Education Expenditure and Sustainable Human Capital Formation: Evidence from OECD Countries

Abstract

This study empirically examines the determinants of sustainable education finance by analyzing how income level, income inequality, fertility rate, and population density influence education expenditure as a share of GDP. Using annual data for 38 OECD countries from 1997 to 2021, the analysis applies fixed-effects and moment quantile regression (MMQR) models to capture both average and distributional dynamics. The results reveal a nonlinear inverted-U-shaped relationship between income and education spending, suggesting that fiscal commitment to education rises at early stages of development but tends to decline once income surpasses a certain threshold. Fertility rates show a significant negative association with education expenditure, while population density exhibits a positive effect. Moreover, the MMQR results highlight heterogeneity across countries, indicating that income growth has a stronger effect in economies with lower initial spending. These findings underscore the need for flexible, inclusive fiscal and institutional frameworks that adapt to national income levels and demographic transitions to ensure the long-term sustainability of education finance.

1. Introduction

Public expenditure on education serves as a cornerstone for the accumulation of human capital and the pursuit of sustainable economic growth. In particular, higher education generates positive externalities by fostering skilled human resources and producing research outcomes with public-good-promoting characteristics, thereby justifying government intervention to correct market failures [1]. Against this backdrop, OECD member countries have continuously sought to enhance labor market competitiveness and promote social cohesion through sustained and equitable public investment in education, both at the higher and basic levels. Such investments are not only an instrument of human capital formation but are also a key mechanism for ensuring long-term social sustainability. However, the level of public education expenditure varies significantly across countries and over time, reflecting the complex interactions of economic capacity, demographic dynamics, and policy priorities.

According to OECD statistics [2], the average share of school education expenditure (from primary to upper secondary) in GDP among OECD countries was 4.9% in 2021, of which public funding accounted for 4.2% and private funding for 0.8%. In comparison, Korea allocates an average of 5.2% of GDP to education, with 4.1% financed by the public sector and 1.1% by the private sector—slightly above the OECD average. In the World Bank’s Education Public Expenditure Review [3], fiscally sustainable education spending is understood as spending that is not only adequate to achieve national education goals but also affordable in the medium and long term, within overall budget constraints. Recent OECD work [4] on education financing likewise emphasizes that governments must balance the expansion of education investments with the need to preserve sound public finances, improve spending efficiency, and ensure equity in access and outcomes. Against this international backdrop, this study seeks to explore the key economic, demographic, and social factors that influence education expenditure in OECD countries and to clarify how these factors shape the sustainability of public education finance and its implications for long-term fiscal and educational policy. Recent international evidence also shows that, despite rising aggregate spending, per-student education expenditure has stagnated or declined in several low- and middle-income countries, raising concerns about the long-term adequacy and sustainability of education expenditure [3].

Figure 1 illustrates the cross-country distribution of education expenditure as a percentage of GDP in the OECD, distinguishing between public and private funding. Public expenditure clearly dominates in all countries, but the private share varies considerably, with Australia, Colombia, Korea, France, and the United Kingdom showing relatively large private contributions compared with most other OECD members. These differences highlight that both the overall level and the financing structure of education spending diverge across countries, underscoring the need to systematically analyze the economic, demographic, and social factors behind such patterns.

Figure 2 presents trends in education expenditure across OECD countries. Between 1997 and 2021, nations such as Australia (AUS), Belgium (BEL), Switzerland (CHE), Chile (CHL), Colombia (COL), Finland (FIN), Greece (GRC), Israel (ISR), Norway (NOR), New Zealand (NZL), and the United States (USA) experienced a steady rise in educational spending. These countries are typically characterized either as welfare-oriented economies or as nations that have strategically prioritized long-term investments in higher education as a foundation for sustainable growth. Notably, Nordic countries have continued to expand public expenditure on education as part of their human-capital-driven development strategies, reinforcing both equity and resilience in their education systems.

By contrast, countries such as Austria (AUT), Canada (CAN), Denmark (DNK), Spain (ESP), Estonia (EST), Hungary (HUN), Ireland (IRL), Korea (KOR), Lithuania (LTU), Poland (POL), Slovakia (SVK), and Türkiye (TUR) have shown declines in education spending. These reductions can be largely attributed to fiscal consolidation efforts, the growing privatization of higher education, or structural adjustments in educational provision in response to declining school-aged populations [5,6,7]. Such fiscal and demographic pressures raise concerns regarding the sustainability of education finance and the equitable distribution of learning opportunities.

A scatter plot of GDP per capita and education expenditure reveals a generally positive correlation between the two variables, suggesting that higher levels of economic development are associated with greater fiscal capacity for public investment in education. However, notable deviations from this pattern exist. Luxembourg (LUX), for instance, records exceptionally high income levels but only moderate education expenditure, while Mexico (MEX), Colombia (COL), and Costa Rica (CRI) remain in the low-income group with correspondingly low spending levels. Korea (KOR), despite allocating a relatively high share of GDP to education, maintains a lower GDP per capita than countries with similar expenditure ratios, implying that the economic and social returns on its educational investment may not yet be fully realized in a sustainable manner.

2. Literature Review

Previous studies have generally found that higher national income tends to be associated with greater government expenditure on education. Higher income levels expand fiscal capacity, enabling governments to invest more effectively in public services such as education [8]. From the perspective of sustainable fiscal management, rising income levels can strengthen a government’s ability to maintain long-term commitments to education spending, which is essential for stable human capital formation.

