metadata: authors: 0: author: Lautharte Junior,Ildo Jose
1: author: de Oliveira,Victor Hugo
2: author: Loureiro,Andre
count: Brazil
docna: 0: docna: Incentives for Mayors to Improve Learning :
            Evidence from state reforms in Ceará, Brazil
docty: Policy Research Working Paper
subtopic: Educational Sciences,Financial Sector Policy,Education for Development (superceded),Educational Policy and Planning - Textbook,Educational Populations,Education For All,Educational Institutions & Facilities,Effective Schools and Teachers
teratopic: Education
abstracts: cdata!: Financial incentives for students,
            teachers, and schools are often used to promote learning.
            Yet, little is known about whether similar incentives for
            mayors produce analogous findings. This paper investigates
            this question by exploring a results-based financing reform
            in Ceará, Brazil, which redistributes state resources to
            municipalities based on education performance. Comparing
            schools on both sides of Ceará's border over key
            implementation periods, the paper shows that ninth  grade
            students who were exposed to the results-based financing
            performed 0.15 standard deviation higher on mathematics and
            language tests. These impacts increase twofold when Ceará
            offers technical assistance to municipalities (pedagogical
            and managerial) and become significant for fifth graders.
            These gains are seen among students in the top performance
            quantiles, but reformulating the results-based financing
            rule to penalize municipalities with more low performers
            significantly reduces learning gaps. The paper discuss
            several mechanisms: the selection of school principals,
            teacher training, the provision and quality of textbooks,
            curriculum coverage, and school homework.
geo_reg_key: 119228,517191
repnme: repnme: Incentives for Mayors to Improve Learning :
            Evidence from state reforms in Ceará, Brazil
display_title: Incentives for Mayors to Improve
            Learning : Evidence from state reforms in Ceará, Brazil
listing_relative_url: /research/2021/01/32752001/incentives-mayors-improve-learning-evidence-state-reforms-ceará-brazil
topicv3: Teachers Management m1326119 1523,Teacher Training m1326786 1532,Textbooks m1326802 2129,Education m1327048 470,Financial Sector Development m1327681 1920
publishtoextweb_dt: 2021-01-15T00:00:00Z
historic_topic: Education
origu: Education LCR (HLCED)
no_of_pages: 54
author_keys: 0: author_key: 1489794
1: author_key: 1209935
model_extractions: Policy Research Working Paper 9509 Incentives for Mayors to Improve Learning Evidence from State Reforms in Ceará, Brazil _Ildo Lautharte Victor Hugo de Oliveira André Loureiro_ Education Global Practice January 2021
Policy Research Working Paper 9509

# **Abstract**

Financial incentives for students, teachers, and schools are often used to promote learning. Yet, little is known about whether similar incentives for mayors produce analogous findings. This paper investigates this question by exploring a results-based financing reform in Ceará, Brazil, which redistributes state resources to municipalities based on education performance. Comparing schools on both sides of Ceará’s border over key implementation periods, the paper shows that ninth grade students who were exposed to the results-based financing performed 0.15 standard deviation higher on mathematics and language tests. These impacts increase twofold when Ceará offers technical assistance to municipalities (pedagogical and managerial) and become significant for fifth graders. These gains are seen among students in the top performance quantiles, but reformulating the results-based financing rule to penalize municipalities with more low performers significantly reduces learning gaps. The paper discuss several mechanisms: the selection of school principals, teacher training, the provision and quality of textbooks, curriculum coverage, and school homework.

This paper is a product of the Education Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at ilautharte@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Incentives for Mayors to Improve Learning: Evidence from state reforms in Ceará, Brazil<sup>_∗_</sup> Ildo Lautharte<sup>_†_</sup> Victor Hugo de Oliveira<sup>_‡_</sup> André Loureiro<sup>_†_</sup>

**Keywords:** Education Incentives for Mayors, Results-Based Financing, Technical Assistance. _JEL Classification: H52, I21, I22._

> _∗_ We would like to thank Halsey Rogers, Pedro Cerdan _−_ Infantes, Renata Lemos, Emanuela DiGroppelo, Caio Piza, Leandro Costa, Bruno Ottoni, and David Evans for the detailed comments. The authors gratefully acknowledge financial support from the REACH Trust Fund at the World B ank. We also thank seminar participants at the World Bank, Instituto IDados, Todos Pela Educação and Brazilian Society of Econometrics for valuable feedback on early drafts of this manuscript. The views expressed by the authors do not reflect the views of IPECE or the World Bank. All errors are, naturally, our own.

The authors gratefully acknowledge financial support from the REACH Trust Fund at the World Bank.

> _†_ Education Global Practice, The World Bank Group

> _‡_ Instituto de Pesquisa e Estratégia Econoômica do Ceará
# **1 Introduction**

Much has been written on how financial incentives can play an important role in promoting student learning. Numerous studies have examined policies rewarding students based on predefined learning goals (Fryer 2011; Bettinger 2012). Others tested, and compared, particular configurations of student incentives across different ages, types of incentives and timeframes (Levitt et al. 2016). A not smaller field investigates the implications of conditioning scholarships on school attendance (Kremer et al. 2009); how to design effective pay-for-performance programs for teachers (Glewwe et al. 2010; Barlevy and Neal 2012); and the effects of distributing school grants based on education outcomes (Das et al. 2013; Gordon 2004). Such an abundance contrasts sharply with relatively no progress made on the design and impacts of similar incentives focused on city mayors.

A context-specific reason for this imbalance may be the result of constitutional arrangements prohibiting top-down fiscal incentives tied to education performance. Or, when legally possible, it may not be politically feasible to design such incentives, because learning is argued to depend on factors outside of the control of the mayor (Hansen et al. 2004). Another explanation for limited empirical evidence is the lack of credible experiments linking financial incentives to education performance at the city level. This paper aims to investigate these gaps. It explores a state reform in _Ceará_ , Brazil, in which state tax revenues are redistributed based on municipal competition on education outcomes. Different from many countries, Brazil provides an ideal opportunity to investigate education incentives to mayors because ( _i_ ) there is administrative autonomy among federal, state and municipal governments and ( _ii_ ) primary and lower secondary education are, in most cases, the responsibility of municipalities.

In 2007, the state government also started to implement non-mandatory technical assistance (TA) for municipalities to address the heterogeneous capacity of municipal governments to implement
education programs. The TA was initially targeted at literacy, and in 2011 was expanded to include support for grades 3 to 5. The state government provided pedagogical and management support to the municipal secretariats of education, including elements like scripted materials for teachers, teacher training focused on classroom practice, effective use of learning assessments, and knowledge exchanges between schools. Another important milestone of the education reforms in Ceará was the reformulation of the RBF rule in 2013 to penalize municipalities with higher percentages of students below minimum thresholds of performance in mathematics and language (Portuguese).

Our empirical strategy explores this timeline and the location of schools across _Ceará_ ’s border in other states to identify RBF effects on learning at the end of primary (5<sup>_th_</sup> grade) and lower secondary (9<sup>_th_</sup> grade) education. Using data from students, teachers, and principals from the _Sistema de Avaliação do Ensino Básico_ (SAEB), we compare the average differences in education outcomes on both sides of the border before and during each implementation stage.<sup>1</sup> In total, this approach generates four parameters. To benchmark our findings and control for pre-existing disparities, we compute the baseline difference in pre-RBF periods (2005 and 2007). The second parameter refers to periods when the RBF was introduced without any complementary program in 2009. The third parameter measures the average difference in periods when the _RBF_ was combined with _TA_ (in 2011 for 5<sup>_th_</sup> grade, and in 2015 for 9<sup>_th_</sup> grade). The last difference considers the reformulation of the RBF rule in 2013 until 2017. We argue that, by comparing these parameters and controlling for student and municipal characteristics, time trends, and border fixed effects, it is possible to estimate whether financial incentives for mayors improved learning and the impacts of providing TA and reformulating the RBF rule.

> 1 It is crucial to highlight two points in this strategy. First, SAEB is not part of the RBF rule in _Ceará_ . Instead, _Ceará_ bases the redistribution criteria on its own _state_ assessment called SPAECE. SAEB is a _national_ assessment with no influence on fiscal redistribution. In this context, using SAEB is empirically important, because it is less susceptible to gaming by municipalities. The second point concerns our definition of schools at the border. Throughout the analysis, we restrict our sample to schools located in the immediate three municipalities on each side of the border between _Ceará_ and adjacent states (See Figure 1). We provide a set of robustness checks testing alternative border

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This framework indicates positive and significant impacts of the RBF reform on student test scores. According to our estimates, students in 9<sup>_th_</sup> grade exposed to the RBF mechanism in _Ceará_ presented 0 _._ 15SD higher scores in mathematics and Portuguese compared to similar students across the state border who were not exposed to the reform. This increase is equivalent, on average, to an additional 3 months of learning. In contrast, at this stage no clear improvement was observed for 5<sup>_th_</sup> graders. However, in periods when the RBF was combined with TA for municipalities, the effects of RBF alone almost doubled, and significant impacts on test scores for 5<sup>_th_</sup> grades emerge. The gains of _combining_ RBF and TA for both grades is equivalent to 5 months of learning in Portuguese and 3 months in mathematics _on the top_ of the effects of RBF alone. Further estimates, disentangling the TA component, indicate that most of these ‘’ _RBF_ + _TA_ ” effects come from providing training and textbooks to schools. Another particularity is the distribution of RBF effects. Quantile regressions show that RBF periods disproportionately benefited students at the top of the distribution, _−_ increasing learning gaps. Providing TA slightly reduces these disparities, but only for periods when the reform reformulated the redistribution rule to penalize municipalities with higher incidences of students below basic levels of performance.

We investigate potential mechanisms for these findings in three groups. As local authorities in Brazil are responsible for selecting and training local staff, we first check for changes in the selection and training of principals and teachers for schools at the border. The estimates show that mayors in _Ceará_ are significantly _less_ likely to directly assign principals to schools and are _more_ likely to _−_ appoint them through formal selection processes (10 _pp_ 20 _pp_ ). This result suggests that replacing political appointments in _Ceará_ with a formal process may represent one channel by which the RBF impacts operate (Mitra Akhtari 2020). Another observed channel is that enrollment rates and the quality of training significantly increased in _Ceará_ relative to its counterparts. After offering TA, and relative to the baseline difference at the border, school principals and teachers were significantly more likely to enroll in TA (11 _._ 5 _pp_ for 5<sup>_th_</sup> grades and 8 _._ 8 _pp_ for 9<sup>_th_</sup> grades) and 4
report that it was useful for their daily work (7 _._ 8 _pp_ for 5<sup>_th_</sup> grades and 12 _pp_ for 9<sup>_th_</sup> grades).

Next, we analyse textbook quality and distribution. Using the SAEB questionnaire of principals, the estimates indicate that schools in _Ceará_ are 10 _pp_ to 25 _pp_ less likely to report a lack of textbooks than similar principals on the other side of the border. This reduction only occurs after TA is introduced. At the same time, 5<sup>_th_</sup> grade teachers in _Ceará_ report that textbooks are at least “ ” “ ” _good_ or _great_ around 9 _._ 5 _pp_ more frequently than their counterparts. Considering concerns raised in previous literature regarding the impacts of textbooks on learning (Glewwe et al. 2009), note that the state of _Ceará_ structured these textbooks to support over-age students. Thus, the distribution of good quality textbooks to municipal schools is argued to be a mechanism explaining our findings.

