Relying on the private sector: The income distribution and public investments in the poor

Journal of Development Economics 107 (2014) 320–342

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Relying on the private sector: The income distribution and public investments in the poor Katrina Kosec ⁎ Stanford University, Graduate School of Business, 655 Knight Way, Stanford, CA 94305, USA

a r t i c l e

i n f o

Article history: Received 25 October 2011 Received in revised form 6 December 2013 Accepted 14 December 2013 JEL classification: D78 H42 H75 I24 O15

a b s t r a c t What drives governments with similar revenues to provide very different amounts of goods with private sector substitutes? Education is a prime example. I use exogenous shocks to Brazilian municipalities' revenue during 1995–2008 generated by non-linearities in federal transfer laws to demonstrate two things. First, municipalities with higher income inequality or higher median income allocate less of a revenue shock to education and are less likely to expand public school enrollment. They are more likely to invest in public infrastructure that is broadly enjoyed, like parks and roads, or to save the shock. Second, I find no evidence that the quality of public education suffers as a result. If anything, unequal and high-income areas are more likely to improve public school inputs and test scores following a revenue shock, given their heavy use of private education. I further provide evidence that an increase in public sector revenue lowers private school enrollment. © 2013 Elsevier B.V. All rights reserved.

Keywords: Fiscal federalism Local government expenditures Political economy Education policy Municipalities

1. Introduction What drives governments with similar revenues to publicly provide very different amounts of goods with private sector substitutes? Education and health care are prime examples; in almost all countries, the public and the private sectors simultaneously provide versions of each. Because access to them may have profound impacts on growth and poverty, it is important to understand what factors lead governments to provide more of the public version versus relying more on the private version. This is especially so since the poor frequently cannot afford a private version. I show that in areas with higher income inequality or higher median income, governments allocate less of an exogenous revenue shock to goods with private substitutes (specifically, education) and more to goods without private substitutes (like parks and roads), which are more broadly enjoyed. Unequal and high-income areas are also more likely to save a revenue shock, running a budget surplus rather than raising consumption in the short run. Importantly, however, I find no evidence that the quality of public education suffers due to this lower propensity to invest in it. If anything, unequal and high-income areas are more likely to use a revenue shock to improve ⁎ 2033 K Street NW, Washington, DC 20006, USA. Tel.: +1 202 421 3393; fax: +1 202 467 4439. E-mail address: [email protected]. 0304-3878/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jdeveco.2013.12.006

public school inputs and standardized test scores, since their heavy use of private education ensures that public education resources are spread less thinly. My results are consistent with the political economy models of Barzel (1973), Besley and Coate (1991), Epple and Romano (1996), Glomm and Ravikumar (1998), and de la Croix and Doepke (2009). They hypothesize that areas with more income inequality have more people who consume private sector versions of publicly-provided goods. Because they are consuming private versions, they vote for low spending on the public sector counterparts. Under majority voting, the government thus provides less of goods with private substitutes. This contrasts somewhat with Meltzer and Richard (1981, 1983), Alesina and Rodrik (1994), and Persson and Tabellini (1994), who predict that the size of public expenditures increases with inequality, as mean income rises relative to the income of the median (decisive) voter. I partly reconcile these models by showing empirically that the type of public investment matters. Government investment in education, which has private substitutes and predominantly benefits the poor, behaves according to the first set of political economy models. Government investment in broadly-enjoyed public goods that lack private sector substitutes (like parks, roads, and other infrastructure) behaves according to the Meltzer–Richard model. My results are also consistent with work modeling control over public policy increasing in income. As inequality grows, the bottom half of the income distribution

