metadata: authors: 0: author: Bastos,Paulo S. R.
1: author: Straume,Odd Rune
count: Brazil
docna: 0: docna: Preschool education in Brazil : does public
            supply crowd out private enrollment ?
docty: Policy Research Working Paper
subtopic: Early Childhood Development,Reproductive Health,Early Child and Children&#39,Early Child and Children's Health,Nutrition,Effective Schools and Teachers,Educational Institutions & Facilities,Educational Sciences,Small Private Water Supply Providers,Town Water Supply and Sanitation,Sanitation and Sewerage,Engineering,Water Supply and Sanitation Economics,Water and Human Health,Health and Sanitation,Sanitary Environmental Engineering,Environmental Engineering,Tertiary Education
teratopic: Water Supply and Sanitation,Environment,Science and Technology Development,Health, Nutrition and Population,Education,Water Resources
abstracts: cdata!: This paper examines whether an expansion
            in the supply of public preschool crowds out private
            enrollment. The paper uses rich data for municipalities in
            Brazil from 2000 to 2006, where federal transfers to local
            governments change discontinuously with given population
            thresholds. The results from a regression-discontinuity
            design reveal that larger federal transfers lead to a
            significant expansion of local public preschool services,
            but show no evidence of crowding out of private enrollment.
            This finding is consistent with a theory in which households
            differ in their willingness to pay for preschool services,
            and private suppliers optimally adjust prices in response to
            an expansion of lower-quality, free-of-charge public supply.
geo_reg_key: 517191
repnme: repnme: Preschool education in Brazil : does public
            supply crowd out private enrollment ?
display_title: Preschool education in Brazil : does
            public supply crowd out private enrollment
listing_relative_url: /research/2016/02/25959162/preschool-education-brazil-public-supply-crowd-out-private-enrollment
topicv3: Teachers Management m1326119 1523,Tertiary Education m1326349 482,Sanitation m1326453 2000,Education m1327048 470,Preschool Education m1327265 1585
publishtoextweb_dt: 2016-02-21T00:00:00Z
historic_topic: Water Supply and Sanitation,Environment,Science and Technology Development,Health, Nutrition and Population,Education,Water Resources
no_of_pages: 44
author_keys: 0: author_key: 1210378
model_extractions: WPS7573 Policy Research Working Paper 7573 Preschool Education in Brazil Does Public Supply Crowd Out Private Enrollment?

_Paulo Bastos Odd Rune Straume_ Development Research Group Trade and International Integration Team February 2016
Policy Research Working Paper 7573

# **Abstract**

This paper examines whether an expansion in the supply of public preschool crowds out private enrollment. The paper uses rich data for municipalities in Brazil from 2000 to 2006, where federal transfers to local governments change discontinuously with given population thresholds. The results from a regression-discontinuity design reveal that larger federal transfers lead to a significant expansion of local public preschool services, but show no evidence of crowding out of private enrollment. This finding is consistent with a theory in which households differ in their willingness to pay for preschool services, and private suppliers optimally adjust prices in response to an expansion of lower-quality, free-of-charge public supply.

This paper is a product of the Trade and International Integration Team, Development Research Group. 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://econ.worldbank.org. The authors may be contacted at pbastos@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
# Preschool Education in Brazil:

Does Public Supply Crowd Out Private Enrollment?<sup>_∗_</sup> Paulo Bastos<sup>_†_</sup> Odd Rune Straume<sup>_‡_</sup> _JEL Classification_ : D12; I21; I28; L21; O15 _Keywords_ : Preschool education; private and public provision; crowding-out.

> _∗_ We thank three anonymous referees for very helpful comments and suggestions. Odd Rune Straume acknowledges the financial support provided by the European Regional Development Fund (ERDF) through the Operational Program Factors of Competitiveness (COMPETE); and by national funds received through the Portuguese Foundation for Science and Technology (FCT) under the research grant PEst-C/EGE/UI3182/2013. Research for this paper has been supported in part by the World Bank’s Multidonor Trust Fund for Trade and Development and through the Strategic Research Partnership on Economic Development.

> _†_ Corresponding author. Development Research Group, The World Bank, 1818 H Street NW, Washington DC, United States. Phone: +12024734332. Email: pbastos@worldbank.org

> _‡_ Department of Economics/NIPE, University of Minho; and Department of Economics, University of Bergen. Email: o.r.straume@eeg.uminho.pt
# **1 Introduction**

Public policies aimed at increasing access to formal preschool education are high on the political agenda in a number of countries. There are probably two main reasons for this. First, a higher supply of formal preschool education is by many seen as a crucial tool for achieving higher (female) participation rates in the labor market.<sup>1</sup> Second, there is now a sizable body of evidence for both developed and developing countries indicating that there are important long-term individual and public benefits to enrollment in preschool education (Cunha et al., 2006; Engle et al. 2007, 2011; Almond and Currie, 2011; Behrman et al. 2013).

Access to formal child care is a particularly important policy issue in developing countries, where enrollment rates are generally much lower, and where private institutions constitute a much larger share of the formal preschool sector, than in developed countries.<sup>2</sup> The generally low and uneven access to preschool education is arguably reflected in the observation of large disparities in cognitive development at the start of primary school in many developing countries. For example, Paxson and Schady (2007) and Schady et al. (2015) document a widening gap in cognitive development between poor and non-poor children in several Latin American nations.<sup>3</sup> After entering primary school, the gap tends to remain constant. Why do these gaps emerge and why do they stop growing? In light of the previously cited studies, a possible explanation lies in the differences in opportunities available _−_ in particular, access to formal child care _−_ to poor and non-poor children in their early years.

In order to remedy such problems, an available policy option is to increase the public supply of (free or widely affordable) preschool education. The intended effects of such a policy are two-fold: (i) to provide more equitable access and (ii) to increase the total supply 1See, e.g., Havnes and Mogstad (2011) and references therein. See also Besamusca et al. (2015) for further discussions and results on the relationship between pre-school enrollment and female labor force participation.

> 2See UNESCO (2008) for statistics and further information about formal preschool in developed and developing countries. Bastos and Cristia (2012) examine supply and quality choices of private suppliers in the city of S ̃ao Paulo, Brazil.

> 3Paxson and Schady (2010) show that conditional cash transfers are unlikely to contribute towards narrowing this gap.

2
of formal child care. However, the successfulness of such a policy depends crucially on the extent to which increased public supply crowds out existing private supply, which in turn depends on how private preschool providers respond strategically to increased competition from public providers. Do private providers respond by lowering their prices and competing more aggressively in all market segments? Or do they react by increasingly targeting higherincome households that do not find public providers attractive? If an expansion in free-ofcharge public supply simply induces households to switch from high-quality private suppliers to lower-quality public centers, negative impacts on child development cannot be excluded.

In the present paper we analyze these questions empirically by examining the effect of changes in the supply of public child care services on private child care provision in Brazil. We use rich municipal-level panel data covering the period 2000-2006 to analyze the effect of increased availability of public child care centers on the quantity of private supply, as measured by private enrollment rates and number of private centers. We also check whether increased public supply has any impact on the quality of private child care, as measured by group size, teacher qualification and quality of infrastructure. To plausibly identify exogenous variation in public supply, we exploit unique features of the allocation mechanism of federal transfers to municipalities in Brazil, where the transfers received by local governments exhibit a non-linear and non-monotonic relationship with given population estimates. Results from a regression-discontinuity design reveal that larger federal transfers to a given municipality lead to a significant expansion of public preschool services (as measured by the number of municipal centers and enrollment), but show no evidence that such an expansion crowds-out private enrollment. If anything, the results suggest that private enrollment also increases. We also find no evidence of adverse effects on the quality of private provision.

To guide the interpretation of our empirical results, we develop a simple theoretical model of vertical differentiation, analyzing the optimal pricing response of a private child care provider to entry of a public competitor. In the model, public preschool education is free of charge (zero price), whereas private providers optimally set prices in a profit-maximizing way and supply higher-quality services. Demand for preschool services comes from two 3
different segments of households, with consumers who differ in average income and therefore differ in willingness-to-pay for preschool education. The private provider optimally chooses between a high-price strategy, serving consumers with high willingness-to-pay only, and a low-price strategy, serving consumers from both segments. An expansion of public supply has ambiguous effects on private enrollment, depending on the difference in willingnessto-pay across consumer segments and on the relative size of each segment. Crowding-out effects of more public provision are less likely when the differences in willingness-to-pay across consumer segments are relatively large.

