## _wp04217

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---

### I. Introduction
- Objective: provide an integrated assessment of the role of social spending and other policy interventions on human capital, economic growth, and social indicators using a panel dataset covering 120 developing countries from 1975 to 2000.
- Model aims:
  - Analyze dynamic direct and indirect effects of social spending on human capital and growth.
  - Account for interaction between education and health interventions.
  - Evaluate implications for the MDGs.
- Structure (as in source): literature review; data and model; empirical results and robustness tests; simulated effects of policy interventions; policy implications and conclusions.

### II. Literature review — key points
- Reduced-form approaches often omit feedback effects across social spending, social indicators, and growth.
- Education and growth:
  - Positive relationships reported in Levine and Renelt (1992), Mankiw and others (1992), Barro and Sala-i-Martin (1995), Barro (1996a and 1996b), Sala-i-Martin (1997).
  - Coulombe and others (2004): literacy scores 1 percent higher → increase in per capita GDP growth of 1.5 percentage points.
  - Counterevidence: Benhabib and Spiegel (1994), Pritchett and Summers (1996).
- Health and growth:
  - Bloom and Canning (2003, 2004) and Gyimah-Brempong and Wilson (2004) find positive contributions; estimated effects about 22 to 30 percent of the growth rate attributed to health capital; one more year of life expectancy associated with higher GDP growth of up to 4 percentage points per year.
- Social spending → social indicators: mixed evidence; education spending often has a greater effect in some studies (Baldacci and others (2003); Gupta and others (2002b)); many studies find weak or insignificant links as well.
- Governance: poor governance mediates weak effectiveness of social spending; including governance helps address omitted-variable bias.

### III. Methodology and model
- Econometric approach: panel data regressions in a recursive system of four equations for:
  1. Real per capita income growth.
  2. Total investment.
  3. Education attainment.
  4. Health status.
- Assumption: disturbances are not correlated across equations; standard least squares produce unbiased and efficient estimates; SUR tests discussed under robustness.
- Growth equation:
  - Neoclassical framework augmented by education and health capital: y = f(sk, he, ed, Ω).
  - Growth modeled as g = f(ed, ∆ed, he, ∆he, sk, Ω).
  - Key variables preserved as in source: it g, i α, t η, log(1−it y), it ks, it Ed, ∆Ed, it He (log under-5 child mortality), ∆he, it n, it m Ω (open, dtot, Balance, p, Highp, LowdefBalance, Lowgov), it u.
- Investment equation: specified as equation [2]; includes levels of education and health indicators, governance (Lowgov), fiscal balance, inflation (p, Highp), population growth, other macro controls.
- Education equation: specified as equation [3]; education capital proxied by composite primary and secondary enrollment rate; explanatory variables include Popu15, y (log real per capita GDP in PPP$), health capital (under-5 mortality), Quality (school repetition rate), EduSpending (current and lagged five-year averages of education spending in percent of GDP; log form), Lowgov interactions, Female (share of female students); lag structure: one lag chosen based on SIC implying impact may take another five years to be fully realized.
- Health equation: log-linear specification for under-5 child survival/mortality includes income level (log real per capita GDP in PPP$), Gender equality (share female students), Urbanization, Poor governance dummy, current health spending (five-year average percent of GDP; log form). Composite enrollment rate dropped as not significant to allow recursive triangular matrix.

### IV. Data and estimation
- Sample: panel dataset covering 120 developing countries, 1975–2000; five-year averages used.
- Data sources: IMF World Economic Outlook 2003, Barro-Lee dataset, World Development Indicators 2003, IMF staff reports social spending database, IMF Government Financial Statistics, ICRG indices.
- Baseline estimator: fixed-effect model (LSDV).
- Robustness/alternative estimators:
  - Robust estimator (controls for outliers).
  - Feasible Generalized Least Squares (FGLS).
  - Error component two-stage least squares (EC2SLS).
  - Fixed-effect instrumental variable estimator (2SLS).
  - System GMM (for lagged variables).
- Overidentification tests reported for instrument validity.

### V. Key descriptive statistics (selected from Table 1)
- Real per capita GDP growth (in percent): Obs. 831; Mean 1.3; Std. dev. 4.0; Min. -20.6; Max. 30.9
- Investment ratio (in percent of GDP): Obs. 883; Mean 22.8; Std. dev. 8.8; Min. 0.3; Max. 50.2
- Composite enrollment rate (in percent): Obs. 792; Mean 130.6; Std. dev. 49.8; Min. 3.0; Max. 238.5
- Under-5 child mortality (per 1000 live births): Obs. 897; Mean 111.0; Std. dev. 78.9; Min. 7.0; Max. 345.0
- Education spending (in percent of GDP): Obs. 689; Mean 3.6; Std. dev. 1.7; Min. 0.6; Max. 10.0
- Health spending (in percent of GDP): Obs. 354; Mean 2.2; Std. dev. 1.5; Min. 0.3; Max. 8.7
- Governance index (1-12): Obs. 364; Mean 5.9; Std. dev. 1.9; Min. 1.0; Max. 11.0
- Poor governance dummy: Obs. 987; Mean 0.2; Std. dev. 0.4; Min. 0.0; Max. 1.0
- Income level (log of real per capita GDP in PPP$): Obs. 968; Mean 9.4; Std. dev. 3.2; Min. -10.7; Max. 16.9
- School repetition rate (in percent): Obs. 512; Mean 12.5; Std. dev. 9.8; Min. 0.1; Max. 38.6

