## wpiea2019204-print-pdf

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---

### Introduction and scope
- Study period: 1995–2016; primary sample: 68 countries that regularly report COFOG data to the GFSY database.
- Primary research question: estimated effects of public social spending (education, health, social protection) on three HDI dimensions: GNI per capita (in PPP in $), expected years of schooling, and life expectancy.
- Data sources: IMF Government Finance Statistics Yearbook (GFSY) COFOG data; UN Global Indicators/HDI database; World Bank Open Data/WDI; IMF WEO; WGI governance indicators.
- Methodological approaches: panel regressions with lagged dependent and explanatory variables; country fixed effects; instrumental variables; Arellano and Bond (1991) GMM estimator; Hausman test to choose between fixed and random effects.

### Model and identification strategies
- Core estimating equation:
  - yᵢₜ = c + α yᵢₜ˗₁ + β xᵢₜ˗₁ + μ Zᵢₜ˗₁ + δᵢ + γₜ + εᵢₜ
- Endogeneity strategies:
  - Lagged explanatory and dependent variables.
  - Country fixed effects and time effects.
  - Instrumental variables and Hausman endogeneity tests.
  - Arellano and Bond (1991) GMM using time-differenced instruments (e.g., yᵢₜ˗₂ for ∆yᵢₜ˗₁).
- Controls included: population, population growth, inflation, investment, terms of trade, literacy rate, Gini index, voice and accountability, political stability and no violence, government effectiveness, rule of law, regulatory quality, control of corruption.

### Key data summary statistics (exact figures from Table 1)
- Dependent variables:
  - GNI per capita in 2011 PPPs (in USD, logs): Mean 21110; Median 17769.7; Maximum 67031.5; Minimum 7164.0; Std. Dev. 15492.6; Observations 1313.
  - Expected years in schooling: Mean 13.6; Median 13.7; Maximum 20.7; Minimum 3.9; Std. Dev. 2.9; Observations 1428.
  - Life expectancy: Mean 72.5; Median 73.7; Maximum 83.7; Minimum 42.1; Std. Dev. 7.6; Observations 1428.
- Explanatory variables (public social spending, percent of GDP):
  - Public educational expenditures as % of GDP: Mean 4.7; Median 4.8; Maximum 9.2; Minimum 921.1; Std. Dev. 1.6; Observations 1149.
  - Public health expenditures as % of GDP: Mean 4.4; Median 4.2; Maximum 28.1; Minimum 0.04; Std. Dev. 3.4; Observations 1142.
  - Public social protection as % of GDP: Mean 10.1; Median 10.7; Maximum 25.6; Minimum 0; Std. Dev. 7.3; Observations 1140.
- Selected controls:
  - Gini index: Mean 36.0; Median 34.25; Maximum 43.45; Minimum 32.29; Std. Dev. 3.4; Observations 1518.
  - Literacy rate: Mean 89.7; Median 89.9; Maximum 91.8; Minimum 84.6; Std. Dev. 1.5; Observations 1518.
  - Total population (in logs): Mean 18.08; Median 18.08; Maximum 18.18; Minimum 17.97; Std. Dev. 0.06; Observations 1518.
  - Investment rates: Mean 21.95; Median 22.20; Maximum 68.94; Minimum 0.0; Std. Dev. 0.10; Observations 1527.

### Main empirical findings — GNI per capita
- Fixed effects OLS (Table 2, selected coefficients):
  - Public education expenditures (logs, lagged): 0.0204*** (standard error 0.0078) in specification (1).
  - Public health expenditures (logs, lagged): −0.0036 (standard error 0.0029) (reported negative in baseline).
  - Public social protection expenditures (logs, lagged): 0.0027** (standard error 0.0012).
  - Lagged dependent variable (GNI per capita in logs, lagged): 0.9295*** (0.0158), 0.9227*** (0.0137), 0.9158*** (0.0139) across specifications.
  - Model fit: R2 = 0.99; Observations: 975, 967, 957 across specifications; Cross-sections reported as 64, 20, 21; Periods reported as 21, 63, 62.
  - Hausman test p-value = 0 → fixed effects preferred.
- Robustness and alternative specifications (Section VI, selected):
  - Educational spending coefficients across specifications: 0.0204*** (spec. (1)), 0.0233*** (spec. (2) with health and social protection), 0.0364** (GMM spec. (3)), other specs: 0.017, 0.018.
  - Public health coefficients often negative in various specifications: e.g., -0.0109**, -0.0097**, -0.0071, -0.0071*, -0.0071*.
  - Public social protection coefficients small but often statistically significant: e.g., 0.0028*, 0.0036**, 0.0052, 0.0042**, 0.0047***, 0.0036**, 0.0030, 0.0035**, 0.0037**.
  - Key robustness conclusion: GMM estimator (0.036 in spec. (3)) is similar in sign and magnitude to fixed effects lagged result (0.020 in spec. (1)); controlling for WGI indicators does not remove statistically significant educational spending effect.
- Authors' interpretation:
  - A 1 percent difference in public educational expenditure leads to a 0.020 (OLS) percent difference in the average GNI per capita in the short run and larger in long run (text statement).
  - Health spending coefficient negative and social protection coefficient small; IV and GMM used for further checks.