The last group of mechanisms analyzed is related to pedagogical practices. During “RBF+TA” periods, 5<sup>_th_</sup> grade students in _Ceará_ became 2 _pp_ more likely to report that their teachers checked their homework (in both mathematics and Portuguese) than students studying in schools located in the circumventing municipalities outside of _Ceará_ . For 9<sup>_th_</sup> grades no significant result was found for this particular outcomes. Importantly, teachers in _Ceará_ were around 8 _pp_ more likely to cover at least 80% of the school curriculum for both grades, and 11 _._ 6 _pp_ for 9<sup>_th_</sup> grades teachers, after the RBF rule was reformulated in 2013.

We also show evidence that the introduction of the RBF increased public spending on education per pupil by 1 _._ 2% relative to the baseline mean in the municipalities of _Ceará_ when compared to municipalities across the border. The introduction of RBF led mayors to invest in school facilities (e.g., internet connections, computer labs, libraries, and sports courts). Moreover, the increase in public spending per capita on complementary public services is even larger, varying from 10 _._ 5% to 21% depending on the type of service. In contrast, the introduction of TA jointly with the RBF and the reformulation of the RBF mechanism did not translate into more education spending in 5
_Ceará_ , and the results suggest that the large gains in student learning after introducing TA and reformulating the RBF rule were attained without increasing municipal public spending.

The paper is organized as follows. After this introduction, section 2 provides background information on _Ceará_ and explains the RBF reform that introduced education incentives for mayors. Section 3 describes the data and presents descriptive statistics. The identification strategy is discussed in section 4. Section 5 illustrates the RBF effects, presents estimation results on test scores, and disentangles the components of TA. Section 6 investigates several mechanisms explaining our results. Section 7 concludes.

# **2 Background**

The state of _Ceará_ is located in northeast Brazil and has approximately 9 _._ 1 million inhabitants (equivalent to Austria or Israel) living in an area of 148 _,_ 895km<sup>2</sup> (equivalent to Bangladesh or Greece). According to 2017 data, its GDP per capita reached _R_ $16 _,_ 395 (or US$7 _,_ 378 PPP), similar to Vietnam (US$7 _,_ 448) and Cabo Verde ( _US_ $7 _,_ 454), which translates into the fifth smallest GDP per capita in Brazil. Three-fourths of its population is concentrated in urban areas, infant mortality is around 13 _._ 2 per 1 _,_ 000 live births, and life expectancy is 74 _._ 3 years _−_ 2 years less than the national average.<sup>2</sup>

## _−_ **2.1 The Results Based Financing Reform in** **_Ceará_**

In this socioeconomic context, in December 2007 _Ceará_ initiated a reform modifying how state consumption tax revenues were redistributed to municipalities. The tax in question is the _Imposto sobre Circulação de Mercadorias e Serviços_ (henceforth, ICMS), an important source of

> 2The information about economic activity, demography, and socioeconomic characteristics of _Ceará_ is from Cavalcante et al. (2019) and de Oliveira et al. (2020).

6
tax revenue for sub-national governments that taxes services and family consumption.<sup>3</sup> A crucial characteristic of the ICMS structure is that the Brazilian constitution establishes that 1/4 of ICMS revenues must be redistributed to municipalities (or 6 _._ 25% of total ICMS revenues), referred to here as _Quota−Parte_ . This redistribution should be based on _discretionary_ state legislation. Thus, the fiscal reform _per se_ focused on changing the _Quota-Parte redistribution_ rule and did not involve the reallocation of _additional_ tax revenues.

Historically, the _Quota-Parte_ rules have been largely based on a common set of variables: municipal population size, municipal area in kilometers, equal distribution, and percentage of treated trash residuals.<sup>4</sup> The state government of _Ceará_ enacted Legislation 14,023/2007 in December 2007 changing that pattern and introducing an results _−_ based financing ( _RBF_ ) model to redistribute ICMS _Quota-Parte_ based on education, health, and environmental performance (Holanda 2006). The law defined indicators for these _RBF_ components and aimed to foster competition among city mayors for better outcomes in critical areas.

The _RBF_ model can be described by the following equation: _QuotaICMS,c_ = 0 _._ 18 _· Educc_ + 0 _._ 05 _· Healthc_ + 0 _._ 02 _· Environmentc_ where _QuotaICMS,c_ is the _Quota−Parte_ for municipality _c_ ; _Educc_ represents the education quality index for municipality _c_ ; _Healthc_ represents average _levels_ and _improvements_ in infant mortality

> 3In most states, the ICMS tax rate varies significantly per product or service, from 7% to 35% according to the state and product; it is the main source of revenue for state governments.

> 4Among the adjacent states of _Ceará_ , _Rio Grande do Norte_ has a _Quota−Parte_ rule largely based on equitable distribution among municipalities, and a smaller fraction based on demographic and/or territorial variables. Other states, such as _Piauí_ and _Paraíba_ , use a similar rule but add a percentage for trash treated and an environment indicator (less than 10%). In the state of _Pernambuco_ , until 2011 tax value added and conservation units also had weight. Still for _Pernambuco_ , from 2011 on-wards 2% of the _Quota−Parte_ was shared with municipalities based on education quality, and only recently, in Law 16 _,_ 616 _/_ 2019, the quota increased to 18% until 2025, as is the case in _Ceará_ . Despite the fact that _Pernambuco_ has adopted the same RBF mechanism as _Ceará_ , it will be only implemented in 2025. Excluding _Pernambuco_ from our estimates results does not change the interpretation in any meaningful way (see Table A.2).

7
rates for municipality _c_ , and _Environmentc_ is a dummy variable indicating whether the municipality _c_ has an operational solid waste management system<sup>5</sup> . As can be seen, _Educc_ receives, by far, the highest weight in the _QuotaICMS,c_ redistribution rule: 18% out of 25% transferred to municipalities depends on education performance. It is also important to mention that the _QuotaICMS,c_ is calculated by an independent think _−_ thank ( _Instituto de Pesquisa e Estratégia Econômica do Ceará_ - IPECE) using information collected by the state government. Municipalities do not collect or report on their _Educc_ , _Healthc_ , and _Environmentc_ data.

This paper focuses on _Educc_ because of its preeminence in the _QuotaICMS,c_ redistribution rule. It has two main components: literacy rates ( _Literacy_ ) and learning scores (Portuguese and Mathematics) in primary education ( _Learning_ ). Literacy rates and learning scores are calculated with a state-managed assessment called SPAECE that is applied to students yearly to monitor the performance in basic education in _Ceará_ . In the original _RBF_ model, proposed in 2007, literacy performance is weighted twice as much as _Learning_ performance to induce greater efforts towards improvements in basic literacy as shown in the following _Educc_ equation: where _Literacyc_ averages the _level_ and _time variation_ of literacy rates per municipality _c_ . On literacy _level_ ( _L_<sup>_w_</sup> _c_<sup>) the formula weights the average literacy rate (</sup> _Lc_ ) by SPAECE _enrollment_ rates _Enroll_ % _<u>,c</u>_ ( _Enroll_ % _,c_ ) times half the standard deviation of Portuguese scores: _L_<sup>_w_</sup> _c_<sup>=</sup> _Lc ×_ 0 _._ 5 _σL_<sup>_<u>c</u>_</sup> . Adding these two weights aims to reduce the potential negative selection of students into SPAECE and to punish municipalities with highly unequal learning performance. Based on the weighted literacy rates ( _L_<sup>_w_</sup> _c_<sup>),thefinalindexforlevelis</sup><sup>_Iliteracy,c_=</sup> _LL_<sup>_w_</sup> _max_<sup>_w_</sup> _<u>c</u>_<sup>_−−LLw_</sup> _<u>min</u>_<sup>_<u>w</u>_</sup> _min_<sup>dividedbythesumof</sup><sup>_Iliteracy,c_forall</sup> municipalities,<sup><u>�</u></sup> _c_<sup>_Iliteracy,c_.Forthetimevariationcomponent,the</sup><sup>_RBF_formulaconsidersthe</sup>

> 5The methodology for computing these indexes was established by Holanda et al. (2008a,b).

8
time difference between _L_<sup>_w_</sup> _ct_<sup>and</sup><sup>_Lw_</sup> _c_ ( _t−_ 1)<sup>inthesameequations.6</sup> The _Learningc_ component of the _RBF_ formula has the same structure as the _Literacyc_ component. It also considers _levels_ and _time variation_ at the municipal level but, instead of _L_<sup>_w_</sup> _c_<sup>and</sup><sup>_Lw_</sup> _ct_<sup>,the</sup> formula considers weighted test scores in 5<sup>_th_</sup> grade named _Tc_<sup>_w_and</sup><sup>_T_</sup> _ct_<sup>_w_.All underlying calculations</sup> to find _ILearning,ct_ follow the same procedures as for _Iliteracy,ct_ . But different from _Literacyc_ , this component includes pass rates ( _Enroll_ % _,c_ ). More explicitly, the final _Learningc_ indicator becomes: _Enroll_ % _<u>,c</u> Ilearning,c_ ∆ _Ilearning,ct Learningc_ = 0 _._ 2 _·_ <u>�</u> _c_<sup>_Enroll_%</sup><sup>_,c_+ 0</sup><sup>_._8</sup><sup>_·_</sup> �0 _._ 4 _·_ <u>�</u> _c_<sup>_Ilearning,c_+ 0</sup><sup>_._6</sup><sup>_·_</sup> <u>�</u> _c_<sup>∆</sup><sup>_Ilearning,ct_</sup> �.

In summary, the original _RBF_ model shows that municipalities with greater improvements in literacy rates, pass rates, and learning scores will receive a higher fraction of _Quota − Parte_ than municipalities with lower overall performance. However, if better test scores are achieved by restricting the participation of students in _SPAECE_ or by widening the gap between high and low performers, municipalities are penalized with a lower _Quota−Parte_ . Overall, the _RBF_ model intends to generate incentives to local authorities to amplify the coverage of students participating in standard exams and, at the same time, reduce learning disparities.

# **2.2 The Reformulation of the RBF Model**

The _RBF_ formula described above was partially reformulated in 2012 by the state government of _Ceará_ . The new decree, 30,796/2011, took effect in 2013 and focused on the _Educc_ component, with _Healthc_ and _Environmentc_ unaltered. In this decree, four reformulations were implemented: (i) _Enroll_ % _,c_ was removed from _Learningc_ and added to the _Educc_ component (weighting 0 _._ 05); (ii) _Literacyc_ replaced the weight for _levels_ by 0 _._ 75 and for _time variation_ by 0 _._ 25, instead of 6Explicitly, the _Literacyc_ equation is illustrated in the RBF mechanism: where ∆ _Iliteracy,ct_ = _L_<sup>_w_</sup> _ct_<sup>_−Lw_</sup> _c_ ( _t−_ 1)<sup>.</sup><sup>_Enroll_%</sup><sup>_,c_=</sup><sup>_<u>NA</u>_</sup> _NEc_<sup>_<u>c</u>NAm_and</sup><sup>_NEm_arethenumberofpupilsassessedand</sup> enrolled in the municipal network, respectively.

9
0 _._ 5 each; (iii) _Learningc_ averaged test scores in Mathematics _and_ Portuguese. These first three modifications focused on increasing the importance of learning levels in the _RBF_ mechanism, inducing equity and preventing gaming (Loureiro et al. 2020).<sup>7</sup> The last modification (iv) substitutes the standard deviation in literacy rates ( _L_<sup>_w_</sup> ) and test scores ( _T_<sup>_w_</sup> ) with the percentage of students below critical levels of learning. Along with simplifying the _RBF_ formula, this particular change reflects the low response of _σ_<sup>_c_</sup> to local policies compared to the percentage of students below thresholds of performance. In specific terms, _Literacyc_ replaces _σL_<sup>_c_by (1</sup><sup>_−Lcritical,c_)3</sup><sup>_·_(1</sup><sup>_−Lpartial,c_)1</sup><sup>_·_(1 +</sup><sup>_Lsatisf,c_)2, where</sup><sup>_Lcritical,c_is the proportion of students</sup> defined as illiterate, _Lpartial,c_ is the proportion of students defined as partially literate, and _Lsatisf,c_ refers to the proportion deemed satisfactorily literate. For _Learningc_ , the weight becomes (1 _− Portlow,c_ )<sup>2</sup> _·_ (1 _−Porthigh,c_ )<sup>2</sup> for Portuguese and Mathematics follows the same structure. In general terms, the reformulation concentrates the fiscal incentives of _Quota−Parte_ in the lower tail part of the distribution by giving more weight to municipalities seeing improvements in students who are lagging behind.

