## 4. Impact on Public Investment and Indirect Impact on Real Per Capita Income Growth of Reducing the Debt Service-to-GDP Ratio from 8.7 Percent to 3.0 Percent

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### I. Key findings from the study
- Empirical evidence for low-income, PRGF-eligible countries supports a nonlinear (Laffer-type) external debt/growth relationship:
  - Threshold estimates: around 30–37 percent of GDP, or around 115–120 percent of exports (from reduced-form growth equations).
  - Alternative threshold estimates when investment is disaggregated:
    - Face value of external debt: around 50 percent of GDP.
    - Net present value (NPV) of external debt: around 20–25 percent of GDP.
    - NPV of external debt: around 100–105 percent of exports (when expressed relative to exports).
- Debt relief projected effects (direct effect on growth):
  - Weighted average NPV of external debt to GDP for the 27 decision point HIPCs is projected to decline from 60 percent prior to debt relief at the decision point to 30 percent by 2005.
  - Based on the system GMM results (second column of Table 2), this reduction from 60 percent to 30 percent NPV/debt-to-GDP would, ceteris paribus, directly add 0.8–1.1 percent to annual per capita GDP growth rates.
  - Applying Pattillo and others (2002) quadratic system GMM results to the same 60 percent → 30 percent reduction yields an increase of 0.4 percentage point per annum.
- Channels and magnitudes:
  - Gross (total) investment has a statistically significant positive impact on real per capita GDP growth.
  - When investment is disaggregated, public investment (not private investment) has the significant growth effect:
    - Each 1 percentage point of GDP increase in public investment raises annual per capita growth by 0.2 percentage point.
  - Debt service shows no robust direct effect on per capita GDP growth once investment is included, consistent with debt service operating indirectly through investment/composition effects.
  - Public investment determinants and crowding-out:
    - Openness is always highly significant and positive for public investment.
    - Urbanization is always highly significant and negative for public investment.
    - Foreign aid is statistically significant and positive in most formulations.
    - The stock of external debt (NPV measures) has no significant short-run impact on public investment.
    - Debt service crowds out public investment nonlinearly; the crowding-out effect intensifies as debt service absorbs a larger share of GDP.
    - Estimated crowding-out magnitude: under linear formulations, a one percentage point of GDP increase in debt service reduces public investment by about 0.2 percent of GDP.
  - Threshold for debt-service crowding-out: empirical diagnostics favored a threshold specification with a cutoff at 5 percent of GDP for debt service.

### II. Empirical approach and data overview
- Sample and period:
  - 55 low-income countries eligible for the IMF’s Poverty Reduction and Growth Facility (PRGF).
  - Data cover the period 1970–99.
  - Three-year averages used for panel regressions.
- Main growth specification (reduced-form):
  - Dependent variable: GRPCY = growth of real per capita income (GDP) (log-level lag included).
  - Explanatory variables include: LYRPC(-1), TOTGR, POPGR, GSEC, GROINV (or private/public investment), FISBAL, OPEN, DEBTSERX, EXTDEBT, and EXTDEBT^2.
  - Four debt-stock indicators used: face value debt/GDP, NPV debt/GDP, face value debt/exports, NPV debt/exports (EXTDEBT measured in natural logs; quadratic term included).
- Estimation methods:
  - Fixed effects and system GMM (Blundell and Bond (1998)) employed.
  - System GMM used to mitigate dynamic panel bias and address potential endogeneity.
- Data sources:
  - External debt and investment: World Bank Global Development Network Growth database.
  - Debt service: Global Development Finance database (World Bank) and World Development Indicators (WDI).
  - NPV of debt: William Easterly dataset.
  - Terms of trade and fiscal balance: World Economic Outlook.
  - Other variables: WDI.