Our paper clearly relates to the more general literature on crowd-out effects of government funding, in particular the strand of the literature dealing with crowd-out effects of public provision of private goods. However, the existing empirical research has mainly been devoted to health care markets. Cutler and Gruber (1996) and Gruber and Simon (2008) analyze the extent to which public health insurance crowds out private insurance, while Cohen et al. (2013) study crowd-out effects of public providers in the US market for outpatient substance abuse treatment. In each case, sizable crowd-out effects are identified.

Among the relatively few empirical studies on child care markets in this strand of the literature, recent contributions include Bassok et al. (2014a) and Bassok et al. (2014b), who find evidence of significant crowding-out of private providers as a result of increased public provision in the child care markets in Oklahoma and Florida, respectively. Cascio and Schanzenbach (2013) also find evidence of crowd-out effects from the expansion of public preschool in Oklahoma and Georgia, particularly for high-income families. Similarly, Cascio (2009) finds evidence of sizable crowd-out effects using US census data over five decades.<sup>4</sup> These mixed findings for the US and Brazilian settings can be rationalized in the context of our model. As noted above, crowding-out effects of more public provision are less likely when the differences in willingness-to-pay across consumer segments are relatively large. These differences are expected to be generally larger in the Brazilian context, where the levels of inequality in parental income are among the highest in the world (World Bank,

> 4There is also a related recent study by Owens and Rennhoff (2012), who examine competition between for-profit and nonprofit child care providers in four Tennessee counties and find no evidence that nonprofit providers crowd out for-profit ones.

4
## 2004).

While there is very little empirical literature on the response of private providers to increased public supply of child care, there exists a considerable literature on the effect of public (or subsidized) child care provision on maternal labor supply, which is a related but still distinctly different issue. Although the reported results from this strand of the literature are quite heterogeneous, most recent studies (applying quasi-experimental approaches) find that increased public financing of child care tends to crowd out existing child care provision, quantitatively ranging from moderate crowd-out effects (e.g., Baker et al., 2008) to almost complete crowd-out with practically no effect on maternal labor supply (e.g., Cascio, 2009, and Havnes and Mogstad, 2011). However, these studies are not always able to distinguish whether public child care provision crowds out private provision of _formal_ or _informal_ child care. While this distinction is irrelevant for the question of maternal labor supply, it is of course crucial if the policy aim is to increase the total supply of formal child care in order to reap the long-term benefits of increased preschool attendance.

The rest of the paper is organized as follows. In the next section we provide information about the institutional characteristics that are important for the implementation of our empirical analysis, and provide a detailed description of the data. The empirical method and results are presented and discussed in sections 3 and 4, respectively. In Section 5 we present a simple theoretical framework to guide the interpretation of our empirical results, where we relate the key model assumptions to the Brazilian reality. Finally, some concluding remarks are given in Section 6.

# **2 Institutional background and data**

This section describes the institutional setting underlying the empirical analysis and the data employed. We first outline the rules determining the allocation of federal transfers across Brazilian municipalities and describe the corresponding data. We then move on to describing the system governing the provision of formal preschool services, as well as the data on public and private preschool providers.

5
# **2.1 Federal transfers to municipal governments**

Brazil has a highly decentralized system of government. Local governments receive large sums of public funds in the form of intergovernmental transfers, and are responsible for an important share of public goods provision, notably in the domain of education and culture, health and sanitation, social assistance and local infrastructure.

A single federal fund _−Fundo de Participa ̧c ̃ao dos Munic ́ıpios_ (FPM) _−_ accounts for about 75% of all federal transfers and 40% of total municipal revenue. Established by the federal constitution, this fund consists of automatic federal transfers to municipal governments. At least 15% of total FPM transfers received by each municipality must be spent on education, 15% must be spent on health care, while the remaining is unrestricted.

The rules governing the allocation of FPM transfers across municipalities provide unique features for our empirical analysis. In particular, the amount of FPM funds transferred to each municipality in a given year depends on population size in a discontinuous way. As discussed in detail below, these discontinuities provide a useful source of exogenous variation in municipal funds available to local governments, part of which must be spent on municipal education.<sup>5</sup> While there is no systematic evidence on how municipalities allocate this additional revenue across the various expenditure items, it is plausible to assume that a significant proportion of such funds is devoted to expanding the supply of municipal preschool education.

The FPM allocation mechanism groups municipalities into population intervals. These intervals determine the coefficients employed to share total state resources earmarked for the FPM. Municipalities in higher population brackets have higher coefficients, and hence receive larger transfers. Each of the 26 federal states receives a different share of the total resources earmarked for FPM.<sup>6</sup> Thus, in a given year, two municipalities from the same state will receive identical transfers if they are in the same interval. Specifically, let _FPMikt_ be the total _FPM_ transfers received by municipality _i_ in state _k_ in year _t_ . The revenue-sharing

> 5The allocation mechanism described below does not apply to municipalities that are state capitals, which are therefore excluded from the analysis.

> 6The federal district (Brasilia) is excluded from the analysis because it contains only one municipality.

6
rule is: where _FPMkt_ is the amount of resources allocated to state _k_ in year _t_ , and _θi_ is the FPM coefficient of municipality _i_ based on its population size.

Due to sample size restrictions, we limit our attention to municipalities with less than 50,940 inhabitants. These municipalities account for about 90% of Brazilian municipalities and 1/3 of the population. The provision of public goods and services in these locations is primarily financed by intergovernmental transfers from the federal and state governments _−_ local taxes represent only about 6% of fiscal revenue. The second column of Table 1 displays the FPM coefficients applied to each population interval. We focus our attention on the initial seven thresholds: 10,189; 13,585; 16,981; 23,773; 30,564; 37,356; and 44,148. The intervals between the initial three thresholds are equal to 3,396, whereas the intervals between the subsequent thresholds amount to twice as much (6,792). For symmetry, we exclude municipalities with fewer than 6,793 inhabitants. In light of these restrictions, it is important to emphasize that the results reported below are specific to the municipalities that are included in the sample, which excludes both very large municipalities and very small ones.

The coefficient _θi_ is assigned to a given municipality by _Tribunal de Contas Uni ̃ao_ (TCU) on the basis of population estimates for the previous year. These population estimates are calculated yearly by _Instituto Brasileiro de Geografia e Estat ́ıstica_ (IBGE), the national statistical institute. IBGE is independent from the government and employs a top-down approach in producing these estimates: municipal-level estimates must be consistent with the state-level estimates; the latter must in turn be consistent with population estimates of the whole country (which draw on birth and mortality rates, and net immigration between Censuses).

However, IBGE population estimates for a given year do not perfectly predict the FPM transfers that each municipality effectively receives in the subsequent year. As noted by Brollo et al. (2013), reasons for such discrepancies may include: (i) imperfect adjustments 7
of the coefficients assigned to municipalities that split during the period of analysis; (ii) other distortions in the application of the FPM allocation procedure, which is not audited.

# **2.2 Data on FPM transfers and population**

We use data on FPM transfers received by each municipality and the IBGE population estimates (the key variables of the FPM revenue-sharing mechanism). Data on FPM transfers for 2000-2006 are made available online by _Tesouro Nacional_ , while population estimates can be obtained in the IBGE website. Using these data, we apply the allocation rule described above to construct the “theoretical transfers” that each municipality should receive in each year. The amount of federal transfers that each municipality receives should be computed according to the IBGE population estimates sent to TCU in the previous year. Hence we use yearly population estimates for the period 1999-2005.

The third and fourth columns of Table 1 report summary statistics by population interval on actual and theoretical FPM transfers. We observe that average actual transfers within intervals are closely aligned with theoretical transfers. We also observe that municipalities in the proximity of the first four thresholds account for about 87% of the observations. Figure 1 plots actual and theoretical FPM transfers over the period 2000-2006 against the corresponding population estimates. The upper-left (lower-left) figure in this figure depicts effectively received (theoretical) transfers, while the seven vertical lines mark the position of the FPM population thresholds. The right panel displays similar associations, but where FPM transfers (actual or theoretical) are averaged over cells of 100 inhabitants, as well as the smoothed average of transfers (represented by the solid line) computed independently within each interval. All diagrams show clear discontinuities at the FPM thresholds. These are somewhat more noisy in the case of actual transfers, suggesting that there exist some cases where FPM transfers are imperfectly assigned to municipalities.<sup>7</sup>

> 7Theoretical transfers exhibit some heterogeneity within intervals due to the different share received by each state.