# **2.3 Technical Assistance**

In 2007, the State of _Ceará_ established the goal that "all students in public schools should read by the end of 2<sup>_nd_</sup> grade (age 7)".<sup>8</sup> Unlike most Brazilian states, in 2007 the large majority of primary

> 7After these modifications, the _RBF_ model has the form:

The second change was in the weights of the _Literacyc_ formula: The third modification adds mathematics to the _Learningc_ formula: _Learningc_ = 0 _._ 5 _· Portuguesec_ + 0 _._ 5 _· Mathematicsc_ where _Portuguesec_ and _Mathematicsc_ are respectively the indicators of learning in Portuguese and Mathematics. 8Formally, the program is called _Programa de Alfabetização na Idade Certa_ (PAIC).

10
education students in _Ceará_ were enrolled in public schools managed by municipalities.<sup>9</sup> Based on this ambitious goal, the government of _Ceará_ elaborated a _non−mandatory_ package of technical assistance (TA) available to _all_ municipalities. This package has three fundamental components:

1. _Literacy Support to Municipalities:_ Provide structured literacy textbooks<sup>10</sup> and teacher training focused on classroom practice.

2. _Knowledge Exchange Practices_ : ( _i_ ) the provision of training for education staff, with a focus on the management of education systems and schools; ( _ii_ ) solid monitoring & evaluation of education policies; ( _iii_ ) incentives for knowledge exchange of best practices among schools; ( _iv_ ) support to reform teacher careers; and ( _v_ ) promotion of meritocratic selection for school principals.

3. _Pedagogical Use of Learning Assessments (SPAECE)_ : state level diagnostics of literacy levels at the beginning and end of _each_ school year to guide pedagogical action.

To coordinate these activities, the state secretariat of education in _Ceará_ created a collaborative governance arrangement structured in three levels. The first is the state coordination team that hires specialists to train and guide regional teams. The regional teams, for instance, disseminate the training to municipal teams (second level) that are, in turn, responsible for training teachers (third level).<sup>11</sup> Because these training activities focus on the use of structured materials and classroom activities<sup>12</sup> , the empirical section investigates each component separately: the incidence and quality of teacher training, curriculum coverage, types of principal selection processes, pedagogical

> 9In the following years, many states accelerated the process of devolving public primary schools to municipal administrations. As of 2018, all states had the majority of primary education students enrolled in municipal schools; in many states this percentage is close to 100%.

> 10These materials proposes detailed guidance on time-use, activities, and pedagogical routines for each class. The materials are aligned with the state curriculum, prioritization of basic skills, and a particular focus on literacy at the right age.

> 11For more details on the technical assistance from the state secretariat of education to municipal governments in _Ceará_ , see (Loureiro et al. 2020).

> 12These activities involved classroom observations by trainers based on text books used daily in the classroom.

11
practices, and quality of materials.

# **3 Data and Descriptive Statistics**

Our main source of information is the _Sistema de Avaliação da Educação Básica_ (SAEB) provided by the Brazilian Ministry of Education between 2005 and 2017. SAEB is a learning quality assessment implemented biannually in Brazil that provides standard test scores in Mathematics and Portuguese, and collects detailed information about students, teachers, and school principals. The SAEB assessment is undertaken at the end of each educational cycle: 5<sup>_th_</sup> grade of primary education, 9<sup>_th_</sup> grade of lower secondary education, and 3<sup>_rd_</sup> grade of upper secondary education. Because virtually only primary and lower secondary education are managed by municipalities in Ceará, and are therefore part of the _RBF_ mechanism, our regression analysis is restricted to 5<sup>_th_</sup> and 9<sup>_th_</sup> grades. Importantly, to reduce the influence of gaming in our findings, note that SAEB is _not_ part of _RBF_ indicators in _Ceará_ . Instead, the RBF uses an independent state-level assessment called SPAECE. An additional advantage of SAEB is to provide unique city identifiers that allow us to explore geographic properties of schools in our identification strategy and control for city fixed effects. In 2005, only a representative sample of schools participated in the assessment; from 2007 on-wards it included all public schools with at least 30 students enrolled in the 5<sup>_th_</sup> or 9<sup>_th_</sup> grade.

The rich information in SAEB allows investigating a comprehensive set of outcomes. At the student level, it provides general characteristics such as gender, age, and race and specific household characteristics as single parenting, household size, number of bathrooms, and parental education. The teacher questionnaire asks about their level of qualification and experience in education, recent participation in training programs, basic contract characteristics, and pedagogical practices in the classroom (e.g., homework correction, materials used, and curriculum coverage). For school prin12
cipals, SAEB similarly provides data on qualifications, experience, and participation in training, but adds how principals were selected and the provision of textbooks. Exploring this information allows us to investigate some mechanisms explaining the _RBF_ effects on learning outcomes.

As our empirical strategy compares schools that are geographically close during the critical periods of the _RBF_ reform, we restrict the working sample to municipalities at the border of _Ceará_ and adjacent states: _Piauí_ , _Rio Grande do Norte_ , _Paraíba_ and _Pernambuco_ . However, the narrower the definition of ‘’border", the smaller is the sample power. Or alternatively, a wide definition of ‘’border" may not effectively control for unobservable factors explaining the differences in learning performance between schools. Thus, we define border as the first _three_ municipalities on each side of the _Ceará_ border. By using this definition, approximately one-third of the municipalities in these five states become part of the working sample (see Figure 1 for an illustration of all municipalities in the sample). Table 1 presents descriptive statistics using this definition.

An immediate evidence from Table 1 is that, during the baseline (2005 _−_ 2007), there is no systematic difference between _Ceará_ and its adjacent states. This is valid for 5<sup>_th_</sup> grade or 9<sup>_th_</sup> grade, test scores, and student characteristics. Other evidence is that for _RBF_ periods from 2009 to 2017, test scores in _Ceará_ steadily increase relative to adjacent states, especially in “ _RBF_ ( _re_ ) + _TA_ ” periods. Considering students in Panel A, around 50% are boys, the students are around 11 years old and, on average, there are 5 people per household. When the re-formulated RBF started (2013), the difference in student performance in test scores between _Ceará_ and adjacent states is 7 _._ 6 points in Portuguese and 9 _._ 2 points in Mathematics comparing 2013 to 2011.

We complement the empirical analysis by merging additional data-sets. In terms of including school _−_ level controls, a useful source of information is the _Censo Escolar_ , which provides comprehensive information on school infrastructure and unique ids that allow us to merge it with the SAEB data. For municipal-level controls, we include data on GDP _per capita_ and population size 13
Table 1 Test Scores and Student Characteristics at the Border of Ceará

|||Panel|A. Stu|dents in 5<sup>_th_</sup>|grad|e|||
|---|---|---|---|---|---|---|---|---|
|**Period**|**1.**|_Baseline_|**2**|**.** _RBF_|**3.**|_RBF_ +_TA_|**4.**|_RBF_(_re_) +_TA_|
|**Years**|(|2005_/_07)||(2009)||(2011)||<br>(2013_/_15_/_17)|
||**Ceará**|**Adj. States**|**Ceará**|**Adj. States**|**Ceará**|**Adj. States**|**Ceará**|**Adj. States**|
|Portuguese Scores|157.7|155.9|168.9|163.3|183.7|169.0|208.2|183.2|
||(37.7)|(35.5)|(42.1)|(37.1)|(45.4)|(38.8)|(52.8)|(45.1)|
|Mathematics Scores|172.5|172.5|184.8|180.8|201.6|184.6|220.7|194.4|
||(38.2)|(37.0)|(44.7)|(39.1)|(48.4)|(38.8)|(54.6)|(42.8)|
|% of Boys|0.50|0.49|0.52|0.51|0.52|0.51|0.51|0.51|
||(0.50)|(0.50)|(0.49)|(0.50)|(0.49)|(0.50)|(0.50)|(0.50)|
|% of White Students|0.27|0.29|0.27|0.28|0.24|0.25|0.22|0.26|
||(0.44)|(0.45)|(0.44)|(0.45)|(0.43)|(0.43)|(0.41)|(0.44)|
|Student Age (in years)|10.9|11.1|11.0|11.3|11.0|11.2|10.8|11.1|
||(1.31)|(1.53)|(1.37)|(1.52)|(1.25)|(1.44)|(1.05)|(1.27)|
|Household Size|5.02|4.98|4.99|4.97|5.07|5.10|5.40|5.37|
||(1.13)|(1.09)|(1.13)|(1.10)|(1.39)|(1.36)|(1.26)|(1.31)|
|% of Mothers with Diploma|0.12|0.14|0.11|0.13|0.12|0.14|0.17|0.18|
||(0.33)|(0.34)|(0.31)|(0.33)|(0.33)|(0.35)|(0.37)|(0.38)|
|**# of Student Observations**|37,437|17,352|47,768|22,011|50,346|21,401|129,350|82,395|
|||Panel|B. Stu|dents in 9<sup>_th_</sup>|grad|e|||
|**Period**|**1.**|_Baseline_|**2**|**.** _RBF_|**3.**|_RBF_(_re_)|**4.**|_RBF_(_re_) +_TA_|
|**Years**|(|2005_/_07)|(|2009_/_11)||(2013)||(2015_/_17)|
|Portuguese Scores|211.0|215.2|226.0|223.0|237.9|227.3|257.8|239.6|
||(40.3)|(40.5)|(44.0)|(42.5)|(46.3)|(43.7)|(47.4)|(44.5)|
|Mathematics Scores|222.8|228.4|230.8|229.8|242.2|231.9|259.6|240.3|
||(38.9)|(40.4)|(44.8)|(42.1)|(48.8)|(42.8)|(51.1)|(43.0)|
|% of boys|0.45|0.40|0.46|0.41|0.48|0.44|0.48|0.46|
||(0.49)|(0.49)|(0.49)|(0.49)|(0.50)|(0.49)|(0.50)|(0.49)|
|% of white students|0.24|0.27|0.22|0.25|0.20|0.23|0.20|0.22|
||(0.43)|(0.44)|(0.41)|(0.43)|(0.40)|(0.42)|(0.40)|(0.41)|
|Student Age (in years)|15.2|15.6|15.2|15.4|14.9|15.1|14.9|15.1|
||(1.56)|(1.76)|(1.31)|(1.50)|(1.18)|(1.35)|(1.01)|(1.24)|
|Household Size|5.23|5.06|4.99|4.90|5.40|5.46|5.31|5.38|
||(1.67)|(1.63)|(1.53)|(1.49)|(1.24)|(1.21)|(1.22)|(1.20)|
|% of Mothers with Diploma|0.12|0.16|0.13|0.17|0.17|0.19|0.19|0.22|
||(0.33)|(0.36)|(0.33)|(0.38)|(0.38)|(0.39)|(0.39)|(0.41)|
|**# of Student Observations**|23,285|10,793|81,125|27,958|40,409|14,619|84,395|32,747|

**Notes.** This table presents descriptive statistics of students at the border between _Ceará_ and adjacent states. All data is from the _Sistema de Avaliação da Educação Básica_ (SAEB), a national assessment implemented biannually. In additional to _Ceará_ , we consider the following adjacent states: _Piauí_ , _Rio Grande do Norte_ , _Paraíba_ and _Pernambuco_ . The definition of border considers the first _three_ municipalities on each side of _Ceará_ ’s border. Panel A considers 5<sup>_th_</sup> graders. Panel B is for 9<sup>_th_</sup> graders. The baseline period of 2005 and 2007 is when neither _Ceará_ nor adjacent states had implemented _RBF_ incentives. The column " _RBF_ " considers 2009 in Panel A, because the _RBF_ law started on January 1, 2009. For 5<sup>_th_</sup> grades, technical assistance ( _TA_ ) initiated in 2011, presented in column " _RBF_ + _TA_ " in Panel A. In Panel B, the column ‘’ _RBF_ ( _re_ )" presents the statistics for 9<sup>_th_</sup> grade when the RBF formula was re-calibrated in 2013, but _TA_ was offered only to 5<sup>_th_</sup> grade classes. In Panels A and B, periods of re-calibration and TA are shown in columns " _RBF_ ( _re_ ) + _TA_ ".

at the municipal level from the _Instituto Brasileiro de Geografia e Estatística_ (IBGE) and live birth records from the Ministry of Health.<sup>13</sup> To investigate potential RBF mechanisms, we use municipal public spending data provided by the National Treasury Bureau ( _Secretaria do Tesouro_

> 13Municipal data on live births can be obtained at the url: `http://www2.datasus.gov.br/DATASUS/index. php?area=0205` .