K. Kosec / Journal of Development Economics 107 (2014) 320–342

becomes less able to make the government invest in publicly-provided goods that the poor use. Prominent studies in this vein include Pande (2003), Foster and Rosenzweig (2003), Keefer and Khemani (2005), Bardhan and Mookherjee (2006), Banerjee and Somanathan (2007), Araujo et al. (2008), and Karabarbounis (2011). This paper's primary contribution is an empirical analysis of how an area's income distribution affects how its government allocates revenue between goods with and without private substitutes. It also examines the public service quality implications of this differential propensity to invest. I focus on education in Brazil, which has abundant private substitutes. The strength of my analysis stems from exploiting a change in Brazil's school finance law which generates exogenous variation in revenue. I focus on education spending in Brazil for three main reasons. First, Brazil has over 5,000 municipalities with enormous discretion over how much to invest in education. This makes it an ideal setting to understand how the local income distribution affects public investment. Second, Brazilian municipalities differ greatly in their income distributions but have similar institutions and constraints that make them comparable. Finally, education is the single largest item in the municipal budget (accounting for about 30% of revenue) and is the chief municipallyprovided service with abundant private substitutes.1 This allows me to cleanly capture tradeoffs between investment in goods with vs. without private substitutes by focusing on education. The analysis faces a significant challenge to identification. Unobserved factors that affect revenue levels may also influence citizens' preferences over goods. For example, if highly-educated individuals place a relatively high value on education and have more taxable income, revenues may be higher precisely where public education is most valued. Endogenous household sorting is likely to exacerbate identification problems. I circumvent these problems by exploiting a 1998 change in Brazil's education finance law that generates exogenous variation in municipalities' revenue. Specifically, I form a simulated instrumental variable that encapsulates the credibly exogenous variation in revenue generated by the law, but which excludes variation due to municipalities' own actions. I instrument for actual (endogenous) revenue with the simulated instrument, thereby testing how different municipalities spend an exogenous shock to revenue, all else equal. Briefly, the law—“Fund for the Maintenance and Development of Fundamental Education and Valorization of Teaching” (FUNDEF)— forced each of Brazil's 26 states to gather 15% of each of its municipalities' revenue in a state fund. Each municipality in the state then received a share of the state's fund equal to its share of public school students in the state (with students at different grade levels weighted differently in different years). Because redistribution took place only within states (and also because of various nonlinearities in the rules), similar municipalities experienced very different changes in their finances. I form a simulated instrument which is the predicted revenue of municipality i in year t. I predict revenue using time variation and discontinuities in the law's parameters applied to municipalities' pre-law (1997) school enrollment and finances. Thus, only the law-induced changes—not municipalities' responses—are incorporated in the simulated instrument. The main results of the paper are as follows. An exogenous revenue increase boosts municipal spending and raises public school enrollment rates. However, more unequal and higher-income municipalities are significantly less likely to expand education spending and public school enrollment. The funds they do not spend on education are more likely to end up in public infrastructure like parks and roads, which lack private substitutes. They are also more likely to save a revenue shock rather than raising short-run consumption.2 Examining the implications of 1 State and federal governments are the main providers of other goods with private substitutes. 2 A budget surplus can also increase access to credit and lower future taxes (Ball and Mankiw, 1995). In Brazil, municipal taxes come primarily from two sources: Taxes on Services (ISS) and Real Estate Taxes (IPTU). The first is a head tax paid by self-employed individuals and enterprise owners. The second is a property tax. Both tax rates vary by municipality.

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these differential spending patterns for public service quality, I find that unequal and high-income areas are actually more likely to use a revenue shock to raise the average quality of public education. While they invest less in education, their more modest increases in public school enrollment more than offset this, leading to greater overall improvements in school quality. Thus, there is no evidence that this lower propensity to invest in education harms the poor. I further provide evidence that an exogenous increase in public sector revenue lowers enrollment in private primary schools. The remainder of the paper is organized as follows. In Section 2, I put the paper into context by describing contrasting predictions in the theory literature. In Section 3, I describe education finance and the political system in Brazil, including the 1998 FUNDEF law and subsequent revisions to it. In Section 4, I outline the empirical strategy and data. In Section 5, I present the empirical results. Section 6 concludes.

2. Theoretical context A large body of theory literature considers the impact of the distribution of income on the demand for publicly-provided goods and income redistribution more generally. This literature is somewhat divided in its predictions. One strand—described in the seminal work of Meltzer and Richard (1981, 1983), and expanded on by Alesina and Rodrik (1994) and Persson and Tabellini (1994)—proposes that under majority rule, an increase in mean income relative to the income of the median voter increases total public spending. An increase in inequality of this type raises public spending by lowering the median (decisive) voter's tax price of raising revenue. In contrast, a second and still burgeoning strand of the literature focuses on the existence of private sector substitutes for publiclyprovided goods. Papers in this vein include Barzel (1973), Besley and Coate (1991), Epple and Romano (1996), Glomm and Ravikumar (1998), de la Croix and Doepke (2009), and Gutiérrez and Tanaka (2009). Their models use a variety of approaches but follow a similar logic. If education quality is a normal good, the existence of private education leads parents past a threshold income to enroll children in private school. This is the income at which the cost of private school is just offset by the utility gain from higher-quality education. In societies with more unequal income or with higher median income, more people are past this threshold and use private schools. They thus oppose spending on public education, leading to less public education under majority voting.3 This is in contrast to government provision of goods like infrastructure, which lack private substitutes.4 Related to this literature, Suárez Serrato and Wingender (2011) model a positive valuation of government services that is larger for unskilled workers. Interestingly, De la Croix and Doepke (2009) model inequality raising public education quality, since greater use of private education lowers the number of children that must be educated publicly. Existing empirical work has not definitively supported or rejected the Meltzer–Richard model. A number of cross-country studies suggest that inequality is associated with less public spending (Lindert, 1994, 1996; Perotti, 1996; Benabou, 1996; Rodríguez, 2004; Moene and Wallerstein, 2001; Schwabish, Smeeding, and Osberg, 2006). Several historical studies also find that unequal 3 A related literature analyzes the effects of the distribution of income on redistribution more generally. Casamatta et al. (2000) describes how a positive level of social security is politically sustainable since retirees and workers with medium wages form a majority coalition supporting it. Bellettini and Ceroni (2007) describe how the poor (liquidity constrained) and the rich may form a coalition to push for low taxes, meaning that the median income voter is not pivotal. 4 While Stiglitz (1974) showed that preferences are not single-peaked when private education is available, several approaches address this and obtain existence of a majority voting equilibrium: imposing a single crossing property in a median voter model (Epple and Romano, 1996; Gutiérrez and Tanaka, 2009), identifying the decisive voter (Barzel, 1973; Glomm and Ravikumar, 1998), and using a probabilistic voting model (de la Croix and Doepke, 2009).