8
# **2.3 Preschool provision**

According to Brazilian law, in the period of analysis preschool services were provided to children aged between 4 and 6. There are two types of preschool providers:

- **(i)** Public preschool centers which are run either by the municipality or the state.

- **(ii)** Private preschool centers which are run independently.

Public centers are financed by the public budget, predominately at the municipal-level, though a number of states have a small number of state public preschool centers as well. Legal provisions mandate that parents seeking to enroll their children in public preschool must do so in a center that is located near their home. Enrollment in public centers is not subject to tuition fees and these centers cannot reject children unless demand exceeds capacity.

Private preschool providers are generally for-profit and have full discretion over tuition fees. While there is no systematic information on prices charged by private centers, data from _Pesquisa de Padr ̃oes de Vida_ for 1996/1997 reveal that households whose children were enrolled in private child care spent about 1,000 Brazilian _reais_ on tuition fees per year, on average. Table 2 reports summary statistics on the household income of families whose children are enrolled in public and private preschool. In line with the price differences described above, we observe that the monthly income of households where children are enrolled in private preschool tends to be considerably higher than that of families that enroll their children in public preschool: mean income is almost twice as large, and marked differences are also observed across several other moments of the distribution of monthly household income.

The market for private preschool services remains highly independent and unregulated. Although education authorities set minimum recommended standards on teacher qualifications and group size, centers were not bound by strict legal constraints on these variables. By contrast, quality standards in the public sector are under direct control of local and central authorities.

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# **2.4 Data on private and municipal preschool centers**

We use administrative data from _Censo Escolar_ on municipal and private preschool centers and their inputs for the years 2000 to 2006. _Censo Escolar_ is a compulsory yearly census conducted by the Ministry of Education, in conjunction with the state-level education departments. This data set gathers information on the universe of public and private preschool centers in Brazil. In each year, it comprises data on enrollment, group size, and teacher qualifications. In addition, it collects information on the infrastructure and equipment of each center, such as whether it has adequate sanitation for preschool, a playground, and a fridge. To ensure that the information is reported accurately, inspections are conducted every year on a random sample of centers. The administrative information from _Censo Escolar_ is widely regarded as highly reliable to monitor developments in the Brazilian public and private child care sectors.

Table 3 reports descriptive statistics on municipal and private preschool centers in different population intervals, using pooled data for the period 2000-2006. We observe that, in the set of municipalities considered, municipal supply accounts for about 88% of enrollment and 84% of the number of centers. We also observe that the proportion of enrollment accounted for by private providers tends to be higher in larger municipalities, reaching about 20% of the total in the largest population intervals. We further observe that participation in preschool among children aged 4 to 6 is at about 49%, of which 43 percentage points is accounted for by municipal enrollment.

It is also important to note that the _Censo Escolar_ data reveal that enrollment in preschool increased considerably over the sample period. In the municipalities that comprise the estimation sample, preschool enrollment rose by about 25%. This overall increase reflects an expansion of enrollment in both the municipal and private sectors (25% and 22.7%, respectively).

Table 4 reports summary statistics on the aforementioned quality indicators of municipal and private providers. We observe that private centers tend to have systematically higher quality indicators: group sizes are considerably smaller, the share of teachers with 10
higher education is slightly higher, and they are more likely to have a playground, adequate sanitation for preschool, and a fridge. We also observe that quality indicators are fairly homogeneous across municipalities of different size.

## **2.5 Additional data**

To perform validity tests to our empirical strategy, we use additional data from _Instituto de Pesquisa Economia Aplicada_ (IPEA) on a number of time invariant attributes of municipalities. These include the area of the municipality (in squared Km), its altitude, latitude, and longitude, as well as the distances to the state and federal union capitals. In addition, we use IBGE data from the 1991 census on a number of municipal attributes, notably the share of females aged at least 10 years old that were economically active, the share of black population, and income per capita.

# **3 Empirical method**

Here we present the econometric strategy for examining the impact of FPM transfers on the supply of municipal and private preschool in Brazilian municipalities. As shown by Brollo et al. (2013), the allocation system of FPM transfers over the time period considered in this paper makes it possible to apply a (fuzzy) Regression Discontinuity (RD) design. A municipality will receive high versus low federal transfers (the treatment) depending on its population size (the running variable) in a stochastic manner, but the likelihood of being treated conditional on the running variable is known to have sizable discontinuities at multiple thresholds.<sup>8</sup> In the neighborhood of a given population threshold separating two population intervals of the FPM revenue-sharing mechanism, “theoretical” transfers sharply increase from a lower to a higher level. Theoretical transfers are therefore a step function of population (the running variable). Due to imperfect compliance or measurement error, transfers effectively received by municipalities may differ from theoretical transfers. Theoretical transfers can

> 8Litschig and Morrison (2013) use the same Brazilian data set on federal transfers for an earlier period in a RD design.

11
therefore be thought of as the treatment assignment and actual transfers as the observed treatment (hence the fuzzy RD design). In the neighborhood of the population thresholds, treatment assignment is exogenous, though the observed treatment may also be influenced by additional factors, such as the ability of local governments to sidestep the exogenous assignment rule. As long as actual transfers depend on theoretical transfers, however, we can use the latter as an instrument in a (fuzzy) regression discontinuity setup.

Provided that the conditional regression functions of potential outcomes are continuous at the population thresholds, we can estimate the effect of higher federal transfers on the outcomes of interest by means of an equation of the form: where _yit_ is the outcome of interest, _g_ ( _Pi_ ) is a high-order polynomial in the population of the municipality in the previous year, _Tit_ is the amount of FPM transfers received by municipality _i_ in year _t_ (instrumented by theoretical transfer), _γs_ are state fixed-effects, _δt_ are year effects, and _μit_ the error term. We cluster the standard errors at the municipality level.<sup>9</sup> In the estimation sample, there is a relatively high proportion of municipalities that cross the FPM population thresholds at least once over the period of analysis (25% of the total). These movements generate discontinuous changes in the amount of theoretical (and actual) transfers allocated to each municipality. Furthermore, by changing the denominator of the revenue sharing rule described in (1), these movements across population thresholds may also affect the actual and theoretical FPM transfers of municipalities that do not cross the FPM population thresholds. We will exploit this source of variation by estimating an equation similar to (2), but including municipality fixed-effects instead of state fixedeffects. In this case, identification of the effects of interest comes from variation over time

> 9The main source of variation we exploit is at the municipality-level and hence we cluster the standard errors at that level. This choice has also been made in previous research exploiting the institutional features of the FPM transfers in Brazil (e.g., Brollo et al, 2013). Although less precisely estimated, the main results of the paper remain qualitatively similar if the errors are clustered at the state-level.

12
in theoretical and actual transfers _within_ municipalities.

# **4 Empirical results**

## **4.1 Validity tests**

One potential concern about the validity of the fuzzy RD design we adopt is potential _−_ manipulation of the running variable for example, if local governments were able to attract more inhabitants to obtain larger transfers, or manipulate the IBGE population estimates sent to the TCU. As we noted above, the way in which IBGE population estimates are constructed makes these sources of potential manipulation unlikely. Even if the official population figures released to obtain the transfers were subject to manipulation, the use of IBGE estimates (rather than TCU data) as an instrument would remove this problem.

We nevertheless inspect for manipulative sorting by formally testing for the presence of discontinuities in the density of IBGE population estimates at the population thresholds we use in our empirical analysis. In line with McCrary (2008), we test for the existence of a density discontinuity at these thresholds by running kernel regressions of the log of density separately on each side of the threshold. We consider all seven thresholds pooled, and also examine the four initial ones separately (for which we have a larger number of observations in the vicinity of each threshold).<sup>10</sup> The results are reported in Figure 2 and do not show evidence that municipalities sort just above the FPM thresholds.

In addition, we perform balance tests on several time-invariant municipal characteristics (reported in the first six columns of Table 5). In the presence of nonrandom sorting, some of these characteristics would likely differ systematically between treated and untreated municipalities around each threshold. The attributes we examine are the area of the municipality (measured in squared Km) and its geographical location (altitude, latitude, longitude, and distances to the state and federal capitals). We inspect for balance by testing for the presence of discontinuities in these attributes at the pooled thresholds. Reassuringly, we do not

> 10Throughout the empirical analysis, we use municipality-year data for the 2000-2006 period, and each municipality enters the estimation sample only once in each year.