However, the relationship between income inequality and education expenditure remains contested. Alesina and Rodrik [9] argued that greater inequality increases redistributive pressures from median-income groups, thereby expanding public expenditure on social programs, including education. Similarly, Easterly and Revelo [10] and Sylwester [11] reported that countries with higher income inequality tend to allocate a larger share of resources to education. In contrast, Perotti [12] suggested that rising inequality weakens social trust and collective support for public goods, resulting in lower levels of government spending. He further argued that inequality in income distribution widens disparities in educational opportunities, thereby undermining sustainable human capital accumulation and long-term economic growth. Conversely, De Gregorio and Lee [13] demonstrated that expanding public expenditure on primary and secondary education contributes to equalizing educational opportunities, ultimately mitigating income inequality. Collectively, these findings indicate that income distribution influences not only the magnitude of public education spending but also its equity and sustainability across different educational levels.

The broader structure of the economy also shapes education expenditure. Gemmell and Kneller [14] emphasized that, for efficient and sustainable resource allocation, governments should prioritize productivity-enhancing sectors such as education and infrastructure. Their findings confirmed that higher income levels are positively associated with a larger share of educational spending. Similarly, Baldacci et al. [15], using panel data from 118 developing countries, found that rising income levels lead to increased education expenditure, especially in low-income economies. They highlighted that investment in education fosters a virtuous and sustainable cycle of human capital development and economic progress.

More recent theoretical and empirical research has increasingly emphasized the possibility that the relationship between income, public education expenditure, and long-run outcomes may be nonlinear rather than strictly monotonic. Angelopoulos, Malley, and Philippopoulos [16,17] develop dynamic general equilibrium models in which public education spending, financed by distortionary taxation, affects growth and welfare. Their results indicate a Laffer-type, inverted-U-shaped relationship between the share of public education expenditure in GDP and long-run growth or lifetime utility, implying the existence of an optimal spending share, beyond which additional expenditure reduces welfare. Using cross-country panel data, Trofimov [18] likewise finds that the positive growth effects of public education spending weaken and eventually turn negative when spending exceeds an empirically estimated optimum, suggesting diminishing returns for education expenditure as a share of GDP. Artige and Cavenaile [19] further show, in an endogenous growth framework, that the effects of public education spending on growth and income inequality are critically shaped by the level of spending and the distribution of human capital, leading to non-monotonic and potentially hump-shaped relationships.

International descriptive evidence reinforces this nonlinear view. The World Bank and UNESCO [20] report that, over the past decade, the average ratio of public education expenditure to GDP tends to rise from low- and middle-income countries but plateaus or even slightly declines among high-income economies, suggesting the presence of saturation effects in the education spending share at higher income levels. Likewise, cross-country data from Our World in Data show that very-low-income countries devote a relatively small share of GDP to education, and that this share increases rapidly in the middle-income range; further increases in income among high-income countries are not always accompanied by proportional increases in the education spending share. These patterns are consistent with an inverted-U-shaped or hump-shaped relationship between income level and education expenditure as a percentage of GDP, rather than a simple linear trend.

Demographic structure has also been identified as a crucial determinant of education expenditure. Countries with high fertility rates or large school-age populations face higher demand for education, necessitating increased public investment [21]. Conversely, in aging societies, policy priorities may shift toward elderly welfare, reducing the share of education expenditure. Yoo [22] reported that, in low-fertility countries such as Korea and Japan, per capita private education expenditure has increased despite declining birth rates. This reflects parental behavior in highly competitive educational environments, where fewer children lead to greater individual investment in private education [23]. Schady and Behrman [24] similarly argued that, although declining fertility may dampen economic growth, it can simultaneously encourage greater household investment in education and health, thereby enhancing the quality and sustainability of human capital. This pattern suggests that demographic transitions can reshape the balance between quantity and quality of human capital accumulation.

In addition, recent political-economy research suggests that the impact of income inequality on education expenditure may itself be nonlinear and contingent on institutional and income-level contexts. Bénabou [25] shows that, in a setting with imperfect credit markets and differentiated public–private education systems, higher inequality can either increase or decrease support for public education, depending on whether richer households can opt out of the public system. Corcoran and Evans [26], using a panel of U.S. school districts, find that rising local income inequality is associated with higher per-pupil spending on public education, consistent with a median-voter framework in which changes in the tax price faced by the median household alter support for school spending. At the same time, Wang et al. [27] document an inverted-U-shaped effect of income gaps on education-related social expenditure in China; they observe that widening inequality initially promotes but eventually dampens education spending once inequality surpasses a certain threshold. Together with earlier cross-country analyses, such as those reported by Sylwester [11] and De Gregorio and Lee [13], these studies imply that the relationship between income inequality and education expenditure can differ between low- and high-income environments and may exhibit threshold or regime-dependent effects.

In summary, the determinants of education expenditure are multidimensional, involving economic, social, and demographic factors, and recent research increasingly points to nonlinear and heterogeneous patterns in how income and inequality translate into education spending. However, much of the existing empirical work either employs linear specifications or does not explicitly distinguish between income groups, leaving the nonlinear and distribution-dependent nature of education finance underexplored. To address this gap, the present study empirically examines the effects of income level, inequality, and demographic structure on education expenditure in OECD countries, with a specific focus on nonlinearities and heterogeneity across income groups. In line with the theoretical and empirical evidence discussed above, we formulate the following hypotheses:

H1. 

There is a nonlinear relationship between income level and education expenditure as a share of GDP.

H2. 

Higher income inequality reduces education expenditure in high-income countries but increases it in low-income countries.

