## _wp15178

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### Introduction: context and motivation
- Public education expenditure (PEE) is a sizable share of government budgets and unit costs of public education have been rising persistently across countries.
- In advanced economies, average per-pupil primary and secondary education expenditures were 18 percent and 23 percent of per capita GDP in 1995–99, rising to 20 percent and 25 percent ten years later (Wolff, Baumol, and Saini, 2014).
- Rising unit costs raise concerns about efficiency; studies point to critical inefficiency in public education, especially in sub-Saharan Africa (Gupta and Verhoeven, 2001; Herrera and Pang, 2005; Grigoli, 2014).
- Key policy question: Do cost increases reflect demographic change or institutional factors (education policy, wage setting, teacher recruitment)?
- Analogous evidence in public health suggests only one-fourth of past medical cost increases are demographic; the remainder (excess cost growth) comes from non-demographic factors including Baumol’s effect and policy/institutional changes (IMF, 2010).

### Decomposition of changes in public education spending
- Aggregate PEE-to-GDP ratio decomposed into:
  - school-age population (as a percent of working-age population),
  - school enrollment (education coverage),
  - per-pupil spending on education (as a percent of GDP per worker).
- Regional patterns (1997–99 to 2007–09):
  - Per-pupil PEE increases drove overall PEE increases in emerging Asia, CEE-CIS, and LAC.
  - In sub-Saharan Africa (SSA), improved school enrollment materially increased public education spending as percent of GDP.
- Per-pupil PEE further decomposed into:
  - teachers’ salaries (price effect),
  - teacher-pupil ratio (demographic/quantity effect),
  - other spending items (other current and capital spending).
- Empirical findings (1997–99 to 2004–06):
  - Growth in per-pupil PEE is driven primarily by increases in teachers’ salaries across all regions.
  - Teachers’ salaries in real terms tended to grow faster than labor productivity in both advanced and non-advanced economies.
  - In emerging Asia, MENA, and LAC, growth in other current and capital expenditure also contributed to higher per-pupil PEE.
  - Higher teacher-pupil ratio (fewer teachers per pupil; larger classes) contributed to higher per-pupil PEE especially in advanced economies and CEE-CIS.
  - Contribution of teacher-pupil ratio smaller in developing countries, where classroom sizes remain large (more than 20 students per teacher), notably in SSA.

### Theoretical framework: modified Baumol’s model and adjusted Baumol’s variable
- Economy split into two sectors:
  - non-progressive sector (education),
  - progressive sector (e.g., manufacturing).
- Nominal wages in both sectors grow with labor productivity in the progressive sector (common-wage growth assumption); model allows time-varying wage premium for teachers.
- Per-pupil PEE growth decomposed into:
  - Baumol’s effect (wages in education rise because wages follow productivity elsewhere),
  - change in wage premium (education wages rising relative to market wages),
  - per-pupil GDP growth (income effect),
  - effects of capital and other recurrent education expenditure and school-age population growth.
- Adjusted Baumol’s variable defined as growth of average wage in excess of growth of economy-wide labor productivity (proxy for Baumol’s disease when education output hard to observe).
- Empirical specification regresses per-pupil PEE growth on:
  - adjusted Baumol’s variable,
  - wage premium change,
  - per-pupil GDP growth,
  - other education spending components,
  - school-age population growth,
  - country and time effects.
- Hypotheses:
  - Hypothesis 1: coefficient on adjusted Baumol’s variable > 0 indicates Baumol’s effect exists.
  - Hypothesis 2: rising wage premium will be a more critical driver of per-pupil PEE growth than Baumol’s effect if wage premium coefficients larger.

### Data and descriptive analysis (sample and coverage)
- Macro panel dataset: 61 advanced and emerging countries, 1995–2009 (country list in Table A.1 in appendix).
- Data sources: UNESCO, UN, World Development Indicators (WDI), ILO, IMF staff calculations.
- Sample composition:
  - Total main-sample countries: 61.
  - High-income countries (HICs; 32) listed in source.
  - Middle-income countries (MICs; 28) listed in source.
  - Low-income countries (LICs; 1): Bangladesh.
- Wage data: ILO labor statistics (average monthly earnings of salaried employees excluding manual workers); where missing, average teacher salary derived from wage bill and employment.
- Data processing: intensive cleaning, unit harmonization, trimming outliers defined as two standard deviations above and below the mean.

### Key summary statistics (sample central tendencies and ranges)
- Average public education expenditure (PEE) (percent of GDP): 4.4 percent (N=150).
- Share of employment in public education sector: about 6 percent on average.
- Range of PEE-to-GDP: 0.9 percent minimum to 12 percent maximum.
- In 1995–2009, real per-pupil PEE increased by 3.3 percent on average.
- Per-pupil basic education expenditure growth: 3.4 percent on average.
- Per-pupil higher education expenditure growth: mean -0.022 (negative average) with larger variance.
- Adjusted Baumol’s variable mean: 3 percent (Adj. Baumol's variable mean 0.031 in table).
- First wage premium measure (teachers’ salaries relative to GDP per capita): mean 0.001, range -25 percent to 39 percent.
- Second wage premium measure (teachers’ salaries relative to manufacturing wage): mean 0.000 (larger variance, smaller sample).
- Capital education expenditure growth: median 4 percent.
- Teacher-pupil ratio change: Dln(teacher-pupil ratio) mean 0.237.