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communities tend to raise less revenue locally and provide lower levels of publicly-provided goods (Goldin and Katz, 1999; Ramcharan, 2010; Galor, Moav and Vollrath, 2009; Zolt, 2009). In contrast, several studies of the U.S. find that inequality is associated with higher public spending and more progressive tax codes (Husted and Kenny, 1997; Chernick, 2005; Schwabish, 2008; Corcoran and Evans, 2010; Boustan et al., 2013). Identification problems complicate the study of the effects of the distribution of income on public expenditures, especially given endogenous household sorting (Tiebout, 1956). Meltzer and Richard (1981) assume that the absolute tax burden increases with income while the benefits of government activity are more equally shared. When a good is predominately consumed by poorer individuals—as is education, in the Brazilian context—the benefits of this expenditure are less equally shared than in the case of a broadly-used good like public infrastructure. Thus, we might expect the distribution of income to differentially affect public investment in education vs. in infrastructure. This motivates the empirical analysis of this paper. A related political economy literature models the distribution of income affecting policy by affecting the distribution of political influence. Theoretical models in this literature give the rich control over policy that is roughly proportionate to their share of income as opposed to their share of votes (Benabou, 1996; Besley and Burgess, 2002; Grossman and Helpman, 1994). They can offer larger campaign contributions and bribes, and may have lower costs of political activity due to personal connections with politicians. However, the rich also have less demand for redistribution. Accordingly, one might expect inequality or higher income to reduce redistribution and the production of publicly-provided goods that mostly benefit the poor. Several empirical studies evaluate these models. Foster and Rosenzweig (2003) find that in democratic villages of rural India, an increase in the share of landless increases road investment (which the landless want) and decreases irrigation investment (which they do not want) more than in non-democratic villages. 5 Mansuri and Rao (2004) demonstrate, in a review of World Bank community-driven development projects, that most projects are dominated by local elites and do not target the poor. Bardhan and Mookherjee (2006) find that Indian villages with high land inequality and large incidence of low-caste status and poverty receive less money from the central government. Within villages, these factors affect the allocation of public goods and the propensity to select projects that generate employment for the poor.6 And Karabarbounis (2011), using panel data from OECD countries, finds that when the income of a group of citizens increases, aggregate redistributive policies tilt towards its most preferred policies. This literature provides an additional political economy mechanism through which higher inequality and income may reduce the size of government. Of course, this literature does not examine the role the existence of private sector substitutes plays in public investment decisions. In summary, the theoretical literature points to two separate channels through which the distribution of income might impact revenue allocation. Specifically, it may affect the number of people who support public education (a “collective choice” channel), or it may affect the relative power and influence of poor individuals, who support public education (a “political power” channel). The bulk of recent literature on both channels would suggest that the propensity to allocate revenue to public

5 Several studies find similar results. Bates (1973, 1976, 1981) shows that some ethnic groups in post-independence Africa increased their access to public funds by increasing their political salience. Varshney (1995), Jaffrelot (2003), Pande (2003), Chandra (2004), and Banerjee and Somanathan (2007) find similar results for low caste groups in India. 6 Keefer and Khemani (2005) describe how political market imperfections like information gaps, social fragmentation, identity-based voting, and credibility problems may drive such findings.

