Federalism and Horizontal Inequalities in Education: Connecting Equalizing Aspirations through a Typology of Municipalities^*

Abstract

Seeking to advance the understanding of the relationship between federalism and horizontal inequalities in Brazil, the objective of this article is to understand the role of the Union in reducing municipal inequities in education beyond the financial dimension of municipal revenues. With the clustering method, the work creates a typology of municipalities based on the functioning structure of educational networks and analyzes how this typology relates to their levels of efficiency in public spending, calculated from the Data Envelopment Analysis (DEA). The results demonstrate that the profile of municipalities is one of the determinants of the efficiency of public educational expenditure. Thus, centrally designed national policies that aim to reduce educational inequities by guaranteeing equal conditions among subnational entities cannot ignore their operating structure to implement the respective public policies.

Resumo

Buscando avançar na compreensão das relações entre federalismo e desigualdades horizontais no Brasil, o objetivo deste artigo é compreender o papel da União na redução das iniquidades municipais em educação para além da dimensão financeira das receitas municipais. Com o método de clusterização o trabalho cria uma tipologia de municípios a partir da estrutura de funcionamento das redes educacionais e analisa como essa tipologia se relaciona com os seus níveis de eficiência do gasto público, calculado a partir da Análise Envoltória de Dados (DEA). Os resultados demonstram que o perfil das municipalidades é um dos determinantes da eficiência do gasto público educacional. Assim, as políticas nacionais desenhadas centralmente que objetivem reduzir as iniquidades educacionais por meio da garantia de condições equânimes entre os entes subnacionais não podem ignorar a sua estrutura de funcionamento para implementar as respectivas políticas públicas.

federalismo; equidade; coordenação federativa; eficiência do gasto público; Fundeb

Résumé

Dans le but d’avancer dans la compréhension des relations entre le fédéralisme et les inégalités horizontales au Brésil, cet article vise à comprendre le rôle de l’Union dans la réduction des inégalités municipales en éducation au-delà de la dimension financière des recettes municipales. En utilisant la méthode de regroupement, l’étude crée une typologie de municipalités à partir de la structure de fonctionnement des réseaux éducatifs et analyse comment cette typologie se rapporte à leurs niveaux d’efficacité des dépenses publiques, calculés à partir de l’Analyse Enveloppement des Données (DEA). Les résultats démontrent que le profil des municipalités est l’un des déterminants de l’efficacité des dépenses publiques en éducation. Ainsi, les politiques nationales conçues de manière centralisée qui visent à réduire les inégalités éducatives en garantissant des conditions équitables entre les entités subnationales ne peuvent ignorer leur structure de fonctionnement pour mettre en œuvre les politiques publiques respectives.

fédéralisme; équité; coordination fédérative; efficacité des dépenses publiques; Fundeb

Resumen

Buscando avanzar en la comprensión de las relaciones entre federalismo y desigualdades horizontales en Brasil, el objetivo de este artículo es comprender el papel de la Unión en la reducción de las iniquidades municipales en educación, más allá de la dimensión financiera de los recursos municipales. Por medio del método de agrupación en clústeres, este trabajo crea una tipología de municipios a partir de la estructura de funcionamiento de las redes educativas y analiza cómo se relaciona esa tipología con los niveles de eficiencia del gasto público, calculado a partir del Análisis por Envoltura de Datos (DEA). Los resultados demuestran que el perfil de las municipalidades es uno de los determinantes de la eficiencia del gasto público en educación. Así, las políticas nacionales diseñadas centralmente que buscan reducir las iniquidades educativas por medio de la garantía de condiciones ecuánimes entre las entidades subnacionales, no pueden ignorar su estructura de funcionamiento para implementar las respectivas políticas públicas.

federalismo; equidad; coordinación federativa; eficiencia del gasto público; Fundeb

Introduction

The 1988 Federal Constitution brought about a series of political and economic changes compared to the previous period. In addition to expanding the range of social policies guaranteed to Brazilian society, the Constitution introduced substantial changes in the management of public policies and the conditions for reforms made in the subsequent period, focusing on formatting social policies. Considering the federative framework created in 1988, decentralization shaped Brazilian federalism by making municipalities autonomous entities and conferring on them a series of authorities and centrality in public policy management and implementation (Arretche, 2002).

The Federal Constitution also guaranteed educational policy on an exceptional basis, a binding of resources at all levels of government so that states and municipalities must allocate at least 25% of tax revenues to the Maintenance and Development of Education (MDE). In comparison, the Union must allocate 18% (Brazil, 1988). The social policy reforms of the 1990s, which followed the significant changes introduced by the Constitution, created the FUNDEF (Fund for Maintenance and Development of Basic Education and the Valorization of Teaching) in 1996. The FUNDEF changed the logic behind financing education within subnational entities by creating twenty-seven financing funds in each federal unit, in which states and municipalities would have part of their revenues sublinked and fully distributed among their respective systems according to the number of enrollments. Therefore, this policy led to a municipalization process that transferred enrollments from the state to the municipal system, making municipalities more prominent in implementing education policies (Arretche, 2002; Gomes, 2009).

With the expiration of the FUNDEF in 2006, the FUNDEB (Fund for the Maintenance and Development of Basic Education and the Valorization of Education Professionals) was instituted. It began to regulate the financing of basic education in the country, the main difference being that it focused on basic education as a whole and no longer on elementary education only. Furthermore, the FUNDEB fixed a percentage of resources for the Union to complement (10% of total revenue). In 2020, the FUNDEB ended and gave way to the New FUNDEB, which, despite maintaining the funding logic of its predecessor, introduced significant changes to the results of education policy results. One of these changes is that it is permanent—that is, it no longer has a time limit like previous policies—and increases the Union’s contribution from 10% to 23% of the total resources in the fund. However, the increased Union resources do not follow the same distribution logic in place until then. Of the additional 13%, 10.5 percentage points would be distributed among education systems without accounting for their federative unit. This way, poorer systems from a better-off state could receive resources. Furthermore, this distribution would consider all revenue from these entities, including municipal resources. The other 2.5 percentage points would be distributed according to the performance improvement and inequality reduction criteria (Brazil, 2020; Peres et al, 2020).