14
_Nacional_ - STN).<sup>14</sup> .

# **4 Identification Strategy**

The results _−_ based financing (RBF) reform in _Ceará_ configures an opportunity to estimate if education incentives for mayors triggers student learning. Given that such a reform occurred at the state level and at clear points in time allows us to explore empirically the geographic and time characteristics in our identification strategy. That being said, we start by restricting our sample to schools located in the three immediate municipalities at the border between _Ceará_ and adjacent states ( _Piauí_ , _Paraíba_ , _Rio Grande do Norte_ and _Pernanbuco_ ). Figure 1 illustrates the municipalities included in the analysis. By limiting our sample to municipalities that are geographically close, but on different sides of the border, we intend to minimize the influence of time-invariant unobserved characteristics of schools and municipalities that affect student learning. Put simply, schools right across the border serve as a good counterfactual for the case that the RBF reform had not been implemented in _Ceará_ .

Another useful characteristic of the _Ceará_ reform is its clear timeline. We leveraged that the RBF and the technical assistance (TA) component were introduced at defined dates to compare the evolution of learning outcomes at the border at different points in time. To make this point clearer, consider the RBF and TA reform for 5<sup>_th_</sup> grades. In the first moment, the state congress enacted the RBF reform in mid-December 2007; so, from January 2008 on-wards, a fraction of Quota-Parte revenues started to be redistributed to municipalities based on learning outcomes. Then, in 2011, schools with students from 3<sup>_rd_</sup> _−_ 5<sup>_th_</sup> grade received a _non−mandatory_ package of training and pedagogical materials (the TA component). In a third and final stage, in 2012 the RBF formula was re-formulated to penalize municipalities with higher percentages of students

> 14 Public spending data can be accessed at `https://siconfi.tesouro.gov.br/siconfi/index.jsf` .

15
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baseline years; _RBFt_ equals one for 2009, two years after the RBF was introduced in _Ceará_ . The dummy _RBFt_ - _TA_ equals one for 2011, when the TA to municipalities was initiated; and _RBF_ ( _re_ )- _TA_ refers to the period after 2013, when the RBF formula was re-calibrated.

Eq. (1) also includes a set of fixed-effects and time trends. _αborder_ is a border fixed-effect that captures unobservable characteristics shared by municipalities at the _same_ border. Including this variable is important, because it makes the RBF impacts emerge from comparing schools that are geographically close instead of simply averaging both sides of the frontier. _αyear_ is a time trend and _tc_ is a city _−_ specific time trend. Time-varying controls in _Xi_ include a set of student (age, race, mother education) and school (if rural school and a dummy if the school offers primary _and_ lower secondary education) characteristics. Finally, _εict_ is the error term clustered by municipality to allow for contemporaneous spatially correlated shocks.

There are four coefficients on which the analysis is based. The baseline difference _β_<sup>_pre_</sup> captures pre-determined differences between _Ceará_ and adjacent states prior to the reform. The parameter _β_<sup>_rbf_</sup> estimates the average difference in the _RBF_ periods _before_ the _TA_ was introduced (2009 for 5<sup>_th_</sup> grade, and 2009 to 2011 for 9<sup>_th_</sup> grade). Next, _β_<sup>_rbf_+</sup><sup>_ta_</sup> represents the estimated difference when the RBF _and_ TA were offered, and _β_<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_ta_</sup> shows the average difference when the _RBF_ formula was reformulated. Based on these coefficients, we report three parameters of interest. First, we estimate the “RBF effect” by _β_<sup>_rbf_</sup> _− β_<sup>_pre_</sup> . This estimate discounts from the average difference in _RBF_ periods the average difference during the baseline years. The second is _β_<sup>_rbf_+</sup><sup>_ta_</sup> _− β_<sup>_rbf_</sup> which measures the _incremental_ effect of _TA and RBF_ on education outcomes. Throughout the analysis, we report this difference as “RBF and Technical Assistance”. Lastly, _β_<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_ta_</sup> _− β_<sup>_rbf_+</sup><sup>_ta_</sup> captures the effect of reformulating the _RBF_ mechanism, and “Results _−_ Based Financing, re” alludes to this parameter in our tables.

However, using these differences to estimate causal effects is only valid under at least two assump17
tions. Primarily, it is assumed that the baseline difference _β_<sup>_pre_</sup> would have remained unaltered if the RBF reform had not been implemented. This assumption echoes the necessary condition that outcomes should have the same trend in the absence of treatment. Secondly, no parallel shock in education outcomes occurred in _Ceará_ at the same time that RBF and TA were introduced. If that is the case, Eq. (1) will erroneously attribute to _RBF_ / _TA_ what is in fact the impact of a contemporaneous shock on education outcomes.

# **5 Estimation Results**

This section starts by presenting the estimated impacts of results _−_ based financing and technical assistance on Mathematics and Portuguese scores. It graphs the evolution of test scores for students at the border across time and presents the results for 5<sup>_th_</sup> and 9<sup>_th_</sup> graders. In the following section, we disentangle the effects of TA components on test scores to understand the mechanisms explaining our findings.

## **5.1 Student Test Scores**

The effects of _RBF_ on test scores are presented in Figure 2. It plots average scores of Mathematics and Portuguese from 2005 to 2017 for municipalities at the border, in accordance with Figure 1. As the federal government applies SAEB biannually and at the end of each school cycle, Figure 2 only includes students in the 5<sup>_th_</sup> and 9<sup>_th_</sup> grades. Dashed vertical lines indicate each stage of the education reform in _Ceará_ . The first line marks when the RBF model starts. The next two lines refer to the introduction of a non-mandatory TA component and the reformulation of RBF (note that these dates differ depending on the grade).

A first indication of how education incentives to local authorities affect test scores is presented 18
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average difference in test scores at the border remains equal when only the _RBF_ mechanism is in place. However, still in Figures 2.A and 2.B, significant differences start to emerge only after TA is offered in 2011 and reinforced after _RBF_ is reformulated in 2013 (see Section 2 for details). As the regression analysis indicates, the provision of TA and the introduction of weights for students below minimum thresholds of performance in the RBF formula had an essential role in these improvements.

The scenario for 9<sup>_th_</sup> grades in Figures 2.C and 2.D is slightly different than 5<sup>_th_</sup> grades. In baseline years, 9<sup>_th_</sup> grade students in _Ceará_ performed significantly _lower_ than those at the border of adjacent states. Additionally, Figure D shows a clearer case for parallel trends during pre-RBF years than Figure C, despite the fact that formal testing cannot reject the equal trends hypothesis before RBF was introduced. This difference in test scores vanishes entirely in _RBF_ years (2009 _−_ 2011) and reflects increases in test scores in _Ceará_ that are not followed by circumventing municipalities. In fact, and similar to 5<sup>_th_</sup> graders, reformulating the RBF model in 2013 and introducing the TA component from 2015 to 2017 consolidated these improvements in the following years in _Ceará_ relative to its counterparts.

Table 2 complements these findings by presenting the RBF effects on test scores using Eq. (1). Columns (1) and (3) present the impacts on Mathematics scores. Columns (2) and (4) are for Portuguese scores. Impact estimates for 5<sup>_th_</sup> graders are presented in columns (1) and (2) and for 9<sup>_th_</sup> graders in columns (3) and (4). The baseline difference between students in _Ceará_ and across the border is shown as “Baseline Difference ( _β_<sup>_pre_</sup> )", and a parallel trends test in pre-RBF years is presented as “Diff(2007) _−_ Diff(2005)". Standard errors are clustered by municipality and p _−_ values are presented in brackets.

At least three main conclusions are drawn from Table 2. Panel A shows that the RBF alone in _Ceará_ increased test scores only for students at the end of lower secondary (9<sup>_th_</sup> grade). In this 20
Table 2

# The Effects of Results _−_ Based Financing on Test Scores (Clustered Standard Errors)

||Mathematics<br>5<sup>_th_ </sup>Grade<br>(1)|Portuguese<br>5<sup>_th_ </sup>Grade<br>(2)|Mathematics<br>9<sup>_th_ </sup>Grade<br>(3)|Portuguese<br>9<sup>_th_ </sup>Grade<br>(4)|
|---|---|---|---|---|
|**A. DD, Results**_−_**Based Financing (RBF)**|||||
|<sup>_rbf pre_</sup>|0_._036|0_._061<sup>_∗_</sup>|0_._155<sup>_∗∗∗_</sup>|0_._153<sup>_∗∗∗_</sup>|
|_β_ _−β_|(0_._040)|(0_._037)|(0_._026)|(0_._023)|
|**B. DD, RBF and Teaching Assistance**|||||
|_β_<sup>_rbf_+</sup><sup>_ta _</sup>_−β_<sup>_rbf_</sup>|0_._220<sup>_∗∗∗_</sup><br>(0_._029)|0_._162<sup>_∗∗∗_</sup><br>(0_._021)|||
|<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_ta rbf_(</sup><sup>_re_)</sup>|||0_._148<sup>_∗∗∗_</sup>|0_._118<sup>_∗∗∗_</sup>|
|_β_ _−β_|||(0_._032)|(0_._028)|
|**C. DD, Results**_−_**Based Financing, re**|||||
|_β_<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_ta _</sup>_−β_<sup>_rbf_+</sup><sup>_ta_</sup>|0_._170<sup>_∗∗∗_</sup><br>(0_._038)|0_._166<sup>_∗∗∗_</sup><br>(0_._032)|||
|<sup>_rbf_(</sup><sup>_re_)</sup> <sup>_rbf_</sup>|||0_._092<sup>_∗∗_</sup>|0_._096<sup>_∗∗∗_</sup>|
|_β_ _−β_|||(0_._035)|(0_._028)|
|**Baseline Diference** (_β_<sup>_pre_</sup>)|_−_0_._022|_−_0_._013|_−_0_._199|_−_0_._142|
||[0_._595]|[0_._738]|[0_._000]|[0_._000]|
|**Dif**(2007) _−_**Dif**(2005)|0_._069|0_._080|_−_0_._022|0_._018|
||[0_._512]|[0_._343]|[0_._891]|[0_._853]|
|**City/Student Controls**|Yes|Yes|Yes|Yes|
|**City**_−_**Specifc Time Trend**|Yes|Yes|Yes|Yes|
|**Border Fixed**_−_**Efects**|Yes|Yes|Yes|Yes|
|**# of Student Observations**|233_,_830|223_,_820|194_,_852|194_,_862|
|**Adj. R**_−_**squared**|0_._188|0_._247|0_._149|0_._185|