- Selected Table 1 entries (preserve exact figures):
  - Public education expenditure/GDP: N 150, Mean 4.419, Median 4.325, Std Dev. 1.714, Min. 0.009, Max 11.988
  - Dln(per-pupil education expenditure): N 1126, Mean 0.0330, Median 0.029, Std Dev. 0.167, Min. -0.738, Max 1.099
  - Dln(per-pupil basic education expenditure): N 1023, Mean 0.0340, Median 0.027, Std Dev. 0.249, Min. -1.657, Max 2.076
  - Dln(per-pupil higher education expenditure): N 969, Mean -0.022, Median -0.007, Std Dev. 0.507, Min. -2.554, Max 2.792
  - Dln(per-pupil wage bill in public education): N 851, Mean 0.039, Median 0.036, Std Dev. 0.135, Min. -0.614, Max 0.964
  - Share of labor in public education sector: N 1560, Mean 0.059, Median 0.059, Std Dev. 0.025, Min. 0.055, Max. 0.128
  - Dln(per capita GDP in PPP$): N 417, Mean 0.046, Median 0.048, Std Dev. 0.042, Min. -0.148, Max 0.159
  - Adj. Baumol's variable: N 417, Mean 0.031, Median 0.020, Std Dev. 0.705, Min. -1.887, Max 1.956
  - Dwage premium 1: N 417, Mean 0.001, Median 0.000, Std Dev. 0.059, Min. -0.254, Max 0.387
  - Dwage premium 2: N 302, Mean 0.000, Median 0.002, Std Dev. 0.097, Min. -0.723, Max 0.771
  - Dln(capital expenditure in education): N 417, Mean 0.028, Median 0.039, Std Dev. 0.343, Min. -3.491, Max 1.853
  - Dln(teacher-pupil ratio): N 417, Mean 0.237, Median 0.178, Std Dev. 0.589, Min. -2.699, Max 6.024

### Testing Baumol model assumptions and wage premium evidence
- Two assumptions tested:
  - (a) constant output ratio (education as a luxury good; income elasticity close to 1 validated in Appendix II using VEC model),
  - (b) common wage growth between education and manufacturing sectors.
- Empirical evidence:
  - Correlation between changes in real teachers’ salaries and real manufacturing wage about 0.58; Figure 4 regression: y = 0.582x + 0.012 with t-statistics (5.40) and (3.25).
- ILO evidence on wage premium (Figure 5):
  - Gap between teachers’ salaries and market wage has grown in many middle-income countries (upward shift after 2000).
  - Wage premium measured as gap between teacher salaries and wages of manufacturing workers.

### Estimation results: testing the Baumol hypothesis (first-differenced panel)
- Estimation approach: first-differenced model (Eqs. (7)–(8)); Dwage premium 1 (teachers’ salaries relative to GDP per capita) and Dwage premium 2 (teachers’ salaries relative to manufacturing wage) included in variants; controls include demographics, capital expenditure, private education dummy, country and year fixed effects.
- Adjusted Baumol's variable coefficients across specifications (columns (1)–(8)): 0.052***, 0.032***, 0.038***, 0.058***, 0.043***, 0.034***, 0.035***, 0.044***.
- Dwage premium 1 coefficients when included: 10.649*** (column 1), 0.555*** (2), 0.329*** (3), 0.303*** (4).
- Dwage premium 2 coefficients when included: 0.470*** (5), 0.250** (6).
- Dln(GDP per capita in PPP$) examples: 1.175*** (1), 1.204*** (2), 0.743*** (3), 0.845*** (4).
- Dln(real capital expenditure in education) significant: 0.076***, 0.072***, 0.072***, 0.092*** in specified columns.
- Dln(teacher-pupil ratio) coefficients small but sometimes significant (e.g., 0.014*, 0.019***, 0.015**, 0.012*).
- Interpretation:
  - Adjusted Baumol’s variable positive and significant but coefficients much smaller than 1 — weaker support for pure Baumol’s (cost disease) mechanism.
  - Wage premium effect significant and typically larger in magnitude, indicating policy-driven wage-setting is a major driver of higher per-pupil PEE and unit labor cost.
  - Change in capital education expenditure contributes to higher per-pupil PEE but with smaller magnitude than wage premium effect.
  - Change in real GDP per capita and teacher-pupil ratio also contribute to unit cost growth.