education is decreasing in both the level of income and income inequality. This paper aims to empirically test whether this is the case. One may suspect that an increase in median income most strongly affects revenue allocation through the collective choice channel, by increasing the number of rich people (who oppose public education expenditure). Conversely, one might suspect that an increase in income inequality (holding median income constant) most strongly affects revenue allocation through the political power channel; the preferences of the median voter are preserved, but the rich are now (relatively) richer and thus more able to influence policy. While the paper cannot empirically distinguish which channel is most important in transmitting the effects of median income on revenue allocation, nor which channel is most important in transmitting the effects of inequality, each of their independent effects may come more from one channel than the other. 3. Background 3.1. Municipal governments and their finances Brazil has over 5000 municipal governments with remarkable political autonomy. They are led by an elected mayor and an elected city council. The mayor is the legislative, budgetary, and administrative leader, and the city council is largely responsible for approving the mayor's policies (Couto and Abrucio, 1995; Wampler, 2007). Federal, state, and municipal governments all publicly provide goods. Municipalities primarily engage in providing pre-primary and primary education, within-city transportation, and public infrastructure. The municipal revenue base is comprised of state and federal government transfers, municipal tax collection, and miscellaneous revenue (e.g., earnings from industrial, agricultural, and mineral activities). Most municipalities depend heavily on transfers for revenue. In 1997, the median municipality got 88% of revenue from transfers. Further, 80% of municipalities got at least 75% of revenue from transfers. See Appendix A for more details. 3.2. Education in Brazil Education is one of the few publicly-provided goods with private substitutes that municipal governments supply. They provide two levels: pre-primary (ages 0–6) and primary (ages 7–15), with higher levels handled by state and federal governments. Primary education must be available to all children and attendance is compulsory. Preprimary is optional for governments and for parents; it takes place in creches for children aged 0–3 and in pre-schools for children aged 4–6. Municipalities must spend at least 25% of revenue on education, though this requirement is non-binding for the vast majority of municipalities; as of 1997, nearly 2/3 of municipalities were spending above the minimum on education. Municipal governments provide most public primary education (83% of students in 2007), but states run some primary schools. Fig. 1 shows the share of children in private school in 2000 by quintile of per capita household income and by child age. For children aged 0–3 (creche aged), 4–6 (pre-school aged) and 7–15 (primary school aged), enrollment rates in private school increase monotonically with income quintile. At the first quintile of income, the private creche enrollment rate is b 1%, the private pre-school enrollment rate is 4%, and the private primary school enrollment rate is 2%. However, at the fifth quintile, the private creche enrollment rate is 14%, the private preschool enrollment rate is 43%, and the private primary school enrollment rate is 33%. Enrollment in pre-primary education is of particular interest for three reasons. First, public and private versions are both widely available. Not only are private creches and pre-schools abundant in Brazil, but also a family that cares for a young child at home uses a private version. Second, Brazilian municipalities have almost full discretion over how much to invest in pre-primary. Third, pre-primary education may

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Fig. 1. Enrollment rate in private schools in 2000 by age and income quintile. Sources: Author's calculations based on data from 2000 Brazilian Census, 11.7% sample (IBGE).

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policy continued under “Fund for the Development of Basic Education and Appreciation of the Teaching Profession” (FUNDEB), which gradually increased the fraction of revenue paid to the fund and added other levels of education to the redistribution algorithm. See Appendix A for more detail. Municipalities benefitting from the reform looked poor compared to others in their state (even if they were rich in the national sense). Table 1 summarizes the frequency of high, moderate, and low net FUNDEF receipts per child in 1998 by high, moderate, and low average income per capita. Many rich municipalities gained while many poor ones lost funds. In 1998, the average municipality got back 1.1 times what it paid in. At the 25th percentile of net receipts, municipalities got back 1/3 of the amount paid in. At the 75th percentile, they got back 1.6 times the amount paid in. As municipalities pay in 15% of revenue, this implies a loss of 10% of revenue at the 25th percentile, and a gain of 9% of revenue at the 75th percentile. These are large effects that should lead municipalities to re-optimize spending. 4. Empirical strategy

have very high returns; Currie and Thomas (1995), Currie (2001), Carneiro and Heckman (2003), Cunha et al. (2006), Engle et al. (2007, 2011), Heckman and Masterov (2007), Berlinski et al. (2009), and Chetty et al. (2011) describe substantial benefits from pre-primary, especially for poor children whose parents cannot privately provide adequate substitutes. Patrinos (2007) estimates a pre-school benefitcost ratio of 2.0 for Brazil—larger than that of most public industrial and agricultural investments. Pre-primary education in Brazil has expanded rapidly but unevenly recently. During 1995–2008, the national enrollment expanded from 8% to 18% among 0–3 year olds (creche aged) and from 48% to 80% among 4–6 year olds (pre-school aged). Yet enrollment rates vary a lot across states; in 2008, the creche enrollment rate ranged from 6% to 32%, and the pre-school enrollment rate ranged from 57% to 91%.7 3.3. The FUNDEF/B education finance reforms Brazil has a history of within- and across-municipality income inequality.8 This has led to high variance in per capita municipal revenue. In 1998, the federal government passed an education finance reform to partially equalize funding across municipalities: “Fund for the Maintenance and Development of Fundamental Education and Valorization of Teaching” (FUNDEF). Federal policymakers worried that disparities in basic education investment threatened national progress. Rich states opposed nation-wide redistribution, and a compromise of within-state redistribution was reached. FUNDEF obligated each of Brazil's 26 states to gather 15% of each municipality's revenue, and 15% of state government revenue, in a state fund. Each municipality then received a share of the fund equal to its share of total public primary school students in the state. Enrollment data come from the Ministry of Education's annual Census of Schools.9 The 15% payment to the state fund did count toward the 25% of revenue minimum expenditure on education, but 10% more was required. All fund receipts had to go to education. If receipts did not reach a federal minimum per primary school child, the federal government would ‘top off’ the fund, bringing it to this level.10 In 2007, the

The roles of inequality and median income in mediating how a revenue shock is spent can be described by the following equation: logðyit Þ ¼ γlogðr it Þ þ δðlogðr it Þ  g i Þ þ θðlogðr it Þ  logðdi ÞÞ þ ηXit þ α i þ βt þ uit