### III. Detailed empirical results (growth equations)
- General diagnostics:
  - Fixed effects and system GMM broadly similar; F-tests reject common intercept; Hausman tests reject random effects; Sargan tests support instrument validity in GMM.
- Coefficients and significance (summary):
  - Lagged per capita income: negative and statistically significant (convergence).
  - Gross investment ratio: positive and statistically significant.
  - Public investment ratio (when disaggregated): positive and statistically significant; private investment ratio: statistically insignificant.
  - Fiscal balance: positive and statistically significant.
  - Population growth and terms-of-trade growth: sometimes significant and negative.
  - Secondary school enrollment (proxy for human capital): statistically insignificant in this low-income sample.
  - Debt service/exports or debt service/GDP: generally statistically insignificant for direct growth effects once investment is included.
  - Debt stock variables enter nonlinearly (log and squared log) with statistically significant coefficients implying a threshold beyond which marginal impact of debt on growth is negative.
- Representative coefficient magnitudes (system GMM, Table 2 basis):
  - Public investment: a 1 percentage point of GDP rise → 0.2 percentage point higher annual per capita growth.
  - Debt NPV reduction example: NPV debt/GDP from 60 percent → 30 percent → +0.8–1.1 percent direct addition to annual per capita growth (system GMM estimate).

### IV. Public investment model and results
- Public investment equation:
  - PUBINV = ßr + ß1 LYRPC + ß2 AIDGNI + ß3 URBAN + ß4 OPEN + ß5 DEBTSERY + ß6 EXTDEBT + ß7 EXTDEBT^2 + υ
  - PUBINV = public investment (% of GDP)
  - DEBTSERY = total debt service (% of GDP) used in reported specifications (alternatives tested include DEBTSERY^2 and threshold dummies).
- Estimation method: fixed effects (system GMM not required given exogeneity of regressors and no lagged dependent variable).
- Main public investment results:
  - Log(income): positive and highly significant.
  - Foreign aid (% of GNI): positive and significant in most specifications.
  - Urbanization ratio: negative and highly significant.
  - Openness: positive and highly significant.
  - Debt service/GDP: negative and statistically significant in many formulations; the square or threshold specification indicates nonlinear, intensifying crowding-out.
  - NPV(debt) measures: coefficients not statistically significant (stock of external debt has no significant short-run impact on public investment).
- Quantified crowding-out:
  - Linear estimate: each 1 percentage point of GDP increase in debt service → public investment declines by about 0.2 percent of GDP.
  - Threshold specification: best fit at a debt-service cutoff of 5 percent of GDP; results with threshold dummy and its square indicate stronger crowding-out above the threshold.
- Model fit:
  - Adjusted R-squared: model explains over half of variation in public investment (Adjusted R-squared values reported around 0.519–0.551 across specifications).

### V. Policy implications and scenarios
- Direct and indirect growth gains from debt relief:
  - Direct channel: reductions in NPV of external debt to GDP (example: 60 percent → 30 percent) can directly raise annual per capita growth by 0.8–1.1 percent (system GMM).
  - Indirect channel via public investment: because debt service crowds out public investment, reductions in debt service can free resources for public investment; however, the observed crowding-out effect is modest (≈0.2 percent of GDP public investment per 1 percentage point of GDP of debt service).
  - Given the modest crowding-out coefficient, ceteris paribus debt relief per se cannot be expected to generate large automatic increases in public investment; much of debt relief may be used for public consumption, deficit reduction, or private consumption/investment unless explicitly allocated.
- Magnitude example (calibration):
  - Reduction in debt service-to-GDP ratio from 8.7 percent (average in 2000 of the 7 most heavily indebted HIPC countries) to 3.0 percent (roughly the average debt service-to-GDP ratio for all HIPC countries in 2002) was used as a calibration exercise.
  - Simulation implications reported:
    - A reduction in debt service of about 6 percentage points of GDP would raise investment by 0.75–1 percentage point of GDP, raising growth modestly by about 0.2 percentage point.
    - If half of the debt service reduction were channeled into higher public investment (instead of one fifth), annual growth would rise by about 0.5 percentage point per annum.
- Policy priorities:
  - To translate debt relief into meaningful growth gains, policies should ensure that at least a meaningful share of freed resources is channeled to high-return public investment rather than only to consumption or financing lower deficits.
  - Improvements in fiscal balances are positively associated with growth; using part of debt relief for sustainable fiscal consolidation can support higher growth.
  - Given the limited short-run sensitivity of public investment to the debt stock (NPV), attention to current fiscal positions and debt service obligations is crucial for public investment planning.
  - Ensure efficiency and productivity of public investment to maximize growth payoffs (since public investment raises growth by 0.2 percentage point per 1 percentage point of GDP in public investment).

