Assumed fiscal multipliers: 1.2 (higher efficiency) and 0.6 (lower efficiency).
  - Under these assumptions, fiscal space can increase significantly, with the payoffs for higher efficiency almost 80 percent larger.
  - Empirical evidence suggests productivity of public capital in LICs is significantly higher than marginal costs of funds under normal financing conditions.
  - Caveats: results do not consider country-specific efficiency, absorption capacity, and crowding-out of private investment.
- Domestic revenue mobilization (DRM):
  - Revenues in non-mineral exporters increased by 2½ percent of GDP in 2010–15 relative to 2005–10.
  - Econometric evidence: the primary balance increases by 0.2 percent of GDP for every one percentage point increase of revenues.
  - If the recent trend continues over the next five years, the primary balance would improve by about ½ percent of GDP.
  - In a scenario where remaining additional revenue is spent on high-efficiency public investment (multiplier of 1.2), fiscal space would increase by as much as six percent of GDP.
  - Note: keeping DRM trends unchanged from recent years will barely meet SDG-related spending needs in many countries—more ambitious DRM is needed.

### Key quantitative findings and model parameters
- SDG incremental annual spending needs: around 30 percent of GDP.
- Impact examples:
  - Financing-mix substitution: decline close to 25 percent for non-mineral exporters.
  - Real depreciation (average annual 4 percent): reduces fiscal space up to 72 percent.
  - Post-switch to external financing plus real depreciation: fiscal space can be as low as 2 percent of GDP.
  - Interest differential shock: increase from 100 bps to 350 bps can reduce fiscal space by more than 70 percent.
  - Real depreciation of 3 percent or more can make fiscal space negative under higher relative costs.
- Public investment multipliers analyzed: 1.2 and 0.6; higher-efficiency payoff almost 80 percent larger.
- DRM historical increase (2010–15 vs 2005–10): 2½ percent of GDP in revenues for non-mineral exporters.
- Estimated primary balance response: 0.2 percent of GDP improvement per 1 percentage point revenue gain.
- Scenario DRM outcome: primary balance improves by about ½ percent of GDP; fiscal space increase up to six percent of GDP when coupled with high-efficiency public investment.
- Residual stock-flow adjustments (SFAs):
  - Average annual residual SFA in sample: 3.2 percent of GDP.
  - Median annual residuals: 2¼ percent of GDP for mineral producers; 1¾ percent of GDP for non-mineral producers.
  - Historical min and max SFA values: -68.8 percent of GDP and 58.4 percent of GDP respectively.
  - SFA cap used in simulations: implicitly set at 3 percent of GDP to avoid bias from outliers.
- Fiscal reaction function primary-balance caps (annual change, resulting ceiling for primary balance level):
  - Mineral exporters: 4¼ (level) and 5 (annual change) percent of GDP.
  - Non-mineral exporters: 1¼ (level) and 1¼ (annual change) percent of GDP.
- Simulation choices:
  - Timeframe aligned with WEO forecast horizon (five-year).
  - Due to data constraints, 2014 is taken as the starting point for simulations.
  - The stochastic simulation draws N sets of variables generating uncertainty (VGU): interest rates (domestic, concessional, non-concessional), growth rate, exchange rate, terms-of-trade, foreign loan disbursements, and the primary balance.
  - The initial “safe” debt level is calibrated so debt stays below the debt ceiling during the five-year timeframe with a 95 percent probability.

### Conclusions and policy implications
- Fiscal policy in LICs is driven more by access to financing than cyclical considerations; exchange rates and terms of trade are major sources of volatility.
- Fiscal space varies widely depending on the nature and magnitude of uncertainty; under benign scenarios fiscal space can be in double digits but is insufficient to meet SDG needs.
- Severe historical-type shocks (e.g., 1990s) could lower fiscal space by a third; large commodity price swings could wipe out fiscal space for mineral exporters.
- Fiscal space could shrink by a factor of eight if financing mixes shift away from concessional loans while real exchange rates reverse recent appreciation.
- Policy responses that enhance resilience—improving public investment efficiency and strengthening domestic revenue bases—can materially increase fiscal space.
- Concessional financing should remain a major source of funding, especially when tighter global financing conditions (e.g., U.S. rate normalization) threaten to constrain fiscal space.
- Shortcomings and further research:
  - Debt limits are taken as given (DSF thresholds), which some may argue do not fully reflect solvency problems; nonetheless, these thresholds signal elevated debt distress risk and influence creditors’ lending decisions.
  - The framework does not account for assets (notably in resource-rich countries) and is deterministic in policy scenario runs.
  - Integrating the framework into a DSGE model is proposed as future research to provide richer insights.