ð1Þ

where i indexes municipalities and t indexes years. yit is a public expenditure outcome such as education expenditure per capita, infrastructure expenditure per capita, the per capita budget surplus, or measures of school enrollment or quality. gi is the Gini coefficient and di is median per capita income. αi are municipality fixed effects and βt are year fixed effects. Xit is a vector of control variables for municipality i in year t, described in Section 4.4. I estimate the model using panel data on Brazil's over 5000 municipalities during 1995–2008. The data come from several sources, matched at the municipality level. They are summarized in Table 3 and described below. By including an interaction of revenue with median income in the regression, I uncover that part of the effect of inequality that is not driven by its correlation with municipal income. In essence, δ measures the effect of a median-preserving spread of per capita income on how revenue is spent. A is a median-preserving spread of B if and only if it has the same median, and the tails of A are uniformly larger than those of B. Malamud and Trojani (2009) describe the relevance of medianpreserving spreads in macroeconomic inequality applications. Similarly, θ uncovers that part of the effect of median income that is not driven by its correlation with inequality. Municipalities may be on different time trends according to their values of the pre-reform (1997) variables used to compute the excluded instruments. I address this concern by including the interaction of a linear time trend with a vector of the 1997 values of per capita revenue, per capita transfer revenue, the public pre-primary school enrollment rate, the public primary school enrollment rate, and the share of primary school students in state or federally-run schools. This allows for heterogeneous secular trends in municipalities with different pre-reform characteristics. 4.1. Identification

7

Averages are based on parental self reports from PNAD (1995–2008). For a discussion of heterogenous trends in access to pre-primary education in Brazil during 1996–2009, see Evans and Kosec (2012). 8 In 2007, GDP per capita was 13,400 (constant 2005 R$). (The average 2005 exchange rate was 0.4 USD/Reais). It ranged from 4,300 R$ in Piauí to 37,700 R$ in the Federal District (IBGE, 2007). 9 State and municipal departments of education must provide data to receive public funds. 10 In 1998, Bahia, Ceará, Maranhão, Pará, Pernambuco, and Piauí had their funds topped off. The per child minimum changes annually. It began varying with age in 2000 and urbanization status in 2005.

There are two identification problems likely to affect this public investment analysis. The first is the potential for omitted variable bias. The second is the potential for observed per capita revenue to be endogenous due to reverse causality. Observed per capita revenue is the result of factors affecting both the supply of public funds and the population's demand for funds. I want to rely solely on variation in revenue that comes from the supply side. Factors which affect demand for revenue may have a direct effect on

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K. Kosec / Journal of Development Economics 107 (2014) 320–342

Table 1 Number of municipalities, by tercile of income Per capita and tercile of net per-child receipts (net per-child benefits) from FUNDEF education finance reform, 1998.

Poorest Middle Richest Total

Lowest receipts

Middle receipts

Highest receipts

51 664 638 1353

372 695 286 1353

710 369 273 1352

Notes: The total number of municipalities in the table is smaller than the national total, due to missing data on per capita municipal income or per-capita FUNDEF receipts data. Sources: Author's calculations based on data from Tesouro Nacional (2011) and IBGE (2007).

Table 2 Means of variables describing quality of educational inputs, which suggest that private education is of higher quality than public. Panel A: pre-primary schools

Students per teacher Fraction of teachers with some post-secondary education Fraction of institutions with own school building Fraction of institutions with electricity Fraction of institutions with indoor bathroom Fraction of institutions with library Fraction of institutions with computer

Panel B: primary schools

Students per teacher Fraction of teachers with some post-secondary education Fraction of institutions with own school building Fraction of institutions with electricity Fraction of institutions with indoor bathroom Fraction of institutions with library Fraction of institutions with computer

Private

Public

Difference

(1)

(2)

(3)

8.8 (0.105) 0.394 (0.001) 0.979 (0.001) 0.997 (0.001) 0.960 (0.001) 0.623 (0.003) 0.849 (0.002)

14.3 (0.132) 0.430 (0.001) 0.949 (0.002) 0.903 (0.001) 0.799 (0.001) 0.197 (0.001) 0.370 (0.002)

5.5 (0.134)*** 0.036 (0.001)*** −0.030 (0.002)*** −0.095 (0.002)*** −0.161 (0.003)*** −0.427 (0.003)*** −0.479 (0.003)***

Private

Public

Difference

(1)

(2)

(3)

8.0 (0.118) 0.801 (0.001) 0.950 (0.001) 0.999 (0.001) 0.959 (0.001) 0.799 (0.003) 0.920 (0.002)

30.4 (0.445) 0.800 (0.001) 0.930 (0.001) 0.871 (0.001) 0.763 (0.001) 0.334 (0.001) 0.447 (0.001)

22.4 (0.416)*** −0.001 (0.001) −0.020 (0.002)*** −0.129 (0.002)*** −0.197 (0.003)*** −0.465 (0.003)*** −0.473 (0.004)***