3. Methodology

3.1. Data

This study empirically examines the determinants of sustainable education finance by analyzing how income level, income inequality, fertility rate, and population density affect education expenditure as a share of GDP. The analysis uses annual data for 38 OECD countries covering the period from 1997 to 2021, enabling a long-term assessment of fiscal and social dynamics relevant to education sustainability. All empirical analyses were conducted using Stata (version 15)

Education expenditure, expressed as a percentage of GDP (https://gpseducation.oecd.org/IndicatorExplorer accessed on 20 November 2024), follows the OECD classification and represents the total expenditure on educational institutions, including both public and private sources. This indicator reflects the fiscal effort devoted to human capital development and provides a comparative measure of the sustainability of public investment in education across countries.

Per capita income is measured by dividing nominal GDP by the total population of each country and adjusting for the Consumer Price Index (CPI) to obtain real income values, thereby eliminating the effects of inflation (https://databank.worldbank.org accessed on 20 November 2024). Income inequality is captured using the Gini coefficient (https://www.oecd.org/en/data/indicators/income-inequality.html accessed on 20 November 2024), a standard metric that enables international comparison and reflects social disparities that may influence education financing. Fertility rate (https://www.oecd.org/en/data/indicators/fertility-rates.html accessed on 20 November 2024) and population density (https://data-explorer.oecd.org accessed on 10 December 2024) are included to account for the demographic pressures that affect both the demand for education and the allocation of fiscal resources.

Descriptions of all variables and summary statistics are reported in

Table 1. Variables, definitions, and sources of data.

Variables	Definition	Source
Education Expenditure (Eduexp)	Total expenditure on educational institutions as a percentage of GDP (2018)	OECD DATA
Income Level (pergdp)	Gross domestic product, current prices (U.S. dollars), Population, CPI (Inflation, average consumer prices)	WEO
Income Inequality (inequ)	Gini Coefficient	OECD DATA
Fertility Rate (ferti)	Total Fertility	OECD DATA
Population Density (pop)	Population density (Persons per square kilometer)	OECD DATA

and

Table 2. Descriptive statistics.

Variables	Max	Min	Mean	Std. Dev.
Eduexp	5.7	1.91	3.097	1.489
lnpergdp	0.919	0.058	0.689	0.777
inequ	0.497	0.217	0.31	0.079
ferti	3.11	0.81	1.679	0.380
pop	5.806	−1.309	2.525	1.513

, providing an overview of the cross-country variations and long-term trends relevant to the fiscal and demographic sustainability of education expenditure.

3.2. Method

This study employs a fixed-effects model to control for time-specific variations and country-specific characteristics, thereby ensuring that the estimated relationships between variables are not biased by temporal or cross-country heterogeneity. One of the main objectives of this study is to examine how the interaction effects between education expenditure, income level, income inequality, and fertility rate influence education spending. To this end, interaction terms among key variables are incorporated into the analysis.

Subsequently, the study applies the Method-of-Moments Quantile Regression (MMQR). Traditional fixed-effects models focus on the mean of the dependent variable and do not account for its entire distribution, which limits their ability to capture heterogeneity across observations. Variables such as education expenditure, where the distribution across countries may exhibit substantial heterogeneity, fail to detect subtle differences and could constrain the interpretation of results. MMQR is therefore adopted to address this limitation.

A key advantage of MMQR is that it estimates effects at multiple points in the conditional distribution of the dependent variable—such as the 10th, 25th, 50th, 75th, and 90th quantiles—thereby complementing traditional linear regression models that concentrate solely on the mean. Using MMQR, this study analyzes the effects of explanatory variables across different quantiles of education expenditure in 38 OECD countries and explores differences between high-income and low-income groups. MMQR, an extension of the quantile regression framework developed by Koenker and Bassett [28], is implemented in this study using the model proposed by Machado and Santos Silva [29], enabling direct comparison with the fixed-effects model results.

Furthermore, to capture structural differences in the determinants of education expenditure arising from disparities in national economic capacity, the analysis is conducted separately for high-income and low-income OECD countries. Following the classification criteria of Na [30], countries are divided into high-income and low-income groups based on whether their per capita GDP (measured in PPP terms) is above or below the sample median (see

Table 3. Group classification of OECD countries.

Classification (Economic Size)	Countries (Abbreviation)
High-Income Countries	USA, GBR, CAN, IRL, AUS, NZL, JPN, DEU, FRA, CHE, SWE, DNK, NOR, FIN, AUT, BEL, NLD, KOR, LUX
Low-Income Countries	ITA, GRC, PRT, ESP, POL, HUN, SVK, SVN, CZE, ISR, ISL, MEX, CHL, EST, TUR, COL, CRI, LVA, LTU

).

Figure 3 classifies OECD countries by income level, with the vertical axis representing each country’s annual education expenditure as a percentage of GDP and its average education expenditure, and the horizontal axis indicating per capita income. Each point represents an individual country. Among high-income countries, a negative relationship is observed in which higher per capita income is associated with a lower share of education expenditure. This pattern may reflect the characteristics of more mature education systems and the increasing private burden of higher education costs in these countries. In contrast, low-income countries exhibit a positive relationship, whereby higher income levels are accompanied by a greater share of education expenditure, suggesting a tendency for government spending on the education sector to expand as income rises.