### Main empirical findings — Expected years of schooling
- Baseline and robustness (Table 3 and Section VI):
  - Static OLS (no fixed effects): a 1 percent increase in public educational spending implies 0.233 percent difference in expected years of schooling.
  - Fixed effects (no lagged dependent): 0.130 and 0.193 percent increases in two specifications.
  - Fixed effects with lagged dependent: short-run coefficient 0.014; long-run coefficient 0.130 (comparable to static fixed-effects).
  - Robustness coefficients (selected): 0.0141*** (fixed effects OLS spec. (1)), 0.0141*** (spec. (2) with Gini), 0.0168*** (GMM spec. (3)), 0.0139***, 0.0148***, 0.0212***, 0.0164** in other specifications.
  - Lagged dependent values: 0.8928***, 0.8791***, 0.8421***, 0.8684***, 0.8686***.
  - Controls with notable coefficients: Gini (in logs, lagged) -0.0132***; population (in logs) 0.0499***; total population (in logs, lagged) 0.0438***; population growth (lagged) 0.0126***; literacy rate (in logs, lagged) -0.0609***; voice and accountability -0.0275**; rule of law -0.0365***.
- Robustness conclusion:
  - A 1 percent increase in public educational spending results in 0.014 percent short-run positive difference in expected years of schooling in the lagged-dependent specification (spec. (1)); GMM confirms magnitude at 0.0168*** (spec. (3)).
  - Relationship robust to inclusion of Gini, population growth, literacy, rule of law, and voice and accountability.

### Main empirical findings — Life expectancy and public health spending
- Baseline and robustness (Table 4, Table 7, Section VI):
  - Static fixed effects: a 1 percent public health expenditure (lagged) implies a percentage increase in life expectancy of 0.017 (text statement).
  - Lagged-dependent specification: short-run coefficient reported as 0.0005*** (table 4 column (4)); long-run effect computed as 0.020 (β/(1-α), text).
  - Table 4 reported public health coefficients: 0.0486**, 0.0498**, 0.0170**, 0.0005*** across columns (1)–(4).
  - Robustness (Table 7) short-run public health coefficients: 0.0005** (spec. (1)), 0.0009*** (spec. (2)), 0.0007** (spec. (3)); GMM spec. (4) 0.0003***.
  - Other reported controls: total population (in logs, lagged) 0.0224***, 0.0065***; literacy rate (in logs, lagged) 0.01880**, 0.0139***; life expectancy (in logs, lagged) 0.9752***, 0.9726***, 0.9834***.
- Robustness conclusion:
  - Short-run effects are quantitatively small (e.g., 0.0005***), but long-run effects (β/(1-α)) are larger and comparable to static fixed effects estimates (text reports long-run 0.020 comparable with 0.017).
  - Including controls such as GNI and Gini does not overturn the positive relationship; one reported figure: a 1 percent increase in public health spending results in 0.0009 percent positive difference in life expectancy (spec. (2) text).

### Robustness — overview of methods and instruments
- Additional controls used: public spending on education, health, social protection; population growth; inflation (in logs); investment; terms of trade; WGI indicators.
- GMM estimators use second lags of dependent and explanatory variables as instruments; some GMM specs include instruments such as total population (in logs) and literacy rate (in logs).
- Hausman test p-value = 0 in main specifications → fixed effects preferred.

### Granger causality (pairwise test results, selected numeric outputs)
- GNI per capita (in logs) does not Granger Cause Public educational expenditures (in logs, share of GDP): Obs 618; F-Statistic 1.87502; Prob. 0.0829.
- Public educational expenditures (in logs, share of GDP) does not Granger Cause GNI per capita (in logs): Obs 618; F-Statistic 2.47266; Prob. 0.0227.
- GNI per capita (in logs) does not Granger Cause Public health expenditures (in logs, share of GDP): Obs 607; F-Statistic 3.78057; Prob. 0.0011.
- Public health expenditures (in logs, share of GDP) does not Granger Cause GNI per capita (in logs): Obs 607; F-Statistic 1.87869; Prob. 0.0823.
- GNI per capita (in logs) does not Granger Cause Public social protection spending (in logs, share of GDP): Lags 2; Obs 834; F-Statistic 3.34294; Prob. 0.0358.
- Public social protection spending (in logs, share of GDP) does not Granger Cause GNI per capita (in logs): Lags 2; Obs 834; F-Statistic 5.07283; Prob. 0.0065.
- Education and schooling (Lags 6): Public educational expenditures → Expected years of schooling: Obs 697; F-Statistic 4.71522; Prob. 0.0001. Expected years of schooling → Public educational expenditures: Obs 697; F-Statistic 1.16388; Prob. 0.3238.
- Health and life expectancy (Lags 6): Public health expenditures → Life expectancy: Obs 694; F-Statistic 1.86936; Prob. 0.0836. Life expectancy → Public health expenditures: Obs 694; F-Statistic 1.29652; Prob. 0.2564.
- Health and life expectancy (Lags 8): Public health expenditures → Life expectancy: Obs 565; F-Statistic 2.99193; Prob. 0.0027. Life expectancy → Public health expenditures: Obs 565; F-Statistic 1.78580; Prob. 0.0772.
- Interpretation from source: bivariate Granger tests indicate some bidirectional causality at 10 percent significance for certain relationships, but are limited because they do not control for other factors.