Notes: Standard errors are in parentheses. ***indicates p b 0.01. Sources: Author's calculations based on school- and teacher-level data from the 2008 Census of Schools.

education and other policy choices. If they do, this would bias estimates of the effects of revenue. There are several possible sources of omitted variable bias (I detail three below). First, having an older population may mean more working adults per capita and more tax revenue. But if it also means fewer children and less need for public education, then ordinary least-squares (OLS) estimates of the effects of revenue on education spending would be (likely downward) biased. The magnitude of the bias might shrink as measures of population-by-age were added Eq. (1), but it would be impossible to eliminate all bias. Second, mayors with high discount rates or who are corrupt may generate higher revenue to maximize private gains.11 However, short-sightedness may also lower investment in education, which has mostly long-term payoffs.

11 de Janvry et al. (2010) suggest such a possibility. They find that second term mayors in Brazilian municipalities, who are not eligible for reelection, have less transparent policies and are less likely to reduce school drop-out rates using federal funds designated for this purpose. Ferraz and Finan (2009a) show that first term mayors misappropriate 27% fewer resources than second term mayors, which they also link to electoral incentives.

This, too, would likely downward-bias the estimates. Finally, municipalities with higher revenue may pay higher wages to public officials. Ferraz and Finan (2009b) show that, in Brazil, this leads to more political competition, and to the election of better-educated, more experienced, more productive candidates. If these qualities increase public education investment, this would likely upward-bias estimates of the effects of revenue on such investment. Municipal revenue per capita can also be a response to education policy—a classic problem of reverse causality. Municipalities that invest heavily in public education may need to levy more taxes to pay for it. One response to these identification problems is a set of valid instruments. These instruments should affect revenue and its interactions with inequality and median per capita income, but should be uncorrelated with factors affecting the demand for revenue. 4.2. Instruments for per capita revenue To address threats to identification, I exploit the federal FUNDEF/B education finance reforms described in Section 3.3, which generated

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Table 3 Summary statistics. Variable

Mean

Std. dev.

Revenue per capita, 100 s 2005 Reais Simulated revenue per capita, 100 s, 2005 Reais Population, 100,000 s Population aged 0–6, 100,000 s Population aged 7–15, 100,000 s Gross municipal product (GMP) per capita, 10,000 s of 2005 Reais Gini coefficient (year 2000, computed by IBGE using full Census data) Median income per capita in 2000, 10,000 s of 2005 Reais Predicted Gini coefficient (computed by author w/Census 11.7% sample) Predicted median income per capita, 10,000 s of 2005 Reais Education spending per capita, 100 s 2005 Reais Infrastructure and urban development spending per capita, 100 s 2005 Reais Budget surplus per capita, 100 s 2005 Reais Municipal public pre-primary school students per age 0–6 population Municipal public primary school students per age 7–15 population Private pre-primary school students per age 0–6 population Private pre-primary school students per age 0–6 population in 1997 Private primary school students per age 7–15 population Private primary school students per age 7–15 population in 1997 Municipal public pre-primary school infrastructure quality index Municipal public primary school infrastructure quality index Private pre-primary school infrastructure quality index Private primary school infrastructure quality index Share of municipal public pre-primary schools w/ own school building Share of municipal public pre-primary schools w/ electricity Share of municipal public pre-primary schools w/ an indoor bathroom Share of municipal public pre-primary schools w/ a library Share of municipal public pre-primary schools w/ a computer Share of municipal public primary schools w/ own school building Share of municipal public primary schools w/ electricity Share of municipal public primary schools w/ an indoor bathroom Share of municipal public primary schools w/ a library Share of municipal public primary schools w/ a computer Share of private pre-primary schools w/ own school building Share of private pre-primary schools w/ electricity Share of private pre-primary schools w/ an indoor bathroom Share of private pre-primary schools w/ a library Share of private pre-primary schools w/ a computer Share of private primary schools w/ own school building Share of private primary schools w/ electricity Share of private primary schools w/ an indoor bathroom Share of private primary schools w/ a library Share of private primary schools w/ a computer Municipal public pre-primary students per teacher Municipal public primary students per teacher Private pre-primary students per teacher Private primary students per teacher Share of municipal public pre-primary teachers w/ post-secondary education Share of municipal public primary teachers w/ post-secondary education Share of private pre-primary teachers w/ post-secondary education Share of private primary teachers w/ post-secondary education Prova Brasil 4th grade Portuguese test score Prova Brasil 4th grade math test score Fraction of population that lived in urban areas in 2000 Labor force participation rate (share of pop. economically active) in 2000 Racial fractionalization index in 2000

9.84 6.12 0.32 0.04 0.06 0.68 0.39 0.23 0.53 0.25 2.67 0.88 0.53 0.25 0.58 0.03 0.02 0.02 0.02 0 0 0 0 0.82 0.82 0.76 0.17 0.22 0.81 0.7 0.66 0.21 0.23 0.75 0.89 0.85 0.49 0.55 0.78 0.86 0.83 0.63 0.64 19.43 26.17 13.66 11.59 0.22 0.31 0.24 0.45 171.92 188.78 0.59 0.55 0.38