**Notes.** _∗∗∗_ denotes significance at 1 percent, _∗∗_ at 5 percent, and _∗_ at 10 percent level. This table shows the estimated impacts of the results _−_ based financing (RBF) reform on student test scores. Data on test scores is from the _Sistema de Avaliação da Educação Básica_ (SAEB), a national standardized exam undertaken by the federal government every two years. Importantly, SAEB is _not_ part of the RBF mechanism in _Ceará_ (instead, they use the state assessment called SPAECE) and for this reason is more appropriate to minimize potential gaming. All regressions restrict the sample to the first three immediate municipalities on each side of the border between _Ceará_ and adjacent states as shown in Figure 1. The municipality controls are: number of births in the municipality _−_ year ( _Sistema de Nascidos Vivos_ (SINASC)); a dummy for rural schools (from SAEB); and a dummy for schools offering grades 1 _−_ 9 (School Census). Student controls come from SAEB and include: a dummy if the student is male, if the student is white, age in years, number of bedrooms, if the mother has higher education and their household size. The estimates also include time trends and city-specific time trends. Border fixed-effects introduces dummies for each border between _Ceará_ and its adjacent states (see the different colors in Figure 1). By including these dummies, the regressions compare students at the same border instead of simply averaging test scores on both sides of the border. Panel A presents _DD_ estimates of _RBF_ impacts. Panel B refers to the effects after introducing the TA component. Panel C shows _DD_ estimates after the RBF formula included weights for the percentage of students below minimum thresholds of performance in Mathematics and Portuguese. The baseline difference at the border, _β_<sup>_pre_</sup> , and a parallel trend test estimating changes in the trends during pre-RBF periods is shown at the bottom of each column. Standard errors are clustered by municipality and shown in parenthesis. P _−_ values are shown in brackets.

21
case, the RBF generates an impact of approximately 0 _._ 15 standard deviation on Mathematics and Portuguese scores. No impacts are found for students in 5<sup>_th_</sup> grade. As shown in Figures 1 _C_ and 1 _D_ , these increases close the score gaps at the border observed during pre-RBF periods. To put these results into another perspective, the _RBF_ effect on 9<sup>_th_</sup> grade translates into an increase equivalent to 3 _._ 7 months of schooling in Mathematics and 3 months in Portuguese.<sup>15</sup> The second finding relates to the gains of providing TA to municipalities. Results from Panel B show that 5<sup>_th_</sup> graders have a significant improvement of 0 _._ 22SD (5 months of schooling) in mathematics and 0 _._ 162SD (3 months of schooling) in Portuguese relative to the difference at the border when only the RBF was in place. For 9<sup>_th_</sup> grade, columns (3) and (4) illustrate a similar conclusion: the TA component almost doubled the RBF impacts in Panel A. One explanation for such gains is that the TA component provides pedagogical materials, teacher training, and knowledge exchange between schools, which benefit municipalities with particularly low capacity to implement similar policies.

Finally, Panel C suggests that reformulating the RBF mechanism by penalizing higher percentages of students performing below minimum levels in SPAECE generates further increases on test scores. Intuitively, this reformulation may reflect that mayors and schools focus on the students who are significantly lagging behind. Observing the estimates in Panel C reinforces this interpretation. When the reformulation occurred without the support TA ( _β_<sup>_rbf_(</sup><sup>_re_)</sup> _− β_<sup>_rbf_</sup> ), the impacts are approximately 0 _._ 092SD (2 _._ 2 months of schooling) for 9<sup>_th_</sup> grade. Yet, when minimum thresholds are introduced in the RBF formula _and_ the TA component is available to municipalities, the impacts on test scores are twice as large (columns (1) and (2), Panel C). Thus, it seems that if mayors understand which students have a stronger impact on the RBF redistribution and TA is available, there are significantly larger impacts on test scores.

> 15 We calculated schooling-equivalent months by the difference in SAEB test scores for the _same_ cohort of students in municipalities outside _Ceará_ between 2007 (when students were in 5<sup>_th_</sup> grade) and 2011 (when these students were in 9<sup>_th_</sup> grade) divided by two. According to the exercise, every two years represents an average gain of 0 _._ 47 _−_ 0 _._ 495 standard deviation in mathematics and 0 _._ 56 _−_ 0 _._ 62 in Portuguese.

22
Two points about these findings are important to highlight. If mayors orient teachers to teach to the SAEB test, our impact coefficients will capture the ability of mayors to artificially influence test scores rather than improvements in learning (for a general discussion, see Barlevy and Neal (2012); Jacob 2005; Glewwe et al. 2010; Carrell and West 2010). However, we argue that this form of gaming is unlikely, because the RBF mechanism is based on SPAECE (the state _−_ level assessment in _Ceará_ ) while our estimates use SAEB (the Brazilian national assessment). As SAEB scores have no influence on the RBF formula and _Quota − Parte_ redistribution in _Ceará_ , mayors have no incentive to game using the test to receive additional funding. Another relevant point is that these conclusions remain consistent after considering different sample definitions, alternative controls, time trends, and combinations of municipalities at the border (see Tables _A._ 1 and _A._ 2 in the appendix for the results).<sup>16</sup> _−_ Another legitimate concern, inherent in outcomes based policies, is whether the RBF mechanism increases learning gaps between low and high performing students. That might be the case, for example, if mayors were to pool their resources to reach high _−_ achieving students or schools to increase average test scores. An opportunity to check whether the RBF reform widened learning gaps is by re-estimating Eq. (1) per quantile. Figure 3 presents the parameters of interest and their respective 95% confidence interval for 5<sup>_th_</sup> and 9<sup>_th_</sup> grades in Portuguese and Mathematics per quantile.

Figure 3 outlines three aspects of RBF effects on low-performing students. First, the RBF alone tends to _increase_ learning gaps, especially for students in the 5<sup>_th_</sup> grades. In Figure 3.A, the effects of RBF measured by _β_<sup>_rbf_</sup> _− β_<sup>_pre_</sup> become significant only for quantiles above 0 _._ 6, while it is not different from zero for students below this point. Secondly, introducing the TA component

> 16An additional concern is whether our estimates are capturing changes in student cohorts in _Ceará_ rather than in performance. To verify this hypothesis, we test whether enrollment rates in public and private schools (in log terms) change after the introduction of RBF and the TA. Table _A._ 3 in the appendix shows that this is not the case. There is no significant change in enrollment rates in public schools in _Ceará_ or negative changes in enrollment rates in private schools.

23
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in the RBF model (Figures 3 _.A_ and 3 _.B_ ) affects significantly low-achieving students but is still not enough to narrow the learning gaps _−_ i.e., _β_<sup>_rbf_+</sup><sup>_ta_</sup> _− β_<sup>_rbf_</sup> is around three times as large for 90<sup>_th_</sup> quantile students compared to 10<sup>_th_</sup> quantile students. Lastly, including in the RBF formula an explicit measure of students below minimum performance thresholds tends to _decrease_ the learning gaps, particularly for students in 9<sup>_th_</sup> grade. In this case, the effects for students in the top quantiles are only slightly larger than students in low quantiles, or even smaller when considering Portuguese scores in 9<sup>_th_</sup> grade. Altogether, Figure 3 indicates that when the RBF formula conditions the redistribution of resources to the performance of students at the lowest bottom (minimum thresholds), it tends to reduce, but not eliminate, the learning enlarged by the RBF mechanism.

# **5.2 The of Technical Assistance**

One explanation for our results is that _reformulating_ the RBF formula and providing technical assistance to municipalities generated larger and more equitable impacts on test scores. As discussed in Section 2, it might be a consequence of the design of the TA program that supports students who are lagging behind in _each grade_ by providing structured materials to schools, offering teacher training and promoting knowledge exchange between schools ( _Escola Nota 10_ program). This section investigates which of these components plays a more important role in RBF impacts on learning.

For that, the first step replaces the _RBF − TA_ dummy in Eq. (1) by three variables indicating each TA activity: one indexing the percentage of teachers that received textbooks and another calculating the percentage of teachers participating in training in the last two years _−_ both as percentages at that school level, and a dummy for schools that participated in the knowledge exchange program _Escola Nota 10_ . Note that in excluding the knowledge exchange dummy, we 25
are unable to measure _directly_ if textbooks or teacher training are offered by the state TA program (PAIC) or a local program in the municipality. So, we only measure TA components indirectly, as textbooks and teacher training can be similarly offered in municipalities on both sides of the border. As a next step, we interacted these variables with _Cearac_ to account for differences at the border between municipalities in _Ceará_ and adjacent states (see Figure 1), exactly as performed in Eq. (1). We therefore estimate the impact of each TA component by using the difference _−_ in _−_ differences in learning scores of: (i) the difference in performance between schools/teachers reporting one TA component at the border; and (ii) the difference in performance between schools at the border during the RBF periods. Table 3 presents the estimated impacts using this strategy for 5<sup>_th_</sup> and 9<sup>_th_</sup> grades.

Results from columns (1) _−_ (4) in Table 3 add important details to our previous findings. Combining the _RBF_ incentives for local mayors with the provision of _textbooks_ to teachers seems to account for a great part of TA effects on learning scores in Panel B. As indicated in columns (1) and (2) in Panel B, if all teachers received textbooks, test scores would increase by 0 _._ 162SD for Portuguese and 0 _._ 253SD for Mathematics, equivalent to around 4 months of learning. In contrast, participation in the knowledge exchange program or providing teacher training does not show significant impacts. A possible explanation for absent impacts of teacher training may emerge from the results in Panel C. After the RBF takes into account clear thresholds of minimum student performance at schools, teacher training shows a strong and significant effect on test scores. For example, for 5<sup>_th_</sup> grade, its impacts are twice as large as providing textbooks to teachers: an increase of 0 _._ 244SD for Portuguese and 0 _._ 290SD for Mathematics, or around 5 months of learning equivalent. The impacts are similarly high for students in 9<sup>_th_</sup> grade, as seen in columns (3) and (4).