13
observe any significant discontinuity along time invariant characteristics of municipalities.

Another potential concern is that municipalities that receive higher transfers (and choose to spend more of that additional revenue on municipal preschool) might have higher demand for preschool services, both private and public. To examine this possibility, in the last three columns of Table 5 we perform balancing tests on pre-determined municipal characteristics that would be expected to be strongly correlated with preschool demand, notably the share of females that were economically active and income per capita (both measured in 1991). In addition, we examine for the presence of discontinuities with regard to the racial composition of the population. The results are reported in the last three columns of Table 6. Reassuringly, they do not point to the presence of any significant discontinuity along these pre-determined municipal characteristics.<sup>11</sup> To the best of our knowledge, and as is also noted by Brollo et al. (2013), there are no other relevant policy discontinuities affecting the outcomes of interest. We can therefore use a fuzzy RD design as a (local) source of exogenous variation in the neighborhoods of the seven FPM thresholds considered.

# **4.2 FPM transfers and the provision of preschool services**

In this section, we implement (2) to examine the impact of transfers on the provision of municipal and private preschool services. The first column of Table 6 reports the estimated first-stage coefficient on the relationship between theoretical transfers and actual FPM transfers. The point estimate is positive, smaller than one, and estimated with a great degree of precision. The fact that the coefficient is smaller than one is in line with the findings of Brollo et al. (2013) and might reflect measurement error, e.g. due to differences between IBGE population estimates and those used by TCU. In the second column, we observe that similar results are obtained when including municipality fixed-effects.

In the third and fourth columns, we observe that theoretical transfers further exhibit a strong positive relationship with total federal transfers (not just FPM transfers) received by municipal governments. This evidence reassures us that the discontinuities of FPM transfers at the thresholds of interest are not offset by systematic changes in other fed-

> 11The balance tests reported in this section are especially relevant for specifications with state fixed-effects.

14
eral transfers _−_ as would be expected in the absence of other relevant policy discontinuities affecting the allocation of transfers around these thresholds.<sup>12</sup> In Table 7 we examine the effects of larger transfers on the quantity of municipal and private preschool, as measured by enrollment and the number of private centers. Panel A reports the effects on municipal supply. The first four columns report reduced-form regressions relating theoretical transfers to municipal enrollment, whereas the last four columns report results from IV specifications where theoretical transfers serve as instruments for actual transfers. In each of these cases, we report results with state fixed-effects and municipal We observe that larger transfers increase significantly the number of and enrollment in municipal preschool centers. We also observe that these results hold both in the reduced form and IV specifications, and remain qualitatively and quantitatively very similar when including state or municipality fixed-effects. Based on the estimates reported in the first and third columns, we observe that, on average, a one standard deviation increase in the amount of FPM transfers (8.84 hundred thousand reais) rises municipal enrollment by about 41 pupils (8.5% of average enrollment), and increases the number of centers by 2.56 (20% of the number of centers, on average). Taken together, these estimates suggest that the marginal municipal centers constructed with the extra FPM revenues tend to be smaller than the average center.

We now turn to the effects of larger transfers on the supply of private preschool (reported in Panel B). Since private suppliers operate independently, the amount of FPM transfers would not be expected to affect private supply other than via the observed expansion in public supply.<sup>13</sup> We observe that there is no robust evidence that an expansion of public

> 12The evidence reported in Table 6 suggests that the effect of theoretical FPM transfers on total transfers exceeds that on FPM transfers. These differences are statistically significant. As noted above, we are not aware of the existence of other policy discontinuities potentially affecting the outcomes of interest. A possible explanation for the larger effect on total federal transfers is that the discontinuous jumps in FPM revenues increase the capacity of local governments to make use of other federal programs. In this case, the policy discontinuities associated with the FPM revenue sharing mechanism would still be the key driving force of the discontinuous jump in total federal transfers received by municipalities.

> 13While increased federal transfers to a given municipality might be expected to have positive income effects, the relatively small weight of total municipal spending on local GDP (about 7% on average in the year 2000) suggests that these effects should be expected to be small.

15
supply crowds out private supply. If anything, there is some evidence that private enrollment also increases. In models with state fixed-effects, we observe a positive and weakly significant (at the 10% level) effect on private enrollment in preschool when considering the first four thresholds. In models with municipality fixed-effects, the coefficients remain positive and of similar magnitude, but are more precisely estimated. These results hold irrespective of whether we consider the reduced-form or IV estimates.

The results in Table 8 show the reduced-form and IV effects of larger transfers on two important measures of quality of municipal and private supply: group size and the share of teachers with higher education. We observe that larger transfers _−_ and the resulting expansion in public supply _−_ have no robust significant impacts on the quality of private supply. In general, we also do not observe robust evidence that the expansion in municipal supply leads to systematic changes in quality indicators of municipal providers. The main exception refers to impacts on the proportion of teachers with higher education, for which we observe some robust evidence of a negative impact when using models with municipality fixed-effects. A plausible explanation for these negative effects is that an expansion in municipal preschool supply may force municipalities to expand the recruitment base to include less qualified teachers.

Table 9 reports reduced-form and IV effects of larger transfers on other quality indicators of municipal and private supply, notably measuring the quality of infrastructure. We see that larger transfers _−_ and the resulting expansion in public supply _−_ have no robust significant impacts on the quality of infrastructure of public or private suppliers.

In the main analysis, we have included a third order population polynomial to absorb a potential direct relationship between municipal population and the outcome of interest. For robustness, in Appendix Tables A1 and A2, we verify if our main findings are sensitive to the choice of the order of the polynomial. Reassuringly, we observe that the results remain similar when considering other functional forms, notably second or fourth order population polynomials.

16
# **5 Theoretical model**

In light of the existing evidence for the US, our finding that an expansion in the supply of municipal preschool does not crowd-out local private enrollment in Brazil might be somewhat surprising. In this section we present a simple theoretical framework in order to rationalize these mixed empirical results.

Consider a market for institutional preschool education with potentially two providers: one private and one public. The private provider offers preschool services at quality _q_ 1 and price _p_ . For simplicity, we take a short-term perspective by assuming that the quality level is fixed, making price the only choice variable of the private provider. The public provider offers preschool education at quality _q_ 0 for free (zero price).<sup>14</sup> We assume that the public provider has lower quality than the private provider: _q_ 1 _> q_ 0. This assumption is fully consistent with the descriptive statistics on the Brazilian child care market presented in Section 3, which show that the quality indicators are systematically higher for private providers.

We assume that consumers have unit demand, where each consumer demands either one unit of child care from the most preferred provider, or zero units if that is the utilitymaximizing choice. The net utility of buying one unit of preschool education is given by where _v_ + _θqi_ is the willingness to pay for one unit of child care of quality _qi_ , with _θ_ being the marginal willingness to pay for quality. A key assumption of our model is that consumers are heterogeneous with respect to the parameters _v_ and _θ_ . More specifically, we assume that demand for preschool services comes from two different demand segments, henceforth referred to as Segment _H_ and Segment _L_ , where each consumer in Segment _H_ is characterized by _v_ = _vH_ and _θ_ = 1, whereas each consumer in Segment _L_ is characterized

> 14The assumption of fixed quality is consistent with the evidence presented in Tables 8 and 9 in Section 4, which shows that an expansion of public supply of preschool has no systematic effect on the quality offered either by private or public providers.

17
by _v_ = _vL < vH_ and _θ ∼ U_ [0 _,_ 1]. Thus, for any quality level, consumers in Segment _H_ has a higher willingness to pay for child care than consumers in Segment _L_ . In addition, whereas consumers in Segment _L_ are heterogeneous with respect to the marginal willingness to pay for quality, with _θ_ being uniformly distributed on the unit interval, each consumer in this segment has a (weakly) lower marginal willingness to pay for quality than consumers in Segment _H_ . We also let the two demand segments be of potentially different sizes by assuming that there are _n_ consumers in Segment _H_ , whereas the total consumer mass in Segment _L_ is normalized to 1.