### VI. Health equation — empirical findings and nexus
- Contribution to growth:
  - Education capital and health capital both positively contribute to output growth via different routes.
  - Education: both stock and flow affect growth; effects from both channels similar in magnitude.
  - Health: direct effect on growth is through flows; stock of health capital affects growth indirectly via investment.
- Social spending effects on social indicators:
  - Education spending dynamics: about two-thirds of the direct effect realized in the first five years; remainder in the next five years.
    - Example: increase in education spending of 1 percentage point of GDP → increase in composite enrollment rate of 6 percentage points within five years and another 3 percentage points in the following period.
    - Note: increase of 6 percentage points in composite enrollment ≡ one more year of schooling (Bils and Klenow (2000)).
  - Health spending:
    - Contemporaneous positive and significant impact on health capital.
    - Increase in health spending of 1 percentage point of GDP → rise in the under-5 child survival rate of 0.2 percentage points, on average, in developing countries.
    - Lagged health spending (five-year average of previous spending) has no effect on current health indicator; impact appears contemporaneous only.
- Interlinkages:
  - Health capital contributes to accumulation of education capital, with an elasticity of about 1.3.
  - Education influences health capital through gender equality (female share of students).
- Governance effects:
  - Health spending particularly sensitive to governance.
  - In countries with poor governance, health spending has no effect on health indicators; education spending impact also much reduced.
  - Poor governance associated with growth about 1.6 percentage points lower per year, other things equal.
  - Poor governance associated with investment-to-GDP ratio about 2 percentage points lower.
- Gender equality quantitative impacts:
  - A 1 percentage point increase in female share of enrolled students is associated with:
    - Increase of 2 percentage points in the composite enrollment rate.
    - Reduction of 0.3 percentage point in the child mortality rate.
- Income effects:
  - GDP per capita robustly and positively correlated with both education and health capital.

### VII. Elasticities, regression magnitudes, and robustness
- Education spending elasticity: 0.25 (elasticity of education indicators with respect to education spending).
- Health spending elasticity: 0.05 (elasticity of health indicators with respect to changes in public health outlays).
- Health–growth elasticities: estimated range from 1.4 to 3.2 across country groups.
- Education–growth: one year of additional primary and secondary schooling associated with increase in growth between 0.4 and 0.8 percentage points per year, depending on country group.
- Selected regression-level magnitudes (examples across estimators preserved):
  - Investment coefficients: 0.111, 0.104, 0.160, 0.143, 0.164, 0.155.
  - Changes in education capital coefficients: 0.118, 0.148, 0.072, 0.200, 0.107, 0.082.
  - Changes in health capital coefficients: 1.099, 0.984, 0.947, -0.416, 2.147, 1.531.
  - Under-5 child mortality effect on education enrollment (selected): -0.188, -0.130, -0.362, -0.319, -0.125, -0.065.
  - Current per capita income effect on under-5 mortality (selected): -9.425, -6.027, -16.422, -22.949, -8.576.