### Regional and income-level public social spending (2016, percent of GDP — selected figures)
- Social Protection by Region:
  - AFR: 5.5; APD: 5.3; EUR: 14.9; MCD: 6.6; WHD: 6.0.
- Social Protection by Country Income Level:
  - LIC: 5.3; LMIC: 8.5; UMIC: 9.4; HIC: 10.2.
- Educational Spending by Region:
  - AFR: 4.8; APD: 4.6; EUR: 5.0; MCD: 4.3; WHD: 3.6.
- Educational Spending by Country Income Level:
  - LIC: 3.3; LMIC: 4.2; UMIC: 4.9; HIC: 5.0.
- Health Spending by Region:
  - AFR: 2.7; APD: 3.7; EUR: 5.4; MCD: 2.7; WHD: 4.0.
- Health Spending by Country Income Level:
  - LIC: 1.1; LMIC: 2.8; UMIC: 3.5; HIC: 6.1.

### Contextual observations reported
- Social protection coverage in Sub-Saharan Africa: covers 17.8 percent of the population; coverage ranges from 48 percent in South Africa to below 10 percent in some West African countries.
- Old-age pensions in Africa cover 29.6 percent of older persons; universal or near-universal coverage in listed African economies.
- Education spending: in most emerging and developing economies education expenditure has increased and "in most" reached 4 percent of GDP; low-income countries around 3 percent of GDP.
- Europe: governments finance more than 80 percent of total education spending; high/very high HDI countries reached expected years of schooling of 14–16 years; medium/low HDI countries: 10–12 years.
- Health coverage gaps: nearly 50 percent of the global population lacks health coverage; rural exclusion from health insurance coverage is 80 percent in Sub-Saharan Africa and 56 percent in South Asia and Pacific.
- Life expectancy averages: 79.5 years in very high HDI countries versus 60.8 in low human development countries.

### Authors' conclusions (as presented)
- Positive long-run effect of public educational spending on GNI per capita.
- No similar statistically meaningful long-run relationship between GNI per capita and public social spending on health and social protection in basic specifications.
- Straightforward long-run relationships found between:
  - public educational spending and expected years of schooling;
  - public health spending and life expectancy.
- Results robust to fixed effects and lagged variables, but authors emphasize need for further robustness checks using instrumental variables and GMM to address potential endogeneity and measurement error.

*Source: wpiea2019204-print-pdf*

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

### References

### Appendices
- Appendix I. Countries Reported For The IMF GFS Yearbook Used The Sample ...................................................................... 34
- Appendix II. Data Methodology and Tests .................................................................................. 36
- Appendix III. Public Social Spending by Regions and Level of Income (figures) ..................... 40

### Tables
- 1. Summary Statistics .................................................................................................................. 16
- 2. Basic Regression Results for GNI per Capita and Public Educational  Spending................... 18
- 3. Basic Regression Results for Expected Years of Schooling .................................................... 20
- 4. Basic Regression Results for Life Expectancy ........................................................................ 21
- 5. Robustness Checks for GNI and Public Social Spending ........................................................ 22
- 6. Robustness Checks for Expected Years of Schooling ............................................................. 25
- 7. Robustness Checks for Life Expectancy ................................................................................. 27
- 8. GFS Functions of Government for Social Spending (GFSM 2014) ........................................ 36
- 9. Granger Causality Test ............................................................................................................ 38

### Figures
- 1. Gini Index by Regions, 1995–2015 ........................................................................................... 7
- 2. Human Development Index by Regions for 2017 ..................................................................... 8
- 3. Government Expenditure per Student in Levels of Education by Regions for 2017   
    (as % of GDP per capita) ......................................................................................................... 10
- 4. Expected Years of Schooling and HDI for 2017 ..................................................................... 10
- 5. Life Expectancy and HDI for 2017.......................................................................................... 11
- 6. Social Protection Spending by Regions for 2016 (percent of GDP) ....................................... 40
- 7. Social Protection by Countries Income Level for 2016 (percent of GDP) .............................. 40
- 8. Educational spending by Regions for 2016 (percent of GDP) ................................................ 41
- 9. Educational spending by Countries Income Level for 2016 (percent of GDP) ....................... 41
- 10. Health Spending by Regions for 2016 (percent of GDP) ...................................................... 42