For the type of utility function given by (3), it is well known (see, e.g., Tirole, 1988, pp. 96-97) that the parameters _v_ and _θ_ can be interpreted as being inversely related to the marginal utility of income. Under the standard assumption of decreasing marginal utility of income, this implies that wealthier consumers are characterized by higher values of _v_ and _θ_ . Thus, we can interpret our model as consumers having identical preferences for preschool services but differing in income, with consumers in Segment _H_ being richer than consumers in Segment _L_ .<sup>15</sup> This also implies that we can use the parameter _vH_ as a measure of the degree of income inequality between the two demand segments.<sup>16</sup> In order to analyze the effect of public preschool supply on private enrollment, we will compare the equilibria under two different scenarios: (i) a private monopoly and (ii) a mixed duopoly with a private and a public provider. Whereas public price and quality are exogenously given, we let the private provider optimally choose its price in order to maximize profits, which is given by where _c ∈_ (0 _,_ 1) is a cost parameter and _D_ := _DH_ + _DL_ is total demand for the private

> 15See the Appendix for technical details.

> 16The key assumption of the model is that there are two distinctly different demand segments where consumers differ in average income. The assumption that only consumers in Segment _L_ are heterogeneous (whereas consumers in Segment _H_ are identical) is made for analytical convenience, without much loss of generality. A model where consumers in Segment _H_ also differ in income would produce similar results, as long as the difference in average income between the two segments is sufficiently high.

18
provider, which is the sum of demand from the two demand segments. Notice that, since all consumers in Segment _H_ are identical, demand from Segment _H_ is either _n_ or 0. On the other hand, demand from Segment _L_ is a continuous function of the price charged by the private provider. Notice also that the cost of meeting higher demand increases with the quality of preschool services offered.<sup>17</sup><sup>_,_18</sup> In order to save notation, and without loss of generality, we set _q_ 1 = _q_ and _q_ 0 = 0, implying that the quality difference between private and public preschool is given by the parameter _q_ . Finally, we assume that it is not possible for the private provider to price discriminate among different types of consumers.

# **5.1 Private monopoly**

The profit-maximization problem of the private provider involves choosing between a highprice strategy which induces demand only from Segment H, and a low-price strategy which induces demand from both segments.

The optimal _high-price strategy_ is to set the highest possible price that still makes consumers in Segment _H_ willing to buy preschool services from the private provider: At this price, all surplus is extracted from consumers in Segment _H_ , and no consumer in Segment _L_ is willing to buy preschool services from the private provider. Total demand with this price strategy is thus _DM_<sup>_high_</sup> = _n_ .

If the provider chooses a _low-price strategy_ , demand from Segment _L_ is given by _DL_ = 1 _− θ_<sup>�</sup> _M_ , where _θ_<sup>�</sup> _M_ :=<sup>_<u>p−vL</u>_</sup> is the marginal willingness to pay for quality for the consumer _q_ in Segment _L_ who is indifferent between buying preschool services or not from the private provider. Notice that consumers in Segment _H_ are always willing to buy preschool from the private provider for any price that makes as least one consumer in Segment _L_ willing to buy; i.e., any price which yields _θ_<sup>�</sup> _M ∈_ (0 _,_ 1). Thus, the optimal price under a low price

> 17The restriction _c <_ 1 is made to ensure equilibrium existence in the mixed duopoly case.

> 18In reality there might also be fixed quality costs. However, as long as quality is exogenously given, such costs are irrelevant for optimal pricing decisions and are therefore dropped.

19
strategy is given by We assume the existence of an interior solution with a low-price strategy, i.e., _θ_<sup>�</sup> _M_ � _p_<sup>_low_</sup> _M_ � _∈_ (0 _,_ 1), which requires _q_ ( _n −_ (1 _− c_ )) _< vL < q_ (1 + _n − c_ ). Demand for the private provider under a low-price strategy is then _DM_<sup>_low_</sup> =<sup><u>1</u></sup> 2<sup>(1 +</sup><sup>_n −c_).Itcaneasilybeshown(seethe</sup> Appendix) that the high-price (low-price) strategy is optimal if _vH_ is above (below) a � threshold value _vH_ . Thus, the optimal solution under a private provider monopoly can be summarized as follows:<sup>19</sup>

**Proposition 1** _A private monopoly provider will optimally choose a high-price strategy, serving consumers from Segment H only, if the difference in willingness-to-pay for child care between the two demand segments is sufficiently large. Otherwise, the provider will choose a low-price strategy and serve consumers from both segments._

This result is quite intuitive. If the willingness-to-pay for preschool is sufficiently higher in Segment _H_ than in Segment _L_ , profits are maximized by setting a price so high that all consumer surplus is extracted from Segment _H_ , at the cost of having no demand from Segment _L_ .

# **5.2 Mixed duopoly**

In a mixed duopoly, the private provider still has a choice between a high-price and a lowprice strategy, but under each strategy the optimal price differs from the corresponding optimal monopoly price. With a public provider in the market offering preschool at zero price, it is no longer feasible for the private provider to follow the same high-price strategy as under monopoly. If the private provider charges a price _p_ = _vH_ + _q_ , all consumers in Segment _H_ would be strictly better off switching to the public provider (which would give

> 19See the Appendix for proofs of all Propositions.

20
these consumers a positive net utility of _vH_ ) and this would leave the private provider with no demand.

In the presence of a public competitor, the optimal _high-price strategy_ for the private provider would now be to set the price equal to the willingness to pay (of consumers in Segment _H_ ) for the quality difference between private and public preschool: This would make all consumers in Segment _H_ (weakly) prefer the private provider while the consumers in Segment _L_ would choose the public provider.<sup>20</sup> The corresponding demand is _DD_<sup>_high_</sup> = _n_ .

If the private provider chooses a _low-price strategy_ , the consumer in Segment _L_ who is indifferent between private and public child care is characterized by _θ_<sup>�</sup> _D_ =<sup>_<u>p</u>_Atthisprice,</sup> _q_<sup>.</sup> all consumers from Segment _H_ prefer the private provider, so total demand for this provider is _n_ + 1 _− θ_<sup>�</sup> _D_ . The profit-maximizing price under a low-price strategy is therefore and is potentially optimal only if it yields _θ_<sup>�</sup> _D ∈_ (0 _,_ 1), which requires _n <_ 1 _− c_ . Otherwise, profits are maximized by choosing the high-price strategy given by (7). Intuitively, a lowprice strategy that targets consumers in both segments is optimal only if the segment with lower willingness-to-pay for child care (Segment L) is sufficiently large relative to the other demand segment. It can easily be confirmed (see the Appendix) that a low-price strategy is always optimal if _n <_ 1 _− c_ . In this case, demand for the private provider is _D_<sup>_low_</sup> =<sup><u>1</u>Thus, the mixed duopoly equilibrium can be characterized as follows:</sup> _D_ 2<sup>(1 +</sup><sup>_n_+</sup><sup>_c_).</sup>

**Proposition 2** _In a mixed duopoly, the private provider will choose a high-price strategy, serving consumers from Segment A only, if n >_ 1 _− c. Otherwise, if n <_ 1 _− c, the provider will choose a low-price strategy and serve consumers from both segments._

> 20Notice that, when public child care is offered at zero price, all consumers (in both demand segments) will buy child care from one of the providers.

21
# **5.3 Does public supply crowd out private enrollment?**

Propositions 1 and 2, when seen in conjunction, reveal that there are three possible outcomes regarding the (qualitative) effect of public child care supply on private enrollment, which are summarized as follows:

**Proposition 3** _(i) If vH <_ � _vH , public supply crowds out private enrollment; (ii) if vH >_ � _vH and n >_ 1 _− c, public supply does not affect private enrollment; (iii) if vH >_ � _vH and n <_ 1 _− c, public supply crowds in private enrollment._

Since private demand is monotonically decreasing in price, public supply crowds out private enrollment only if the private provider finds it optimal to use a low-price strategy in the absence of competition from a public provider. As we know from Proposition 1, this requires that the difference in willingness-to-pay for child care between the two demand segments is sufficiently low ( _vH < v_ � _H_ ). The degree of private crowd-out depends on the private provider’s pricing strategy in the presence of public competition. There is less crowd-out if the private provider maintains a low-price strategy also after the introduction of public supply.<sup>21</sup> This requires that the segment with higher willingness-to-pay is relatively small. However, if Segment _H_ is sufficiently large, the private provider will respond to public supply by switching from a low-price to a high-price strategy, which increases the crowd-out On the other hand, if the difference in willingness-to-pay between the two demand segments is sufficiently high ( _vH >_ � _vH_ ), the private supplier prefers a high-price strategy in the absence of a public provider and public supply of child care will therefore not crowd out private enrollment. If, in addition, the size of the demand segment with higher willingnessto-pay is relatively large ( _n >_ 1 _− c_ ), the private provider maintains a high-price strategy also in the face of competition from a public provider, which implies that public supply has no effect on private enrollment. The private provider simply targets different consumers than those who are prone to choose a public provider.