26
Table 3 The Effects of Technical Assistance Components on Test Scores (Clustered Standard Errors)

||Portuguese<br>5<sup>_th_ </sup>Grade<br>(1)|Mathematics<br>5<sup>_th_ </sup>Grade<br>(2)|Portuguese<br>9<sup>_th_ </sup>Grade<br>(3)|Mathematics<br>9<sup>_th_ </sup>Grade<br>(4)|
|---|---|---|---|---|
|**A. DD, Results**_−_**Based Financing (RBF)**|||||
|<sup>_rbf pre_</sup>|0_._033|0_._012|0_._156<sup>_∗∗∗_</sup>|0_._149<sup>_∗∗∗_</sup>|
|_β_ _−β_|(0_._043)|(0_._042)|(0_._025)|(0_._028)|
|**B. DD, RBF** + **Technical Assistance**|||||
|Knowledge Exchange, _β_<sup>_rbf_+</sup><sup>_Knowledge _</sup>_−β_<sup>_rbf_</sup>|_−_0_._019<br>(0_._054)|0_._022<br>(0_._067)|||
|Teacher Training (%), _β_<sup>_rbf_+</sup><sup>_Training _</sup>_−β_<sup>_rbf_</sup>|0_._007<br>(0_._050)|_−_0_._002<br>(0_._061)|||
|Textbooks (%), _β_<sup>_rbf_+</sup><sup>_TextBooks _</sup>_−β_<sup>_rbf_</sup>|0_._162<sup>_∗∗∗_</sup><br>(0_._055)|0_._253<sup>_∗∗∗_</sup><br>(0_._064)|||
|**C. DD, Results**_−_**Based Financing, re**<br>_β_<sup>_rbf_(</sup><sup>_re_)</sup> _−β_<sup>_rbf_</sup>|||0_._127<sup>_∗∗∗_</sup>|0_._167<sup>_∗∗∗_</sup>|
||||(0_._029)|(0_._032)|
|KldEh<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_Knowledge rbf_</sup>|0_._016|0_._103|_−_0_._023|0_._160|
|nowege xcange, _β_ _−β_|(0_._071)|(0_._088)|(0_._182)|(0_._294)|
|ThTii%<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_Training rbf_</sup>|0_._244<sup>_∗∗∗_</sup>|0_._290<sup>_∗∗∗_</sup>|0_._182<sup>_∗∗∗_</sup>|0_._177<sup>_∗∗_</sup>|
|eacer ranng (), _β_ _−β_|(0_._045)|(0_._054)|(0_._061)|(0_._071)|
|bk%<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_TextBooks rbf_</sup>|0_._109<sup>_∗_</sup>|0_._128<sup>_∗_</sup>|0_._045|0_._144<sup>_∗∗_</sup>|
|Textoos (), _β_ _−β_|(0_._055)|(0_._066)|(0_._067)|(0_._073)|
|**City/Student Controls**|Yes|Yes|Yes|Yes|
|**City**_−_**Specifc Time Trend**|Yes|Yes|Yes|Yes|
|**Border Fixed**_−_**Efects**|Yes|Yes|Yes|Yes|
|**# of Student Observations**|228_,_418|228_,_428|191_,_285|191_,_275|
|**Adj. R**_−_**squared**|0_._244|0_._184|0_._187|0_._150|

**Notes.** _∗∗∗_ denotes significance at 1 percent, _∗∗_ at 5 percent, and _∗_ at 10 percent level. This table shows the impacts of technical assistance on test scores for 5<sup>_th_</sup> and 9<sup>_th_</sup> grades. Test scores are from _Sistema de Avaliação da Educação Básica_ (SAEB), the national standardized exam undertaken every two years. All regressions restrict the sample to students in municipalities at the border as indicated in Figure 1. The municipality controls are: the number of births per year ( _Sistema de Nascidos Vivos_ , SINASC); a dummy for rural schools (SAEB); and a dummy for schools offering grades 1 to 9. Student controls include: if male, if white, age in years, the number of bedrooms, if the mother has higher education and household size. Municipality-specific time trends and border fixed-effects are included. Panel A presents the impacts of the RBF mechanism. Panel B shows the impacts of providing RBF and each technical assistance component. The variable _textbooks_ is the percentage of teachers in the school who received textbooks. _Training_ is the percentage of teachers participating in training in the last two years, and _Knowledge_ is a dummy for schools that participated in the knowledge exchange program _Escola Nota 10_ . Panel C estimates the effects by introducing in the RBF formula the percentages of students below minimum performance thresholds in the city.

27
# **6 Mechanisms**

The next sections explore four potential channels for our findings: ( _i_ ) the selection and training of school principals, ( _ii_ ) the provision of training to teachers, and ( _iii_ ) the distribution of pedagogical materials. For these, we use detailed questionnaires from _SAEB_ applied to school principals, teachers, and students. The last mechanism, ( _iv_ ), is the changes in different domains of public spending and school facilities. The following sections discuss these points individually.

## **6.1 Selection and Training of School Principals**

The results so far suggest that combining education incentives for mayors with technical assistance produces sharp improvements in test scores. Interestingly, these effects reduce by half when RBF was implemented without any technical support. Because the selection and training of school principals in Brazil is generally provided by municipal authorities, even when the selection occurs by community voting, we now turn our attention to how RBF reform has altered the selection and training of school principals in _Ceará_ .

Two additional challenges emerge from using the questionnaire of principals from SAEB. Primarily, a large proportion of principals manage schools with either primary or lower secondary students. Therefore, it is not possible to perform separate regressions for each school type and identify when the technical assistance was introduced; if it was in 2011 or 2015. Secondly, the questionnaire for principals and teachers only became comprehensive after 2005, giving us only 2007 as a baseline difference. Because of these limitations, we had to adapt our empirical strategy in Eq. (1) to a dynamics model as in the following regression: 28
where _yit_ refers to the outcome of interest for principal _i_ in time _t_ ; _αborder_ is the border fixed-effects as defined for Eq. (1); _αt_ is a time trend; and _αct_ is a municipality-specific time trend. _Ceara_ is a dummy for schools at _Ceará_ ’s borders and zero for schools on the other side of the border (Figure 1); therefore, _β_ 0 measures the DD in the baseline period. _αyear_ is a set of exclusive dummies per year, i.e., from 2007 to 2017. The variable _DiDt_ interacts _αyear_ and _Ceara_ ; _γXi_ is a set of controls for principals’ characteristics (five age categories, race, and gender); and _εit_ is the error term. Because principals manage schools of different sizes, Eq. (2) weights the coefficients by school size, according to the school census. As before, the parameters of interest are the yearly differences in outcomes ( _βt_ ) at the border _relative_ to the difference during the baseline year of 2007.

Figure 4 plots the DD coefficients of interest for principal selection. Selection types are merged in four categories: "Election", "Designated", "Formal Selection", and "Hybrid".<sup>17</sup> Thus, Figures 4 _.A_ and 4 _.B_ present the _βt_ , and their respective 95% confidence intervals, relative to the difference in the baseline, in this case 2007.

The first result from Figure 4 is the opposite behavior shown by designations and formal selection of principals. Figure 4 demonstrates that municipalities in _Ceará_ had around a 10 _pp_ decrease in the probability of school principals being designated during the RBF period (2009 _−_ 2011) and almost a 20 _pp_ decrease after the RBF was reformulated (2013 _−_ 2017). In contrast, there is an increase in formal selection: when the RBF was introduced, principals in Ceará were around 10 _pp −_ 15 _pp_ more likely to go through a formal selection process than principals on the other side of the border. The second finding is that either "Hybrid" or “Election” selection processes present no significant change. Overall, these findings are in accordance with the interpretation

> 17The referred question in SAEB is " _Did you assume this position by:_ ". The outcome "Election" equals one when principals respond " _Election only_ " and zero otherwise. The outcome "Designated" equals one when principals answer " _Designation only_ " and zero otherwise. From SAEB 2011 backwards, this variable also includes principals who respond " _Political Indication_ " and " _Technical Indication_ ". "Formal Selection" considers principals admitted by " _Selection Only_ ". "Hybrid" encompasses the combinations of " _Selection and Election_ " or " _Selection and Indication_ ". This combination was chosen because these options remain in SAEB from 2007 to 2017.

29
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that mayors become more likely to undertake formal selection processes after tax resources are conditioned upon education performance.

_−_ By formalizing the selection process, mayors may attract high quality principals and avoid hiring low _−_ quality professionals. A fast _−_ growing body of research has shown that school principals play an important role in student performance (Lavy 2008; Grissom and Bartanen 2019). It has been found that better _−_ qualified principals affect graduation rates and English test scores (Coelli and Green 2012), and performance in primary education (Dhuey 2018). In addition to formal selection, local authorities can aim to improve the general quality of principals by providing, or by adopting, the training offered by the state government. To examine the provision and quality of training, we use two outcomes of principals derived from SAEB: a dummy " _if principals enrolled in training in the last_ 2 _years_ " and a dummy " _if they considered the training useful for their daily work_ ".

According to Figure 5, school principals in _Ceará_ were significantly more likely to participate in training after 2013. The DD coefficients indicate that training participation increased by 20 _pp_ after RBF reformulation, maintaining a positive and significant impact between 20 _pp −_ 30 _pp_ in the following years. Along with training participation, principals in _Ceará_ are around 10 _pp_ more likely to report that the training was useful than principals on the other side the border. For instance, as the question used to identify participation in training refers to the last two years, such increases might reflect the availability of technical assistance since 2011 in the state of _Ceará_ . Another argument is that it may have taken some time for principals to participate in training and, consequently, evaluate its usefulness.

# **6.2 Selection and Training of Teachers**

The second part of our analysis relates to the selection and training of teachers. Table 4 presents the estimations for several teacher outcomes using Eq. (1). Panel A column (1) shows the results 31
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errors are clustered at the municipal level and shown in parenthesis.

|B. Selection and Classroom Hours<br>**if permanent**<br>**if temporary**<br>**20 Classroom**<br>**40 Classroom**<br>**Teacher**<br>**Teacher**<br>**Hours per wk**<br>**Hours per wk**<br>(3)<br>(4)<br>(5)<br>(6)<br>5_th_ Grade _−_Teachers<br>_−_0_._133_∗∗∗_<br>0_._057<br>_−_0_._162_∗∗∗_<br>0_._109_∗∗_<br>(0_._033)<br>(0_._023)<br>(0_._046)<br>(0_._054)<br>0_._058<br>0_._027<br>0_._033<br>0_._003<br>(0_._041)<br>(0_._029)<br>(0_._041)<br>(0_._042)<br>_−_0_._014<br>_−_0_._010<br>_−_0_._095_∗∗∗_<br>_−_0_._053<br>(0_._036)<br>(0_._037)<br>(0_._035)<br>(0_._042)<br>9_th_ Grade _−_Teachers<br>_−_0_._021<br>0_._076_∗∗_<br>_−_0_._081_∗∗∗_<br>0_._133_∗∗∗_<br>(0_._044)<br>(0_._033)<br>(0_._029)<br>(0_._049)<br>_−_0_._007<br>_−_0_._053<br>0_._015<br>_−_0_._029<br>(0_._041)<br>(0_._035)<br>(0_._012)<br>(0_._040)<br>_−_0_._068_∗_<br>0_._032<br>_−_0_._129_∗∗∗_<br>0_._012<br>(0_._039)<br>(0_._036)<br>(0_._018)<br>(0_._038)<br>**Teacher**<br>**Teacher**<br>**Teacher**<br>**Teacher**<br>his table presents the DD coefcients of RBF efects on teacher training,<br>_istema de Avaliação da Educação Básica_ (SAEB). Column (1) is for a<br>achers perceived the training as useful. column (3) is if teachers had an<br> for teachers with contracts of 20 or 40 hours per week. All regressions<br> _Pernambuco_ and _Paraíba_ as illustrated in Figure 1. The defnition of<br>municipality controls: the number of births in the municipality_−_year,<br>ded provided by _SAEB_; and a dummy for schools ofering from the 1_st_<br>up (as they are provided in 7 categories. It also includes: time trends,<br>ghted by school Size. The line "DD, Results_−_Based Financing" reports<br>ween RBF and pre_−_RBF periods. The line "DD, Teaching Assistance"<br>erence in the coefcients _rbf_ +_ta_ (or _rbf_(_re_) +_ta_ for 9_th_) and _rbf_ (or<br>e estimated impacts of reformulating the RBF model. Standard errors|
|---|
|aining<br>**if training**<br>**helped**<br>(2)<br>0_._001<br>(0_._008)<br>0_._011<br>(0_._006)<br>0_._078_∗∗∗_<br>(0_._023)<br>0_._017<br>(0_._011)<br>0_._120_∗∗∗_<br>(0_._034)<br>_−_0_._021<br>(0_._037)<br>**Teacher**<br>ercent level. T<br>naires in the _S_<br> considers if te<br> (5) and (6) is<br>_ande do Norte_,<br>sions include <br>l schools provi<br>es per age gro<br>cients are wei<br> the border bet<br> testing the dif<br> re" reports th|
|A. Tr<br>**If had**<br>**training**<br>(1)<br>**DD, Results**_−_**Based Financing (**_βrbf −βpre_**)**<br>_−_0_._087_∗∗_<br>(0_._035)<br>**DD, Teaching Assistance (**_βrbf_+_ta −βrbf_**)**<br>0_._115_∗∗∗_<br>(0_._026)<br>**DD, Results**_−_**Based Financing, re (**_βrbf_(_re_)+_ta −βrbf_+_ta_**)**<br>0_._057_∗_<br>(0_._029)<br>**DD, Results**_−_**Based Financing (**_βrbf −βpre_**)**<br>0_._075_∗∗_<br>(0_._033)<br>**DD, Teaching Assistance (**_βrbf_(_re_)+_ta −βrbf_(_re_)**)**<br>0_._088_∗∗∗_<br>(0_._027)<br>**DD, Results**_−_**Based Financing, re (**_βrbf_(_re_)_−βrbf_**)**<br>0_._007<br>(0_._027)<br>**Questionnaire Respondent**<br>**Teacher**<br>**Notes.** *** denotes signifcance at1percent, ** at5percent, and * at10p<br>selection and classroom hours. All outcomes come from teacher question<br>dummy equal to one teachers had training in the past 2 years. Column (2)<br>open_−_ended contract and column (4) is for temporary contracts. Columns<br>restrict to municipalities at the border between _Ceará_ and _Piauí_, _Rio Gr_<br>border considers the three immediate municipalities at each side. Regres<br>according to the _Sistema de Nascidos Vivos_ (SINASC); a dummy for rura<br>to the 9_th_ grades. The students controls include: if male, if white, dummi<br>municipal_−_specifc time trends, and border fxed_−_efects. Regression coef<br>the impacts of introducing the _RBF_ alone by comparing the diferences at <br>estimates the impacts of combining the RBF with technical assistance by <br>_rbf_(_re_) for 9_th_) periods. Finally, the line "DD, Results_−_Based Financing, <br>are clustered by municipality and shown in parenthesis.|