*Source: wpiea2019204-print-pdf - References.*

### 11. Health Spending by Countries Income Level for 2016 (percent of GDP) ............................. 42

### 11. Health Spending by Countries Income Level for 2016 (percent of GDP)

### Introduction and scope
- Study period: 1995–2016; primary sample: 68 countries that regularly report COFOG data to the GFSY database.
- Primary research question: estimated effects of public social spending (education, health, social protection) on three HDI dimensions: GNI per capita (in PPP in $), expected years of schooling, and life expectancy.
- Data sources: IMF Government Finance Statistics Yearbook (GFSY) COFOG data; UN Global Indicators/HDI database; World Bank Open Data/WDI; IMF WEO for inflation and investment; WGI for governance indicators.
- Main methodological approaches: panel regressions with lagged dependent and explanatory variables; country fixed effects; instrumental variables; Arellano and Bond (1991) GMM estimator; Hausman test to choose between fixed and random effects.

### Model and identification strategies
- Core estimating equation (distributed lag, fixed effects panel):
  yᵢₜ = c + α yᵢₜ˗₁ + β xᵢₜ˗₁ + μ Zᵢₜ˗₁ + δᵢ + γₜ + εᵢₜ
- Strategies to address endogeneity:
  - Use of lagged explanatory and dependent variables (causality flows forward).
  - Country fixed effects and time effects to control for time-invariant and common shocks.
  - Instrumental variables and Hausman endogeneity tests.
  - GMM (Arellano and Bond, 1991) using time-differenced instruments (e.g., yᵢₜ˗₂ for ∆yᵢₜ˗₁).
- Control variables included (list preserved): population, population growth, inflation, investment, terms of trade, literacy rate, Gini index, voice and accountability, political stability and no violence, government effectiveness, rule of law, regulatory quality, control of corruption.

### Key data summary statistics (exact values from Table 1)
- Dependent variables:
  - GNI per capita in 2011 PPPs (in USD, logs): Mean 21110; Median 17769.7; Maximum 67031.5; Minimum 7164.0; Std. Dev. 15492.6; Observations 1313.
  - Expected years in schooling: Mean 13.6; Median 13.7; Maximum 20.7; Minimum 3.9; Std. Dev. 2.9; Observations 1428.
  - Life expectancy: Mean 72.5; Median 73.7; Maximum 83.7; Minimum 42.1; Std. Dev. 7.6; Observations 1428.
- Explanatory variables (public social spending, percent of GDP):
  - Public educational expenditures as % of GDP: Mean 4.7; Median 4.8; Maximum 9.2; Minimum 921.1; Std. Dev. 1.6; Observations 1149.
  - Public health expenditures as % of GDP: Mean 4.4; Median 4.2; Maximum 28.1; Minimum 0.04; Std. Dev. 3.4; Observations 1142.
  - Public social protection as % of GDP: Mean 10.1; Median 10.7; Maximum 25.6; Minimum 0; Std. Dev. 7.3; Observations 1140.
- Selected controls (means and observations):
  - Gini index: Mean 36.0; Median 34.25; Maximum 43.45; Minimum 32.29; Std. Dev. 3.4; Observations 1518.
  - Literacy rate: Mean 89.7; Median 89.9; Maximum 91.8; Minimum 84.6; Std. Dev. 1.5; Observations 1518.
  - Total population (in logs): Mean 18.08; Median 18.08; Maximum 18.18; Minimum 17.97; Std. Dev. 0.06; Observations 1518.
  - Investment rates: Mean 21.95; Median 22.20; Maximum 68.94; Minimum 0.0; Std. Dev. 0.10; Observations 1527.

### Main empirical findings — summary of estimated effects
- GNI per capita (log) — fixed effects OLS results (Table 2, specifications (1)–(3)):
  - Public education expenditures (logs, lagged) → coefficient 0.0204*** (standard error 0.0078). Interpretation in paper: "a 1 percent difference in public educational expenditure leads to a 0.020 (OLS) percent difference in the average GNI per capita in the short run and larger in long run."
  - Public health expenditures (logs, lagged) → coefficient −0.0036 (standard error 0.0029); statistically significant reporting: coefficient is negative (not meaningful).
  - Public social protection expenditures (logs, lagged) → coefficient 0.0027** (standard error 0.0012).
  - Lagged dependent variable (GNI per capita in logs, lagged) → coefficients across specifications: 0.9295*** (0.0158), 0.9227*** (0.0137), 0.9158*** (0.0139).
  - Model fit: R2 = 0.99; Observations: 975, 967, 957 across specifications; Cross-sections (countries) reported as 64, 20, 21 in table; Periods reported as 21, 63, 62 (as shown).
  - Hausman test p-value = 0 → fixed effects preferred over random effects.
  - Authors note: health spending coefficient negative and social protection coefficient small; results require further examination with IV and GMM.