### Robustness checks and heterogeneity
- Intertemporal parameter stability (pre-crisis 1999–2006 vs 2007–09):
  - Adjusted Baumol's variable coefficients: 0.047*** (1999–2006) and 0.006 (2007–09) for Dln(real per pupil wage bill); 0.043*** and 0.025 for Dln(real per pupil education expenditure).
  - Dwage premium 1: 0.556*** (1999–2006) and 0.652** (2007–09) for wage bill; 0.471*** and 0.045 for PEE.
  - Conclusion: wage premium remains significantly large in pre-crisis period; Baumol coefficients remain < 1.
- Asymmetry by country groups:
  - Baumol’s and wage premium effects stronger for developing economies than advanced economies.
  - Weaker Baumol’s effect in HICs; stronger effects in MICs.
  - Wage premium effect significantly positive primarily for countries with large classroom size.
  - Selected interaction results: Adj. Baumol's variable baseline 0.049***, interaction x * Advanced = -0.043***; Dwage premium 1 baseline 0.338***, interaction y * Advanced = -0.181 (varies by spec).
- Basic vs Higher education:
  - Basic education: estimates similar to total PEE; stronger wage premium effect for basic education.
  - Higher education: Baumol’s effect and capital expenditure matter more for higher education unit-cost growth.
  - Selected coefficients:
    - Adj. Baumol's variable: 0.049** (basic mean), 0.032* (basic pre-crisis mean), 0.070** (higher mean), 0.063** (higher pre-crisis mean).
    - Dwage premium 1: 0.274* (basic mean), 0.451* (basic pre-crisis mean), 0.190 (higher mean), 0.245 (higher pre-crisis mean).
    - Dln(real capital expenditure in education): 0.097*** (basic), 0.093*** (basic pre-crisis), 0.112*** (higher), 0.130** (higher pre-crisis).

### Econometric methods and key test results (Appendix I summary)
- Panel unit root tests (ADF-Fisher) on logs and first differences:
  - Log (real per-pupil education spending): 88.648 StatProb 0.118 (All); 78.810 StatProb 0.101 (Pre-crisis).
  - DLog (real per-pupil education spending): 155.519 StatProb 0.000 (All); 115.757 StatProb 0.000 (Pre-crisis).
  - Log (per capita GDP in PPP$): 67.116 StatProb 0.702 (All); 22.400 StatProb 1.000 (Pre-crisis).
  - DLog (per capita GDP in PPP$): 63.265 StatProb 0.703 (All); 109.781 StatProb 0.000 (Pre-crisis).
  - Log (real teachers' salaries): 74.228 StatProb 0.471 (All); 76.052 StatProb 0.144 (Pre-crisis).
  - DLog (real teachers' salaries): 183.794 StatProb 0.000 (All); 109.700 StatProb 0.000 (Pre-crisis).
  - First-differenced series reject unit root for pre-crisis period.
- Johansen Fisher panel cointegration test supports model is I(1) with one cointegrating vector.
- Vector Error Correction (VEC) model (one cointegrating vector; one-year lag; intercept and linear time trend):
  - Panel A. Cointegrating equation (long-term relationship):
    - Ln(per capita GDP in PPP$) (lag1): Column (1) All: 0.546*** (standard error 0.195); Column (2) Pre-crisis: 1.155*** (standard error 0.097)
    - Ln(real teachers' salaries) (lag1): Column (1) All: -0.030 (0.076); Column (2) Pre-crisis: -0.015 (0.039)
  - Panel B. Main equation (short-term relationship):
    - Error correction term: All: -0.035*** (0.010); Pre-crisis: -0.077*** (0.025)
    - DLn(per capita GDP in PPP$): All: 0.195 (0.128); Pre-crisis: 0.213 (0.184)
    - DLn(real teachers' salaries): All: 0.116*** (0.041); Pre-crisis: 0.112*** (0.048)
    - Observations: All: 408; Pre-crisis: 287
    - Adjusted R-squared: All: 0.136; Pre-crisis: 0.145
    - Wald test F-stat: All: 13.822; Pre-crisis: 10.705
  - Interpretation:
    - Long-term income elasticity = 0.55 for whole sample (significant); pre-crisis long-term income elasticity = 1.15 (close to unity).
    - Short-term error correction negative and significant, confirming long-term relationship.
    - Short-term price elasticity (teachers’ salaries) positive and significant, indicating teachers’ salaries drive short-term variation in per-pupil PEE.
    - Conclusion: Public education can be considered a luxury good in the long run consistent with Wagner’s hypothesis for education.

### Appendix III — Wage premium case studies (Indonesia and South Africa)
- Methods and data:
  - Oaxaca-Blinder decomposition and quantile regression (median); bootstrapped standard errors (50 replications).
  - Data: Indonesia — Susenas; South Africa — PALMS. For South Africa some comparisons restricted to union members.
- Distributional wage gap (selected figures):
  - Indonesia (2004): Log wage in education mean 13.923; manufacturing mean 13.533; wage gap mean 0.390 (quartile and percentile details in source).
  - Indonesia (2007): Log wage in education mean 14.210; manufacturing mean 13.709; wage gap mean 0.501.
  - South Africa (2004): Log wage in education mean 8.318; manufacturing mean 7.338; wage gap mean 0.980.
  - South Africa (2007): Log wage in education mean 8.382; manufacturing mean 7.536; wage gap mean 0.847.
- Oaxaca-Blinder decomposition selected results:
  - Indonesia 2004: Raw wage gap (mean) = 0.367 (0.052); Explained = 0.189 (0.045); Unexplained = 0.178 (0.058). Median raw = 0.550.
  - Indonesia 2007: Raw = 0.430 (0.054); Explained = 0.254 (0.037); Unexplained = 0.177 (0.055). Median raw = 0.693.
  - South Africa 2004: Raw = 0.864 (0.025); Explained = 0.783 (0.034); Unexplained = 0.082 (0.039). Median raw = 1.104.
  - South Africa 2007: Raw = 0.724 (0.025); Explained = 0.744 (0.027); Unexplained = -0.019 (0.031). Median raw = 1.027.
- Interpretation:
  - Public education workers paid higher salaries than manufacturing workers at all quartiles in both countries; wage gap tends to narrow toward upper percentiles.
  - In Indonesia the explained component (observable skills) increased from 2004 to 2007, suggesting higher skill premium for high-skill public education workers.
  - In South Africa the unexplained component grew larger at the median in 2007, suggesting institutional or policy-driven increases in wage premium.
  - Policy implication: wage premium increases arise from a mix of observable skill differences and unobservable rent components (institutional factors, union strength, wage-setting policies); country-specific labor market institutions matter.