33
Table 4 indicates significant increases in the participation of teachers in training, particularly after the technical assistance periods. From Column (1), 5<sup>_th_</sup> grade teachers are 11 _._ 5 _pp_ more likely to participate in training, while 9<sup>_th_</sup> grade teachers are 8 _._ 8 _pp_ more likely than their counterparts across the border. Still in column (1), DD coefficients during RBF periods show negative impacts for 5<sup>_th_</sup> grade (8 _._ 7 _pp_ ) and positive impacts for 9<sup>_th_</sup> grade (7 _._ 5 _pp_ ). Similar to both grades, after TA teachers report significantly more that training was useful, reaching 12 _pp_ for 9<sup>_th_</sup> grade. Relative to the baseline difference, for either 5<sup>_th_</sup> or 9<sup>_th_</sup> grade, there is a significant increase in the percentage of teachers _Ceará_ enrolling in training and reporting that it was useful.

The second piece of evidence comes from Panel B, Table 4. Despite significant changes in the selection of principals, no clear pattern is seen for teachers in Figure 4, Table 4 columns (3) and (4). On the other hand, columns (5) and (6) suggest a strong substitution of teachers from 20hours per week contracts to 40-hours per week contracts. In column (5), it is possible to observe a decrease of 16 _._ 2 _pp_ in the percentage of 5<sup>_th_</sup> grade teachers with 20-hours per week contracts; for 9<sup>_th_</sup> grade, the decrease is 8 _._ 1 _pp_ . At the same time, the percentage of teachers reporting a 40-hour per week contracts in column (6) increases by 10 _._ 9 _pp_ for 5<sup>_th_</sup> grade and 13 _._ 3 _pp_ for 9<sup>_th_</sup> grade. This reduction repeats when the RBF is reformulated for both grades. Therefore, while the TA impacts on the incidence and quality of training, introducing the RBF model results in significantly more teachers with 40-hours per week contracts than on the other side of the border.

If teacher training and selection improves pedagogical skills and learning, the results from Table 4 may partially explain how the RBF mechanism and TA influence student outcomes. Previous literature reinforces this argument. Angrist and Lavy (2001) evaluate the impacts of in _−_ service training for teachers in Jerusalem and find significant positive effects on test scores. Bressoux et al. (2009) show that teacher training substantially improves student test scores in mathematics in France. Therefore, better training and longer classroom hours are potential channels explaining 34
our findings.<sup>19</sup>

# **6.3 Pedagogical Support**

Table 5 presents the impacts of RBF and TA policies on pedagogical support. It divides the analysis into three parts: Panel A shows if teachers are more likely to check school homework in mathematics (Column (1)) and Portuguese (Column (2)); Panel B concentrates on book quality, according to teachers’ perspectives<sup>20</sup> ; Panel C shows if teachers cover more than 80% of the curriculum in column (4) and if they cover less than 40% in column (5). Table 5 reports the results for 5<sup>_th_</sup> and 9<sup>_th_</sup> grades.

Table 5 suggests that teachers in _Ceará_ are significantly more likely to check school homework and " " " " see their pedagogical materials as _good_ or _great_ than their cross-border counterparts. Table 5 column (1) shows that 1 _._ 8 _pp_ more teachers check school homework in mathematics, and 2 _._ 3 _pp_ in Portuguese, when technical assistance was introduced. For 9<sup>_th_</sup> grade, the results are generally insignificant. Similarly, improvements in textbook quality in Panel B are only observed for 5<sup>_th_</sup> grade. That can be seen in column (3) by significant increases of 9 _._ 4 _pp_ with TA and more than a 10 _._ 3 _pp_ increase after RBF was reformulated. If the use of better pedagogical materials influences performance as previous literature suggests (Leme et al. 2012), textbooks of higher quality may explain the improvements of student performance in 5<sup>_th_</sup> grade in _Ceará_ .

Another potential channel explaining our findings comes from Panel C columns (4) and (5). Column (4) Panel C shows 5<sup>_th_</sup> grade teachers in _Ceará_ were 8 _._ 1 _pp_ more likely to cover 80% of the curriculum after TA was implemented than teachers on the other side of the border. The effect

> 19Further analysis using the probability of teachers having a master’s shows insignificant results for both grades. So, we cannot consider that better-certified teacher is a channel explaining our findings. (See Ehrenberg and Brewer (1994) and Clotfelter et al. (2006) for similar results in the literature.)

> 20The question used in _SAEB_ is: " _What is your opinion about the book(s) used in the subject you lecture in the class_ ?". The " _book quality_ " variable in Panel B equals one when teachers say " _Good_ " or " _Great_ " and zero otherwise.

35
Table 5 Pedagogical Practices, Textbook Quality and Curriculum Coverage (Clustered Standard Errors)

||A. Pedagogica|l Practices|B. Book Quality|C. Curricu|lum Coverage|
|---|---|---|---|---|---|
||**Teacher Checks**<br>**Maths Homework**<br>(1)|**Teacher Checks**<br>**Port Homework**<br>(2)|**Textbook**<br>**is good/great**<br>(3)|**Covers**<br>_≥_80%<br>(4)|**Covers**<br>_≤_40%<br>(5)|
|||5<sup>_th_ </sup>Grade|_−_Teachers/Students|||
|**DD, Results**_−_**Based Financing (**_β_<sup>_rbf _</sup>_−β_<sup>_pre_</sup>**)**|0_._008|0_._006|_−_0_._051|0_._002|0_._018|
||(0_._010)|(0_._010)|(0_._056)|(0_._032)|(0_._019)|
|**DD, Teaching Assistance (**_β_<sup>_rbf_+</sup><sup>_ta _</sup>_−β_<sup>_rbf_</sup>**)**|0_._018<sup>_∗_</sup>|0_._023<sup>_∗∗_</sup>|0_._094<sup>_∗∗_</sup>|0_._081<sup>_∗_</sup>|_−_0_._036<sup>_∗∗_</sup>|
||(0_._010)|(0_._010)|(0_._046)|(0_._043)|(0_._017)|
|**DD, Results**_−_**Based Financing, re (**_β_<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_ta _</sup>_−β_<sup>_rbf_+</sup><sup>_ta_</sup>**)**|0_._010|0_._004|0_._103<sup>_∗∗_</sup>|0_._010|0_._004|
||(0_._009)|(0_._009)|(0_._043)|(0_._036)|(0_._011)|
|**# of Observations**|225_,_869|224_,_593|2_,_310|2_,_310|2_,_310|
|**Adj. R**_−_**squared**|0_._006|0_._634|0_._084|0_._549|0_._484|
|||9<sup>_th_ </sup>Grade|_−_Teachers/Students|||
|**DD, Results**_−_**Based Financing (**_β_<sup>_rbf _</sup>_−β_<sup>_pre_</sup>**)**|0_._016<sup>_∗_</sup>|0_._010|0_._000|0_._051|_−_0_._005|
||(0_._008)|(0_._008)|(0_._038)|(0_._042)|(0_._014)|
|**DD, Teaching Assistance (**_β_<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_ta _</sup>_−β_<sup>_rbf_(</sup><sup>_re_)</sup>**)**|0_._009|0_._010|_−_0_._014|0_._081<sup>_∗∗_</sup>|0_._018<sup>_∗∗_</sup>|
||(0_._009)|(0_._008)|(0_._038)|(0_._039)|(0_._008)|
|**DD, Results**_−_**Based Financing, re (**_β_<sup>_rbf_(</sup><sup>_re_)</sup> _−β_<sup>_rbf_</sup>**)**|0_._007|0_._006|0_._034|0_._116<sup>_∗∗∗_</sup>|_−_0_._027<sup>_∗∗∗_</sup>|
||(0_._008)|(0_._008)|(0_._044)|(0_._042)|(0_._009)|
|**# of Observations**|191_,_503|191_,_764|2_,_310|2_,_310|2_,_310|
|**Adj. R**_−_**squared**|0_._005|0_._005|0_._084|0_._549|0_._484|
|**Questionnaire Respondent**|**Student**|**Student**|**Teacher**|**Teacher**|**Teacher**|

**Notes.** *** denotes significance at 1 percent, ** at 5 percent, and * at 10 percent level. This table presents the effects of RBF and technical assistance on pedagogical practices, textbook quality, and curriculum coverage. Data comes from teacher questionnaires in the _Sistema de Avaliação da Educação Básica_ (SAEB) and all regressions are restricted to municipalities at the border between _Ceará_ and its adjacent states as shown in Figure 1. The regressions include municipality controls for the number of births per year in _Sistema de Nascidos Vivos_ (SINASC), a dummy for rural schools (SAEB); if schools offer from the 1<sup>_st_</sup> to the 9<sup>_th_</sup> grade. A time trend, municipal-specific trends, and a border fixed-effect are also included. The teacher/student controls are: if male, if white, and dummies per age group. Weights for school size, in terms of number of students, are considered in columns (3) to (5). The “ _DD_ , Results _−_ Based Financing" shows the _RBF_ impacts. The “ _DD_ , Teaching Assistance” refers to the effects of introducing the technical assistance component and “ _DD_ , Results _−_ Based Financing, re” shows _DD_ estimates reformulating the RBF mechanism. The baseline difference at the border is _β_<sup>_pre_</sup> . Standard errors are clustered by municipality and shown in parenthesis.

on curriculum coverage is even stronger for teachers in 9<sup>_th_</sup> grade. In addition to the 8 _._ 1 _pp_ increase during TA periods, teachers were 11 _._ 6 _pp_ more likely to cover 80% of the curriculum after RBF reformulation. However, reinforcing this argument, an opposite movement is observed in column (5). It shows a 3 _._ 6 _pp_ decrease in the percentage of 5<sup>_th_</sup> grade teachers reporting covering less than 40% of the curriculum during the TA periods, and 2 _._ 7 _pp_ less likely among 9<sup>_th_</sup> grade teachers after RBF was reformulated. In the same way that textbook quality plays a prominent role in explaining the gains in performance for students in 5<sup>_th_</sup> grade, greater curriculum coverage by teachers seems to be an important driver for learning improvement in 9<sup>_th_</sup> grade.