- Expected years of schooling — basic results (Table 3 summary text):
  - Static OLS (no fixed effects): a 1 percent increase in public educational spending implies 0.233 percent difference in expected years of schooling.
  - Fixed effects specifications (without lagged dependent variable): 1 percent increase in public educational spending → 0.130 and 0.193 percent increase in expected years of schooling (two fixed-effects specifications).
  - Fixed effects with lagged dependent variable: short-run coefficient 0.014; long-run coefficient 0.130 (authors note these are comparable to fixed-effects static results).
  - Hausman test p-value = 0 → fixed effects appropriate.
  - Authors note: to address potential endogeneity, results require further investigation with IV and GMM.

- Life expectancy and public health spending — qualitative result reported in introduction and summary:
  - Estimated regressions imply a "straightforward relationship" between public spending on health and life expectancy in the long run (paper states: "Our estimations for expected year of schooling and life expectancy as dimensions of human development imply a straightforward relationship with public spending on education and health respectively in the long run").

### Contextual and policy-relevant observations from the text
- IMF commitment and SDG alignment:
  - IMF committed in 2015 to work with member countries toward the Sustainable Development Goals (Lagarde, 2015).
  - SDG indicator 1.a.2: "Proportion of total government spending on essential services (education, health and social protection)" — highlights importance of COFOG public expenditure data.
- Regional and coverage facts (exact values preserved as presented):
  - Social protection in Sub-Saharan Africa covers only 17.8 percent of the population; coverage ranges from 48 percent in South Africa to below 10 percent in some West African countries.
  - Old-age pensions in Africa now cover 29.6 percent of older persons; universal or near-universal coverage in Botswana, Cabo Verde, Lesotho, Mauritius, Namibia, Seychelles, South Africa, Eswatini and Zanzibar (United Republic of Tanzania).
  - In most emerging and developing economies, education expenditure has increased and "in most" reached 4 percent of GDP; low-income countries keep spending at around 3 percent of GDP.
  - Europe: governments finance more than 80 percent of total education spending; countries with high/very high HDI reached expected years of schooling level of 14–16 years; medium/low HDI countries: 10–12 years; mean years of schooling used as 15 years benchmark for many country groups by 2025.
  - Health coverage gaps: nearly 50 percent of the global population lacks health coverage; rural exclusion from health insurance coverage is 80 percent in Sub-Saharan Africa and 56 percent in South Asia and Pacific.
  - Life expectancy: averages 79.5 years in very high HDI countries versus 60.8 in low human development countries.

### Authors' conclusions (as presented)
- Positive long-run effect of public educational spending on GNI per capita.
- No similar statistically meaningful long-run relationship found between GNI per capita and public social spending on health and social protection in the basic specifications reported.
- Straightforward long-run relationships found between:
  - public educational spending and expected years of schooling;
  - public health spending and life expectancy.
- Results reported as robust to inclusion of fixed effects and lagged variables, but authors underline the need for further robustness checks using instrumental variables and GMM estimators to address potential endogeneity and measurement error.

*Source: IMF staff paper (chapters and tables drawn from wpiea2019204-print-pdf).*

### Section VI.

### Section VI.

### Robustness — overview
- The section applies additional controls, instrumental variables, and GMM estimators to check robustness of baseline results for GNI per capita, expected years of schooling, and life expectancy.
- Control variables added include: public spending on education, health and social protection; population growth; inflation (in logs); investment; terms of trade; and WGI indicators — voice and accountability, political stability and no violence, government effectiveness, rule of law, regulatory quality, and control of corruption.
- GMM estimators use the second lag of the dependent and explanatory variables as instruments; some GMM specifications also include instruments such as total population (in logs) and literacy rate (in logs).