5.92 2.98 1.92 0.21 0.3 0.58 0.03 0.13 0.08 0.12 1.42 0.82 1.01 0.14 0.29 0.05 0.03 0.03 0.03 1.73 1.81 1.78 1.91 0.33 0.34 0.36 0.28 0.35 0.34 0.37 0.38 0.31 0.35 0.38 0.31 0.33 0.4 0.42 0.38 0.34 0.36 0.42 0.43 7.96 12.87 7.18 6.87 0.27 0.31 0.28 0.34 18.93 23.35 0.23 0.09 0.12

Notes: Data are summarized over 1995–2008 over all municipalities for which data are available, except where a specific year is indicated. (N = 59,424). Sources: Author's calculations based on data from IBGE, Ministry of Education, Tesouro Nacional, IPEA, MEC, TSE, and BNDES.

exogenous variation in municipalities' revenue. These laws redistributed revenue within states according to an algorithm handed down by the federal government, and thus exogenous to any one municipality's investment decisions. The rules changed slightly each year, but always identify two things: how much each municipality has to pay into its state's education fund (always a set fraction of its revenue), and how much of the fund is given to each municipality (equal to its share of total public school students in the state, with students at different grade levels weighted differently each year). Given municipal public school enrollment and revenue data for all municipalities, the algorithm delivers a new (i.e. adjusted) revenue to each municipality. It is lower

for net losers and higher for net winners from the reform. Each year, there is a slightly different algorithm. These reforms almost certainly induced endogenous revenue and enrollment responses by municipalities and parents (Gordon, 2004; Hoxby, 2001). A good instrument should encapsulate the credibly exogenous variation in revenue generated by the law, but exclude variation due to municipalities' own actions. To do this, for each year I simulate the revenue each municipality would have if the current year's algorithm were applied to 1997 (pre-reform) enrollment and revenue data. I then instrument for actual (endogenous) net revenue with the simulated instrument, which allows me to test how different

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municipalities differentially spend an exogenous shock to revenue, all else equal. I instrument for the interaction of per capita revenue with covariates using the interaction of simulated per capita revenue with those covariates.12 See Appendix B for further details on construction of the instruments. The first stage equations state that per capita revenue and its interactions with the Gini coefficient and per capita median income are a function of simulated per capita revenue, sit and its interactions with inequality and per capita median income: log ðr it Þ ¼ λ1 log ðsit Þ þ π 1 ðlog ðsit Þ  g i Þ þ ϕ1 ðlogðsit Þ  log ðdi ÞÞ þ μ 1 Xit þ ρ1;i þ κ 1;t þ ϵ1;it

ð2Þ

log ðr it Þ  g i ¼ λ2 log ðsit Þ þ π2 ðlog ðsit Þ  g i Þ þ ϕ2 ðlog ðsit Þ  log ðdi ÞÞ þ μ 2 Xit þ ρ2;i þ κ 2;t þ ϵ2;it

ð3Þ

log ðr it Þ  logðdi Þ ¼ λ3 logðsit Þ þ π3 ðlogðsit Þ  gi Þ þ ϕ3 ðlogðsit Þ  logðdi ÞÞ ð4Þ þ μ 3 Xit þ ρ3;i þ κ 3;t þ ϵ3;it : ρi are municipality fixed effects and κt are year fixed effects. In Section 5, I demonstrate that these instruments satisfy the inclusion restriction: they are correlated with observed per capita revenue and with its interactions with inequality and per capita median income. The exclusion restriction should hold since the instruments depend only on prereform municipality characteristics (captured by fixed effects) and time-varying federal government rules, which are exogenous to any particular municipality's investments. 4.3. Data and variable measurement 4.3.1. Inequality and median income I take two approaches to measure gi. First, I take the Gini coefficient at one point in time and assume that it broadly characterizes the average level of inequality in a municipality over 1995–2008. Specifically, gi is the Gini coefficient computed by the Brazilian Institute of Geography and Statistics (IBGE, 2010) using 2000 Census data, and it only appears in interaction in Eq. (1). This seems appropriate as the national Gini coefficient was 0.59 in 1960—the first year the Census collected household income data—and also 0.59 in 2000 (Skidmore, 2004). It can also be defended on practical grounds given that the only Census during the sample period was in 2000, and only Census data permit calculation of a municipality-specific Gini.13 Second, I predict a timevarying municipal Gini, as in Boustan et al. (2013). If national trends mask changes in the distribution of income in individual municipalities, such an approach is important.14 Using Integrated Public Use Microdata Series (IPUMS) Census data, I find that the correlation coefficient between the 1991 and 2000 municipal Gini coefficients is only 0.16—suggesting changes over time. Barros et al. (2009) also note that inequality declined steadily since the 2000 Census, from a Gini of 0.59 in 2001 to 0.55 in 2007 as per estimates from the National Household Sample Survey (PNAD). I thus use both approaches (the 2000 Gini and a time-varying, predicted Gini), showing that they yield substantially similar results. I predict each municipality's Gini coefficient for each year during 1995–2008 as follows. I first take actual per capita income observations on the over 5 million households from the 2000 Census and compute the percentile of the national income distribution 12