By analyzing the three education financing policies of recent decades, it is evident that although subnational entities are responsible for their implementation—especially municipalities—the Union is responsible for formulating them nationally. As noted by Arretche (2012) in other policies, subnational entities do not partake in this decision-making process. Despite the Union’s equality-generating movements based on this institutional arrangement ensured by the Federalism of 1988 (Arretche, 2010), it is apparent that one of the great challenges facing this same arrangement is how to make nationally standardized policies in the presence of territorial inequalities. In other words: the question is how the Union, responsible for formulating and shaping public policy design, addresses the different capabilities and needs of subnational entities in its search to provide equity between Brazil’s 5570 municipalities, 27 states, and federal district. Subsidies for financing education policies should be created to allow the transfer of Union resources to subnational entities and the redistribution of resources between these entities – municipalities, above all, based on the municipalities’ different capabilities to use their respective resources efficiently to operate equally.

Given this, this study aims to evaluate the role of the Union in reducing municipal inequalities in education, considering different capabilities among municipalities to implement their own education policy. To this purpose, a typology of municipalities was created based on the education system structure to analyze how this typology relates to the efficiency levels of public education spending in the respective municipalities. This study applied cluster multivariate analysis techniques, ANOVA, and Data Envelopment Analysis (DEA) on indicators of the structure of municipal systems’ public elementary education service supply. The measurement and concept of the supply structure are according to the following indicators: school management complexity, teaching effort, teacher regularity, adequacy of teacher training, school infrastructure, and average pay for teachers today. The connection between this study’s objective and empirical analyses is based on the following points:

1. if the operating structure of education systems is a determinant of efficiency levels of public education spending in municipalities, and the Union does not take this into account when designing funding policies, then it tends to have a limited role in reducing municipal education inequities, to the extent that it does not consider municipal conditions to achieve their education results;

2. if the systems’ structure is not a determinant of efficiency levels, then there is no reason for the Union to consider the profile of municipalities to design basic education-funding policies to promote equity among systems.

From the results, this typology of municipalities is expected to inform—both in theory and empirically—discussions about the design of public policies given the territorial inequalities in which policy executing units have different conditions to carry out their implementation activities and demand different levels of resources to operate on an equal footing with their counterparts. In addition, the equalizing aspirations of education policy should consider the particularities of the heterogeneous Brazilian municipalities.

This paper has five other sections: the first presents the theoretical framework, based on the approach of Brazilian federalism and its relation with territorial inequalities, and the approach addressing the management of public education spending. The second section presents methodological choices. The third section presents and the fourth discusses the results of the study. Finally, the fifth section presents final considerations, followed by references.

Theoretical Framework

Territorial Inequalities within Brazilian Federalism

Brazil’s federative arrangement established by the 1988 Federal Constitution combines centralizing and decentralizing dynamics visible in the public policies’ outcomes and, in turn, their level of inequalities. Contrary to the expectations of Brazilian federalism’s decentralizing nature, the literature points to its centralizing character: the central government has ample power to design and formulate public policies. Subnational governments will then implement these public policies without participating in decision-making (Arretche, 2012). Arretche (2012) further differentiates centralization and decentralization dimensions with policy decision-making and policymaking. According to the author, the first category concerns decision-making to formulate public policies, while the latter refers to their execution. In this sense, she notes that policymaking was decentralized in 1988, referring to the role of subnational entities. Policy decision-making, which refers to the Union’s role in drawing public policies, remained centralized—thereby revealing the centralizing nature of Brazilian federalism.

The consequences of this arrangement on public policy inequalities are visible in the Union’s ability to reduce them. By standardizing the drawing of public policies nationally and forcing subnational entities to implement them, the tendency for the implemented policies to be uniform among the different entities increases (Arretche, 2010). However, the central government’s actions that generate equality do not consider the different specificities and capabilities of different states and municipalities to implement their respective public policies.

When analyzing a set of policies that are regulated and not regulated by the federal government, Arretche (2010) notes that regulated policies, i.e., those that the central government normatively regulates, have lower levels of inequality in spending than non-regulated policies. This leveling happens because when determining national standards for regulated policies while simultaneously supervising how units adhere to such regulations, there is a reduction in inequalities. As for education policy, the regulations are established by linking at least 25% of tax revenues--which must be applied across municipalities and later the FUNDEF, which creates new rules for the distribution of education resources. The result of these mechanisms is the reduction of inequalities in municipal education spending measured by the Gini index, which decreased from 0.304 in 1996 to 0.232 in 2006 (Arretche, 2010). However, one should consider that the reduction in inequalities expressed above refers to inequalities of a specific condition in which a policy may operate. They are reductions in inequalities of outputs, which do not necessarily mean a decrease in inequalities of policy results--that is, in inequalities of outcomes (Arretche, 2016).

Beyond the analytical dimensions of centralization versus decentralization, there are also other dimensions of federative analysis to explore and which impact public policies and their inequalities, like Federative coordination. Federative coordination is the capacity and/or possibility of a federative entity—usually the most comprehensive—to influence and guide the actions of other entities or to promote cooperation to achieve certain goals (Abrucio, 2005; Machado; Palotti, 2015; Segatto; Abrucio, 2018). In this regard, the FUNDEF was instituted bearing in mind that “the assumption of these actions was that in redistributive problems, particularly in a federation, the federal government’s action is necessary to prevent the worsening of inequalities” (Abrucio, 2005:53). It is also noteworthy the possibility of the central government, in the context of Brazilian federalism and with a coordinating prerogative, to produce actions of immediate effect on subnational governments without the need for them to adhere to the respective policy, as occurred with the FUNDEF and later FUNDEB (Gomes, 2009).

When the FUNDEF was established in 1996, one of the results of this policy was the reduction of intra-state inequalities: of municipal and state systems within the same federative unit (FU). Yet there was no reduction of inter-state inequalities--that is, of systems from different FUs (Vazquez, 2005). After the end of the FUNDEF, ten years after its establishment, the FUNDEB emerged. Just like the previous policy, the FUNBEB came from the central government through Constitutional Amendment 53/2006, which maintained the FUNDEF’s financing logic. However, besides covering all basic education, the FUNDEB increased the amount of resources that the entities should spend on the fund (from 15% to 20% of the 25% linked to MDE) and fixed the Union’s contribution of another 10%. This led to a decrease in intra-state and inter-state funding inequalities (Pinto, 2014; Bernardo et al., 2020).