### GNI per Capita and Public Social Expenditures
- Including public spending on education, health and social protection and additional controls:
  - Effect of educational spending on GNI per capita changes from 0.020 to 0.023 in specification (2) when health and social protection expenditures are included.
  - Coefficients reported:
    - Public education expenditures as % of GDP (in logs, lagged): 0.0204*** (specification (1)), 0.0233*** (specification (2)), 0.0364** (GMM specification (3)).
    - Public health expenditures as % of GDP (in logs, lagged): -0.0109** (in specification (2)); additional specifications report -0.0097**, -0.0071, -0.0071*, -0.0071* in various specifications.
    - Public social protection expenditures as % of GDP (in logs, lagged): 0.0028* (specification (2)); other specifications report 0.0036**, 0.0052, 0.0042**, 0.0047***, 0.0036**, 0.0030, 0.0035**, 0.0037**.
  - Other reported coefficients (selected):
    - GNI per capita in 2011 PPPs $ prices (in logs, lagged): 0.9295***, 0.9229***, 0.9095** (across specifications).
    - Population growth (lagged): -0.0306**, -0.0556*** in some specifications.
    - Inflation (in logs, lagged): -0.0037* in one specification; 0.0158** in another.
    - Investment (lagged): 0.3619*** in some specifications; -0.0020*** reported in another.
    - Terms of trade (lagged): -0.0011***, -0.0015***, -0.0075*** in different specifications.
    - WGI indicators show varying significant coefficients (examples):
      - Voice and accountability: -0.2425*** in one specification, 0.1089*** in another.
      - Political stability and no violence (lagged): -0.1148*** in one spec, 0.0331*** in another.
      - Government effectiveness (lagged): 0.2729***, 0.0632* across specifications.
      - Regulatory quality (lagged): -0.5742*** in one specification.
      - Control of corruption (lagged): 0.1693***, 0.2195*** in different specs.
- Key robustness conclusions for GNI per capita:
  - The GMM estimator of 0.036 in specification (3) is similar to the fixed effects lagged result of 0.020 in specification (1).
  - A 1 percent difference in public educational spending leads to an increase in GNI per capita of 0.018 (OLS) percent (text statement).
  - Specifications (4) and (5) with additional instruments produce coefficients of 0.017 and 0.018 for educational spending.
  - Controlling for WGI indicators in specifications (6) and (11) does not change the statistically significant effect of educational spending on GNI per capita.
  - Public health coefficients are often negative and interpreted as not meaningful for growth; social protection effects are statistically significant but much smaller in magnitude than educational spending (e.g., 0.002).

### Expected Years of Schooling and Public Educational Spending
- Main robustness findings and reported coefficients:
  - Public education expenditures as % of GDP (in logs, lagged):
    - 0.0141*** (fixed effects OLS, specification (1))
    - 0.0141*** (specification (2) with Gini)
    - 0.0168*** (GMM estimator, specification (3))
    - 0.0139*** and 0.0148*** in specifications (4) and (5)
    - 0.0212*** and 0.0164** reported in other specifications
  - Expected years of schooling (in logs, lagged): 0.8928***; other reported lagged values: 0.8791***, 0.8421***, 0.8684***, 0.8686***.
  - Additional controls and reported coefficients:
    - Gini (in logs, lagged): -0.0132*** (specification (2))
    - Population (in logs): 0.0499*** (specification with population)
    - Total population (in logs, lagged): 0.0438*** (specification (4))
    - Population growth (lagged): 0.0126*** (specification (4))
    - Literacy rate (in logs, lagged): -0.0609*** (specification (4))
    - Voice and accountability: -0.0275** (specification (4))
    - Rule of law: -0.0365*** (specification (4))
- Robustness conclusions for schooling:
  - Inclusion of controls leads to similar coefficients as the lagged-dependent-variable specifications.
  - The basic econometric result: a 1 percent increase in public educational spending results in 0.014 percent short run positive difference in expected years of schooling in the lagged dependent specification (specification (1)).
  - The GMM estimator with instruments confirms magnitude at 0.0168*** in specification (3).
  - Relationship between public educational spending and expected years of schooling is robust to inclusion of Gini, population growth, literacy, rule of law, and voice and accountability.

### Life Expectancy and Public Health Spending
- Baseline and robustness coefficients (selected):
  - OLS static fixed effects model without lagged dependent variable: a 1 percent public health expenditure (lagged) implies a percentage increase in life expectancy of 0.017 (text statement).
  - Specification with lagged explanatory and dependent variables: short-term coefficient 0.0005*** (table 4 column (4)); reported long-run effect of 0.020 (text statement, computed as β/(1-α)).
  - Table 4 reported coefficients:
    - Public health expenditures as % of GDP (in logs, lagged): 0.0486**, 0.0498**, 0.0170**, 0.0005*** across columns (1)–(4).
    - Life expectancy (in logs, lagged): 0.9752*** (when included).
  - Robustness checks (Table 7) report:
    - Public health expenditures as % of GDP (in logs, lagged): 0.0005** (specification (1)), 0.0009*** (specification (2)), 0.0007** (specification (3)).
    - GNI per capita (in logs, lagged) reported as 0.0025*** in one specification.
    - Gini index (in logs, lagged): -0.0081** in one specification.
    - GMM specification (4) finds 0.0003*** (short run) for public health expenditures as % of GDP (in logs, lagged).
    - Specifications with additional controls report 0.0002** and 0.0003*** for public health expenditures in some specifications.
    - Other controls reported:
      - Total population (in logs, lagged): 0.0224***, 0.0065*** in different specifications.
      - Literacy rate (in logs, lagged): 0.01880**, 0.0139*** in different specifications.
      - Life expectancy (in logs, lagged): 0.9726***, 0.9834*** in different specifications.
- Robustness conclusions for life expectancy:
  - The short-run effect is small (e.g., 0.0005***), while the long-run effect (β/(1-α)) is larger and comparable to the static fixed effects estimate (text cites long-run 0.020 comparable with 0.017).
  - Including controls such as GNI per capita and Gini does not overturn the positive relationship; one reported figure: a 1 percent increase in public health spending results in 0.0009 percent positive difference in life expectancy (specification (2) text).
  - GMM with additional instruments produces a smaller short-run magnitude (0.0003 percent).