3.3. The Empirical Model

In this study, we conducted an empirical analysis in three steps. First, we estimated a baseline fixed-effects panel model for the full sample of OECD countries as well as for the high-income and low-income subsamples. This specification captures the average within-country association between income, inequality, fertility, and education expenditure, while controlling for time-invariant heterogeneity across countries. Second, to explore whether the effect of income depends on demographic and distributional conditions, we augment the baseline model with interaction terms between income and income inequality and between income and the fertility rate. These interaction terms allow us to explicitly test whether the impact of income on education expenditure differs with the level of inequality and demographic pressure and whether such effects vary between high- and low-income countries. Third, motivated by the substantial differences found between income groups, we apply the Method-of-Moments Quantile Regression estimator to investigate how the determinants of education expenditure behave across the conditional distribution of education spending. This three-step strategy distinguishes our study from much of the existing literature and provides a more nuanced assessment of how income level, income inequality, and fertility jointly shape sustainable education finance.

To account for unobserved heterogeneity across countries, this study employs a fixed-effects panel model, which effectively controls for time-invariant country-specific characteristics and common time shocks. The general form of the linear panel regression model is expressed as

$$y_{i,t}=\alpha +x_{i,t}\prime \beta +c_i+{\lambda }_t+u_{i,t}$$

where $y_{i, t}$ denotes the dependent variable for country i at time t; $x_{i, t}$ is a vector of explanatory variables; $c_{i, t}$ captures unobserved, time-invariant country-specific effects; ${\lambda }_t$ represents time effects common to all countries; and $u_{i, t}$ is the idiosyncratic error term.

Because $c_{i, t}$ may be correlated with the regressors, the FE model eliminates this potential bias by applying a within transformation, which subtracts the time mean from each observation within a country. The transformed model is therefore expressed as

$${ỹ}_{i,t}={\left( x_{i,t}+{\overline{x}}_{i,t}\right)}^{\prime }\beta +( {\lambda }_t-\lambda )+{ũ}_{i,t}$$

This transformation removes the unobserved individual effects ($c_i$) and ensures that estimation relies solely on within-country variation over time. When time dummies are included, the FE specification can be rewritten as

$$y_{i,t}={\alpha }_i+y_t+x_{i,t}\prime \beta +u_{i,t}$$

where ${\alpha }_i$ denotes country-specific fixed effects and $y_t$ represents time fixed effects.

The empirical framework consists of two specifications: a baseline model that captures the general relationships among the key variables, and an interaction model that examines how the effects of income on education expenditure vary conditionally with demographic and inequality factors. The two models are specified as follows:

• Baseline Model

$${Eduexp}_{i,t}={\alpha }_0+{\alpha }_1{lnpergdp}_{i,t}+{\alpha }_2{lnpergdp}_{i,t}^2+{\alpha }_3{inequ}_{i,t}+{\alpha }_4{ferti}_{i,t}+{\alpha }_5{lnpop}_{i,t}+{\epsilon }_{i,t}$$

(1)

B.

Interaction Model

$${Eduexp}_{i,t}={\beta }_0+{\beta }_1{lnpergdp}_{i,t}+{\beta }_2{lnpergdp}_{i,t}^2+{\beta }_3{inequ}_{i,t}+{\beta }_4{ferti}_{i,t}+{\beta }_5{lnpop}_{i,t}+{\beta }_6{lnpergdp}_{i,t}·{inequ}_{i,t}+{\beta }_7{lnpergdp}_{i,t}·{ferti}_{i,t}+{ϵ}_{i,t}$$

(2)

Here, $i$ denotes the country, $t$ denotes the time period, ${Eduexp}_{i, t}$ represents the share of education expenditure in GDP for country $i$ at time t, ${lnpergdp}_{i,t}$ is the log-transformed per capita GDP, ${inequ}_{i,t}$ represents income inequality, ${ferti}_{i,t}$ denotes the fertility rate, ${lnpop}_{i, t}$ is the log-transformed population density, and ${\epsilon }_{i,t}$ is the error term.

The independent variables in this study are defined as follows. First, per capita GDP, representing economic performance, is included based on the premise that income levels influence both the demand for and provision of education [1]. According to Wagner’s Law, public sector expenditure tends to increase proportionally with income, and education, as a representative public good, is expected to follow this pattern, with government spending rising alongside economic growth.

Second, higher income inequality may strengthen the social legitimacy for greater government involvement in education. However, prior studies have reported mixed findings: while some suggest that greater inequality prompts expanded public investment in education, others argue that it leads to elite-focused education spending and potentially reduces overall educational expenditure. This warrants empirical investigation.

Third, higher fertility rates increase the school-aged population, thereby placing a greater fiscal burden on public education budgets. Since fertility rate directly affects the demand for education, it is included as a key demographic variable.

Lastly, Hwang [1] and Sylwester [11] suggest that higher population density can reduce the cost of establishing and maintaining an education system, as agglomeration effects from population concentration allow for economies of scale.

When analyzing the effect of income on education expenditure, assuming a purely linear relationship—where education spending rises proportionally with per capita income—may not fully capture reality. Hartwig [31] reported that, beyond a certain income threshold, education expenditure growth may slow or even decline; this implies that, while education behaves as a normal good at lower income levels, saturation or substitution effects may emerge once income surpasses a certain point [32]. To account for this potential nonlinearity, the square term of per capita income, ${lnpergdp}_{i,t}^2$, is included in the baseline model.