In light of efforts to reduce inequalities by the FUNDEB fixing a complementary percentage of resources, the expectations for the New FUNDEB’s equalizing effect are even more optimistic given the increase from 10% to 23% and the introduction of new mechanisms to distribute this increase, which tend to benefit education systems with the lowest student/year values even more. The most innovative mechanism introduced refers to the 2.5 percentage points distributed according to the criteria of improved quality of education with inequality reduction, thus showing the tendency to “determine the control over the result of spending on education and encourage systems that prove to be efficient with increased funding” (Peres et al., 2020c).

When combining the aims of increased efficiency in public spending and reduced horizontal inequalities into a single policy, it is key to understand the conditions of the units implementing said education policy to achieve these aims. Given the territorial and education inequalities among municipalities and their different conditions to use public resources and manage education policies, treating all units as having equal implementation capabilities tends not to explore the State’s full potential in reducing these inequalities. In short, policies formulated by the Union in a centralized manner should consider the different types of municipalities, their respective capabilities, and needs to equitably distribute the resources that will be implemented locally.

Despite the merit behind research seeking to analyze and measure the central government’s ability to reduce horizontal inequalities within education—more specifically, inequality in funding—one should also consider municipalities’ ability to produce results with these very resources. Hence, this paper seeks to analyze whether municipalities with different operating structures of education policy have different conditions to manage their education resources and thus use them efficiently. From these results, one hopes to understand the Union’s potential to reduce horizontal inequities while considering the specificities of the country’s different education systems.

Management and Efficiency in Public Education Spending

Studies addressing the economic aspects of resource allocation in education systems widely discuss the efficiency of public education spending. Based on the human capital theory, economic research on education emerged in the 1960s. Yet, several classical 18th and 19th-century economists, such as Adam Smith, Alfred Marshall, and John Stuart Mill, discussed the importance of education as a national investment tool and how to fund it (Woodhall, 1987:1).

The efficiency criterion of welfare economics is called Pareto efficiency and defines welfare as “a condition where it is not possible to increase total utility by reallocating resources, if any reallocation which makes one group of individuals better off would make another group worse off “ (Woodhall, 1987:2). According to Pareto efficiency, resources are not used most efficiently if all groups improve their situation, altering the balance between different goods and services. However, if any change benefits one group over another, this condition is described as Pareto optimal (Woodhall, 1987).

In addition to efficiency, equity is also a criterion for making decisions on resource allocation even though efficiency measurement techniques have not addressed this issue so that “the dominant paradigm utilized in analyzing the effects of educational resources on student outcomes over the last few decades has been the education production function”. (Hedges et al., 1994:6). Thus, for Pritchett and Filmer (1999:224), the education function “is an expression for the maximum amount of output possible for an amount of inputs”. Therefore, it is a relationship between the inputs and outputs of a production system.

According to Hanushek (1995), budget differences do not represent the main factor in performance differences--resource allocation becomes the determining factor in this process (Hanushek, 1995). Thus, according to the author (1986:1162), the strategy of allocating more resources to public schools, irrespective of how the money is spent, is ineffective as there is no strong relationship between education spending and student performance. Thus, defining an effective budget structure to allocate spending efficiently is not just about increasing spending. This way, it is possible to identify municipalities with fewer resources but students with satisfactory performance (Rothstein, 2000; Hanushek, 2004; Andrade, 2009).

Several studies in Brazil over recent decades have shown that despite a significant increase in the education budget, this increase has not necessarily been reproduced in the quality of public education (Crozatti et al., 2014; Diaz, 2010; Menezes Filho; Amaral, 2009; Campos; Cruz, 2009; Franco et al., 2007; Menezes Filho; Pazello, 2004, Crozatti, 2021). These resources have increased with the decentralization process and the adoption of policies to transfer resources to municipalities because of the FUNDEF and FUNDEB’s funding mechanisms (Crozatti et al., 2014). However, in addition to evaluating the efficiency of public spending based on the relationship between spending and school performance, the various factors that strengthen or limit the production dynamics of results from spending should control this measurement, given that the arrangements for its management also produce effects on results (Crozatti, 2021; Machado et al., 2022).

Methodology

This study ought to be considered exploratory explanatory, since it associates Brazilian municipalities’ efficiency level with the supply of basic education’s structural characteristics, categorizing the municipalities into distinct clusters.

Database and Sample Sizes

This study used the following databases to conduct its research:

1. The 2015 School Census;

2. The 2015 Prova Brasil / National Basic Education Assessment System (SAEB) results;

3. The National Treasury’s 2014 Municipal Reports;

4. National Institute for Educational Studies and Research’s (INEP) 2015 Education Indicators.

INEP, in partnership with municipal education departments, conducts the School Census yearly. It provides the number of students enrolled in the municipal education systems’ early and final elementary school years. The Prova Brasil is a school performance assessment applied to public school students and is part of the National Basic Education Assessment System (SAEB). In this case, the student’s evaluation scores were obtained from the scores of the municipal education systems for the Portuguese and Mathematics tests applied to fifth and ninth-grade students. INEP’s portal Indicadores Educacionais provided each system’s Socioeconomic Level score (INSE).

Municipal public finances information was obtained from the National Treasury Secretariat’s portal: spending on elementary schools for each municipality was used to calculate the average expenditure per student enrolled. Finally, the bases from INEP’s Educational Indicators portal give statistical value to the quality of education, focusing on student performance and schools’ economic and social circumstances.

It is worth noting that we used the overall data from municipalities to develop a typology of them. For the efficiency analysis, we segmented the results with specific scores for the Early and Final elementary school years. The literature shows a range of factors that create differences between these cycles (Barros, 2001), which this study will not describe.

Data Envelopment Analysis (DEA)

For Engert (1996: 252), Data Envelopment Analysis is the best way to determine how efficient organizations are, given how simple it is to handle multiple outputs. Authors like Bates (1997), Ruggiero (1999), Chakraborty et al. (2001), Mizala et al. (2002), who compared the method with others of similar function also favor DEA results due to its great flexibility.

This study used Haynes and Dinc’s (2005:612) described protocol, to which there are three steps: 1) define and select the Decision Making Units (DMUs) which should use the same types of inputs to produce the same types of outputs and perform similar tasks, with similar objectives, under the same technological apparatus and market conditions. For this reason, this study considers all Brazilian municipalities and compares municipal education systems’ profiles to evaluate their efficiency and compare each group (profile); 2) determine the input and output variables used to evaluate the relative efficiency of DMUs; 3) apply one of the DEA models and analyze results. This study uses the Banker, Charnes and Cooper (1984) model of a convex production frontier. It seeks to optimize performance in managing the inputs applied by increasing outputs, thus using the output-oriented model.