### Main conclusions and policy implications
- Main conclusions:
  - Persistent rise in per-pupil PEE largely driven by change in teachers’ salaries.
  - Baumol (cost disease) effect is positive and significant but much weaker than the theoretical prediction (coefficients << 1) and weaker than Baumol’s effect found for health care.
  - Rising wage premium for teachers (policy-driven) significantly contributes to per-pupil PEE growth; effect robust to pre-crisis sample restriction.
  - Wage premium effect particularly strong in middle-income countries and in countries with large classroom size; stronger for basic education.
  - For tertiary education, Baumol’s effect and growth of capital education expenditure contribute more to cost growth.
- Policy questions and recommendations:
  - Scrutinize policies that drove the strong wage premium effect, especially in middle-income countries.
  - Key policy question: does the wage premium reflect legitimate skill premium for teachers or overpayment driven by institutional and political factors?
  - Case studies (Indonesia and South Africa) suggest institutional/political drivers in those countries and point to need for reforms to rationalize wage-setting policies to improve cost-effectiveness of public education.
  - Further research needed:
    - Use micro surveys for other countries to assess whether higher teachers’ salaries and wage premium lead to better educational outcomes.
    - Examine whether educational performance could be improved with less education spending in advanced economies (noting prior findings that overcompensation correlated with lower OECD PISA scores).

*Source: _wp15178 - 1. Summary Statistics; Appendix I; Appendix III (IMF staff paper excerpt).*

### 1. Summary Statistics...................................................................................................

### 1. Summary Statistics

### Introduction: context and motivation
- Public education expenditure (PEE) is a sizable share of government budgets and unit costs of public education have been rising persistently across countries.
- In advanced economies, average per-pupil primary and secondary education expenditures were 18 percent and 23 percent of per capita GDP in 1995–99, rising to 20 percent and 25 percent ten years later (Wolff, Baumol, and Saini, 2014).
- Rising unit costs raise concerns about efficiency: despite increased budget allocations, educational performance has not improved in some regions; studies point to critical inefficiency in public education, especially in sub-Saharan Africa (Gupta and Verhoeven, 2001; Herrera and Pang, 2005; Grigoli, 2014).
- Key question for policymakers: Do cost increases reflect demographic change or institutional factors (education policy, wage setting, teacher recruitment)?
- Analogous evidence in public health suggests only one-fourth of past medical cost increases are demographic; the remainder (excess cost growth) comes from non-demographic factors including Baumol’s effect and policy/institutional changes (IMF, 2010).

### Decomposition of changes in public education spending (aggregate identity)
- A public education spending-to-GDP ratio is decomposed into three components:
  - school-age population (as a percent of working-age population),
  - school enrollment (education coverage),
  - per-pupil spending on education (as a percent of GDP per worker).
- Regional patterns (1997–99 to 2007–09):
  - Despite demographic ageing reducing demand in some regions, per-pupil PEE increases drove overall PEE increases in many emerging regions: emerging Asia, Central Eastern Europe and the Commonwealth of Independent States (CEE-CIS), and Latin America (LAC).
  - In sub-Saharan Africa (SSA), improved school enrollment materially increased public education spending as percent of GDP.
- Figure 1 (Decomposition of Change in Public Education Spending, from 1997–99 to 2007–09) shows median regional contributions of:
  - school age population,
  - school enrollment,
  - per-pupil spending,
  to the change in education spending (Percent of GDP).

### Decomposition of changes in per-pupil education spending
- Per-pupil PEE is further decomposed into:
  - teachers’ salaries (price effect),
  - teacher-pupil ratio (demographic/quantity effect),
  - other spending items (other current and capital spending).
- Empirical findings (1997–99 to 2004–06):
  - Growth in per-pupil PEE is driven primarily by increases in teachers’ salaries across all regions.
  - Teachers’ salaries in real terms tended to grow faster than labor productivity in both advanced and non-advanced economies.
  - In advanced economies, salary growth reflects higher willingness to pay for public education.
  - In many developing countries, past underpayment of teachers relative to market wages contributed to low motivation and attrition to other sectors (UNESCO, 2011); recent salary increases have narrowed wage gaps in some countries (examples cited: Nicaragua, Peru, Uruguay, Ecuador; emerging European countries such as Czech Republic, Iceland, Latvia, Slovak Republic had low initial teacher pay).
  - For emerging Asia, MENA, and LAC, growth in other current and capital expenditure also contributed to higher per-pupil PEE, reflecting scarcity of education materials and facilities.
  - Higher teacher-pupil ratio (fewer teachers per pupil; larger classes) contributed to higher per-pupil PEE especially in advanced economies and CEE-CIS, where declining school-age population led to rising teachers-per-pupil and an overstaffed system.
  - Contribution of teacher-pupil ratio is smaller in developing countries, where classroom sizes remain large (more than 20 students per teacher), notably in SSA.
- Figures referenced:
  - Figure 2. Decomposing the Change in Per-Pupil Education Spending, from 1997–99 to 2004–06 (Percent of GDP per capita).
  - Figure 3. Evolution of Student-Teacher Ratio (source: World Development Indicators).