Subsequently, the MMQR model proposed by Machado and Silva [29] is applied. The quantile regression framework defines the conditional quantile function $Q_Y\left(\tau |X\right)$ as the minimum value at which the conditional cumulative distribution function $F_{\left.Y\right|X}\left(y\right)$ reaches a given quantile, τ, as follows:

$$Q_Y\left(\tau |X\right)=inf\left\{y:F_{\left.Y\right|X}\left(y\right)\ge \tau \right\}$$

In this framework, quantile regression estimates are obtained by solving the following minimization problem:

$$\widehat{\mathsf{\beta }}\left(\tau \right)=\arg min\sum _{i=1}^N\sum _{t=1}^N{\rho }_{\tau }(y_{i,t}-X_{i,t}^{\prime }\beta )$$

Here, ${\rho }_{\tau }\left(u\right)$ denotes the quantile loss function, defined as

$${\rho }_{\tau }\left(u\right)=\left\{\begin{array}{c}\tau u if u\ge 0\\ \left(\tau -1\right)u if u<0\end{array}\right.$$

Based on this general framework, the MMQR model specified in this study is as follows:

$$Q_{eduexpi,t\left(\tau |X\right)}={\gamma }_0\left(\tau \right)+{\gamma }_1\left(\tau \right){lnpergdp}_{i,t}+{\gamma }_2\left(\tau \right){lnpergdp}_{i,t}^2+{ \gamma }_3\left(\tau \right){inequ}_{i,t}+{ \gamma }_4\left(\tau \right){ferti}_{i,t}+{\gamma }_5\left(\tau \right){lnpop}_{i,t}+{\mu }_I+ {\theta }_{i,t}$$

(3)

Here, ${\mu }_i$ represents country-specific, time-invariant characteristics, which are included to control for structural differences that may affect education expenditure. In Equation (3), the analysis is conducted for quantiles τ = 0.1, 0.25, 0.5, 0.75, and 0.9, allowing for an examination of how the effects of explanatory variables differ between countries with low levels of education expenditure (lower quantiles) and those with high levels (upper quantiles).

Before proceeding to the regression analysis, preliminary correlation diagnostics indicated no evidence of problematic autocorrelation in the data. Diagnostic tests, however, confirmed the presence of heteroskedasticity in the residuals: the Breusch–Pagan/Cook–Weisberg test after the baseline pooled OLS regression rejects the null of homoskedasticity (χ²(1) = 7.56, p = 0.006). Accordingly, all panel regressions are estimated with country-clustered robust standard errors, which provide a heteroskedasticity-robust inference.

4. Empirical Result

4.1. Fixed-Effects Model

Table 4. Results of the fixed-effects model.

	All Countries	High-Income Countries	Low-Income Countries
$lnpergdp$	0.396 *** (0.17)	0.241 (0.20)	4.571 *** (1.53)
$ln{pergdp}^2$	−0.690 *** (0.21)	−0.515 (0.18)	−6.773 *** (2.92)
inequ	−3.240 * (1.79)	−5.432 *** (1.49)	3.149 * (3.02)
ferti	−0.835 *** (0.22)	0.244 (0.21)	−0.221 * (0.45)
lnpop	0.003 * (0.001)	0.002 (0.00)	0.046 ** (0.14)
C	2.205 *** (1.00)	6.891 *** (1.18)	−3.607 ** (2.32)
$R^2$	0.41	0.32	0.31
Obs.	912	456	456

Note: Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

reports the baseline fixed-effects estimates for the full panel of 38 OECD countries and for the groups of high-income and low-income countries. For all countries taken together and for the low-income countries, the logged per capita income is significantly nonlinearly related to education expenditure: the coefficient on lnpergdp is positive, and the coefficient on its squared term is negative, both significant at the 1% level. This pattern implies an inverted-U relationship in which the share of education spending in GDP increases with income at lower income levels and decreases once income exceeds a certain threshold. This result is consistent with theoretical contributions, arguing that public education outlays have an inverted-U effect on long-run growth and welfare, with an interior optimum beyond which marginal benefits [18,33]. In the early stages of development, governments may allocate a larger share of fiscal resources to education to foster human capital accumulation and inclusive growth; in contrast, at higher income levels, the education share tends to fall, reflecting fiscal rebalancing and a greater reliance on private education finance.

For the group of high-income countries, by contrast, neither the level nor the squared term of lnpergdp is statistically significant. Hence, for these economies, the data do not provide clear evidence of a systematic income–expenditure relationship once a country’s fixed effects are controlled for, and any potential nonlinearity should be interpreted with caution rather than as a robust pattern.

Second, income inequality is negatively and significantly associated with education expenditure in all countries and in the high-income countries, indicating that greater inequality tends to be accompanied by a smaller share of education expenditure in GDP. The magnitude of the coefficient is larger for high-income countries, which is consistent with political-economy arguments that rising inequality can weaken middle-class support for tax-financed public education in advanced economies [26]. For the low-income countries, however, the coefficient is positive and significant at the 10% level, suggesting that, in less developed OECD economies, higher inequality may be associated with higher public education expenditure when policymakers explicitly prioritize inequality reduction [11,27]. Given the relatively large standard errors for this country group, these estimates should be viewed as indicative and interpreted with due caution.

Third, the fertility rate is negatively and significantly related to the share of education expenditure in GDP for all countries and for the low-income countries, whereas for high-income countries, the estimated fertility coefficient is not statistically significant, and no firm conclusion can be drawn about the effect of fertility on education expenditure.

Finally, population density is positively and significantly related to education expenditure for all countries and for the low-income countries, indicating that higher density increases both the demand for education and the cost of maintaining adequate education [34]. Densely populated countries, therefore, need policy measures that enhance the efficiency of education investment while ensuring equitable access, in line with the broader goals of sustainable and inclusive urban development. All regressions are estimated with country-clustered robust standard errors that are heteroskedasticity-consistent. In some specifications for the high- and low-income country groups, standard errors are relatively large, reflecting the smaller number of countries and greater within-group heterogeneity; accordingly, the corresponding coefficients are interpreted primarily in terms of their sign and overall pattern rather than precise magnitudes.