### VIII. Simulation results — selected policy intervention scenarios (Table 7)
- Simulation assumptions: policy change at end of baseline year; increased social spending maintained; rise in spending is deficit-neutral; elasticities from recursive model persist; other variables held constant except captured income effects.
- Increase education spending by 1 percent of GDP:
  - Composite enrollment: baseline 154.0 → T+1 160.0 → T+2 167.2 → T+3 172.5 (absolute changes: 6.0, 7.2, 5.4).
  - Implied net primary enrollment: baseline 89.7 → 93.2 → 97.5 → 100 (absolute changes: 3.5, 4.3, 1.0).
  - Per capita GDP growth (in percent): baseline 1.3 → 1.8 → 2.0 → 2.7 (absolute changes: 0.5, 0.2, 0.7).
  - Under-5 child mortality (per 1000 live births): baseline 76.0 → 76.0 → 70.9 → 64.7 (absolute changes: 0.0, -5.1, -6.2).
  - Implied headcount ratio: baseline 100.0 → 95.2 → 89.9 → 82.9 (absolute changes: -4.8, -5.3, -7.0).
  - Interpretation: increase in education spending of 1 percentage point of GDP is associated with 3 more years of schooling on average and a total increase in growth of 1.4 percentage points in 15 years; per capita growth rate would rise by about 0.5 percentage point per year on average over the simulation period; poverty headcount could fall by about 17 percent over 15 years.
- Increase health spending by 1 percent of GDP:
  - Under-5 child mortality: baseline 76.0 → T+1 73.6 → T+2 69.9 → T+3 69.9 (absolute changes: -2.4, -3.7, 0.0).
  - Composite enrollment: 154.0 → 154.4 → 157.7 → 157.7 (absolute changes: 0.4, 3.3, 0.0).
  - Implied net primary enrollment: 89.7 → 90.0 → 91.8 → 91.9 (absolute changes: 0.3, 1.9, 0.0).
  - Per capita GDP growth: 1.3 → 1.7 → 1.7 → 1.7 (absolute changes: 0.4, 0.0, 0.1).
  - Implied headcount ratio: 100.0 → 95.6 → 91.2 → 86.7 (absolute changes: -4.4, -4.4, -4.5).
  - Interpretation: raising health spending by 1 percent of GDP would reduce under-5 child mortality from 76 per thousand in 2000 to 70 per thousand in 2015; the MDG target of 62 per 1,000 cannot be met under this scenario; net enrollment rate would rise by about 2 percentage points (from 90 to 92); growth would rise by a total of 0.5 percentage points over 15 years.
- Improving governance to be above the world average:
  - Under-5 child mortality: 76.0 → 70.8 → 70.8 → 69.7 (absolute changes: -5.2, 0.0, -1.2).
  - Composite enrollment: 154.0 → 159.3 → 172.4 → 173.5 (absolute changes: 5.3, 13.2, 1.0).
  - Implied net primary enrollment: 89.7 → 92.8 → 100 → 100 (absolute changes: 3.1, 7.7, 0.6).
  - Per capita GDP growth: 1.3 → 2.9 → 2.7 → 2.8 (absolute changes: 1.6, -0.2, 0.1).
  - Implied headcount ratio: 100.0 → 92.5 → 85.5 → 78.2 (absolute changes: -7.5, -7.0, -7.3).
  - Interpretation: discrete jump from low-governance to high-governance associated with increase in growth rate of 1.6 percentage points; improving governance comparable to increasing education spending by 1 percent of GDP in impact.
- Reduce inflation by 10 percentage points:
  - Per capita GDP growth: 1.3 → 1.8 → 1.8 → 1.8 (absolute changes: 0.5, 0.0, 0.0).
  - Implied headcount ratio: 100.0 → 95.2 → 90.5 → 85.7 (absolute changes: -4.8, -4.8, -4.8).
  - Additional marginal change from high inflation to below 20 percent: growth effect 0.1 percentage point (from baseline 1.3 → 1.4), implied headcount ratio declines by -3.6 each period shown.
- Reduce fiscal deficit by 1 percent of GDP:
  - Per capita GDP growth: 1.3 → 1.8 → 1.8 → 1.8 (absolute changes: 0.5, 0, 0).
  - Implied headcount ratio: 100.0 → 95.3 → 90.6 → 86.0 (absolute changes: -4.7, -4.7, -4.7).
  - Interpretation: improving fiscal balance by 1 percentage point of GDP associated with increase in per capita GDP growth by 0.5 percentage point; effect assumed deficit reduction achieved without affecting social spending.
- Note: 1 percent of GDP of all developing countries ≈ $60 billion in 2000 (simulation context note from source).

### IX. Policy implications and recommendations
- Increase social spending:
  - Education: raising education spending by 1 percentage point of GDP yields meaningful long-term gains—3 more years of schooling on average and 1.4 percentage points total growth increase over 15 years; two-thirds of direct impact realized within five years, full impact in 10–15 years.
  - Health: raising health spending by 1 percentage point of GDP yields immediate reduction in under-5 mortality and a rise of 0.5 percentage point in annual per capita GDP growth over 15 years.
- Improve governance:
  - Strengthening governance can replicate or exceed impacts of higher social spending: immediate reduction in child mortality, substantial gains in enrollment, and a 1.6 percentage point increase in per capita GDP growth.
  - Reducing corruption and increasing accountability for public spending are as important as increasing spending.
- Maintain macroeconomic stability:
  - Reducing inflation (by 10 percentage points) and lowering fiscal deficits (by 1 percentage point of GDP) both yield a 0.5 percentage point increase in annual per capita GDP growth and reduce poverty headcount through growth.
- Targeting and efficiency:
  - Given moderate effects relative to spending costs, improving efficiency and targeting of social outlays is critical.
- Country heterogeneity:
  - Returns to social spending are highest in low-income countries and sub-Saharan Africa; marginal returns decline with higher initial levels of social outlays.
- Design considerations:
  - Simulations assume spending increases are deficit-neutral and governance and macro environment remain unchanged; effectiveness would be diminished if accompanied by deterioration in these areas.

### X. Appendix Table 8 — Short-Run Total Effects Decomposition: Selected Endogenous Variables (as reported)
- Total effects
  - Real per capita GDP growth: 0.000, 0.702, 0.091, 0.165
  - Investment ratio: 0.000, 0.000, 0.000, 0.035
  - Gross enrollment rate: 0.000, 0.000, 0.000, 0.188
  - Under-5 Child survival rate: 0.000, 0.000, 0.000, 0.000
- Direct effects
  - Real per capita GDP growth: 0.000, 0.702, 0.091, 0.124
  - Investment ratio: 0.000, 0.000, 0.000, 0.035
  - Gross enrollment rate: 0.000, 0.000, 0.000, 0.188
  - Under-5 Child survival rate: 0.000, 0.000, 0.000, 0.000
- Indirect effects
  - Real per capita GDP growth: 0.000, 0.000, 0.000, 0.042
  - Investment ratio: 0.000, 0.000, 0.000, 0.000
  - Gross enrollment rate: 0.000, 0.000, 0.000, 0.000
  - Under-5 Child survival rate: 0.000, 0.000, 0.000, 0.000

*Source: _wp04217 - Authors’ calculations and simulations reported in the IMF working paper (_wp04217)._*

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

### References (Excerpt) — _wp04217

### I. Introduction
- Human capital is identified as a key determinant of growth and human development (references include Romer (1986), Lucas (1988), Squire (1993), Ravallion and Chen (1997), Sen (1999), Schultz (1999)).
- The paper examines the role of public policy, particularly social spending, in helping countries meet the Millennium Development Goals (MDGs).
- Key research objective: provide an integrated assessment of the role of social spending and other policy interventions on human capital, economic growth, and social indicators using a panel dataset covering 120 developing countries from 1975 to 2000.
- Model aims:
  - Analyze dynamic direct and indirect effects of social spending on human capital and growth.
  - Account for interaction between education and health interventions.
  - Evaluate implications for the MDGs.
- Structure of the paper:
  - Section II: Literature review.
  - Section III: Data and model.
  - Section IV: Empirical results and robustness tests.
  - Section V: Simulated effects of policy interventions.
  - Section VI: Policy implications and conclusions.