### VI. Table 4 (selected reported coefficients and indirect growth effects)
- Growth of Impact on Public Investment (in percent of GDP) — Fixed Effects / System GMM (selected rows)
  - Results with net present value of debt in percent of GDP:
    - Debt service/GDP: 0.95 / 0.20 / 0.17
    - [Debt service/GDP]2: 0.70 / 0.15 / 0.13
    - Debt-service threshold dummy: 0.92 / 0.20 / 0.17
    - [Debt-service threshold dummy]2: 0.78 / 0.17 / 0.14
  - Results with net present value of debt in percent of exports:
    - Debt service/GDP: 1.12 / 0.27 / 0.22
    - [Debt service/GDP]2: 0.71 / 0.17 / 0.14
    - Debt-service threshold dummy: 1.22 / 0.29 / 0.24
    - [Debt-service threshold dummy]2: 0.79 / 0.19 / 0.15
- Indirect growth effect reported: indirectly raise real per capita GDP growth by 0.1–0.2 percent annually under baseline assumptions.

### VII. Conclusions and suggested further research
- Conclusions:
  - External debt affects growth directly (via resource efficiency) and indirectly (via public investment through debt service crowding-out).
  - The positive effects of debt relief may already be reflected in some healthier growth experienced by HIPCs in recent years relative to the 1990s.
  - GDP per capita grew by an average of 1.2 percent per annum in 2000–2002, compared with 0.2 percent during the 1990s.
- Suggested additional research:
  - Further evaluate other indirect channels through which external debt affects growth, including the relationship between debt and public sector deficits.
  - Assess how debt interfaces with other macroeconomic determinants of growth, and examine the ambiguous theoretical impact of aid on both revenues and expenditures.

*Source: IMF working paper excerpt (section 4) on external debt, public investment, and growth in low-income countries.*

### References..............................................................................................................

### _wp03249 - References..............................................................................................................

### References
- References................................................................................................................................22

### Tables
- 1. Impact of Gross Investment and External Debt on Per Capita Income Growth ..................10
- 2. Impact of Private/Public Investment and External Debt on Per Capita Income Growth.....12
- 3. Impact of External Debt/Debt Service on Public Investment ..............................................16

*Source: _wp03249 - References..............................................................................................................*

### 4. Impact on Public Investment and Indirect Impact on Real Per Capita Income Growth of

### 4. Impact on Public Investment and Indirect Impact on Real Per Capita Income Growth of Reducing the Debt Service-to-GDP Ratio from 8.7 Percent to 3.0 Percent