### Theoretical framework: modified Baumol’s model
- The economy is split into two sectors:
  - non-progressive sector (education),
  - progressive sector (e.g., manufacturing).
- Productivity growth assumptions:
  - non-progressive sector productivity grows at rate (notation in source),
  - progressive sector productivity grows faster at rate (notation in source).
- Long-run nominal wages in both sectors are related and grow with labor productivity in the progressive sector (common-wage growth assumption). The model allows a time-varying wage premium for teachers (to capture skill premia, overcompensation, bargaining power, or minimum wage interventions).
- Key modelling implications:
  - Unit labor cost in education depends on productivity growth differences between sectors and changes in the wage premium.
  - Per-pupil PEE growth can be decomposed into:
    - Baumol’s effect (education salaries rising because wages follow productivity growth elsewhere),
    - change in wage premium (education wages rising relative to market wages),
    - per-pupil GDP growth (income effect),
    - plus effects of capital and other recurrent education expenditure and school-age population growth.
- Adjusted Baumol’s variable:
  - Defined as growth of average wage in excess of growth of economy-wide labor productivity (following Colombier, 2012; Bates and Santerre, 2013).
  - Economy-wide labor productivity is constructed from sectoral outputs and labor inputs under the model’s assumptions; the adjusted Baumol’s variable approximates a measurable proxy for Baumol’s disease when education output is hard to observe.
- Final empirical specification (Eq. (8) in source):
  - Per-pupil PEE growth regressed on adjusted Baumol’s variable, wage premium change, per-pupil GDP growth, other education spending components, school-age population growth, plus country and time effects.
- Hypotheses tested:
  - Hypothesis 1: Baumol’s effect exists if per-pupil PEE growth is directly proportional to the adjusted Baumol’s variable (i.e., coefficient on adjusted Baumol’s variable > 0).
  - Hypothesis 2: If teachers are paid increasingly higher salaries relative to market wages (wage premium increases), the wage premium effect will be a more critical driver of per-pupil PEE growth than the Baumol’s effect.

### Data and descriptive analysis (sample and coverage)
- Macro panel dataset used to test hypotheses covers 61 advanced and emerging countries from 1995 to 2009 (further details and country lists are in Table A.1 in the appendix of the source).
- Data sources cited in descriptive sections include UNESCO, UN, World Development Indicators, ILO, and IMF staff calculations.

### Main results summarized (from the paper’s executive summary)
- Decomposition analysis: historical increase in per-pupil PEE has been driven by growth of teachers’ salaries.
- Regression analysis findings:
  - Baumol’s effect is much weaker than predicted by the theoretical model and weaker than found for medical care spending in earlier work.
  - The rising wage premium paid to teachers in public schools (excess over manufacturing sector wages) contributes more significantly to growth of per-pupil PEE.
  - The wage premium effect is stronger in middle-income countries and in countries with larger classroom size.
  - The wage premium effect predominantly drives higher cost growth in basic education.
  - For tertiary education, Baumol’s effect and growth of capital education expenditure contribute more to cost growth.
- Case studies (Appendix III) for Indonesia and South Africa suggest that rising wage premium for teachers may reflect institutional characteristics governing teachers’ wage setting.

*Source: _wp15178 - 1. Summary Statistics (IMF staff paper excerpt provided).*

### Appendix I for details).

### Appendix I. Data Description

### Appendix I. Data Description

### Data sources and variables
- Education expenditure:
  - Main source: United Nations Educational, Scientific and Cultural Organization (UNESCO) Institute for Statistics (public education expenditure including primary, secondary, and tertiary).
  - Missing values filled by: Organization for Economic Cooperation and Development’s (OECD’s) Education database and World Bank’s World Development Indicators (WDI).
  - Data include: educational expenditure as a share of GDP and per-pupil expenditure levels for primary, secondary, and tertiary; expenditure by nature (educational personnel, other current expenditures, capital expenditures).
- Wage data:
  - Source: International Labor Organization (ILO) labor statistics database (average monthly earnings of salaried employees excluding manual workers) for education and manufacturing sectors.
  - Earnings coverage: gross remunerations in cash and in kind for time worked, bonuses, allowances, and benefits; exclude severance and termination payments.
  - Classification: Disaggregated by economic activity according to ISIC Rev. 3.1 and Rev. 4.
  - Units and conversion: Expressed in local currency; recorded mainly as monthly wages (but hourly, daily, weekly, or annual in some cases). Converted into annual wages in the current local currency unit. Outliers (two standard deviations above and below the mean) are trimmed.
  - When ILO wage data is missing: average teacher salary computed by dividing the wage bill for public education by total employees in public education. Wage bill also computed from total public education spending and the share of recurrent spending for educational personnel. Total employment in education drawn from ILO labor statistics.
- Other independent variables:
  - Baumol’s variable computed using average economy-wide wage growth (ILO), change in labor productivity (real GDP from WDI divided by total employment from ILO), and share of employment in public education.
  - Real per capita GDP in PPP international dollars, teacher-pupil ratio, school-age population, and school enrollment from WDI and United Nations (2013).