### II. Literature review — key points
- Empirical literature often uses reduced-form equations and typically does not capture feedback effects across social spending, social indicators, and growth.
- Education and growth:
  - Several studies (Levine and Renelt (1992), Mankiw and others (1992), Barro and Sala-i-Martin (1995), Barro (1996a and 1996b), Sala-i-Martin (1997)) find a positive relationship between enrollment/schooling and growth.
  - Coulombe and others (2004): literacy scores 1 percent higher → increase in per capita GDP growth of 1.5 percentage points.
  - Counterevidence: Benhabib and Spiegel (1994), Pritchett and Summers (1996) — at best weak macro link from education attainment to output growth.
- Health and growth:
  - Fewer studies, but Bloom and Canning (2003, 2004) and Gyimah-Brempong and Wilson (2004) find positive contributions of health capital to aggregate output.
  - Estimated effects: about 22 to 30 percent of the growth rate attributed to health capital; improvements equivalent to one more year of life expectancy associated with higher GDP growth of up to 4 percentage points per year.
- Social spending → social indicators:
  - Mixed evidence. Baldacci and others (2003) and Gupta and others (2002b) find social spending important for education and health outcomes; education spending often has a greater effect.
  - Other studies find weak or insignificant links between public education outlays and education indicators (Noss (1991), Mingat and Tan (1992, 1998), Flug, Spilimbergo, and Wachtenheim (1998)).
  - Health spending effects on infant/child mortality often small or insignificant in several studies (Kim and Moody (1992), McGuire and others (1993), Musgrove (1996), Pritchett (1996), Filmer and Pritchett (1997), Filmer and others (1998)); Gupta and others (2003) find positive effects on the poor.
- Interaction of education and health:
  - Education raises awareness and capacity to address health needs; better health enhances effective use of education (Schultz (1999)); better health can reduce depreciation of education capital (Barro (1996b)).
  - Few integrated-system studies; Arjona and others (2001) for OECD countries finds positive association between selected social spending types and growth; Gyimah-Brempong and Wilson (2004) find positive link between health investment and growth in sub-Saharan Africa and OECD.
- Governance and institutions:
  - Poor governance mediates weak effectiveness of social spending (Mauro (1998), Abed and Gupta (2002), Gupta and others (2002a), Rajkumar and Swaroop (2002)).
  - Including governance helps address omitted-variable bias in the spending–outcomes relationship.

### III. Data and model — Methodology and equation system
- Econometric approach: panel data regressions in a recursive system of four equations for:
  1. Real per capita income growth.
  2. Total investment.
  3. Education attainment.
  4. Health status.
- Assumption: disturbances are not correlated across equations; standard least squares produce unbiased and efficient estimates. SUR tests are discussed under robustness checks in the paper.
- Sample: panel dataset covering 120 developing countries from 1975 to 2000.

- Growth equation
  - The growth equation is based on a neoclassical framework augmented by education and health capital.
  - Per capita output y is specified as y = f(sk, he, ed, Ω) where sk is the investment ratio, he is health capital, ed is education capital, and Ω is macro and institutional controls.
  - Growth of real per capita GDP g is modeled to depend on both initial stock and increment in human capital: g = f(ed, ∆ed, he, ∆he, sk, Ω).
  - Baseline growth equation presented as equation [1] (symbols and full functional form preserved in the source).
  - Definitions and key variable measurements:
    - it g: real per capita GDP growth.
    - i α and t η: country-specific and period-specific effects.
    - log(1−it y): lagged logarithm of per capita income to control for conditional convergence.
    - it ks: investment ratio measured as gross capital formation (private and public) in percent of GDP.
    - it Ed: stock of education capital proxied by the composite primary and secondary enrollment rate; ∆Ed: changes in education capital.
    - it He: stock of health capital proxied by logarithm of under-5 child mortality; ∆he: changes in health capital.
    - it n: rate of growth of total population.
    - it m Ω: control variables include trade openness (open = (imports + exports)/GDP), changes in terms of trade (dtot), fiscal balance (Balance), inflation (p), high inflation dummy (Highp) where inflation > 20 percent per year, LowdefBalance interaction (fiscal balance × low-deficit dummy where deficit below 3 percent of GDP), and Lowgov (poor governance dummy based on anticorruption and democratic accountability indices from ICRG).
    - it u: error term.
  - The model includes both levels and changes (stocks and increments) of human capital variables.

- Investment equation
  - Investment is modeled as influenced by education and health human capital and macro/institutional factors.
  - Specified as equation [2] in the source.
  - Explanatory variables include levels of education and health indicators, governance (Lowgov), fiscal balance, inflation (p and Highp), population growth, and other macro controls as defined in the growth equation.