The DEA was performed in two stages to estimate the efficiency frontier. Based on the inputs directly impacting the education production function and the outputs represented by the performance of education system(s), each municipality’s efficiency score was defined. In this first stage, the input used was the average expenditure per elementary school student (all expenditures, regardless of the source of revenue). The selected outputs were: average Portuguese and Mathematics Prova Brasil/SAEB scores, the promotion rate, and the age-grade distortion indicator, all for the elementary school in the municipal education systems. In the second stage, the Socioeconomic Level Indicator (INSE) was introduced as a non-discretionary variable so that the new input was the input over which the manager has no short-term control; the efficiency score calculated in the first stage was used as the output (Diniz, 2012:101). These two stages aim to adjust efficiency levels according to students’ socioeconomic levels. It is important to note that given the specific challenges of each stage of education, we organized the outputs for the Early Years and the Final Years of elementary school so that the efficiency scores were also calculated and analyzed for the two points in this education stage.

Due to the relationship between school performance and students’ social, economic, and cultural profiles in several countries and at different times (Soares; Alves, 2013a), this study uses INSE to contextualize the results obtained by municipal education systems in the Prova Brasil/SAEB evaluation.

Implementing SAEB, starting in 2005, made it possible to produce data that enabled research on the national school system to develop. It showed the main extra and intra-school factors associated with school performance. These studies showed a significant link between the socioeconomic status of students and other elements, such as color/race and educational backwardness, and student performance on cognitive tests (Ferrão et. al., 2001; Albernaz; Ferreira; Franco, 2002; César; Soares, 2001; Soares; Collares, 2006; Alves; Ortigão; Franco, 2007; Andrade; Laros, 2007; Soares, Alves, 2013a). Therefore, these studies have shown that school performance tends to increase as students belong to higher social statuses. Thus, we can understand the education systems that face greater challenges and those that have successfully promoted teaching and student learning by outlining the conditions under which these processes occur along with other indicators (Soares; Alves, 2013b).

However, this connection is not deterministic. Studies such as Raudenbush and Willms (1995) and Soares and Alves (2013a) show that by estimating the effect of school on student performance, controlling for the influence of students’ demographic and contextual characteristics, there are both schools with results strongly associated with students’ backgrounds and those that can increase their knowledge acquisition through education policies and practices.

This analysis of the issues that govern the relationship between school and society ratifies the demand to understand students’ conditions in the social hierarchy strata when analyzing school performance in external evaluations. For this reason, such research can contribute to formulating and implementing a group of public policies aimed at collaborating with improving student flow rates and student learning and reducing social inequalities still in evidence. It provides targeted government support to systems with higher adversity levels and disseminates pedagogical experiences that proved successful (Ronca, 2013).

Cluster Analysis

Cluster analysis is a multivariate technique that aims to collect elements or variables into groups with minimum internal and maximum variance between groups. The literature establishes several grouping methods for forming clusters (Hair et al., 2009: 427-80). This study employs Ward’s method, which, according to Hair et al. (2009), is an agglomerative hierarchical clustering technique in which the magnitude of similarity used to unite the conglomerates is estimated as the sum of squares between the two clusters performed on all selected variables. It organizes a set of units into groups with the most common units. This method is considered hierarchical because the groups are hierarchically connected: each unit belongs to a subgroup, which, in turn, belongs to a larger group and this one to a larger group until arriving at a group that contains all (Hair et al., 2009). With this clustering technique, municipalities are grouped by how similar their education functioning structure so that each cluster shows a municipality profile of a more homogeneous set of municipalities. The indicators used in this study that indicate the operating structure of municipal education systems and that were used to group the municipalities into management structure profiles are shown in Table 1 below.

Table 1
: Frequency of municipalities per clusters

Cluster	Frequency	%	Accumulated %
1	867	18	18
2	1327	27.5	45.4
3	532	11	56.5
4	663	13.7	70.2
5	1439	29.8	100
Total	4828	100

Thus, it is possible to assess the education system’s profile with these variables and locate it in a typology capable of describing said profile. Using the clustering method and the typification variables described above, we propose classifying Brazilian municipalities into five categories or groups, defined by the clustering method that accounts for the particular characteristics of education systems.

Analysis of Variance (ANOVA) on Clusters of Municipalities

ANOVA evaluates the significance of one or more factors by comparing the means of response variables at different levels of this factor (Hair et al., 2009:303-55). The ANOVA test will check the following hypotheses:

• H₀: the average efficiency score of each of the municipal elementary education systems clusters is equal to those of the other clusters;

• H₁: the average efficiency score of each of the municipal elementary education systems clusters is different for at least one of the other clusters.

The study used box plot graphs (Hair et al., 2009:51-5) of averages for the same variables for each cluster to visually test and identify outliers and the difference in averages in municipalities. As a result, a similar dispersion is seen. Furthermore, some outliers present results above and/or below the average in all clusters.

The results obtained in the ANOVA show a p-value of less than 5%. Therefore, we have evidence that at least one cluster differs. This finding is already a partial answer but adds little to our research as we wish to know which clusters show discrepancies--or rather, we want to be able to compare the clusters and see which of them are statistically similar or distinct in terms of their operating structure.

To this end, we performed Tukey’s (1953) proposed test, also known as Tukey’s Honestly Significant Difference (HSD) test. The HSD test revealed that the average efficiency performance of clusters is significantly different. Furthermore, as for p-values, we note that except for clusters 4 and 5 in the Early and Late Years, and 1 and 3 in the Late Years, the other clusters have significance levels than the adopted significance level (p-value < 0.05). This finding leads to the conclusion that the average efficiency score of these clusters is significantly different from the others.

As Giraldi, Cargnelutti, and Storck (2009) point out, we used the Brown-Forsythe test, or the Welch test, to validate the results--to assess the equality of means when the clusters are unequal in sample size. The results of this test show that the statistics have significant differences at the 0.05 level, so we reject the null hypothesis that the groups have equal means. All the results of the ANOVA tests are featured in Appendix I through XIII.