### Conclusion (section VII summary points reiterated here)
- Overall findings:
  - Positive long run effects of public educational spending and social spending on GNI per capita.
  - Positive effect of public educational spending on expected years of schooling.
  - Positive effect of public health spending on life expectancy.
- Specific empirical conclusions:
  - Public educational spending shows positive small effects on GNI per capita in the short run and larger effects in the long run.
  - Health spending shows no evidence of positive effects on GNI per capita when appropriate controls are included; social protection effects are statistically significant but much smaller in magnitude than educational spending.
  - The OLS estimator with fixed cross-country effects indicates a positive relation between public educational spending and expected years of schooling, and reduced income inequality in the long run.
  - The relationship between public health spending and life expectancy is statistically significant and larger in the long run compared to immediate effects.

*Source: wpiea2019204-print-pdf - Section VI.*

### References

### References and Methodological Appendices (wpiea2019204-print-pdf)

### Literature and thematic foundations
- Citations cover human capital, public expenditure, inequality, and growth. Representative topics include:
  - Human capital theory and schooling (Becker, 1964; Barro, 2001; Barro and Lee, 2015; Jones and Klenow, 2010).
  - Public spending and growth or productivity (Aschauer, 1989; Blanchard and Perotti, 2002; Bose, Haque and Osborn, 2003; Spilimbergo et al., 2009).
  - Social spending, welfare states, and health outcomes (Fritzell and Lundberg, 2007; Human Development Report; World Bank reports).
  - Inequality and redistribution (Benabou, 2000; Pagano, 2004; Melo and Tiongson, 2003).
  - Econometric and panel-data methodology (Andersen and Hsiao, 1982; Arellano and Bond, 1991; Baltagi, 2005; Davis, 2002).

### Public social spending: definitions and classification
- Public social spending scope applied in analysis includes:
  - Health;
  - Education; and
  - Social protection.
- Source and classification:
  - COFOG methodology for functions of government expenditures as described in GFSM 2014.
  - Social public spending primarily part of individual consumption of households.
- GFSM 2014 GFS functions for social spending (extract of categories):
  - Health: Medical products, appliances, and equipment; Outpatient services; Hospital services; Public health services; R&D Health.
  - Education: Pre-primary and primary education; Secondary education; Postsecondary non-tertiary education; Tertiary education.
  - Social protection: Sickness and disability; Old age; Survivors; Family and children; Unemployment; Housing.
- Notes:
  - COFOG classifies expenditures into ten categories distinguishing individual consumption and collective consumption.

### Human Development Index (HDI) indicators and thresholds
- HDI is the geometric mean of indices for education, health, and income, scaled 0 to 1.
- HDI country groupings used:
  - Very high level: HDI above 0.8
  - High level: HDI above 0.7
  - Medium level: HDI 0.56-0.7
  - Low level: HDI below 0.56
- HDI dimension indicators with minimum and maximum values:
  - Health: Life expectancy (years) — Minimum 20, Maximum 85
  - Education: Expected years of schooling — Minimum 0, Maximum 18; Mean years of schooling — Minimum 0, Maximum 15
  - Standard of Living: Gross National Income per capita (in PPP in $) — Minimum 100, Maximum 75000
- Source: United Nations, Human Development Report 2017, Technical Notes.

### Inequality measure and data considerations (Gini index)
- Gini index definition and interpretation:
  - Measures area between Lorenz curve and line of absolute equality, expressed as percentage of maximum area.
  - Gini index of 0 represents perfect equality; index of 100 implies perfect inequality.
  - Gini measures relative, not absolute, wealth; increases in Gini can coexist with reductions in absolute poverty.
- Data and adjustments:
  - Distribution data from nationally representative household surveys or best available grouped data.
  - Adjusted for household size to measure per capita income or consumption.
  - No adjustment for spatial differences in cost of living within countries due to data unavailability.
  - Survey year is year underlying household survey data were collected (or year with most data if spanning two years).

### Time series and panel-data statistical approach
- Unit root and stationarity testing:
  - Panel unit root tests used to determine whether variables should be entered in levels or first differences.
  - Log transformations of time series variables tended to produce stationary series.
  - Test result summary: natural logarithms of public spending time series reject null hypothesis of unit root.
    - Levin, Lin and Chu method: probability of unit root is zero.
    - Im, Pesaran and Shin, ADF and PP methods: confirm stationarity at confidence between 90 and 99 percent.
  - Other dependent and control variables (in natural logarithms) are stationary in levels.
- Purpose: avoid spurious regressions (Granger and Newbold 1974) and determine appropriate model specification.