- Education equation
  - Education capital (composite primary and secondary enrollment rate) is modeled as a function of education spending and other determinants.
  - Specified as equation [3] in the source.
  - Key explanatory variables and definitions:
    - Popu15: share of population below 15 years old (school-age population).
    - y: logarithm of real per capita GDP in PPP dollars.
    - Health capital: under-5 child mortality rate as proxy.
    - Quality: school repetition rate (higher repetition → lower quality).
    - EduSpending: current five-year average and lagged five-year average of education spending in percent of GDP; logarithmic functional form used.
    - Lowgov: poor governance dummy interacting with spending terms to capture governance effects on spending effectiveness.
    - Female: share of female students in primary and secondary schools (gender equality effect).
  - Lag structure: one lag chosen based on Schwartz Information Criteria (SIC) in a distributed lag specification; implies impact of education spending during a five-year period may take another five years to be fully realized.

### Tables and appendixes referenced in the source excerpt
- Tables listed in the document (table numbers and titles preserved):
  - Table 1. Summary Descriptive Statistics
  - Table 2. Growth Equation-Dependent Variable: Average Real Per Capita GDP Growth
  - Table 3. Investment Equation-Dependent Variable: Average Annual Investment Ratio
  - Table 4. Education Equation-Dependent Variable: Average Composite Enrollment Rate
  - Table 5. Health Equation-Dependent Variable: Average Annual Under-5 Child Mortality Rate
  - Table 6. Summary of Total Effect Coefficients by Country Group
  - Table 7. Simulation on the Impact on Growth and Social Indicators from Various Policy Interventions
- Appendixes:
  - Appendix I. Derivation of the Growth Equation with Human Capital
  - Appendix II. List of Countries Included in the Sample and Data Sources
- Appendix tables referenced:
  - Table 8. Short-Run Total Effects Decomposition: Selected Endogenous Variables
  - Table 9. Short-Run Total Effects Decomposition: Selected Exogenous Variables

*Source: _wp04217 - References (PDF excerpt).*

### 4. Health equation

### 4. Health equation

### Health equation specification
- Functional form (log-linear) used to model health indicator (under-5 child survival / mortality) includes:
  - Income level (log of real per capita GDP in PPP$).
  - Gender equality (share of female students as proxy).
  - Urbanization (share of urban population).
  - Poor governance (measured as in the education equation; a poor governance dummy is 1 for countries below the average governance index).
  - Current health spending (five-year average of health spending as a percent of GDP; logarithmic functional form adopted to control for decreasing returns).
- Note: The composite enrollment rate (proxy for aggregate education level) was not significant in the health equation and was dropped to allow a recursive, triangular coefficient matrix across the four equations (growth, investment, education, health).

### Decomposition of short-run effects (system structure)
- Recursive system form: ξΓxByy++=, reduced form: y = Πx+ξ.
- Definitions:
  - y = vector of endogenous variables.
  - x = vector of exogenous variables.
  - B = lower triangular matrix of direct effects between endogenous variables (βij ≠ 0 and βji = 0 for i>j).
  - Γ = matrix of direct effects of exogenous variables on endogenous variables.
  - ξ = vector of error terms.
- Total effect calculation: Π = (I − B)−1 Γ.
- Indirect effect calculation: Θ = (I − B)−1 B Γ (equivalently indirect effects = total effects − direct effects).
- Decomposition assumptions: current and lagged spending increases are independent; lagged education and health capital are predetermined. Decomposition focuses on short-run relationships; long-run effects analyzed in simulations in Section V.

### Data and estimation
- Panel dataset: 120 developing countries, 1975–2000; five-year averages used.
- Sources: IMF World Economic Outlook 2003, Barro-Lee dataset, World Development Indicators 2003, IMF staff reports social spending database, IMF Government Financial Statistics, ICRG index of corruption and democratic accountability.
- Variable measurement highlights:
  - Output growth = five-year average of annual growth rate of real per capita GDP.
  - Education and health capital = proxied by enrollment and child mortality/survival indicators.
  - Social spending = percent of GDP (five-year averages).
- Baseline estimator: fixed-effect model (LSDV).
- Robustness/alternative estimators used:
  - Robust estimator (controls for outliers).
  - Feasible Generalized Least Squares (FGLS) (controls for heteroskedasticity and first-order autocorrelation).
  - Error component two-stage least squares (EC2SLS).
  - Fixed-effect instrumental variable estimator (2SLS).
  - System GMM (for equations with lagged variables to address endogeneity, measurement error, omitted variables).
- Overidentification tests reported for instrument validity.