Results: Relationship Between the Operating Structure of Education and the Efficiency of Public Spending

A Typology of Municipalities

Table 1 below presents the frequency and percentage of municipalities in each cluster. This results from applying the clustering method on the variables that identify the operating structure of each municipality’s elementary education system. The clusters were numbered from 1 to 5 for identification. The total frequency of municipalities in table 1 differs from the total number of municipalities in the country because some municipalities do not have an elementary school system.

The two largest clusters in the study are clusters 2 and 5, with 1,327 and 1,439 municipalities, respectively. In addition to the data in Table 1, it was noted that medium and large municipalities (with more than 100,000 inhabitants) are primarily found in cluster 5. In contrast, small municipalities are distributed in all categories. Identifying municipalities of the same size with different structures for operating education is still possible.

Table 2 presents the distribution of the municipalities by geographical region. Clusters 1 and 2, with the least favorable indicators (Table 4), are mainly composed of municipalities in the country’s Northeast region. In contrast, clusters 4 and 5, having the highest indicators, are concentrated in municipalities in the South and Southeast. The number of municipalities does not bias the presentation of this data in the different regions since Table 3 shows that most municipalities in the North and Northeast regions are concentrated in clusters 1 and 2. In contrast, most municipalities in the Southeast and South are concentrated in clusters 4 and 5. Figure 1 shows the map of Brazil, identifying the municipalities by clusters 1 to 5.

Table 2
: Share of municipalities from each cluster in each geographic region

Region	Cluster					Total
	1	2	3	4	5
Central-West	6.92%	4.22%	4.51%	18.80%	10.08%	8.49%
Northeast	46.83%	50.64%	34.96%	5.86%	5.14%	28.51%
North	6.00%	12.28%	3.57%	7.82%	2.99%	6.81%
Southeast	19.95%	25.47%	32.71%	54.14%	35.51%	32.22%
South	20.30%	7.39%	24.25%	13.38%	46.28%	23.98%
All	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%

Table 4
: Descriptive analysis of municipality indicators by cluster

Category	Variables	1	2	3	4	5	All
Management level	Average number of students per class	20.33	19.13	19.23	18.99	20.17	19.65
	Average enrollment per system	2,776	2,405	1,430	880	4,702	2839
	System Attendance rate	4.18	3.72	4.51	4.63	4.87	4.36
	Complexity of management	54.94	75.49	66.83	80.15	66.48	68.82
Student Performance	Average Prova Brasil Score Early Years	406.13	389.00	421.37	438.72	440.45	417.64
	Average Prova Brasil Score Final Years	488.29	471.90	495.65	508.67	516.19	492.27
Grade Promotion/Retention Rate	Average class hours per day	4.50	4.53	4.62	4.62	4.51	4.54
	Promotion	84.89	82.48	87.16	91.21	89.42	86.70
	Average % of student dropouts in the system	3.65	4.34	3.18	2.59	2.52	3.30
Teaching Level	% teachers with higher education [degrees]	73.90	67.20	84.11	87.17	90.41	79.93
	Turnover	5.46	14.82	46.03	8.16	2.60	12.02
	Adequacy of teaching	69.97	62.75	81.48	84.84	87.86	76.63
	Teaching effort	42.08	55.00	51.18	71.05	37.14	49.15
Public spending	Education spending per capita (R$)*	791.69	758.48	797.20	761.66	803.87	782
	Average expenditure on/per student/year	6458.45	6613.31	8152.83	9470.48	8406.14	7683
	Average teacher salary/month	2175.67	2318.09	2528.98	2375.49	3314.13	2620
	Infrastructure	0.55	0.39	0.57	0.62	0.67	0.55
Socioeconomic	Socioeconomic Level	45.40	43.19	47.19	48.77	51.02	47.11
	GDP per capita*	16.74	12.83	19.81	19.49	30.68	20.545
	Demographic Density	127.24	39.18	43.53	38.69	276.75	126

• Source: research data.
• Note: values highlighted in red are expressively positive, while values highlighted in yellow are negative in terms of what is expected from a quality system. *Values in R$ 1,00.

Table 3
: Share of Municipalities from each geographic region by cluster

Region	Cluster					Total
	1	2	3	4	5
Central-West	14.63%	13.66%	5.85%	30.49%	35.37%	100%
Northeast	29.48%	48.80%	13.51%	2.83%	5.37%	100%
North	15.81%	49.54%	5.78%	15.81%	13.07%	100%
Southeast	11.12%	21.72%	11.18%	23.14%	32.84%	100%
South	15.20%	8.46%	11.14%	7.69%	57.51%	100%

Figure 1
: Map of Brazil with municipalities by typology of operating structure

Analyzing each category, we can observe that the only variable that stands out for its heterogeneity among the clusters at the Management Level is the one that represents Management Complexity. We highlight that cluster 2 has the lowest indicators for the remaining categories, but it shows a low rate of management complexity.

In the student performance category, we observe clusters 4 and 5 present the highest scores for the Early and Final years, while cluster 2 has the lowest values for this category. As shown in Table 4 and below, clusters 4 and 5 display the best results for the variables analyzed, while cluster 2 displays the worst values. This result shows a relationship between the profile of systems and their performance as measured by standardized tests. This finding corroborates Coleman’s (1968) findings that the factors captured by the categories present in Table 4 have a positive impact on student performance.

In the promotion variable, cluster 2’s low value shows that this group of municipalities has a relatively low level of promotion compared to the other groups, which is ultimately reflected in the average school dropouts— the highest among the groups. As shown in Tables 1 and 2, most of the municipalities in cluster 2 are found in Brazil’s Northern and Northeastern regions which are also the most vulnerable in socioeconomic terms. In this regard, Neri (2015) highlights that in municipalities that are more vulnerable and display lower socioeconomic levels, the impact on students’ permanence in the school network is more significant since they end up entering the labor market (formal and informal) to help support the family income.

When analyzing teaching level, it is possible to observe that while cluster 5 has the best results in teacher training and adequacy of teaching, cluster 2 presents the lowest values. Cluster 2 also has the lowest values in the school units’ infrastructure indicator, while clusters 4 and 5 show the best results.

Only cluster 3 presents results significantly above average in the teacher turnover indicator. The literature shows that higher teacher turnover can negatively impact students’ results in standardized tests (Duarte, 2009). Finally, the variable that measures the Average Elementary Teacher Salary/month in each group of municipalities shows that only cluster 5 has results above the national average among the typologies formulated. Part of the explanation is in the public spending category since cluster 5 spends approximately R$ 1,000.00 more on the average salary of its teachers compared to cluster 2. In this regard, Barbosa (2014:511) points out that “the remuneration of teachers is an important element in improving the quality of education and is directly related to the financial resources allocated to it”. Crozatti’s (2022) study points out a similar effect when analyzing the Basic Education Development Index (IDEB) and the average expenditure per student on staff of São Paulo’s elementary education systems.