Figure 6 complements Table 5 by showing that _Ceará_ is distributing textbooks where they are scarcer. Using school principal questionnaires from SAEB and plotting the _DD_ coefficients from Eq. (2), Figure 6 shows no change in the provision of pedagogical materials by the municipal council (blue bars), but significant decreases in the incidence of schools reporting a lack of text36
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content and language barriers hampered the capacity of textbooks to improve learning in Kenya. In contrast, textbooks in _Ceará_ overcome both limitations: they are designed for students who are lagging behind in their grade and are produced in students’ native language (Portuguese).

# **6.4 Municipal Public Spending**

An important aspect of _Ceará_ ’s RBF model is that fiscal resources conditioned on education performance do not necessarily need to be spent on education. If mayors foresee the need to build a new hospital or a bridge or even invest in security, there is nothing that prevents them from using the resources disbursed based on education performance. The idea underlying the fact that the RBF resources are not earmarked to education expenditures is to generate stronger incentives for mayors to prioritize improving learning. This section estimates whether RBF, and TA, affects municipal public spending. Table 6 presents the estimation results on several public spending categories.

The effect related to RBF on municipal public spending is displayed in Panel A of Table 6. In column (1), the RBF increased public spending on education per pupil by 1 _._ 2% relative to the baseline mean. For the other sectors, the variations are even larger. Public spending per capita on sanitation, housing, and urbanization increased by 13 _._ 9% with the introduction of the RBF. On social spending (i.e., social security and social assistance), per capita spending increased by 10 _._ 5%, and by 21 _._ 6% for spending on culture, sports and leisure. Municipal public spending on health also increased with the introduction of the RBF, but the coefficient is statistically significant only at the 10% level. As a whole, the introduction of the RBF contributed to an increase of 2% in municipal public spending in _Ceará_ relative to the baseline mean when compared with their counterparts in the adjacent states.

Panel B displays the incremental effect of combining TA and RBF. The introduction of teaching 38
Table 6 The RBF effects on Public Spending of Municipalities (Clustered Standard Errors)

||Education<br>(1)|Health<br>(2)|Sanitation,<br>Housing and<br>Urbanization<br>(3)|Social<br>(4)|Sport,<br>Culture<br>and Leisure<br>(5)|Total<br>spending<br>(6)|
|---|---|---|---|---|---|---|
|**A. DD, Results**_−_**Based Financing**<br>_β_<sup>_rbf _</sup>_−β_<sup>_pre_</sup>|0.095***<br>(0.021)|0.223*<br>(0.125)|0.671***<br>(0.139)|0.462***<br>(0.090)|0.691***<br>(0.112)|0.153***<br>(0.024)|
|**B. DD, Teaching Assistance**|||||||
|_β_<sup>_rbf_+</sup><sup>_ta _</sup>_−β_<sup>_rbf_</sup>|0.038|-0.259*|0.081|0.054|-0.015|-0.05|
||(0.031)|(0.141)|(0.175)|(0.125)|(0.173)|(0.033)|
|**C. DD, Results**_−_**Based Financing, reformulated**<br>_β_<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_ta _</sup>_−β_<sup>_rbf_+</sup><sup>_ta_</sup>|-0.006|0.039|-0.213|-0.056|-0.134|-0.024|
||(0.024)|(0.070)|(0.174)|(0.184)|(0.182)|(0.021)|
|**Variation relative to the baseline mean**<br>|||||||
|_β_<sup>_rbf _</sup>_−β_<sup>_pre_</sup><br>|1.16%|3.70%|13.88%|10.46%|21.57%|2.05%|
|_β_<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_ta _</sup>_−β_<sup>_rbf_+</sup><sup>_ta_</sup>|0.46%|-4.30%|1.68%|1.22%|-0.47%|-0.67%|
|_β_<sup>_rbf_(</sup><sup>_re_)+</sup><sup>_ta _</sup>_−β_<sup>_rbf_+</sup><sup>_ta_</sup>|-0.07%|0.65%|-4.41%|-1.27%|-4.18%|-0.32%|
|**Spending Defnition**|per student|per capita|per capita|per capita|per capita|per capita|
|**Dep. var. mean**|8.193|6.021|4.834|4.417|3.204|7.466|
|**Dep. var. SD**|0.375|0.504|0.948|0.843|0.988|0.276|
|**# of municipality Observations**|4,163|4,160|4,256|4,256|4,256|4,163|
|**Adj. R**_−_**Squared**|0.702|0.223|0.065|0.13|0.078|0.381|

**Notes.** _∗∗∗_ denotes significance at 1 percent, _∗∗_ at 5 percent, and _∗_ at 10 percent level. The dependent variables come from National Treasury Bureau ( _Secretaria do Tesouro Nacional_ (STN). All regressions restrict the sample to the 330 municipalities at the border between Ceará and adjacent states. The definition of border considers the three imediate municipalities at each side of _Ceará_ and _Piaúi_ , _Rio Grande do Norte_ , _Pernambuco_ and _Paraíba_ . municipality controls include the number of births in the municipality _−_ year according to the _Sistema de Nascidos Vivos_ (SINASC), and GDP per capita as provided by IBGE. The vector of dependent variables includes: (1) Natural log of education spending per student; (2) Natural log of health spending per capita; (3) Natural log of spending on sanitation, housing and urbanism per capita; (4) Natural log of spending on social assistance and social security per capita; (5) Natural log of spending on sport, leisure and culture per capita; (6) Natural log of total spending per capita. Public spending variables are deflated by the General Price Index (2017 = 100) of the _Fundação Getúlio Vargas_ . Time trends and Municipal specific time trends are included. To compare municipalities close geographically, sharing the same state border, all regressions include Border Fixed Effects. The bottom of each column presents in Panel A the DD estimates of RBF impacts, Panel B presents the effects after introducing teaching assistance, the TA component in our model; and Panel C shows the estimates of reformulating the RBF to weights for minimum standards. Standard errors are clustered by municipality and shown in parenthesis.

assistance did not affect the public spending of municipalities, especially on education. The exception is the reduction in health spending per capita (see column (2)), about _−_ 4 _._ 3% relative to the baseline mean but significant only at the level of 10%. The health sector shares some complementary services with education, such as health prevention (e.g., obesity prevention and immunization), guidance on sexual and reproductive health, etc. The efficient provision of such services with the introduction of teaching assistance might have contributed to reducing health spending, especially on primary health care. Panel C, in turn, shows that the reformulation of the RBF did not have implications on municipal public spending. The large gains in leaning with the introduction of TA and the reformulation of the RBF (see Panels B and C of Table 2) were 39
attained without increasing spending on education per pupil.

An emerging literature investigates the importance of how governments are financed for public investment. Gadenne (2017) argues that increases in municipal governments spending based on tax revenues tends to benefit citizens more than increases based on grants. In the specific cases of constitutional transfers, Litschig and Morrison (2013) show that extra transfers from the federal government to municipalities based on the _Fundo de Participação dos Municípios_ (FPM) increased local public spending per capita by approximately 20%, leading to an increase of 7% in schooling and 4 _pp_ in literacy rates. Carvalho Filho and Litschig (2020) show that extra resources from the FPM transfers not only increased spending on education but also on housing, urban infrastructure, and transportation by about 20% in early 1980s. More recently, Cruz and Silva (2020) have analyzed the importance of budget structure for government spending in education by estimating the effects of a minimum spending rule and a set of intergovernmental transfers. The authors show that the minimal spending rule decreases the efficiency of education spending for high-spending municipalities, despite increasing the education investment of low-spending municipalities.

Our results are in accordance with this literature and indicate that the introduction of RBF led municipalities to increase their spending per capita not only in the provision of education, but also of other public services. The reforms have led to an increase in the total public spending of municipalities in _Ceará_ compared with municipalities across the border. In the case of education services, the introduction of the RBF led mayors to invest in the quality of school facilities, such as internet connections, computer labs, libraries, and sports courts (see Table _A_ 4 in the appendix). School facilities improved with the introduction of TA as well, suggesting that mayors see them as complementary inputs to improve learning (Glewwe and Kremer 2006; Glewwe and Muralidharan 2016). For Latin American countries, evidence has shown that the provision of school facilities improves student learning, despite the lack of high-quality research (Cuesta et al. 2016).

40
# **7 Conclusion**

This paper presents new evidence that fiscal incentives to local governments can be an effective tool to improve learning. Exploring a results _−_ based financing (RBF) reform in the state of _Ceará_ (Brazil) that redistributes resources to municipalities based mainly on education outcomes, we investigate whether education incentives for mayors affect learning. While vast literature has already shown the importance of financial incentives for students, teachers, and schools for academic performance, little is known about whether similar mechanisms targeting head of local governments would produce similar impacts. Because city mayors in Brazil are responsible for delivering most educational services and to allocate budget to programs, distributing fiscal resources in exchange for better education outcomes presents itself as a valuable option for public policy.

Comparing test scores in schools located in municipalities at the border between _Ceará_ and adjacent states, we show that the RBF increased student performance in Portuguese and mathematics by approximately 3 months’ learning equivalent for 9<sup>_th_</sup> grade. For 5<sup>_th_</sup> grade, no impacts were found. For instance, when the reform combines RBF and technical assistance (TA) to municipalities (i.e., provision of textbooks, training, and knowledge exchange between schools) the _RBF_ + _TA_ increased learning outcomes around 3 months’ learning equivalent for both grades, but now significant and slightly higher for students in 5<sup>_th_</sup> grade. Investigating the role of each TA component, it seems that providing textbooks and training teachers were the main drivers of TA impacts.

Our findings also confirm the concern that RBF programs increase inequality. Quantile estimates suggest that implementing the RBF produces effects that are three, sometimes four, times higher for students from 0 _._ 20 higher quantiles than for students from the top 0 _._ 20 quantiles, increasing learning gaps. This scenario only changes after the reformulation of the RBF criteria penalized municipalities based on the percentage of students performing below minimum threshold scores. During the period of the reformulated RBF, the impacts are smaller than in previous periods 41
0 _._ 92SD (or 2 months of schooling) but with strong implications for distribution, with greater impacts on 9<sup>_th_</sup> grade students from low quantiles and significantly reduced impacts for 5<sup>_th_</sup> grade students.

We use detailed data on teachers, principals and public spending to analyze several mechanisms for these findings. First, there are significant reductions in principals “ _Designated_ " to schools and replaced by those going through formal selection processes. Second, there is a strong indication that both principals and teachers in _Ceará_ are more likely to be involved in training and report it as useful for their daily work compared to similar principals and teachers in the immediate municipalities outside _Ceará_ ’s border. Fourth, after the RBF reform, teachers in _Ceará_ are more likely to be hired on 40-hour contracts (both grades), check school homework more often (5<sup>_th_</sup> grade), and cover at least 80% of the curriculum (both grades). Finally, schools in _Ceará_ report significantly less frequent lack of pedagogical materials at the same time that significantly more teachers consider these books to be at least “good”.

Exploring different formats of the RBF model in _Ceará_ in time provides a clear contribution to public policy design. Particularly, introducing the RBF in combination with technical assistance boosts learning impacts in at least two _−_ fold relative to RBF alone. Elaborating textbooks and providing training to teachers, based on student test scores, is the main source of these impacts. Another important contribution to policy design is that redistributing fiscal resources exclusively based on education performance tends to widen learning gaps. Such inequalities are significantly reduced, when penalizing municipalities where there is a high percentage of students below certain thresholds of performance.

All these gains in student learning in _Ceará_ were obtained without increasing public spending on education. This means that the large gains in student learning and education quality followed the efficient allocation of public spending to municipalities in _Ceará_ .

42