### Key descriptive statistics (Table 1, sample sizes and central measures)
- Real per capita GDP growth (in percent): Obs. 831; Mean 1.3; Std. dev. 4.0; Min. -20.6; Max. 30.9
- Investment ratio (in percent of GDP): Obs. 883; Mean 22.8; Std. dev. 8.8; Min. 0.3; Max. 50.2
- Composite enrollment rate (in percent): Obs. 792; Mean 130.6; Std. dev. 49.8; Min. 3.0; Max. 238.5
- Primary school enrollment rate (in percent): Obs. 801; Mean 88.5; Std. dev. 26.9; Min. 3.0; Max. 174.7
- Secondary school enrollment rate (in percent): Obs. 798; Mean 42.1; Std. dev. 29.5; Min. 0.0; Max. 126.6
- Under-5 child mortality (per 1000 live births): Obs. 897; Mean 111.0; Std. dev. 78.9; Min. 7.0; Max. 345.0
- Education spending (in percent of GDP): Obs. 689; Mean 3.6; Std. dev. 1.7; Min. 0.6; Max. 10.0
- Health spending (in percent of GDP): Obs. 354; Mean 2.2; Std. dev. 1.5; Min. 0.3; Max. 8.7
- Population growth (in percent): Obs. 831; Mean 2.0; Std. dev. 1.3; Min. -3.3; Max. 8.2
- Trade openness (in percent of GDP): Obs. 838; Mean 81.8; Std. dev. 89.1; Min. 0.1; Max. 1120.5
- Changes in terms of trade: Obs. 821; Mean 2.1; Std. dev. 15.5; Min. -21.2; Max. 365.9
- Fiscal balance (in percent of GDP): Obs. 713; Mean -4.9; Std. dev. 6.0; Min. -29.8; Max. 18.3
- Fiscal balance in low-deficit countries (deficit lower than sample mean): Obs. 713; Mean 0.0; Std. dev. 1.9; Min. -3.0; Max. 18.3
- Income level (log of real per capita GDP in PPP$): Obs. 968; Mean 9.4; Std. dev. 3.2; Min. -10.7; Max. 16.9
- Inflation rate (log of changes in CPI): Obs. 884; Mean 0.2; Std. dev. 0.4; Min. -0.1; Max. 3.4
- High inflation dummy (inflation >20 percent): Obs. 884; Mean 0.2; Std. dev. 0.4; Min. 0.0; Max. 1.0
- Governance index (1-12; higher value equals better governance): Obs. 364; Mean 5.9; Std. dev. 1.9; Min. 1.0; Max. 11.0
- Poor governance dummy (1 for countries below the average governance index): Obs. 987; Mean 0.2; Std. dev. 0.4; Min. 0.0; Max. 1.0
- Fertility rate (per 1000 people per year): Obs. 951; Mean 4.7; Std. dev. 1.8; Min. 1.1; Max. 10.0
- Share of under-15 population (in percent): Obs. 931; Mean 39.3; Std. dev. 8.1; Min. 16.6; Max. 51.2
- Urbanization (share of urban population): Obs. 980; Mean 39.1; Std. dev. 20.1; Min. 2.4; Max. 91.4
- School repetition rate (in percent): Obs. 512; Mean 12.5; Std. dev. 9.8; Min. 0.1; Max. 38.6

### Main empirical results relating to health and broader nexus (selected findings)
- Contribution to growth:
  - Both education capital and health capital positively contribute to output growth, but via slightly different routes.
  - Education: both stock and flow affect growth; effects from both channels similar in magnitude.
  - Health: only direct effect on growth is through flows; stock of health capital affects growth indirectly via investment.
  - Social spending affects education and health indicators, so social spending boosts growth via human capital.
- Education spending dynamics:
  - Education spending has immediate and lagged effects on education capital.
  - About two-thirds of the direct effect realized in the first five years; the remainder in the next five years.
  - Example: increase in education spending of 1 percentage point of GDP → increase in composite enrollment rate of 6 percentage points within five years and another 3 percentage points in the following period.
  - Note: an increase of 6 percentage points in composite enrollment is equivalent to one more year of schooling (following Bils and Klenow (2000)).
- Health spending effects:
  - Contemporaneous positive and significant impact on health capital.
  - Increase in health spending of 1 percentage point of GDP → rise in the under-5 child survival rate of 0.2 percentage points, on average, in developing countries.
  - Lagged health spending (five-year average of previous spending) has no effect on current health indicator; impact appears contemporaneous only.
- Interlinkages between education and health:
  - Health capital contributes to accumulation of education capital, with an elasticity of about 1.3.
  - Education influences health capital through gender equality (female share of students).
- Governance and its role:
  - Governance has significant direct effects on links between social spending and social indicators; health spending is particularly sensitive to governance.
  - In countries with poor governance, health spending has no effect on health indicators; impact of education spending is also much reduced.
  - Poor governance reduces growth mainly through its impacts on human capital and investment:
    - Countries with poor governance have growth about 1.6 percentage points lower per year, other things equal.
    - Poor governance associated with investment-to-GDP ratio about 2 percentage points lower.
  - The effect of governance on growth is transmitted through indirect channels via social indicators and investment.
- Gender equality and quantitative impacts:
  - Female share of enrolled students positively associated with education capital and negatively associated with child mortality.
  - A 1 percentage point increase in female share of enrolled students (e.g., from 40 percent to 41 percent) is associated with:
    - Increase of 2 percentage points in the composite enrollment rate.
    - Reduction of 0.3 percentage point in the child mortality rate.
- Income effects:
  - GDP per capita is robustly and positively correlated with both education and health capital, indicating mutual reinforcement between income and human capital.
- Heterogeneity:
  - Impact of education and health capital on growth varies across income and regional groups (results referenced in Table 6; details not reproduced here).