Table 5. Results of the interaction term model.

	All Countries			High-Income Countries			Low-Income Countries
lnpergdp	2.674 *** (0.51)	5.497 *** (0.55)	5.014 *** (0.46)	1.384 (1.54)	3.80 1 ** (1.91)	3.978 *** (1.02)	4.924 *** (2.54)	4.687 * (2.64)	4.515 *** (2.95)
$ln{Pergdp}^2$	−1.484 *** (0.15)	−1.566 *** (0.14)	−1.464 *** (0.15)	−0.603 ** (0.26)	−0.596 ** (0.25)	−1.451 *** (0.14)	−5.624 *** (2.81)	−5.487 *** (2.99)	5.376 *** (2.65)
Inequ	0.411 * (0.53)	1.574 (0.51)	1.241 * (0.52)	−5.210 *** (1.00)	1.247 (2.14)	1.090 * (0.47)	−1.947 ** (0.52)	−2.341 ** (1.00)	−2.320 ** (1.10)
Ferti	−0.441 * (0.20)	−0.021 (0.11)	−0.424 * (0.20)	0.788 (0.24)	0.724 *** (0.15)	−0.756 ** (0.18)	−0.987 *** (0.29)	−0.548 *** (0.45)	−1.048 *** (0.32)
pergdp × ferti	0.855 ** (0.33)		0.814 ** (0.37)	−0.450 (0.54)		0.807 * (0.22)	2.054 ** (0.78)		1.879 ** (0.88)
pergdp × inequ		−6.245 *** (2.00)	−6.740 *** (2.01)		−7.241 * (4.27)	−7.040 *** (2.13)		5.917 (5.27)	4.400 (5.03)
Lnpop	0.001 ** (0.00)	0.003 *** (0.00)	0.003 *** (0.00)	0.000 * (0.00)	0.002 * (0.00)	0.003 *** (0.00)	0.021 *** (0.00)	0.021 *** (0.00)	0.023 *** (0.02)
C	2.132 *** (0.24)	1.541 (0.27)	2.310 *** (0.32)	3.475 (1.20)	1.029 (1.42)	9.406 *** (2.50)	2.147 * (1.28)	2.104 ** (1.64)	2.614 *** (1.67)
$R^2$	0.31	0.38	0.30	0.29	0.31	0.32	0.31	0.31	0.32
Obs.	912	912	912	456	456	456	456	456	456

Note: Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

reports the estimates from the specifications that augment the baseline model with interaction terms between logged per capita income and the fertility rate, and between logged per capita income and income inequality. For all countries and for the low-income countries, the interaction between lnpergdp and ferti is positive and statistically significant in most specifications, indicating that, in countries with higher fertility rates, increases in income tend to be accompanied by a stronger rise in education expenditure as a share of GDP. For the group of high-income countries, by contrast, the interaction term is generally small and statistically insignificant, and only one specification yields a weakly significant coefficient. Overall, these results suggest that fertility effects are significant only in lower-income OECD economies; for richer countries, the estimated coefficient on fertility is statistically insignificant, and thus no systematic influence of fertility on education expenditure can be confirmed.

The interaction between lnpergdp and inequ is negative and statistically significant for all countries and for the high-income countries, but positive and statistically significant for the low-income countries. However, some interaction terms involving inequality show marginal significance in certain models, and the evidence is mixed and does not allow for a definitive conclusion. Given the relatively large standard errors for the low-income country group, however, the positive interaction effect in these countries should be regarded as suggestive rather than definitive. Even so, the coefficients point to an asymmetric impact of income inequality on education expenditure across income groups.

For the group of high-income countries, the interaction specifications show some indications of a nonlinear pattern, although the evidence is not fully consistent across models, and several coefficients are statistically insignificant. In these specifications, the coefficient on lnpergdp is positive, whereas the coefficient on its squared term (lnpergdp²) is negative and statistically significant. The joint effects of income with fertility and inequality, therefore, modify the standalone impact of income, so that the marginal effect of income on education expenditure depends on the demographic and distributional context [35]. In other words, the influence of income on education expenditure is not fixed but varies with changes in fertility and inequality.

4.2. MMQR Model

To gain deeper insights into how the determinants of education expenditure differ across the distribution, this study conducts an additional analysis using the Method-of-Moments Quantile Regression (MMQR) approach (see

Table 6. MMQR method.