In the public spending on education category, we observe an effect similar to the analysis of the other categories among clusters: clusters 1 and 2 have the lowest values. In contrast, clusters 4 and 5 have the highest values. Possible correlations of these values with the other performance indicators are found in Sobreira and Campos’s (2008) study, whose results point to the importance of financial support and the qualification of teachers to improve the quality of public education. In this study, this idea is visible through standardized test results in Portuguese and Mathematics.

From the efficiency analysis in the next section, we will have enough information to identify whether the education management profile of municipalities is linked to their efficiency level.

Efficiency Analysis of Municipal Systems’ Elementary Schooling

Table 5 presents descriptive statistics and the number of observations of municipalities per cluster, with their respective efficiency scores. DEA allows us to obtain an efficiency score for each decision-making unit (DMUs), which are this study’s municipal education systems. Therefore, each network was given an efficiency index ranging from 0 to 1, where 0 indicates maximum inefficiency and 1 indicates maximum efficiency. These scores made it possible to calculate descriptive statistics for each cluster, which included average efficiency.

Table 5
: Efficiency Index Mean and Standard Deviation and Frequency of Observations

Cluster	Early Years			Final Years
	Average	Standard Deviation	Frequency	Average	Standard Deviation	Frequency
1	0.649314	0.104859	793	0.679732	0.117716	621
2	0.604932	0.098193	1,212	0.623277	0.095934	903
3	0.681768	0.112130	470	0.697839	0.130759	280
4	0.733556	0.086427	597	0.756080	0.104519	137
5	0.729079	0.076113	1,304	0.753168	0.100668	746
All	0.675769	0.107582	4,376	0.686928	0.119491	2,687

The efficiency score for the Early Years of elementary school showed a mean value of 0.67, with a standard deviation of 0.11 and a positive dissymmetric distribution, or to the right, and observations predominantly with above average values. For the Final Years, the efficiency shows an average of 0.68, with a standard deviation of 0.12, with a normal distribution, showing a prevalence of observations with values close to the average, with few observations dispersed around the average. We also observe that clusters 4 and 5 have the highest efficiency averages, followed by clusters 3, 1, and 2, with the lowest averages for the early and final elementary school years.

Notably, these patterns are visible in more than average terms. Figure 2 below shows the distribution of municipal efficiency levels by cluster for the elementary school’s initial and final years. However, there are observations from all the clusters at practically all efficiency levels, clusters 4 and 5 concentrate the largest numbers of municipalities at the highest efficiency levels. Moreover, it is also possible to observe that the first quartile of clusters 4 and 5 is higher than the third quartile of cluster 2.

Figure 2
: Efficiency Score by Cluster of Municipalities for Early and Final Years of Elementary School

Applying Savian and Bezerr (2013) and Lourenço et al.’s (2017) classification that deems municipalities with scores of 1 efficient and those with scores orbiting between average plus one standard deviation (0.67 + 0.11 = 0.78 | 0.68 + 0.12 = 0.80) and less than 1 are considered weakly inefficient; with moderate inefficiency, the municipalities with scores lower than 0.864 and equal or higher than the average subtracted from the standard deviation (0.67 - 0.11 = 0.56 | 0.68 - 0.12 = 0.56); and those with scores lower than the other intervals as strong efficiency, it is possible to evaluate analytically municipalities’ efficiency, as shown in Table 6.

Table 6
: Frequency of Municipalities by Efficiency and Inefficiency Levels

Level	Early Years			Final Years
	Freq.	%	c. %	Freq.	%	c. %
Efficient	5	0.1	0.1	6	0.2	0.2
Weak Inefficiency	754	16.3	16.4	522	17.9	18.1
Moderate Inefficiency	2970	64.0	80.4	1905	65.5	83.6
Strong Inefficiency	911	19.6	100	477	16.4	100
All	4640	100		2910	100

According to Table 6, only 16.4% of the education systems that offer Early Years and 18.1% of the systems that offer Final Years were efficient or showed weak inefficiency, even though the vast majority of municipalities (64% for the Early Years and 65.5% for the Final Years) showed moderate inefficiency. This result agrees with Silva et al. (2015) and Lourenço et al. (2017). We observe a somewhat unfavorable scenario in which 83.6% of the municipalities in Early Years and 81.9% of Final Years find themselves in the two worst performance strata (Moderate Inefficiency and Strong Inefficiency).

The high inefficiency indicates the potential for promoting better public education services (Santos, Carvalho, Lírio, 2008). It is essential to optimize the management of resources by making better use of the existing operating structures or by expanding and improving them.

Table 7 shows the average input, output, and operating structure variables for the efficient municipalities and those with weak inefficiency, compared to the group that presents strong inefficiency.

Table 7
: Efficiency and Inefficiency Indicators (Weak and Strong)

Level of Education		Anos Iniciais		Anos Finais
Efficiency Level		Eficientes + Inefic.Fraca	Inefic. Forte	Eficientes + Inefic.Fraca	Inefic. Forte
N		759	911	528	477
Average Efficiency Index		0.821	0.511	0.854	0.509
Inputs	Average spending per student	7776.71	5293.46	6,362.62	5,442.67
	Socioeconomic level	51.131	41.223	50.027	41.501
Outputs	Prova Brasil	477.661	357.276	536.810	456.211
	Promotion	97.026	80.163	89.503	62.672
	Age-grade distortion	4.863	25.545	18.442	50.021
Operating Structure	Infrastructure	0.653	0.398	0.649	0.413
	Salary	2788.46	2337.68	2810.90	2507.98
	Teaching Effort	50.252	50.871	42.369	49.496
	Turnover	8.978	16.300	7.453	16.406
	Management complexity	73.495	61.616	63.531	62.470
	Adequacy of teaching	85.852	57.771	84.413	61.310

Socioeconomic conditions should be examined carefully—according to Andrews and Vries (2012), they are one of the explanatory factors behind school performance levels. According to the authors, local economic development projects can significantly impact school performance more than education policies based on input factors or on holding schools and teachers accountable. In this work, the results measured by the DEA indicate that the group of municipalities classified as efficient present Socioeconomic Level indicator values ​​below the average (the average of ‘efficient’ municipalities for the Initial Years was 41.93, while the general average was 46.83, and 43.08 for the Final Years compared to the general average of 45.33), and above the average for the Prova Brasil score (average of 415.39 for the Initial Years and 490.01 for the Final Years). However, technical efficiency does not necessarily mirror the fact that the municipality has reached quality education. However, this may be due to it achieving reasonable scores in Portuguese and Mathematics standardized tests given its low socioeconomic background.