### Sample composition
- Total main-sample countries: 61.
- High-income countries (HICs; 32): Australia, Austria, Bahrain, Belgium, Canada, Cyprus, Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Israel, Italy, Japan, South Korea, Lithuania, Luxembourg, Malta, New Zealand, Norway, Poland, Portugal, Russia, Spain, Sweden, Switzerland, United Kingdom, United States, Uruguay.
- Middle-income countries (MICs; 28): Argentina, Armenia, Azerbaijan, Brazil, Bulgaria, Chile, Costa Rica, Croatia, Dominican Republic, Ecuador, Egypt, El Salvador, Georgia, Indonesia, Kazakhstan, Kyrgyz Republic, Latvia, Malaysia, Mauritius, Mexico, Moldova, Nicaragua, Panama, Peru, Philippines, Romania, Thailand, Ukraine.
- Low-income countries (LICs; 1): Bangladesh.
- Income group classification note: based on World Bank Atlas method with thresholds in 2013: low-income GNI per capita $1,045 or less; middle-income more than $1,045 but less than $12,746; high-income $12,746 or more.

### Data processing and quality considerations
- Intensive data cleaning for nominal wage series consistency due to differing units and currency redenominations.
- Trimming of outliers defined as two standard deviations above and below the mean.
- Limitation: ILO education wage data provides average wage for public education workers as a whole (no disaggregation by education level or type of worker) and covers workers in both public and private institutions.
- Limitation: Average wages mostly from monthly payroll data (censuses, establishment sample surveys, household surveys); insufficient hourly-wage observations to define wage premium at hourly frequency.

### Econometric methods and key test results
- Panel unit root tests:
  - Fisher-type panel unit root tests (ADF-Fisher) applied to log differences of real per-pupil education spending, real per capita GDP, and real teachers’ salaries for an unbalanced panel.
  - Reported ADF-Fisher Chi-sq statistics (sample = All; Pre-crisis 1995–2006):
    - Log (real per-pupil education spending): 88.648 StatProb 0.118 (All); 78.810 StatProb 0.101 (Pre-crisis).
    - DLog (real per-pupil education spending): 155.519 StatProb 0.000 (All); 115.757 StatProb 0.000 (Pre-crisis).
    - Log (per capita GDP in PPP$): 67.116 StatProb 0.702 (All); 22.400 StatProb 1.000 (Pre-crisis).
    - DLog (per capita GDP in PPP$): 63.265 StatProb 0.703 (All); 109.781 StatProb 0.000 (Pre-crisis).
    - Log (real teachers' salaries): 74.228 StatProb 0.471 (All); 76.052 StatProb 0.144 (Pre-crisis).
    - DLog (real teachers' salaries): 183.794 StatProb 0.000 (All); 109.700 StatProb 0.000 (Pre-crisis).
  - Once first-differenced, the ADF test rejects the null of unit roots for the pre-crisis period.
- Cointegration testing:
  - Johansen Fisher panel cointegration test performed with a one-year time lag; critical value of 95 percent used.
  - Test supports the model is I(1) with one cointegrating vector under different intercept and trend assumptions (trace test and max eigenvalue test: reported "111" across specifications).
- Vector Error Correction (VEC) model:
  - Model includes one-year lag and time trend of per-pupil real education expenditure; cost function determinants include per capita GDP (Wagner variable, constant 2005 PPP-adjusted U.S. dollars) and real teachers’ salaries (deflated by GDP deflator).
  - VEC estimation results (assumes one cointegrating vector; includes intercept and linear time trend):
    - Panel A. Cointegrating equation (long-term relationship), Ln(per capita GDP in PPP$) (lag1):
      - Column (1) All: 0.546*** (standard error 0.195)
      - Column (2) Pre-crisis: 1.155*** (standard error 0.097)
    - Panel A. Ln(real teachers' salaries) (lag1):
      - Column (1) All: -0.030 (0.076)
      - Column (2) Pre-crisis: -0.015 (0.039)
    - Panel B. Main equation (short-term relationship):
      - Error correction term:
        - All: -0.035*** (0.010)
        - Pre-crisis: -0.077*** (0.025)
      - DLn(per capita GDP in PPP$):
        - All: 0.195 (0.128)
        - Pre-crisis: 0.213 (0.184)
      - DLn(real teachers' salaries):
        - All: 0.116*** (0.041)
        - Pre-crisis: 0.112*** (0.048)
      - Constant:
        - All: 0.009 (0.013)
        - Pre-crisis: 0.006 (0.015)
      - Observations:
        - All: 408
        - Pre-crisis: 287
      - Adjusted R-squared:
        - All: 0.136
        - Pre-crisis: 0.145
      - Wald test F-stat:
        - All: 13.822
        - Pre-crisis: 10.705
  - Interpretation:
    - Long-term income elasticity ( ) = 0.55 for whole sample (significant).
    - Pre-crisis long-term income elasticity = 1.15 (close to unity).
    - Short-term error correction negative and significant, confirming long-term relationship.
    - Short-term price elasticity (teachers’ salaries) positive and significant, indicating teachers’ salaries drive short-term variation in per-pupil PEE.
  - Conclusion: Public education can be considered a luxury good in the long run consistent with Wagner’s hypothesis for education, given estimated elasticities.