*Source: IMF staff analysis (wp17110).*

### 0.3 percent and steps (i-iii) are repeated.

### wp17110 - 0.3 percent and steps (i-iii) are repeated.

### Simulation methodology: shock distributions and sampling
- Results presented in this paper are based on N=2000.
- Shocks are drawn from country-specific multivariate normal distributions with k-dimensional mean and covariance matrix:
  - k is the number of variables considered.
- Multivariate Student’s t-distribution used as an alternative to capture tail risk; degrees of freedom denoted by scalar and positive v.
  - The larger v, the closer the t-distribution resembles the normal distribution (converging towards the normal distribution for v).
  - The smaller v, the fatter the tails become.
  - In the special case v = 1, the distribution becomes a multivariate Cauchy distribution.
- For the simulations in this paper, the degrees of freedom are set to 4.
- Matlab sampling note:
  - Matlab can sample from a normalized multivariate Student’s t-distribution with zero mean, normalized variances and a pre-defined covariance structure Σ.
  - Each generalized draw  is converted to fit the real data as follows:
    - X() = diag(μ) +  Σ. (as presented in source)
- Illustration:
  - Figure A3.2 compares random draws for Bolivia’s growth rates under a normal and a Student’s t-distribution (v = 4) — used to illustrate heavier tails under the t-distribution.

### Fiscal reaction function: specification and endogeneity issues
- Baseline fiscal reaction function specification (notation retained from source):
  - The equation captures how the primary balance reacts endogenously to current economic conditions and outstanding stock of public debt (Bohn 1998).
  - Error term decomposition:
    - ݁௜௧ with ߙ௜ (country specific, time-invariant) and ݒ௜௧ (idiosyncratic to each country and time period).
- Endogenous variables to contemporaneous error term ݁௜௧ include:
  - Lagged dependent variable ܾ݌௜,௧ିଵ (lagged primary balance as percentage of GDP): comprises lagged error term ݁௜,௧ିଵ which includes ߙ௜.
  - Lagged gross public debt ݀௜,௧ିଵ: determined by lagged primary balance ܾ݌௜,௧ିଵ and further lags, hence endogenous via ߙ௜.
  - Regressors in ݔ௜௧ (e.g., output gap, disbursements on external public and publicly guaranteed debt) may be endogenous if omitted factors/shocks in ݁௜௧ affect both primary balance and regressors.

### Estimation approach: System GMM
- Main estimator: System GMM dynamic panel estimator (Blundell and Bond 1998).
  - Relies on two types of moment conditions:
    - (i) Those relating to the econometric equation in first differences.
    - (ii) Those relating to the econometric equation in levels.
  - Differencing purges time-invariant component ߙ௜; differenced error term becomes ݒ௜௧ ݒெ௜,௧ିଵ (an MA(1) process).
  - Instruments for differenced lagged dependent variables and differenced lagged debt ratio: second lagged levels (ܾ݌௜,௧ିଶ and ݀௜,௧ିଶ), and further lagged levels.
  - Instruments for lagged differences of endogenous variables in ݔ௜௧ constructed using lagged levels and exogenous variables (e.g., terms of trade gap).
- Potential drawback:
  - Lagged levels may be poor instruments for differenced variables if endogenous variables are highly persistent (e.g., debt ratio).
- Level-equation moment conditions:
  - Use lagged differences as instruments for endogenous variables in levels; differencing assumed to purge fixed effects making instruments exogenous to ߙ௜ and ݒ௜௧.
- Post-estimation specification tests performed:
  - A Test for Second Order Serial Correlation in the Differenced Error Term:
    - Null hypothesis: no second order serial correlation of the differenced error term.
    - Presence of second order serial correlation implies first order serial correlation of levels ݒ௜௧ and may invalidate use of second lagged levels as instruments.
  - Hansen Test of Over-identification:
    - Null hypothesis: instruments are valid.

### Alternative estimator: Generalized Least Squares (GLS) and FGLS
- Alternative specification used as robustness test:
  - Adds country dummies (fixed effects) to capture country specific intercepts ߚ௜, assumed to capture time-invariant component ߙ௜.
  - Lagged dependent variable omitted; persistence of primary balance captured by error term assumed generated by AR(1): ݒ௜,௧ = ݒߩ௜,௧ିଵ + ݑ௜௧ with ݑ௜௧ ~ (0, ݪ).
- Estimator:
  - Feasible Generalized Least Squares (FGLS) is used to account for serial correlation in the error term.
  - This approach follows Abiad and Ostry (2005) and is similar to Ghosh and others (2013).