As shown in Table 8, the efficient municipalities have a lower average score than those with weak inefficiency in the Prova Brasil scores for the initial and final years. This observation confirms that efficiency is not necessarily related to the best school performance results but to the relationship between performance and expenditure allocated to education activities. Thus, a more efficient municipality does not obtain the best results or spend the most resources but makes the best use of its resources to obtain the best results with the least amount of resources possible (Faria et al., 2008).

Table 8
: Mean, Maximum, Minimum, and Standard Deviation of Prova Brasil Score and Socioeconomic Level of Municipalities

Level	Efficiency Level	Freq.	Prova Brasil				Socioeconomic Level
			Mean	Max	Min	SD	Mean	Max	Min	SD
Early Years	Efficient	5	455.2	581.1	375.0	94.5	41.9	47.3	38.6	3.5
	Weak Inefficiency	754	477.8	566.1	386.6	20.7	51.2	60.3	34.8	4.1
	Strong Inefficiency	911	357.3	442.4	310.5	18.8	41.2	52.6	32.3	2.7
Final Years	Efficient	6	527.8	619.6	477.5	57.3	43.1	51.3	38.6	5.1
	Weak Inefficieny	522	536.9	616.4	481.3	26.2	50.1	59.9	34.8	4.8
	Strong Inefficiency	477	456.2	536.8	363.9	24.9	41.5	54.8	33.4	3.1

The data presented (Table 7) demonstrate that, for the Initial Years, the averages of the group of municipalities classified as ‘Efficient + Weakly Inefficient’ are more favorable in all categories of indicators — Inputs, Outputs, and Operating Structure —, except for the teaching effort indicator, which, even so, presents a very similar result between the groups. For the Final Years, the only variable that presents favorable results for municipalities with strong inefficiency is that related to teaching effort.

Finally, Table 9 below presents the results of a linear regression model that takes clusters 1 to 5 as the independent variable and the efficiency score as the dependent variable to determine the correlation between a municipality’s belonging to one of these clusters and its efficiency level by education level. For early years, belonging to clusters 1 or 2 harms efficiency levels, while belonging to clusters 4 or 5 has a positive effect, and all coefficients obtained are statistically significant (p-value < 0.01). For final years, belonging to any of the clusters negatively affects efficiency levels. However, cluster 4 was omitted due to collinearity, and cluster 5 has no statistical significance (p-value > 0.10). At least for the early years model, these models corroborate the finding that the profile of municipalities’ education service supply structure at the elementary level is one of the determinants of the efficiency of municipal education spending in elementary education.

Table 9
: Regression Model Results for Efficiency Levels

	Early years	Final years
Cluster 1	-0.0324*** (0.0054)	-0.0763*** (0.0100)
Cluster 2	-0.0768*** (0.0050)	-0.1328*** (0.0098)
Cluster 3	-	-0.0582*** (0.0111)
Cluster 4	0.0517*** (0.0057)	-
Cluster 5	0.0473*** (0.0050)	-0.0029 (0.0099)
Constant	0.6817*** (0.0043)	0.7560*** (0.0091)
R2	24.4%	19.95%
N	4376	2687

• Source: research data.
• Note: cluster 3 in the Early Years model and cluster 4 in the Late Years model were automatically omitted due to collinearity. Statistical significance levels: *** < 1%, ** < 5%, * < 10%.

The Union’s Role in Reducing Education Inequities between Municipalities

The results presented in section 3 show that the clusters of municipalities developed in this study have particular characteristics regarding their operating structure and levels of efficiency in public education spending. It saw that while cluster 2 has the worst operating structure indicators (11 out of 14 indicators analyzed), clusters 4 and 5 presented the best. In practical terms, this shows that municipalities in clusters 4 and 5 have better potential to obtain better results from education policy. In contrast, municipalities in the second group are at a disadvantage.

In turn, cluster 2 municipalities also have, on average, the worst efficiency level among all the clusters (60.4% according to Table 5), while cluster 4 and 5 municipalities display the best efficiency levels (73.3% and 72.9%, respectively). Although averages are being compared here, the grouping technique by internal similarity and the ANOVA test allowed us to identify that municipalities in the different clusters are statistically different from each other and, therefore, relatively homogeneous within each group. This observation lets us conclude that the systems’ operating structure helps determine their efficiency level. Based on the tests carried out, the results contained in the appendices of this study ratify the findings reported earlier regarding ANOVA, which reject the null hypothesis that the samples (efficiency score) come from equally distributed populations, thus indicating that at least one of the clusters is distinct from the others.

Efficiency derives from the relations established between input and output so that maximum efficiency is the lowest input level possible, obtaining the highest output level. In this regard, an education system that aims to improve its efficiency levels must: 1) increase its output by maintaining its input; 2) decrease its input by maintaining its output; or 3) increase its input by further increasing its output. Since one of the goals of education policy is to increase the results of the systems and ensure students’ adequate promotion, which this paper shows through the improvement of students’ learning measured by their ability to respond to the Prova Brasil standardized tests, by promotion rates and age-grade distortions, respectively, then the second option is unreasonable. As for the first option, we assume that the increase in efficiency comes from the management’s better use of the resource. However, the work focuses instead on the volume of spending and its relation to efficiency. It also highlights that, historically, Brazil spends little on education policy compared to other countries, whose spending per student corresponds to 43.5% of the average spending of OECD countries for early childhood and primary education and 39% for secondary education in 2015 (TPE, 2021). Therefore, maintaining or decreasing education spending (input) cannot be an option. Thus, this study’s reflections should be steered by the third option, according to which an increase in inputs can be efficient if an increase in outputs accompanies it.