### Appendix III — Wage premium case studies (Indonesia and South Africa)
- Context and method:
  - Investigates whether wage premium between public education and manufacturing arises from observable characteristics (skill, gender, etc.) or unobservable rent payments.
  - Uses Oaxaca-Blinder decomposition and quantile regression (median) for decomposition; standard errors for median estimated by bootstrapping 50 times.
  - Data sources: Indonesia — National Socio-Economic Household Survey (Susenas); South Africa — Post-Apartheid Labor Market Surveys (PALMS).
  - For South Africa, analysis restricted to union members in some comparisons to control for unionization effects.
- Distributional wage gap findings (Table A.5):
  - Indonesia (2004):
    - N = 942
    - Log wage in education (2004) mean/p25/p50/p75/p90 = 13.923 / 13.682 / 14.078 / 14.241 / 14.457
    - Log wage in manufacturing (2004) mean/p25/p50/p75/p90 = 13.533 / 13.218 / 13.528 / 13.816 / 14.221
    - Wage gap in 2004 (education - manufacturing): 0.390 / 0.464 / 0.550 / 0.425 / 0.236
  - Indonesia (2007):
    - N = 907
    - Log wage in education (2007) = 14.210 / 13.911 / 14.403 / 14.604 / 14.897
    - Log wage in manufacturing (2007) = 13.709 / 13.305 / 13.700 / 14.078 / 14.509
    - Wage gap in 2007 = 0.501 / 0.606 / 0.703 / 0.526 / 0.388
  - South Africa (2004):
    - N = 1514
    - Log wage in education (2004) = 8.318 / 8.006 / 8.517 / 8.854 / 9.018
    - Log wage in manufacturing (2004) = 7.338 / 6.764 / 7.352 / 7.903 / 8.517
    - Wage gap in 2004 = 0.980 / 1.242 / 1.166 / 0.950 / 0.501
  - South Africa (2007):
    - N = 1899
    - Log wage in education (2007) = 8.382 / 8.006 / 8.700 / 8.995 / 9.240
    - Log wage in manufacturing (2007) = 7.536 / 6.987 / 7.575 / 8.086 / 8.700
    - Wage gap in 2007 = 0.847 / 1.019 / 1.125 / 0.910 / 0.541
  - Pattern: Public education workers paid higher salaries than manufacturing workers at all quartiles in both countries; wage gap narrows toward upper percentiles.
- Oaxaca-Blinder decomposition results (Table A.6):
  - Indonesia:
    - 2004:
      - Raw wage gap (mean) = 0.367 (0.052)
      - Explained component (mean) = 0.189 (0.045)
      - Unexplained component (mean) = 0.178 (0.058)
      - Median decomposition: Raw = 0.550 (0.018); Explained = 0.286 (0.028); Unexplained = 0.264 (0.004)
    - 2007:
      - Raw wage gap (mean) = 0.430 (0.054)
      - Explained component (mean) = 0.254 (0.037)
      - Unexplained component (mean) = 0.177 (0.055)
      - Median: Raw = 0.693 (0.009); Explained = 0.491 (0.066); Unexplained = 0.203 (0.017)
    - Interpretation: In Indonesia, the explained component increased from 2004 to 2007, suggesting a higher skill premium for high-skill public education workers.
  - South Africa:
    - 2004:
      - Raw wage gap (mean) = 0.864 (0.025)
      - Explained component (mean) = 0.783 (0.034)
      - Unexplained component (mean) = 0.082 (0.039)
      - Median: Raw = 1.104 (0.020); Explained = 0.900 (0.064); Unexplained = 0.204 (0.014)
    - 2007:
      - Raw wage gap (mean) = 0.724 (0.025)
      - Explained component (mean) = 0.744 (0.027)
      - Unexplained component (mean) = -0.019 (0.031)
      - Median: Raw = 1.027 (0.015); Explained = 0.764 (0.055); Unexplained = 0.263 (0.015)
    - Interpretation: In South Africa, the unexplained component grew larger in 2007 at the median, suggesting institutional or policy-driven increases in wage premium.
- Evolution of median wage gap by education level (Figure A.1):
  - Wage gap reported as percent of manufacturing sector wage for Primary, Secondary, Tertiary in 2004 and 2007.
  - Observed changes (visualized in figure):
    - Indonesia: median wage gap increased over time, particularly for Primary.
    - South Africa: median wage gap increased over time, particularly for Primary.
  - Axis labels / ticks shown: -5%, -3%, -1%, 1%, 3%, 5%, 7% (Wage gap in percent of manufacturing sector wages).
  - Note: For South Africa, sample restricted to union members to control for unionization effects.
- Policy-relevant interpretation:
  - Wage premium increases are driven by both observable characteristics (skills) and unobservable rent components (institutional factors, wage-setting policies, union strength), varying by country.
  - Low-skilled public education workers experienced rising wage premiums relative to manufacturing workers, consistent with stronger public-sector compensation, job security, unionization, and political clout.
  - Country-specific labor market institutions determine the source of wage premium; micro-level analyses in other countries are needed to inform policy design on public education expenditure.

*Source: _wp15178 - Appendix I. Data Description*

### References

### References

### Baumol’s cost disease and health-care expenditure
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- IMF, 2010, “Macro-Fiscal Implications of Health Care Reform in Advanced and Emerging Economies,” (Washington: International Monetary Fund).