*Source: _wp04217 - 4. Health equation*

### 0.1 percentage point increase in per capita GDP growth. This effect is 1.5 times that

### _wp04217 - 0.1 percentage point increase in per capita GDP growth. This effect is 1.5 times that

### Key empirical findings
- Education spending elasticity: 0.25 (elasticity of education indicators with respect to education spending).
- Health spending elasticity: 0.05 (elasticity of health indicators with respect to changes in public health outlays).
- Health–growth elasticities: estimated range from 1.4 to 3.2 for different country groups (compared with Bloom and Canning (2003) and Bloom and Sevilla (2004) estimates of 1.3 and 1.9).
- Education–growth: one year of additional primary and secondary schooling is associated with an increase in growth ranging between 0.4 and 0.8 percentage points per year, depending on country group.
- Regression-level magnitudes (selected):
  - Investment coefficients range (examples across estimators): 0.111, 0.104, 0.160, 0.143, 0.164, 0.155.
  - Changes in education capital coefficients (examples): 0.118, 0.148, 0.072, 0.200, 0.107, 0.082.
  - Changes in health capital coefficients (examples): 1.099, 0.984, 0.947, -0.416, 2.147, 1.531.
  - Under-5 child mortality effect on education enrollment (selected): -0.188, -0.130, -0.362, -0.319, -0.125, -0.065.
  - Current per capita income effect on under-5 mortality (selected): -9.425, -6.027, -16.422, -22.949, -8.576.

### Summary of total-effect coefficients (selected from Table 6)
- All developing countries (dy/dx impacts):
  - Real per capita GDP growth: 0.09 (composite enrollment), 0.17 (under-5 child survival rate), 0.54 (current education spending), 0.39 (current health spending), 0.25 (lagged education spending).
  - Composite enrollment rate: 0.00 (on composite), 0.19 (on under-5 child survival), 6.00 (on current education spending), 0.44 (on current health spending), 2.72 (on lagged education spending).
- Low-income countries:
  - Real per capita GDP growth: 0.12, 0.11, 0.59, 0.48, 0.27 (same variable order as above).
- Sub-Saharan Africa:
  - Real per capita GDP growth: 0.13, 0.10, 0.55, 0.48, 0.25.

### Robustness and comparison with literature
- Education elasticity (0.25) is close to upper range in the literature (Psacharopoulos (1994); Psacharopoulos and Patrinos (2002); Baldacci and others (2003)).
- Health elasticity (0.05) is consistent with Schultz (1999) and Gupta and others (2002b).
- Health–growth elasticities of 1.4–3.2 compare with Bloom and Canning (2003) and Bloom and Sevilla (2004) elasticities of 1.3 and 1.9.
- Education-year effect comparisons: literature estimates 0.3 to 3 percentage points per year (Levine and Renelt (1992); Barro (1996a); others); this paper: 0.4 to 0.8 percentage points per additional year (composite enrollment basis).
- Results robust across estimators: robust regression, two-stage least squares, system GMM; qualitatively consistent when solving system simultaneously (Seemingly Unrelated Regression) and under alternative education and health indicators.

### Simulation results (policy interventions, Table 7)
- Assumptions: policy change at end of baseline year; increased social spending maintained; rise in spending is deficit-neutral; elasticities from recursive model persist; other variables held constant except captured income effects.
- Increase education spending by 1 percent of GDP:
  - Composite enrollment: baseline 154.0 → T+1 160.0 → T+2 167.2 → T+3 172.5 (absolute changes: 6.0, 7.2, 5.4).
  - Implied net primary enrollment: baseline 89.7 → 93.2 → 97.5 → 100 (absolute changes: 3.5, 4.3, 1.0).
  - Per capita GDP growth (in percent): baseline 1.3 → 1.8 → 2.0 → 2.7 (absolute changes: 0.5, 0.2, 0.7).
  - Under-5 child mortality (per 1000 live births): baseline 76.0 → 76.0 → 70.9 → 64.7 (absolute changes: 0.0, -5.1, -6.2).
  - Implied headcount ratio: baseline 100.0 → 95.2 → 89.9 → 82.9 (absolute changes: -4.8, -5.3, -7.0).
  - Interpretation in text: increase in education spending of 1 percentage point of GDP is associated with 3 more years of schooling on average and a total increase in growth of 1.4 percentage points in 15 years; per capita growth rate would rise by about 0.5 percentage point per year on average over the simulation period; poverty headcount could fall by about 17 percent over 15 years.
- Increase health spending by 1 percent of GDP:
  - Under-5 child mortality: baseline 76.0 → T+1 73.6 → T+2 69.9 → T+3 69.9 (absolute changes: -2.4, -3.7, 0.0).
  - Composite enrollment: 154.0 → 154.4 → 157.7 → 157.7 (absolute changes: 0.4, 3.3, 0.0).
  - Implied net primary enrollment: 89.7 → 90.0 → 91.8 → 91.9 (absolute changes: 0.3, 1.9, 0.0).
  - Per capita GDP growth: 1.3 → 1.7 → 1.7 → 1.7 (absolute changes: 0.4, 0.0, 0.1).
  - Implied headcount ratio: 100.0 → 95.6 → 91.2 → 86.7 (absolute changes: -4.4, -4.4, -4.5).
  - Text interpretation: raising health spending by 1 percent of GDP would reduce under-5 child mortality from 76 per thousand in 2000 to 70 per thousand in 2015; the MDG target of 62 per 1,000 cannot be met under this scenario; net enrollment rate would rise by about 2 percentage points (from 90 to 92); growth would rise by a total of 0.5 percentage points over 15 years.
- Improving governance to be above the world average:
  - Under-5 child mortality: 76.0 → 70.8 → 70.8 → 69.7 (absolute changes: -5.2, 0.0, -1.2).
  - Composite enrollment: 154.0 → 159.3 → 172.4 → 173.5 (absolute changes: 5.3, 13.2, 1.0).
  - Implied net primary enrollment: 89.7 → 92.8 → 100 → 100 (absolute changes: 3.1, 7.7, 0.6).
  - Per capita GDP growth: 1.3 → 2.9 → 2.7 → 2.8 (absolute changes: 1.6, -0.2, 0.1).
  - Implied headcount ratio: 100.0 → 92.5 → 85.5 → 78.2 (absolute changes: -7.5, -7.0, -7.3).
  - Text interpretation: a discrete jump from low-governance to high-governance is associated with an increase in the growth rate of 1.6 percentage points; change from lower- to higher-than-average governance yields immediate reduction of 0.5 percentage point in child mortality, increase of 6 percentage points in composite enrollment, and rise of 1.6 percentage points in per capita GDP growth; elevating governance is comparable to increasing education spending by 1 percent of GDP in impact.
- Reduce inflation by 10 percentage points (e.g., from 40 percent to 30 percent):
  - Per capita GDP growth: 1.3 → 1.8 → 1.8 → 1.8 (absolute changes: 0.5, 0.0, 0.0).
  - Implied headcount ratio: 100.0 → 95.2 → 90.5 → 85.7 (absolute changes: -4.8, -4.8, -4.8).
  - Additional marginal change from high inflation to below 20 percent: growth effect 0.1 percentage point (from baseline 1.3 → 1.4), implied headcount ratio declines by -3.6 each period shown.
- Reduce fiscal deficit by 1 percent of GDP:
  - Per capita GDP growth: 1.3 → 1.8 → 1.8 → 1.8 (absolute changes: 0.5, 0, 0).
  - Implied headcount ratio: 100.0 → 95.3 → 90.6 → 86.0 (absolute changes: -4.7, -4.7, -4.7).
  - Text interpretation: improving fiscal balance by 1 percentage point of GDP is associated with increase in per capita GDP growth by 0.5 percentage point; effect assumed deficit reduction achieved without affecting social spending.