> 21There is still a crowd-out effect, since _DDlow < DM_<sup>_low_.</sup>

22
However, since public supply pushes the price of private child care downwards, sticking to a high-price strategy is optimal only if the relative size of the high-valuation segment is sufficiently large. If Segment _H_ is relatively small ( _n <_ 1 _− c_ ), the private provider will optimally respond to public preschool supply by switching from a high-price strategy to a low-price strategy, leading to the somewhat counterintuitive outcome where public supply _crowds in_ private enrollment. In this case, the presence of a public provider forces the private provider to compete for consumers (in Segment _L_ ) who would otherwise not be profitable for the private provider to target. As a result, the demand for private child care increases. Thus, using our interpretation of the two demand segments as differing in average income, public supply crowding in private enrollment might occur if demand for child care consists of a segment of consumers who are much richer than the rest but relatively few in numbers.

In light of this theoretical framework, a plausible explanation for the lack of any evidence that public supply crowds out private enrollment in Brazilian child care markets, is a demand side that is characterized by relatively large inter-household income inequalities, which implies that private providers might find it profitable to exclusively (or to a large extent) target high-income households by offering high-quality services at prices that are not affordable to low-income segments. An increase in the public supply of preschool will then fully (or mainly) benefit those households that previously could not afford private preschool, rather than crowding out private enrollment.

# **6 Concluding remarks**

We have examined if and how an expansion in the supply of public preschool affects private provision. Using rich data for municipalities in Brazil from 2000-2006, we have used an RD design to exploit the fact that federal transfers received by local governments exhibit a non-linear and non-monotonic relationship with given population estimates. The results reveal that larger federal transfers lead to a significant expansion of municipal preschool, as measured by the number of centers and enrollment, but show no evidence of crowding out of 23
local private enrollment, nor of negative impacts on the quality of private providers. These findings are consistent with a theoretical model in which households differ in willingnessto-pay for preschool services, and private suppliers optimally adjust prices in response to an expansion of lower-quality, free-of-charge public supply. In the context of the model, the absence of crowding-out effects of more municipal preschool providers can be rationalized by the existence of relatively large differences in willingness-to-pay for preschool services across different demand segments. Our theoretical and empirical findings therefore suggest that in developing country settings characterized by relatively high income inequality, an expansion in public preschool supply will likely significantly increase enrollment among the poorest segments of society, and need not have adverse effects on the quantity or quality of local private supply.

# **Appendix**

## **Alternative functional forms for population polynomial**

In the main analysis, we have included a third order population polynomial to absorb a potential direct relationship between municipal population and the outcome of interest. In Tables A1 and A2, we observe that our main results remain similar when including instead second or fourth order population polynomials, respectively.

## **Interpretation of the utility function**

Suppose that consumers have identical ordinal preferences and differ only in income. The utility for consumer _i_ of buying one unit of child care at quality _q_ and price _p_ is given by an additive separable utility function where _yi_ is consumer _i_ ’s income and _μ_ is the utility of net income, ( _yi − p_ ). Suppose that _p_ is small relative to _yi_ (implying that expenditures on child care constitute only a small 24
fraction of total income). In this case, the utility function in (A1) can be approximated by a first-order Taylor expansion around _p_ = 0, as follows: which, by a monotonic transformation, is equivalent to a utility function _<u>μ</u>_ <u>(</u> _<u>yi</u>_ <u>) 1</u> where _vi_ := _μ_<sup>_<u>′</u>_</sup> ( _yi_ )<sup>and</sup><sup>_θi_:=</sup> _μ_<sup>_<u>′</u>_</sup> ( _yi_ )<sup>.If</sup><sup>_μ_isstrictlyconcave,</sup><sup>_yi>yj_implies</sup><sup>_vi>vj_and</sup> _θi > θj_ ; i.e., richer consumers have a higher willingness to pay for child care of any quality ( _v_ + _θq_ ) and a higher marginal willingness to pay for quality ( _θ_ ).

# **Proofs**

**Proof of Proposition 1** The maximum profits with a high-price strategy, given by (5), is

whereas the maximum profits with low-price strategy, given by (6), is Comparing (A4) and (A5) yields From (A6) it is easily verified that the profit difference is monotonically increasing in _vH_ , and that _πM_<sup>_high_</sup> _− πM_<sup>_low_</sup> _<_ 0 if _vH → vL_ . Thus, a low-price (high-price) strategy is 25
optimal if _vH_ is below (above) a threshold level _v_ � _H_ , given by _Q.E.D._

**Proof of Proposition 2** With a low-price strategy, given by (8), the marginal willingnessto-pay for quality of the consumer who is indifferent between the public and private provider is given by

Since _θ_<sup>�</sup> _D >_ ( _<_ ) 1 if _n <_ ( _>_ ) 1 _− c_ , it follows that a low-price strategy is potentially optimal only if _n <_ 1 _− c_ . Since the profit function is discontinuous at the price that yields _θ_<sup>�</sup> _D_ = 1, it remains to show that a low-price strategy that yields _θ_<sup>�</sup> _D <_ 1 always gives higher profits than a high-price strategy. Maximum profits with a lowand high-price strategy, respectively, are given by and A comparison of (A8) and (A9) yields is true which confirms that the low-price strategy given by (8) is always optimal for _n <_ 1 _−c_ . _Q.E.D._

**Proof of Proposition 3** The results follow directly from a comparison of Proposition 1 and 2, when noting that private enrollment is lower under mixed duopoly than under private monopoly when the private provider chooses a low-price strategy in both cases.

26
This is confirmed by comparing and _Q.E.D._

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# **Figure 1: Actual and theoretical FPM transfers**

<!-- Start of picture text --> 10189 13585 16981 23773 30565 37356 44148 10189 13585 16981 23773 30565 37356 44148<br>Population Population<br>10189 13585 16981 23773 30565 37356 44148 10189 13585 16981 23773 30565 37356 44148<br>Population Population<br>60 60<br>FPM transfers 4020 FPM transfers 4020<br>60 60<br>40 40<br>20 20<br>Theoretical FPM transfers Theoretical FPM transfers<br><!-- End of picture text --> _Notes_ : The upper left panel plots actual FPM transfers versus population size; the upper right scatterplot is averaged over 100-inhabitant bins plus running-mean smoothing performed separately in each interval between two thresholds. The lower left panel plots theoretical FPM transfers versus population size; the lower right scatterplot is averaged over 100-inhabitant bins plus running-mean smoothing performed separately in each interval between two thresholds.

1
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**Table 1: FPM coefficients, actual and theoretical transfers**

|Population|FPM<br>coefficient|Actual<br>transfers|Theoretical<br>transfers|Obs.|
|---|---|---|---|---|
|6,793-10,188|0.6|13.91|13.11|5211|
|10,189-13,584|0.8|18.20|17.65|3982|
|13,585-16,980|1|22.48|22.28|2931|
|16,981-23,772|1.2|26.77|26.78|3931|
|23,773-30,564|1.4|31.12|31.17|2312|
|30,565-37,356|1.6|35.35|35.60|1412|
|37,357-44,148|1.8|39.55|39.80|907|
|44,149-50,940|2|43.81|44.43|542|
|Total|-|23.42|23.13|21168|

_Notes:_ Actual and theoretical FPM transfers are in hundred thousand Brazilian _reais_ at 2000 prices.