### I. Key findings from the study
- Empirical evidence for low-income, PRGF-eligible countries provides support for a nonlinear (Laffer-type) external debt/growth relationship:
  - Threshold estimates: around 30–37 percent of GDP, or around 115–120 percent of exports (from reduced-form growth equations).
  - Alternative threshold estimates when investment is disaggregated:
    - Face value of external debt: around 50 percent of GDP.
    - Net present value (NPV) of external debt: around 20–25 percent of GDP.
    - NPV of external debt: around 100–105 percent of exports (when expressed relative to exports).
- Debt relief projected effects (direct effect on growth):
  - Weighted average NPV of external debt to GDP for the 27 decision point HIPCs is projected to decline from 60 percent prior to debt relief at the decision point to 30 percent by 2005.
  - Based on the system GMM results (second column of Table 2), this reduction from 60 percent to 30 percent NPV/debt-to-GDP would, ceteris paribus, directly add 0.8–1.1 percent to annual per capita GDP growth rates.
  - By comparison, applying Pattillo and others (2002) quadratic system GMM results to the same 60 percent → 30 percent reduction yields an increase of 0.4 percentage point per annum.
- Channels and magnitudes:
  - Gross (total) investment has a statistically significant positive impact on real per capita GDP growth.
  - When investment is disaggregated, public investment (not private investment) has the significant growth effect:
    - Each 1 percentage point of GDP increase in public investment raises annual per capita growth by 0.2 percentage point.
  - Debt service shows no robust direct effect on per capita GDP growth once investment is included, consistent with debt service operating indirectly through investment/composition effects.
  - Public investment determinants and crowding-out:
    - Openness is always highly significant and positive for public investment.
    - Urbanization is always highly significant and negative for public investment.
    - Foreign aid is statistically significant and positive in most formulations.
    - The stock of external debt (NPV measures) has no significant short-run impact on public investment.
    - Debt service crowds out public investment nonlinearly; the crowding-out effect intensifies as debt service absorbs a larger share of GDP.
    - Estimated crowding-out magnitude: under linear formulations, a one percentage point of GDP increase in debt service reduces public investment by about 0.2 percent of GDP.
  - Threshold for debt-service crowding-out: empirical diagnostics favored a threshold specification with a cutoff at 5 percent of GDP for debt service.

### II. Empirical approach and data overview
- Sample and period:
  - 55 low-income countries eligible for the IMF’s Poverty Reduction and Growth Facility (PRGF).
  - Data cover the period 1970–99.
  - Three-year averages used for panel regressions.
- Main growth specification (reduced-form):
  - Dependent variable: GRPCY = growth of real per capita income (GDP) (log-level lag included).
  - Explanatory variables include: LYRPC(-1), TOTGR, POPGR, GSEC, GROINV (or private/public investment), FISBAL, OPEN, DEBTSERX, EXTDEBT, and EXTDEBT^2.
  - Four debt-stock indicators used: face value debt/GDP, NPV debt/GDP, face value debt/exports, NPV debt/exports (EXTDEBT measured in natural logs; quadratic term included).
- Estimation methods:
  - Fixed effects and system GMM (Blundell and Bond (1998)) employed.
  - System GMM used to mitigate dynamic panel bias and address potential endogeneity.
- Data sources:
  - External debt and investment: World Bank Global Development Network Growth database.
  - Debt service: Global Development Finance database (World Bank) and World Development Indicators (WDI).
  - NPV of debt: William Easterly dataset.
  - Terms of trade and fiscal balance: World Economic Outlook.
  - Other variables: WDI.

### III. Detailed empirical results (growth equations)
- General diagnostic results:
  - Fixed effects and system GMM broadly similar; F-tests reject common intercept; Hausman tests reject random effects; Sargan tests support instrument validity in GMM.
- Coefficients and significance (summary across specifications):
  - Lagged per capita income: negative and statistically significant (convergence).
  - Gross investment ratio: positive and statistically significant.
  - Public investment ratio (when disaggregated): positive and statistically significant; private investment ratio: statistically insignificant.
  - Fiscal balance: positive and statistically significant.
  - Population growth and terms-of-trade growth: sometimes significant and negative.
  - Secondary school enrollment (proxy for human capital): statistically insignificant in this low-income sample.
  - Debt service/exports or debt service/GDP: generally statistically insignificant for direct growth effects once investment is included.
  - Debt stock variables enter nonlinearly (log and squared log) with statistically significant coefficients implying a threshold beyond which marginal impact of debt on growth is negative.
- Representative coefficient magnitudes (system GMM, Table 2 basis):
  - Public investment: a 1 percentage point of GDP rise → 0.2 percentage point higher annual per capita growth.
  - Debt NPV reduction example: NPV debt/GDP from 60 percent → 30 percent → +0.8–1.1 percent direct addition to annual per capita growth (system GMM estimate).