### Education, teacher pay, and public-private wage differentials
- Asadullah, M., 2006, “Pay Differences between Teachers and Other Occupations: Some Empirical Evidence from Bangladesh,” Journal of Asian Economics, Vol. 17, pp. 1044–65.
- Glewwe, P., and M. Kremer, 2006, “Schools, Teachers, and Education Outcomes in Developing Countries,” Chapter 16 in Handbook of the Economics of Education, Vol. 2, pp. 945–1017.
- Mizala, A., and H. Nopo, 2012, “Evolution of Teachers’ Salaries in Latin America at the Turn of the 20th Century: How Much Are They (Under or Over) Paid?” IZA Discussion Paper No. 6806.
- Hazans, M., 2010, “Teacher Pay, Class Size and Local Governments: Evidence from the Latvian Reform,” IZA Discussion Paper No. 5291.
- Podgursky, M., and R. Tongrut, 2006, “(Mis-)Measuring the Relative Pay of Public School Teachers: Education Finance and Policy,” Education Finance and Policy, Vol. 1, No. 4, pp. 425–40.
- Zymelman, M., and J. DeStephano, 1989, “Primary School Teachers’ Salaries in Sub-Saharan Africa,” World Bank Discussion Paper 45 (Washington: World Bank).
- UNESCO Institute for Statistics, 2010, Methodological Guide for the Analysis of Teacher Issues (Paris: UNESCO).
- UNESCO Institute for Statistics, 2011, Financing Education in Sub-Saharan Africa: Meeting the Challenges of Expansion, Equity, and Quality (Paris: UNESCO).
- Organisation for Economic Co-operation and Development, Education at a Glance 2012: OECD Indicators (Paris).
- Organisation for Economic Co-operation and Development, Education at a Glance 2013: OECD Indicators (Paris).
- Mishel, L., and R. Rothstein, 2002, “The Class Size Debate,” Economic Policy Institute, Washington, DC.
- Mitch, D., 2004, “School Finance,” in International Handbook on the Economics of Education, G. Johnes and J. Johnes, eds., Cheltenham, UK: Edward Elgar Publishing, pp. 260–98.
- Wolff, E., W. Baumol, and A. Saini, 2014, “A Comparative Analysis of Education Costs and Outcomes: The United States vs. Other OECD Countries,” Economics of Education Review, Vol. 39, pp. 1–21.
- Psacharopoulos, G., and H. Patrinos, 2004, “Returns to Investment in Education: A Further Update,” Education Economics, Vol. 12, No. 2, pp. 111–34.

### Public spending, Wagner’s law, and efficiency of expenditure
- Akitoby, B., B. Clements, S. Gupta, and G. Inchauste, 2006, “Public Spending, Voracity, and Wagner’s Law in Developing Countries,” European Journal of Political Economy, Vol. 22, pp. 908–24.
- Kuckuck, J., 2014, “Testing Wagner’s Law at Different Stages of Economic Development,” FinanzArchiv, Vol. 70, No. 1, pp. 128–68.
- Lamartina, S., and A. Zaghini, 2011, “Increasing Public Expenditure: Wagner’s Law in OECD Countries,” German Economic Review, Vol. 12, pp. 149−64.
- Gupta, S., and M. Verhoeven, 2001, “The Efficiency of Government Expenditure: Experiences from Africa,” Journal of Policy Modeling, Vol. 23, pp. 433–67.
- Herrera, S., and G. Pang, 2005, “Efficiency of Public Spending in Developing Countries: An Efficiency Frontier Approach,” World Bank Policy Research Working Paper No. 3645 (Washington: World Bank).
- Verhoeven, M., V. Gunnarsson, and S. Carcillo, 2007, “Education and Health in G7 Countries: Achieving Better Outcomes with Less Spending,” IMF Working Paper WP/07/263 (Washington: International Monetary Fund).
- IMF, 2013, “Portugal: Rethinking the State—Selected Expenditure Reform Options,” IMF Country Report No. 13/6 (Washington: International Monetary Fund).
- IMF, 2014, “Public Expenditure Reform: Making Difficult Choices,” Fiscal Monitor, April.
- Grigoli, F., 2014, “A Hybrid Approach to estimating the Efficiency of Public Spending on Education in Emerging and Developing Economies,” IMF Working Paper WP/14/19 (Washington: International Monetary Fund).
- Clements, B., S., Gupta, I., Karpowicz, and S. Tareq, 2010, “Evaluating Government Employment and Compensation,” IMF Fiscal Affairs Department, Technical Notes and Manuals (Washington: International Monetary Fund).

### Econometric and panel-data methods cited
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- Maddala, G.S., and S. Wu, 1999, “A Comparative Study of Unit Root Tests with Panel Data and New Simple Test,” Oxford Bulletin of Economics and Statistics, Vol.61, pp.631–52.
- Nielsen, H., and M. Rosholm, 2001, “The Public-Private Sector Wage Gap in Zambia in the 1990s: A Quantile Regression Approach,” Empirical Economics, Vol. 26, pp.169–82.
- Melly, B., 2005, “Public-private Sector Wage Differentials in Germany: Evidence from Quantile Regression,” Empirical Economics, Vol. 30, pp. 505–20.

*Source: _wp15178 - References.*

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