**Table 2: Preschool enrollment and household income, 2001**

||% of total<br>enrollment|Mean|10th percentile<br>Household inc|Median<br>ome (mont|90th percentile<br>hly)|
|---|---|---|---|---|---|
|Enrollment in public preschool|0.68|586.93|120|400|1200|
|Enrollment in private preschool|0.32|1079.26|280|950|3980|

_Notes:_ Data come from _Pesquisa Nacional por Amostra de Domicilios_ (PNAD). Household income is measured in Brazilian _reais_ at current prices.
**Table 3: Municipal and private preschool, 2000-2006**

|||En|ratio between<br>rollment||#centers||
|---|---|---|---|---|---|---|
|Population|mean|% of total<br>enrollment<br>|<br>enrollment and<br>population aged 4-6|mean|% of total<br>centers|Obs.|
|_Panel A: Munici_|_pal supply_||||||
|6,793-10,188|240.1|0.93|0.45|7.1|0.90|5211|
|10,189-13,584|320.8|0.90|0.43|9.9|0.86|3982|
|13,585-16,980|409.8|0.89|0.43|12.2|0.85|2931|
|16,981-23,772|519.9|0.85|0.41|14.9|0.82|3931|
|23,773-30,564|691.1|0.82|0.41|17.5|0.80|2312|
|30,565-37,356|863.5|0.80|0.42|21.4|0.77|1412|
|37,357-44,148|1042.6|0.80|0.41|22.9|0.76|907|
|44,149-50,940|1245.8|0.81|0.43|25.6|0.75|542|
|Total|480.1|0.88|0.43|13.0|0.84|21168|
|_Panel B: Private_|_supply_||||||
|6,793-10,188|16.4|0.07|0.03|0.5|0.10|5211|
|10,189-13,584|32.7|0.10|0.04|0.9|0.14|3982|
|13,585-16,980|50.7|0.11|0.05|1.3|0.15|2931|
|16,981-23,772|78.4|0.15|0.06|1.9|0.18|3931|
|23,773-30,564|135.4|0.18|0.08|2.9|0.20|2312|
|30,565-37,356|192.7|0.20|0.09|3.9|0.23|1412|
|37,357-44,148|226.6|0.20|0.09|4.5|0.24|907|
|44,149-50,940|264.5|0.19|0.09|5.2|0.25|542|
|Total|75.5|0.12|0.06|1.7|0.16|21168|

_Notes:_ This table provides descriptive statistics based on the estimation sample for 2000-2006. Indicators are first computed at the municipal-year level and then averaged across municipalities and years within each population bracket. Data on municipal population aged 4 to 6 used to compute participation in public and private preschool come from the 2000 census.
**Table 4: Quality indicators of preschool providers**

|Population|Group<br>size|% teachers<br>with higher<br>education|Playground|<sup>Adequate</sup><br>sanitation|Fridge|Obs.|
|---|---|---|---|---|---|---|
|_Panel A: Munici_|_pal supply_||||||
|6,793-10,188|23.64|0.22|0.24|0.25|0.62|5170|
|10,189-13,584|24.17|0.20|0.22|0.21|0.59|3936|
|13,585-16,980|24.34|0.20|0.21|0.21|0.56|2899|
|16,981-23,772|24.36|0.21|0.20|0.21|0.57|3901|
|23,773-30,564|25.18|0.20|0.21|0.20|0.57|2301|
|30,565-37,356|24.74|0.25|0.23|0.23|0.59|1397|
|37,357-44,148|24.67|0.25|0.26|0.24|0.64|903|
|44,149-50,940|24.75|0.27|0.26|0.25|0.66|540|
|Total|24.28|0.21|0.22|0.22|0.59|20982|
|_Panel B: Private_|_supply_||||||
|6,793-10,188|14.04|0.22|0.62|0.49|0.68|1874|
|10,189-13,584|14.53|0.23|0.67|0.56|0.71|2153|
|13,585-16,980|14.65|0.24|0.68|0.57|0.70|1834|
|16,981-23,772|15.51|0.24|0.69|0.60|0.72|3009|
|23,773-30,564|16.20|0.25|0.69|0.62|0.75|1970|
|30,565-37,356|16.33|0.27|0.71|0.64|0.75|1287|
|37,357-44,148|16.17|0.28|0.76|0.69|0.78|873|
|44,149-50,940|15.57|0.31|0.77|0.68|0.77|515|
|Total|15.26|0.25|0.68|0.59|0.72|13471|

_Notes:_ This table provides descriptive statistics based on the estimation sample for 2000-2006. Indicators are first computed at the municipal-year level and then averaged across municipalities and years within each population bracket.
**Table 5: Balance tests of time-invariant and pre-determined municipal attributes**

||Area|Elevation|Latitude|Longitude|Distance<br>to federal<br>capital|Distance<br>to state<br>capital|Share of woman<br>(age >9) that were<br>economically<br>active in 1991|<br>Share of black<br>population in<br>1991|<br>Income per<br>capita in 1991|
|---|---|---|---|---|---|---|---|---|---|
|Thresholds 1-7|-47.643|0.737|0.001|0.000|0.334|-0.326|-0.003|0.000|-0.000|
||[32.080]|[1.460]|[0.009]|[0.010]|[1.006]|[0.950]|[0.005]|[0.000]|[0.000]|
|Obs.|21124|21124|21124|21124|21124|21124|19036|19080|19120|
|Thresholds 1-4|-21.432|0.516|-0.001|0.007|1.664|-0.357|-0.005|0.000|-0.000|
||[24.250]|[1.790]|[0.011]|[0.013]|[1.198]|[1.150]|[0.006]|[0.000]|[0.000]|
|Obs.|18321|18321|18321|18321|18321|18321|16354|16367|16401|

_Notes:_ Estimates from reduced-form regressions relating time-invariant or pre-determined municipal attributes to theoretical transfers observed in the period 2000-2006. Data for 1991 come from the corresponding population census. All regressions include a three order population polynomial, state and year fixed effects. Robust standard errors clustered at the municipal level in brackets. *, **, *** represent significance at the 10%, 5% and 1% level, respectively.
# **Table 6: Actual and theoretical transfers**

||FPM tr|ansfers|All Tr|ansfers|
|---|---|---|---|---|
|Thresholds 1-7|0.804***|0.773***|0.989***|0.984***|
||[0.010]|[0.012]|[0.040]|[0.028]|
|Obs.|21168|21168|21168|21168|
|F-statistic|59336.48|54124.90|12366.89|13070.67|
|Thresholds 1-4|0.753***|0.710***|0.853***|0.816***|
||[0.012]|[0.013]|[0.037]|[0.024]|
|Obs.|18365|18365|18365|18365|
|F-statistic|29612.69|10949.45|5042.12|8357.66|
|Municipality fixed-effects|No|Yes|No|Yes|
|State fixed-effects|Yes|No|Yes|No|

_Notes:_ Estimates from reduced-form regressions relating theoretical transfers to actual FPM transfers and all federal transfers. All regressions include a three order population polynomial and year fixed-effects. Robust standard errors clustered at the municipal level in brackets. *, **, *** represent significance at the 10%, 5% and 1% level, respectively.
**Table 7: FPM transfers and preschool supply**

|||Reduce|d form|||IV<br>|||Obs.|
|---|---|---|---|---|---|---|---|---|---|
||Enroll|ment|#cen|ters|Enroll|ment|#ce|nters||
|Panel A: Municipal supply||||||||||
|Thresholds 1-7|3.750**|5.230***|0.232***|0.200***|4.666**|6.765***|0.289***|0.258***|21168|
||[1.551]|[1.424]|[0.082]|[0.061]|[1.926]|[1.684]|[0.101]|[0.072]||
|Thresholds 1-4|4.016***<br>[1.415]|5.019***<br>[1.221]|0.187**<br>[0.084]|0.192***<br>[0.060]|5.333***<br>[1.879]|7.064***<br>[1.571]|0.249**<br>[0.111]|0.270***<br>[0.078]|18365|
|Panel B: Private supply||||||||||
|Thresholds 1-7|0.831|1.467***|0.000|0.000|1.035|1.898***|0.000|0.001|21168|
||[0.702]|[0.386]|[0.011]|[0.007]|[0.874]|[0.458]|[0.014]|[0.008]||
|Thresholds 1-4|1.045*|1.118***|-0.002|0.071*|1.387*|1.573***|-0.003|0.008|18365|
||[0.559]|[0.375]|[0.011]|[0.041]|[0.743]|[0.484]|[0.015]|[0.008]||
|Municipality fixed-effects|No|Yes|No|Yes|No|Yes|No|Yes||
|State fixed-effects|Yes|No|Yes|No|Yes|No|Yes|No||