### Granger causality test results (pairwise tests)
- Test setup: Pairwise Granger causality with specified lags; variables generally in logs and public social spending expressed as share of GDP.
- Key findings (Null Hypothesis, Obs, F-Statistic, Prob.):
  - GNI per capita (in logs) does not Granger Cause Public educational expenditures (in logs, share of GDP): Obs 618; F-Statistic 1.87502; Prob. 0.0829.
  - Public educational expenditures (in logs, share of GDP) does not Granger Cause GNI per capita (in logs): Obs 618; F-Statistic 2.47266; Prob. 0.0227.
  - GNI per capita (in logs) does not Granger Cause Public health expenditures (in logs, share of GDP): Obs 607; F-Statistic 3.78057; Prob. 0.0011.
  - Public health expenditures (in logs, share of GDP) does not Granger Cause GNI per capita (in logs): Obs 607; F-Statistic 1.87869; Prob. 0.0823.
  - GNI per capita (in logs) does not Granger Cause Public social protection spending (in logs, share of GDP): Lags 2; Obs 834; F-Statistic 3.34294; Prob. 0.0358.
  - Public social protection spending (in logs, share of GDP) does not Granger Cause GNI per capita (in logs): Lags 2; Obs 834; F-Statistic 5.07283; Prob. 0.0065.
- Causality between public educational spending and expected years of schooling (Lags 6):
  - Public educational expenditures (in logs, share of GDP) does not Granger Cause Expected years of schooling (in logs): Obs 697; F-Statistic 4.71522; Prob. 0.0001.
  - Expected years of schooling (in logs) does not Granger Cause Public educational expenditures (in logs, share of GDP): Obs 697; F-Statistic 1.16388; Prob. 0.3238.
- Causality between public health spending and life expectancy:
  - Lags 6:
    - Public health expenditures (in logs, share of GDP) does not Granger Cause Life expectancy (in logs): Obs 694; F-Statistic 1.86936; Prob. 0.0836.
    - Life expectancy (in logs) does not Granger Cause Public health expenditures (in logs, share of GDP): Obs 694; F-Statistic 1.29652; Prob. 0.2564.
  - Lags 8:
    - Public health expenditures (in logs, share of GDP) does not Granger Cause Life expectancy (in logs): Obs 565; F-Statistic 2.99193; Prob. 0.0027.
    - Life expectancy (in logs) does not Granger Cause Public health expenditures (in logs, share of GDP): Obs 565; F-Statistic 1.78580; Prob. 0.0772.
- Interpretation notes from source:
  - Granger tests indicate bi-directional causality at 10 percent significance between GNI per capita and public spending on education and health for certain specifications.
  - With two lags, one-directional causality from GNI per capita to public social protection, and one-directional causality of public spending on life expectancy and expected years of schooling.
  - Bivariate tests are limited because they do not control for other factors; regressions in the paper include additional controls for a fuller picture.

### Regional and income-level public social spending (selected numeric values from figures for 2016, percent of GDP)
- Social Protection Spending by Region (2016, percent of GDP):
  - AFR: 5.5
  - APD: 5.3
  - EUR: 14.9
  - MCD: 6.6
  - WHD: 6.0
- Social Protection by Country Income Level (2016, percent of GDP):
  - LIC: 5.3
  - LMIC: 8.5
  - UMIC: 9.4
  - HIC: 10.2
- Educational Spending by Region (2016, percent of GDP):
  - AFR: 4.8
  - APD: 4.6
  - EUR: 5.0
  - MCD: 4.3
  - WHD: 3.6
- Educational Spending by Country Income Level (2016, percent of GDP):
  - LIC: 3.3
  - LMIC: 4.2
  - UMIC: 4.9
  - HIC: 5.0
- Health Spending by Region (2016, percent of GDP):
  - AFR: 2.7
  - APD: 3.7
  - EUR: 5.4
  - MCD: 2.7
  - WHD: 4.0
- Health Spending by Country Income Level (2016, percent of GDP):
  - LIC: 1.1
  - LMIC: 2.8
  - UMIC: 3.5
  - HIC: 6.1

### Country sample for IMF GFS Yearbook (level of government represented)
- The sample lists countries and the level of government reported (examples):
  - Albania (ALB) — General government
  - Angola (AGO) — Budgetary central government
  - Australia (AUS) — General government
  - China, P.R.: Mainland (CHN) — General government
  - India (IND) — Budgetary central government
  - United States (USA) — General government
- (Full country-level listing appears in the appendix of the source.)

*Source: wpiea2019204-print-pdf - References (wpiea2019204-print-pdf)*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019204-print-pdf.pdf_