	All Countries					High-Income Countries					Low-Income Countries
	Q.10	Q.25	Q.50	Q.75	Q.90	Q.10	Q.25	Q.50	Q.75	Q.90	Q.10	Q.25	Q.50	Q.75	Q.90
lnpergdp	5.264 *** (1.17)	7.112 *** (0.35)	2.924 *** (0.33)	2.141 *** (0.27)	1.624 *** (0.30)	0.998 (2.00)	0.789 (0.53)	2.014 *** (0.50)	3.354 *** (0.14)	3.954 *** (0.78)	4.924 (3.37)	6.001 *** (3.25)	6.248 *** (2.20)	9.405 (3.60)	8.693 ** (3.33)
${lnPergdp}^2$	−1.925 ** (0.28)	−1.957 *** (0.20)	−1.624 *** (0.17)	−1.112 *** (0.20)	−1.095 * (0.21)	−0.354 (1.16)	−0.384 (0.20)	−0.705 *** (0.21)	−1.113 *** (0.13)	−1.164 *** (0.21)	−6.651 (5.50)	−7.625 *** (4.28)	−7.320 *** (4.30)	−9.854 (4.85)	−9.004 ** (4.62)
inequ	−1.064 (0.70)	−0.752 (1.50)	−0.324 (1.50)	−0.687 (0.98)	−0.100 (0.92)	−2.241 (2.21)	−3.248 *** (2.31)	−3.756 ** (1.50)	3.320 (1.60)	2.754 (1.62)	1.321 *** (0.43)	1.357 ** (0.70)	1.654 (1.10)	1.762 (1.64)	1.778 (1.71)
ferti	−0.536 (0.35)	−0.120 (0.27)	0.367 *** (0.34)	0.435 *** (0.27)	0.467 *** (0.15)	1.210 *** (0.19)	1.124 *** (0.12)	0.120 *** (0.12)	0.121 *** (0.15)	0.119 *** (0.20)	−0.627 ** (0.34)	−0.798 *** (0.31)	−0.627 ** (0.24)	−0.533 ** (0.21)	−0.492 ** (0.21)
lnpop	0.002 ** (0.00)	0.000 *** (0.00)	0.001 * (0.00)	0.001 *** (0.00)	0.002 *** (0.00)	0.002 * (0.00)	0.002 *** (0.00)	0.000 (0.00)	0.000 (0.00)	0.000 (0.00)	0.022 *** (0.00)	0.025 *** (0.00)	0.010 *** (0.00)	0.009 *** (0.00)	0.009 *** (0.00)
c	1.354 * (0.68)	1.657 (0.72)	1.546 ** (0.71)	1.924 *** (0.68)	3.648 *** (0.69)	4.681 ** (1.62)	4.038 *** (1.38)	3.067 *** (0.67)	2.681 ** (0.52)	2.689 (0.68)	−3.910 (0.60)	−2.618 ** (0.54)	−1.985 ** (0.61)	1.761 (1.10)	1.927 *** (0.95)
Obs.	912	912	912	912	912	456	456	456	456	456	456	456	456	456	456

Note: Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

). The results indicate that increases in logged per capita income are associated with higher education expenditure in OECD countries, with notable heterogeneity across quantiles.

For all countries, lnpergdp is positively and statistically significantly associated with education expenditure at every quantile, while its squared term, lnpergdp², is negative and statistically significant across the entire distribution. Moreover, the coefficients on lnpergdp are larger at the lower quantiles (Q10 and Q25) and gradually decline toward the upper quantiles. This pattern indicates that the marginal effect of income on education spending is stronger in countries that devote a relatively low share of GDP to education, although the inverted-U-shaped relationship between income and education expenditure is evident throughout the distribution.

For the group of high-income countries, the coefficients on lnpergdp and lnpergdp² are small and statistically insignificant at the lower quantiles (Q10 and Q25). From the median quantile (Q50) onward, however, lnpergdp becomes positive and statistically significant, while lnpergdp² is negative and statistically significant. The absolute values of these coefficients increase toward the upper quantiles (Q75 and Q90), indicating that a nonlinear income effect is statistically significant only in the middle and upper quantiles (Q50–Q90), while no significant income effect is found at the lower quantiles.

For the low-income countries, lnpergdp is positive and statistically significant across all quantiles, and its coefficient increases from the lower to the upper part of the distribution, with the largest values at higher quantiles. By contrast, the squared term lnpergdp² is negative and statistically significant at every quantile, with larger absolute values at the upper quantiles. Taken together, these results indicate that income has a strong and progressively larger impact on education expenditure in low-income countries that allocate a higher share of GDP to education, while the negative squared term confirms an inverted-U-shaped pattern in which the marginal effect of additional income eventually diminishes. From a policy perspective, this suggests that low-income countries should use periods of income growth to expand and lock in public education spending, especially once education outlays begin to account for a larger share of GDP, while at the same time adopting fiscal frameworks that prevent the erosion of education budgets as economies mature [14,15,18].

5. Conclusions

5.1. Summary of Analysis

This study examined the determinants of education expenditure as a share of GDP in 38 OECD countries over the period 1997–2021, with particular attention to the sustainability of public education finance. Using annual panel data, the analysis followed a three-step empirical strategy. First, baseline fixed-effects models were estimated for all countries and separately for groups of high-income and low-income countries, allowing within-country relationships to be identified while controlling for time-invariant heterogeneity.

Second, interaction terms between income and inequality and between income and fertility were introduced to examine whether the impact of income on education expenditure depends on demographic and distributional conditions. Third, Method-of-Moments Quantile Regression (MMQR) was applied to explore how these relationships vary across the conditional distribution of education expenditure.

The empirical results provide strong evidence of a nonlinear, inverted-U-shaped relationship between income and education expenditure for all countries taken together and for the group of low-income countries. Logged per capita income has a positive and statistically significant effect on the education spending share, while its squared term is negative and significant, indicating that the marginal effect of income diminishes and may eventually become negative as income rises. For the group of high-income countries, the baseline fixed-effects estimates do not show a precisely estimated nonlinear pattern. However, once interaction terms are included and the MMQR estimates across quantiles are considered, the joint evidence for high-income countries suggests a nonlinear income–expenditure relationship that is statistically significant only at the middle and upper quantiles, while no significant income effect is found at the lower quantiles.