_Notes_ : Reduced form regressions relate the relevant outcome to theoretical transfers. In the IV regressions, theoretical transfers serve as instrument for actual transfers. All regressions include a three order population polynomial and year fixed effects. Robust standard errors clustered at the municipal level in brackets. *, **, *** represent significance at the 10%, 5% and 1% level, respectively.
**Table 8: FPM Transfers, group size and teachers’ education**

|||Reduc|ed form<br>|||I|V<br>|||
|---|---|---|---|---|---|---|---|---|---|
||||eac|ers w|||eac|ers w|s|
||Grou|p size|<br>higher e|<br>ducation|Grou|p size|<br>higher e|<br>ducation|.|
|Panel A: Municipal supply||||||||||
|Thresholds 1-7|0.061<br>[0.041]|0.019<br>[0.048]|-0.001<br>[0.001]|-0.004***<br>[0.001]|0.075<br>[0.051]|0.025<br>[0.057]|-0.001<br>[0.001]|-0.005***<br>[0.001]|20990|
|Thresholds 1-4|0.108**<br>[0.050]|0.015<br>[0.063]|-0.002*<br>[0.001]|-0.004***<br>[0.001]|0.144**<br>[0.066]|0.021<br>[0.082]|-0.003*<br>[0.002]|-0.005***<br>[0.002]|18207|
|Panel B: Private supply||||||||||
|Thresholds 1-7|0.010<br>[0.036]|0.044<br>[0.029]|0.000<br>[0.002]|-0.002<br>[0.002]|0.012<br>[0.045]|0.057<br>[0.035]|0.001<br>[0.002]|-0.002<br>[0.002]|13471|
|Thresholds 1-4|0.043<br>[0.049]|-0.002<br>[0.002]|-0.001<br>[0.002]|-0.002<br>[0.002]|0.058<br>[0.066]|0.103*<br>[0.053]|-0.001<br>[0.003]|-0.003<br>[0.003]|10840|
|State fixed-effects|Yes|No|Yes|No|Yes|No|Yes|No||
|Municipality fixed-effects|No|Yes|No|Yes|No|Yes|No|Yes||

_Notes_ : Reduced form regressions relate the relevant outcome to theoretical transfers. In the IV regressions, theoretical transfers serve as instrument for actual transfers. All regressions include a three order population polynomial and year fixed effects. Robust standard errors clustered at the municipal level in brackets. *, **, *** represent significance at the 10%, 5% and 1% level, respectively.
**Table 9: FPM Transfers and the quality of infrastructure in preschool centers**

|||R|educed fo<br>|rm<br>|||||IV<br>|||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
||Playgr|ound|Ade<br>sanit|quate<br>ation|Fri|dge|Playg|round|Ade<br>sanit|uate<br>ation|Fri|dge|Obs.|
|Panel A: Municipal supply||||||||||||||
|Thresholds 1-7|0.002<br>[0.001]|0.002<br>[0.001]|-0.000<br>[0.001]|0.001<br>[0.001]|0.001<br>[0.002]|-0.000<br>[0.001]|0.003<br>[0.002]|0.002*<br>[0.001]|-0.000<br>[0.002]|0.001<br>[0.001]|0.001<br>[0.002]|-0.000<br>[0.001]|20990|
|Thresholds 1-4|0.003<br>[0.002]|0.003*<br>[0.001]|-0.001<br>[0.002]|0.000<br>[0.001]|0.001<br>[0.002]|-0.000<br>[0.001]|0.003<br>[0.002]|0.004**<br>[0.002]|-0.001<br>[0.002]|0.000<br>[0.002]|0.002<br>[0.002]|-0.000<br>[0.002]|18207|
|Panel B: Private supply||||||||||||||
|Thresholds 1-7|-0.001<br>[0.002]|-0.001<br>[0.002]|0.002<br>[0.002]|0.001<br>[0.002]|0.000<br>[0.002]|0.000<br>[0.002]|-0.002<br>[0.003]|-0.001<br>[0.002]|0.003<br>[0.003]|0.001<br>[0.002]|0.000<br>[0.003]|0.000<br>[0.002]|13471|
|Thresholds 1-4|-0.003<br>[0.003]|-0.001<br>[0.002]|0.004<br>[0.003]|0.001<br>[0.003]|0.001<br>[0.003]|0.001<br>[0.002]|-0.005<br>[0.004]|-0.002<br>[0.003]|0.006<br>[0.005]|0.002<br>[0.004]|0.001<br>[0.004]|0.001<br>[0.003]|10840|
|State fixed-effects|Yes|No|Yes|No|Yes|No|Yes|No|Yes|No|Yes|No||
|Municipality fixed-effects|No|Yes|No|Yes|No|Yes|No|Yes|No|Yes|No|Yes||

_Notes_ : Reduced form regressions relate the relevant outcome to theoretical transfers. In the IV regressions, theoretical transfers serve as instrument for actual transfers. All regressions include a three order population polynomial and year fixed effects. Robust standard errors clustered at the municipal level in brackets. *, **, *** represent significance at the 10%, 5% and 1% level, respectively.
**Table A1: FPM transfers and preschool supply, controlling for second order population polynomial**

|||Reduce<br>|d form|||IV<br>|||Obs.|
|---|---|---|---|---|---|---|---|---|---|
||Enrol|lment|#ce|nters|Enrol|lment|#ce|nters||
|Panel A: Municipal supply||||||||||
|Thresholds 1-7|3.646**<br>[1.658]|5.151***<br>[1.425]|0.216**<br>[0.089]|0.197***<br>[0.061]|4.522**<br>[2.053]|6.668***<br>[1.686]|0.268**<br>[0.110]|0.255***<br>[0.072]|21168|
|Thresholds 1-4|4.054***<br>[1.334]|5.025***<br>[1.197]|0.183**<br>[0.077]|0.188***<br>[0.059]|5.411***<br>[1.778]|7.029***<br>[1.531]|0.244**<br>[0.103]|0.262***<br>[0.076]|18365|
|Panel B: Private supply||||||||||
|Thresholds 1-7|0.214|1.494***|-0.008|0.001|0.266|1.935***|-0.010|0.001|21168|
||[0.742]|[0.381]|[0.011]|[0.006]|[0.920]|[0.453]|[0.014]|[0.008]||
|Thresholds 1-4|1.151**|1.168***|0.003|0.006|1.537**|1.634***|0.004|0.009|18365|
||[0.532]|[0.371]|[0.011]|[0.006]|[0.711]|[0.477]|[0.014]|[0.008]||
|State fixed-effects|Yes|No|Yes|No|Yes|No|Yes|No||
|Municipality fixed-effects|No|Yes|No|Yes|No|Yes|No|Yes||

_Notes_ : Reduced form regressions relate the relevant outcome to theoretical transfers. In the IV regressions, theoretical transfers serve as instrument for actual transfers. All regressions include a second order population polynomial and year fixed effects. Robust standard errors clustered at the municipal level in brackets. *, **, *** represent significance at the 10%, 5% and 1% level, respectively.
**Table A2: FPM transfers and preschool supply, controlling for fourth order population polynomial**

|||Reduce<br>|d form<br>|||IV<br>|||Obs.|
|---|---|---|---|---|---|---|---|---|---|
||Enrol|ment|#cen|ters|Enroll|ment|#ce|nters||
|Panel A: Municipal supply||||||||||
|Thresholds 1-7|3.946**|5.236***|0.242***|0.199***|4.934**|6.766***|0.302***|0.257***|21168|
||[1.558]|[1.424]|[0.083]|[0.061]|[1.944]|[1.684]|[0.103]|[0.072]||
|Thresholds 1-4|4.246***|5.018***|0.195**|0.187***|5.575***|7.065***|0.256**|0.268***||
||[1.471]|[1.228]|[0.080]|[0.060]|[1.930]|[1.571]|[0.106]|[0.078]|18365|
|Panel B: Private supply||||||||||
|Thresholds 1-7|0.786|1.467***|-0.000|0.000|0.982|1.898***|-0.000|0.001|21168|
||[0.712]|[0.386]|[0.012]|[0.007]|[0.890]|[0.458]|[0.014]|[0.008]||
|Thresholds 1-4|1.626***<br>[0.608]|1.188***<br>[0.379]|0.007<br>[0.012]|0.007<br>[0.007]|2.136***<br>[0.800]|1.573***<br>[0.484]|0.009<br>[0.016]|0.008<br>[0.008]|18365|
|State fixed-effects|Yes|No|Yes|No|Yes|No|Yes|No||
|Municipality fixed-effects|No|Yes|No|Yes|No|Yes|No|Yes||

_Notes_ : Reduced form regressions relate the relevant outcome to theoretical transfers. In the IV regressions, theoretical transfers serve as instrument for actual transfers. All regressions include a fourth order population polynomial and year fixed effects. Robust standard errors clustered at the municipal level in brackets. *, **, *** represent significance at the 10%, 5% and 1% level, respectively.