### IV. Public investment model and results
- Public investment equation:
  - PUBINV = ßr + ß1 LYRPC + ß2 AIDGNI + ß3 URBAN + ß4 OPEN + ß5 DEBTSERY + ß6 EXTDEBT + ß7 EXTDEBT^2 + υ
  - PUBINV = public investment (% of GDP)
  - DEBTSERY = total debt service (% of GDP) used in reported specifications (alternatives tested include DEBTSERY^2 and threshold dummies).
- Estimation method: fixed effects (system GMM not required given exogeneity of regressors and no lagged dependent variable).
- Main public investment results:
  - Log(income): positive and highly significant.
  - Foreign aid (% of GNI): positive and significant in most specifications.
  - Urbanization ratio: negative and highly significant.
  - Openness: positive and highly significant.
  - Debt service/GDP: negative and statistically significant in many formulations; the square or threshold specification indicates nonlinear, intensifying crowding-out.
  - NPV(debt) measures: coefficients not statistically significant (stock of external debt has no significant short-run impact on public investment).
- Quantified crowding-out:
  - Linear estimate: each 1 percentage point of GDP increase in debt service → public investment declines by about 0.2 percent of GDP.
  - Threshold specification: best fit at a debt-service cutoff of 5 percent of GDP; results with threshold dummy and its square indicate stronger crowding-out above the threshold.
- Adjusted R-squared: model explains over half of variation in public investment (Adjusted R-squared values reported around 0.519–0.551 across specifications).

### V. Policy implications and scenarios
- Direct and indirect growth gains from debt relief:
  - Direct channel: reductions in NPV of external debt to GDP (example: 60 percent → 30 percent) can directly raise annual per capita growth by 0.8–1.1 percent (system GMM).
  - Indirect channel via public investment: because debt service crowds out public investment, reductions in debt service can free resources for public investment; however, the observed crowding-out effect is modest (≈0.2 percent of GDP public investment per 1 percentage point of GDP of debt service).
  - Given the modest crowding-out coefficient, ceteris paribus debt relief per se cannot be expected to generate large automatic increases in public investment; much of debt relief may be used for public consumption, deficit reduction, or private consumption/investment unless explicitly allocated.
- Magnitude example noted in text (policy-relevant scenario):
  - Reduction in debt service-to-GDP ratio from 8.7 percent (average in 2000 of the 7 most heavily indebted HIPC countries) to 3.0 percent (roughly the average debt service-to-GDP ratio for all HIPC countries in 2002) was used as a calibration exercise; detailed calculations are reported in Table 4 of the source.
- Policy priorities implied by results:
  - To translate debt relief into meaningful growth gains, policies should ensure that at least a meaningful share of freed resources is channeled to high-return public investment rather than only to consumption or financing lower deficits.
  - Improvements in fiscal balances are positively associated with growth; using part of debt relief for sustainable fiscal consolidation can support higher growth.
  - Given the limited short-run sensitivity of public investment to the debt stock (NPV), attention to current fiscal positions and debt service obligations is crucial for public investment planning.
  - Because public investment raises growth (0.2 percentage point of growth per 1 percentage point of GDP in public investment), ensuring the efficiency and productivity of public investment is important to maximize growth payoffs.

*Source: IMF working paper excerpt (section 4) on external debt, public investment, and growth in low-income countries.*

### 8.7 to 3.0 percent of GDP would increase public investment by 0.7–0.8 percent of GDP, and

### _wp03249 - 8.7 to 3.0 percent of GDP would increase public investment by 0.7–0.8 percent of GDP, and

### Key empirical findings on debt, investment, and growth
- High levels of debt can depress economic growth in low-income countries.
- Debt appears to affect growth via its effect on the efficiency of resource use, rather than through its depressing effect on private investment.
- The debt-overhang hypothesis: debt has a deleterious effect on growth only after it reaches a threshold level.
  - Threshold levels estimated:
    - around 50 percent of GDP for the face value of external debt.
    - around 20–25 percent of GDP for the estimated net present value of external debt.
  - External debt indicators expressed as a ratio to exports are somewhat weaker, but indicate a threshold level for the net present value of external debt at around 100–105 percent of exports.
- Projected HIPC debt reduction implications:
  - The substantial reduction in external debt projected for the HIPCs by the time most reach their completion points in 2005 would, ceteris paribus, directly add 0.8–1.1 percent to their per capita GDP growth rates.
  - GDP per capita grew by an average of 1.2 percent per annum in 2000–2002, compared with 0.2 percent during the 1990s.