Furthermore, the analysis shows that the effect of income inequality on education expenditure is not uniform across income groups. In the full sample and among high-income countries, higher inequality is associated with a lower share of education expenditure in GDP, suggesting that more unequal high-income societies devote a smaller portion of national income to public education. By contrast, for low-income countries, income inequality has a positive and statistically significant association with education expenditure; this result indicates that, in these countries, rising inequality can be accompanied by stronger redistributive efforts through the education budget.

Fertility rates are negatively associated with education expenditure in all countries and in low-income countries, whereas this relationship is not statistically significant in high-income countries. Population density is generally positively associated with the education spending share, especially in low-income countries, reflecting both increased demand for schooling and higher costs of providing adequate infrastructure in densely populated areas. A supplementary analysis that incorporates an education quality indicator based on SDG 4.1.1 suggests a positive association between spending levels and learning outcomes, although data limitations prevent the inclusion of this variable in the main specification (see Appendix A for detailed results).

Overall, the results indicate that education expenditure in OECD countries is shaped by a combination of income, inequality, and demographic factors, and that these relationships are nonlinear and heterogeneous across income groups and across the distribution of education spending. This highlights the need to move beyond simple linear models and average effects when assessing the sustainability of education expenditure.

5.2. Policy Recommendations

The empirical results of this study suggest several concrete directions for the design of education finance policy in OECD countries. The first implication concerns the use of income growth in countries with relatively low education spending. For the low-income group, income has a consistently positive and statistically significant effect on the education spending share across all quantiles, while the squared term is negative, indicating an inverted-U-shaped pattern. In other words, when income starts from a low base, additional growth is strongly associated with an expansion of education expenditure; however, the marginal effect weakens as the education spending share becomes larger. This pattern implies that low-income OECD countries, or those currently allocating a relatively small share of GDP to education, should treat periods of income growth as an opportunity to raise the education spending share to a sustainable medium-run level and then stabilize it, rather than allowing spending to fluctuate with the business cycle [36]. Medium-term expenditure frameworks that include explicit floors or reference ranges for education spending could help lock in these gains and support the gradual accumulation of human capital.

Second, the role of income inequality differs clearly between income groups and should be reflected in policy design. In high-income countries, higher inequality is associated with a lower share of education expenditure in GDP, and some interaction terms between income and inequality are negative and occasionally statistically significant; however, the evidence is mixed and does not support a definitive conclusion about how inequality modifies the effect of income on education spending. Overall, these empirical patterns are broadly consistent with political-economy arguments that high inequality may weaken middle-class support for tax-financed public education [9,12]. In practical terms, high-income OECD members that combine high income levels with rising inequality may need to protect the education budget explicitly within fiscal rules, for example, by ensuring that funding formulas favor disadvantaged schools and regions, and by making the distributive effects of education spending more transparent. In contrast, for the low-income group, inequality is positively associated with education expenditure, suggesting that, where education is used as a key redistributive tool, rising inequality can be matched by higher public effort. In these countries, linking redistributive education programs to the tax and transfer system can help in ensuring that additional spending effectively reaches groups that are most affected by inequality [37].

Third, the results underline the fact that demographic pressures should be explicitly incorporated into education budget planning. In low-income countries, higher fertility is associated with a lower education spending share, while population density is positively related to education expenditure. This combination suggests that densely populated systems with high fertility face a strong demand for schooling but have difficulty maintaining high spending ratios. For such countries, multi-year education plans that pre-emptively account for projected school-aged cohorts, along with investments in cost-effective infrastructure (for example, multi-shift schools or shared facilities), can help prevent per-student spending from eroding as enrolment increases. In addition, where high density already coincides with high education spending shares, the inverted-U-shaped income effect found at upper quantiles indicates that further increases in spending should prioritize quality improvements and efficiency gains rather than simply expanding the aggregate budget [38].

Finally, the nonlinear and distribution-dependent patterns found in this study suggest that a uniform rule—such as targeting a fixed optimal education spending ratio—may not be appropriate for all OECD countries. Instead, education finance strategies should differentiate between (i) countries that are still below the point where the marginal effect of income on education spending begins to weaken, and (ii) countries that have already reached or passed this threshold. For the former, the priority is to raise and stabilize the education spending share as income grows; for the latter, the priority is to preserve the public component of education finance in the face of fiscal consolidation and private-sector expansion, while making better use of existing resources. In both cases, the results of this study point to the need for education budgets that are explicitly linked to income dynamics, inequality profiles, and demographic trends, rather than being adjusted solely in response to short-term fiscal pressures.

6. Limitations and Prospects

This study has several limitations. First, although a supplementary analysis was conducted using an education quality indicator based on SDG 4.1.1, this variable could not be incorporated into the main empirical model because its temporal and cross-country coverage is limited, and many OECD country–year observations are missing. For this reason, the core specifications focus on education expenditure as a share of GDP and do not fully reflect cross-country differences in education quality. Future research would benefit from richer and more consistent indicators of education quality that would allow a more comprehensive assessment of the link between spending, outcomes, and the sustainability of education expenditure.

Second, the baseline analysis covers the period up to 2021 and therefore only partially includes the COVID-19 period. The study does not capture the medium-term fiscal and educational consequences of the pandemic, such as temporary school closures, emergency spending, and post-pandemic consolidation. As post-COVID data on education expenditure, inequality, and demographic indicators become more complete, future work could extend the panel and explicitly compare pre- and post-pandemic patterns. This would make it possible to determine whether the nonlinear income–expenditure relationship and the inequality effects identified in this paper have changed in the aftermath of COVID-19 and to evaluate the robustness of the present findings in a new fiscal and social environment.