### Policy implications and recommendations
- Increase social spending:
  - Education: raising education spending by 1 percentage point of GDP yields meaningful long-term gains—3 more years of schooling on average and 1.4 percentage points total growth increase over 15 years; two-thirds of direct impact realized within five years, full impact in 10–15 years (important lag).
  - Health: raising health spending by 1 percentage point of GDP yields immediate reduction in under-5 mortality (0.6 percentage point increase in under-5 survival rate reported) and a rise of 0.5 percentage point in annual per capita GDP growth.
- Improve governance:
  - Strengthening governance can replicate or exceed impacts of higher social spending: immediate reduction in child mortality, substantial gains in enrollment, and a 1.6 percentage point increase in per capita GDP growth.
  - Reducing corruption and increasing accountability for public spending are as important as increasing spending.
- Maintain macroeconomic stability:
  - Reducing inflation (by 10 percentage points) and lowering fiscal deficits (by 1 percentage point of GDP) both yield a 0.5 percentage point increase in annual per capita GDP growth and reduce poverty headcount through growth.
- Targeting and efficiency:
  - Given the moderate effects relative to spending costs, improving efficiency and targeting of social outlays is critical.
- Country heterogeneity:
  - Returns to social spending are highest in low-income countries and sub-Saharan Africa; marginal returns decline with higher initial levels of social outlays.
- Design considerations:
  - Simulations assume spending increases are deficit-neutral (through grants, increased revenues, or reallocation) and that governance and macro environment remain unchanged; effectiveness would be diminished if accompanied by deterioration in these areas.

### Notes on methodology (selected)
- Model: neoclassical growth model augmented with human capital decomposed into education capital and health capital; recursive system of growth, investment, education, and health equations estimated.
- Data: five-year averages; variables from WEO, WDI, Barro-Lee (2003), IMF databases, and ICRG governance components.
- Simulations: partial equilibrium, assume elasticities persist; initial baseline averages for developing countries; 1 percent of GDP of all developing countries ≈ $60 billion in 2000.

*Source: Authors’ calculations and simulations reported in the IMF working paper (_wp04217)._*

### Appendix Table 8. Short-Run Total Effects Decomposition: Selected Endogenous Variables

### Appendix Table 8. Short-Run Total Effects Decomposition: Selected Endogenous Variables

### Total effects
- Real per capita GDP growth: 0.000, 0.702, 0.091, 0.165
- Investment ratio: 0.000, 0.000, 0.000, 0.035
- Gross enrollment rate: 0.000, 0.000, 0.000, 0.188
- Under-5 Child survival rate: 0.000, 0.000, 0.000, 0.000

### Direct effects
- Real per capita GDP growth: 0.000, 0.702, 0.091, 0.124
- Investment ratio: 0.000, 0.000, 0.000, 0.035
- Gross enrollment rate: 0.000, 0.000, 0.000, 0.188
- Under-5 Child survival rate: 0.000, 0.000, 0.000, 0.000

### Indirect effects
- Real per capita GDP growth: 0.000, 0.000, 0.000, 0.042
- Investment ratio: 0.000, 0.000, 0.000, 0.000
- Gross enrollment rate: 0.000, 0.000, 0.000, 0.000
- Under-5 Child survival rate: 0.000, 0.000, 0.000, 0.000

*Appendix Table 8. Short-Run Total Effects Decomposition: Selected Endogenous Variables*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp04217.pdf_