### Impact of debt service on public investment and indirect effects on growth
- The stock of public debt does not appear to depress public investment, but debt service does.
- The relationship between debt service and public investment is nonlinear, with crowding out intensifying as the ratio of debt service to GDP rises.
- Average effect:
  - Every 1 percentage point increase in debt service as a share of GDP reduces public investment by about 0.2 percentage point.
- Simulation implications:
  - A reduction in debt service of about 6 percentage points of GDP would raise investment by 0.75–1 percentage point of GDP, raising growth modestly by about 0.2 percentage point.
  - If half of the debt service reduction were channeled into higher public investment (instead of one fifth), annual growth would rise by about 0.5 percentage point per annum.
- Caveat:
  - Greater public investment bolsters growth only if it is matched by other revenue and expenditure measures that do not lead to higher budget deficits.

### Table 4: Impact on Public Investment and Indirect Impact on Real Per Capita Income (selected reported coefficients)
- Growth of Impact on Public Investment (in percent of GDP) — Fixed Effects / System GMM
  - Results with net present value of debt in percent of GDP:
    - Debt service/GDP: 0.95 / 0.20 / 0.17
    - [Debt service/GDP]2: 0.70 / 0.15 / 0.13
    - Debt-service threshold dummy: 0.92 / 0.20 / 0.17
    - [Debt-service threshold dummy]2: 0.78 / 0.17 / 0.14
  - Results with net present value of debt in percent of exports:
    - Debt service/GDP: 1.12 / 0.27 / 0.22
    - [Debt service/GDP]2: 0.71 / 0.17 / 0.14
    - Debt-service threshold dummy: 1.22 / 0.29 / 0.24
    - [Debt-service threshold dummy]2: 0.79 / 0.19 / 0.15
- Indirect growth effect reported: indirectly raise real per capita GDP growth by 0.1–0.2 percent annually under baseline assumptions.

### Policy implications and recommendations
- Allocation of debt relief:
  - One viable option for country authorities to raise growth and combat poverty is to allocate a substantial share of debt relief for public investment.
  - In practice, most HIPCs have been raising public investment in the context of their PRGF-supported programs; on average, these countries have targeted an increase of 0.5 percentage point of GDP in this spending, relative to the pre-PRGF year.
- Fiscal consistency:
  - To reap positive effects of debt relief on investment and growth, higher spending on capital outlays must be matched by spending cuts, higher external grants, or increases in domestic revenues to prevent an increase in the budget deficit.
- Design of adjustment programs:
  - Reducing the stock of debt alone—rather than an immediate reduction in debt service—is unlikely to induce governments to increase their spending on public investment.
  - Cutting debt-service obligations can provide breathing space to raise public investment, but debt relief per se is likely to lead to just a modest rise in this spending unless deliberately channeled to investment.

### Conclusions and suggested further research
- Conclusions:
  - External debt affects growth directly (via resource efficiency) and indirectly (via public investment through debt service crowding-out).
  - The positive effects of debt relief may already be reflected in some healthier growth experienced by HIPCs in recent years relative to the 1990s.
- Suggested additional research:
  - Further evaluate other indirect channels through which external debt affects growth, including the relationship between debt and public sector deficits.
  - Assess how debt interfaces with other macroeconomic determinants of growth, and examine the ambiguous theoretical impact of aid on both revenues and expenditures.

*Source: IMF working paper content excerpt.*

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