### Robustness checks and key empirical findings (Table A4.1)
- General note: Dependent variable in all specifications is general government primary balance (percent of GDP). ‘TOT’ denotes terms of trade; ‘min. exp.’ are mineral exporting countries; ‘ext. disb.’ are external disbursements; AR(x) indicates autoregressive order ‘x’.
- Main robustness findings summarized from specifications (columns 1–5 in Table A4.1):
  - Specification (1) Baseline (without external disbursements) — System GMM:
    - Lagged primary balance: 0.171 (0.056)***.
    - Lagged debt: 0.006 (0.01).
    - TOT gap (min. exp.): 0.097 (0.051)*.
    - TOT gap (non-min. exp.): -0.024 (0.023).
    - External disbursements: -0.215 (0.078)*** (note: excluded in this specification).
    - Debt relief dummy: 1.492 (0.708)**.
    - Constant: -1.67 (0.46)***.
    - Estimator: System GMM.
    - AR(2) test p-value: 0.208.
    - Hansen test p-value: 0.211.
    - Instruments: 18.
    - Observations: 292.
    - Countries: 27.
    - Years per country (average): 10.81.
  - Specification (2) Output Gap (without external disbursements) — System GMM:
    - Lagged primary balance: 0.027 (0.069)**.
    - Lagged debt: 0.003 (0.013).
    - Output gap (min. exp.): -0.182 (0.42).
    - Output gap (non-min. exp.): 0.568 (0.422).
    - External disbursements: -0.165 (0.076 )** (excluded in this specification).
    - Debt relief dummy: 1.467 (0.67)**.
    - Constant: -1.492 (0.626)**.
    - Estimator: System GMM.
    - AR(2) test p-value: 0.284.
    - Hansen test p-value: 0.343.
    - Instruments: 18.
    - Observations: 292.
    - Countries: 27.
    - Years per country (average): 10.81.
  - Specification (3) Baseline (GLS) (AR(1) Error Structure and Fixed Effects):
    - Lagged primary balance: (omitted in GLS specification) reported as blank.
    - Lagged debt: 0.018 (0.006)***.
    - TOT gap (min. exp.): 0.093 (0.034)***.
    - TOT gap (non-min. exp.): -0.01 (0.017).
    - External disbursements: (noted range in spec. 5) — see specification (5) for ranges.
    - Debt relief dummy: 0.587 (0.221)***.
    - Constant: 1.239 (1.064).
    - Estimator: GLS.
    - Observations: 292.
    - Countries: 27.
    - Years per country (average): 10.81.
  - Specification (4) Output Gap (GLS) (AR(1) Error Structure and Fixed Effects):
    - Lagged debt: 0.017 (0.006)***.
    - TOT gap (min. exp.): (not reported in this column).
    - Output gap (min. exp.): 0.571 (0.277)**.
    - Output gap (non-min. exp.): 0.26 (0.069)***.
    - Debt relief dummy: 0.55 (0.216)**.
    - Constant: 1.24 (1.049).
    - Estimator: GLS.
    - Observations: 292.
    - Countries: 27.
    - Years per country (average): 10.81.
  - Specification (5) Eliminating One Country at a time (range of coeff. estimates shown) — System GMM with 26 countries in each regression:
    - Lagged primary balance: range 0.109 – 0.164.
    - Lagged debt: range 0.009 – 0.021.
    - TOT gap (min. exp.): range 0.07 – 0.148.
    - TOT gap (non-min. exp.): range -0.04 - -0.012.
    - External disbursements: range -0.62 - -0.362.
    - Debt relief dummy: range 0.729 – 1.518.
    - Constant: range -0.975 - -0.094.
    - Estimator: System GMM.
    - Observations: 292.
    - Countries: 26 (per regression).
    - Years per country (average): 10.81.
- Robustness conclusions highlighted in text:
  - Key features of baseline are robust to omission of the external disbursements term:
    - (i) There is persistence of the primary balance.
    - (ii) The lagged debt term is statistically insignificant under baseline GMM but small, positive and statistically significant under GLS.
    - (iii) The terms of trade gap is statistically significant for mineral exporting countries.
  - Using output gap instead of TOT gap (GMM): output gap remains statistically insignificant — suggests fiscal policy does not react in a counter-cyclical way to stabilize business cycle fluctuations (under System GMM).
  - GLS estimates (without lagged primary balance):
    - A small, positive and statistically significant coefficient on lagged debt is found.
    - Output gap found statistically significant under GLS (contrasting GMM results), indicating lack of robustness regarding output gap importance.
  - Sequential country omission (specification 5):
    - Coefficients for lagged primary balance and terms of trade gap (mineral exporters) always positive — robustness of persistence and terms of trade importance.
    - Coefficients on external disbursements always negative and less than one in absolute value — reductions in external financing cannot be fully substituted by increases in domestic financing.

*Source: wp17110 - 0.3 percent and steps (i-iii) are repeated.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17110.pdf_