According to the Section 3 results, the systems’ operating structure profile and the cluster to which they belong help determine their efficiency levels. We can thus expect higher levels of efficiency from systems with better structures. The causal mechanism behind this logic is that better-structured systems provide better conditions for students to obtain better results, thus decreasing the burden of education spending on student performance. The significance of thinking about the efficiency of public education spending is seen in how it translates into the ability of systems to manage their resources to obtain desirable education outcomes. Therefore, for education policy to achieve its goals by improving education performance, it is necessary that public spending take into account efficiency. For that, one cannot disregard the context in which public spending occurs because, as this paper seeks to show, one cannot address its efficiency while disregarding the operating structure of the education system—a determinant of efficiency.

Policies that seek to reduce education inequalities among municipalities must not disregard municipalities’ capabilities have to manage their resources or the factors that affect those resources’ efficiency levels. The two major education funding policies, the FUNDEF and FUNDEB, have significantly reduced horizontal inequalities in education (Arretche, 2010; Vazquez, 2005, 2014). However, this dimension of inequality concerns budget revenues. The main criterion for the distribution of fund revenues was the number of enrollments in systems (FUNDEF), or the number of enrollments and enrollment weightings (FUNDEB). Thus, both policies did not try to reduce the unequal conditions municipalities have to manage their resources since they did not account for the structure of systems or aspects related to management capabilities.

Considering that the FUNDEF, FUNDEB and New FUNDEB were created in a federative context in which the Union designs national public policies, highlighting that the three policies were instituted through two constitutional amendments and regulated by the National Congress through Ordinary Laws. Furthermore, their design did not seek to promote equal conditions for the subnational entities to be equitable in promoting education policy. Thus, at least in this aspect, the Union’s role was limited in reducing horizontal inequities in education. Its equalizing movements that seek to reduce these inequalities by reducing inequalities in conditions should consider the different capabilities that subnational entities have to implement their local public policies.

Final Considerations

In order to transpose political-administrative delimitations to address municipal inequalities in education, this paper formulated a typology of municipalities so that not only factors of state or regional location but also particular characteristics would express inequalities among these units: this study formulated a typology of municipalities based on their operating structure of municipal education systems. It verified to what extent these typologies correlate with the respective systems’ efficiency indexes of public education spending. The next step was to explore the role of the Union in reducing municipal inequities in education.

The results showed that the operating structure of the municipal systems correlates with their efficiency levels of public education spending so that the municipalities in the cluster with the worst operating structure obtain the worst efficiency levels, and those in clusters with better structures obtain the best efficiency rates. Therefore, education policies that aim to reduce education inequities should prioritize structuring systems with the worst conditions for education policy to the detriment of networks that are already relatively structured and have better relative conditions to offer such policy.

The Union, in the context of 1988 Brazilian federalism and based on its ability to centrally design national policies for subnational entities to implement (Arretche, 2012), can create institutional arrangements to reduce horizontal education inequities based on management and implementation conditions. Thus, this work contributes to the theoretical field that deals with understanding the implications of Brazilian federalism for public education policies—especially on its inequalities, shedding light on the need to understand horizontal inequalities from its multiple dimensions.

This study is also purposive, as its results may help municipal education managers identify which management elements contribute to increasing the efficiency of public education spending. At the same time, the results provide subsidies for the Union to identify which sort of municipality is less efficient, so it can design education policies that reduce horizontal inequities.

It is also noteworthy that, besides the municipal education management structure, other elements affect student performance and, consequently, municipalities’ efficiency level: the students’ race, for example, so that the promotion of equity among the municipalities includes the promotion of racial equity that should be considered when designing education financing policies. The lack of this perspective on inequalities is a limitation of this study and a suggestion for future ones. Besides this, it is also recommended to deepen the understanding of the Union’s role in reducing horizontal inequalities by controlling municipalities’ ability to implement public education policies and using their values of redistribution from the fund policies. A further understanding and measuring such inequalities with specific metrics and methods tends to shed light on aspects that are still little explored in existing literature.

Chart 1
: Indicators used to group municipalities

Indicator	Dimensions	Nature	Interpretation	Manipulation
Complexity of school management	(a) school size; (b) number of school shifts; (c) complexity of the stages offered by the school (d) number of stages/modalities offered.	ordinal	The complexity groups/levels are numbered from 1 to 6 in order from least to most complex management.	we selected categories 1 and 2, which represent less complexity, added the percentages and generated a continuous variable, where the highest values demonstrate less complexity in system management.
Teaching effort	(a) number of schools; (b) number of shifts; (c) number of students; and (d) number of stages in which they teach.	ordinal	The groups/levels of teaching effort are listed from 1 to 6 in order from lowest to highest effort. Higher categories indicate greater teacher effort	we select the categories from 1 to 3, which represent the lowest teaching effort, add up the percentages and generate a continuous variable.
Teaching regularity	regularity of teachers’ tenure in schools over the last five years..	Continuous	higher values of this indicator represent higher teacher turnover	There is none
Adequacy of teacher training	Coherence between the teacher’s training and the classes taught	continuous	higher values represent more adequate teacher training	There is none
School infrastructure	(a) equipment ratio; (b) basic services ratio ( running water, sewage, internet); and (c) school environment ratio (court, playground, library)	continuous	higher values indicate that the municipality has better infrastructure in the elementary school system	There is none
average pay for teachers today	Average pay for faculty members in the system	discrete	average pay for different levels of territorial aggregation and administrative dependence in classroom performance	There is none

• Source: Prepared by the authors.
• Note: the infrastructure indicator used to build the clusters derives from the 2015 Basic Education School Census, and all other indicators are from the 2015 INEP Education Indicators. All indicators refer to the elementary school stage in the municipal systems.

^* This article was previously presented at the 45th Anpocs Meeting, in the Public Policies Working Group, coordinated by Marta Arretche (USP/CEM) and Sandra Gomes (UFRN), whom we thank for the opportunity to discuss it, as well as the debater Anna Venturini (CEBRAP) for her comments and suggestions. We would also like to thank the anonymous reviewers of Dados for their evaluations, comments and suggestions. Part of the results of this article come from the first author’s master’s dissertation, entitled “Análise da eficiência em educação fundamental das municipalidades mediante a elaboração de uma tipologia de municípios”. We would also like to thank the anonymous reviewers of Dados for their assessments, comments and suggestions.

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Publication Dates

• Publication in this collection
  17 Feb 2025
• Date of issue
  Jan 2025

History

• Received
  6 Apr 2022
• Reviewed
  10 Oct 2022
• Accepted
  12 Dec 2022