In a similar vein, Martínez-Fritscher et al. (2010) use commodity price shocks in Brazil during 1889–1930 as an instrument for state capacity to spend on publicly-provided goods. They find that education expenditures increased during this period in response to positive price shocks. 13 No other survey indicates municipality of residence for individuals in all Brazilian municipalities. 14 For example, if the incomes of the poor are rising more rapidly than those of the rich, then poor areas will see greater increases in the share of revenue from local taxes. And Gadenne (2012) shows that revenue from taxes (rather than transfers) is relatively more likely to go into education.

(1st, 2nd, …, and 99th) to which each household belongs. Second, I take household-level per capita income data from PNAD for each year during 1995–2008; while these data do not identify the household's municipality of residence, they provide useful information on national patterns of income growth. I use them to compute the annual income growth rate for each percentile of the income distribution (1st, 2nd, …, and 99th) during 1995–2008. Third, I apply these national income patterns to estimate what was each of the 5 million 2000 Census households' per capita income in each year during 1995–1999 and 2001–2008. For example, during 2001–2007, the incomes of the poorest decile grew by 7% while those of the richest decile grew by only 1.1% (Barros et al., 2009).15 Accordingly, I would predict that the incomes of poor households (as of the 2000 Census) would growth more over 2001–2008 than would the incomes of richer households. Finally, armed with predicted incomes of each household in each year, I compute a predicted Gini (and also a predicted median per capita household income) for each municipality i in each year t. I similarly measure di (median income) in two ways: the actual 2000 Census median per capita income, and a time-varying, predicted median per capita income. By design, changes in the predicted Gini and predicted median income cannot be influenced by endogenous responses to revenue levels (including household sorting); they capture expected changes in the municipal income distribution driven purely by national trends, such as changes in the return to skill or other aspects of the labor market. When using time-varying, predicted values, I estimate a modified variant of Eq. (1) that also includes the Gini and median per capita income in their non-interacted forms: log ðyit Þ ¼ γp log ðr it Þ þ δp ðlog ðrit Þ  g it Þ þ θp ðlog ðr it Þ  log ðdit ÞÞ þ ψg it þ ωlog ðdit Þ þ σXit þ υi þ χ t þ εit :

ð5Þ

Results using the actual vs. predicted distribution of income naturally have different interpretations. When I use the actual income distribution (and interpret δ and θ from Eq. (1)), I test whether municipalities characterized by relatively high inequality or high median income in 2000 spend exogenous shocks to revenue during 1995–2008 differently. When I use the predicted income distribution (and interpret δp and θp from Eq. (5)), I test whether municipalities that one expects to become more unequal or to reach a higher median income during 1995–2008 (due to prevailing national income patterns) spend an exogenous shock to revenue differently than do municipalities in which one does not anticipate such large, exogenously-driven increases. 4.3.2. Public expenditure and revenues I measure education expenditure, infrastructure expenditure, and the budget surplus in Reais per capita spent by municipality i in year t (in 100 s of constant, 2005 $R).16 I similarly measure revenue in net Reais per capita (net of FUNDEF/B receipts) in municipality i in year t (in 100 s of constant, 2005 $R) using data from Tesouro Nacional (2011). As a nominal amount of currency has more purchasing power in some areas—possibly in poorer or more rural areas—than in others, I convert all measures of expenditure, revenue, and income to constant, 2005 São Paulo currency using a set of spatial income deflators for Brazil computed by Ferreira et al. (2003). 4.3.3. School enrollment levels The Ministry of Education's annual Census of Schools (Censo Escolar) provides detailed school-level data on the number of students 15 Rather than computing national income growth rates by decile as in Barros et al. (2009), I compute them by percentile—thus computing 100 different rates rather than 10. 16 These jointly account for about half of municipal revenue. Additional revenue goes to administrative costs (e.g., paying public employees and operating the judiciary), public assistance (welfare), and a number of smaller uses which make it difficult to identify the beneficiaries of the spending.

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enrolled by grade level and type of school (public or private) for each year during 1995–2008. Combining these data with population by age data, I also compute the share of 0–6 year olds and 7–15 year olds enrolled in school (public and private).17 4.3.4. Public education quality The Census of Schools also provides detailed information on teachers and school infrastructure in each municipality i in each year t. I compute several measures of the average quality of educational inputs: students per teacher (i.e. class size), the fraction of teachers with at least some post-secondary education,18 and the fraction of schools with a designated school building,19 electricity, an indoor bathroom, a library, and a computer. Table 2 summarizes these variables for public vs. private pre-primary and primary schools in 2008.20 Private schools outperform public on all metrics but the education level of pre-primary teachers (public teachers are 3.6 percentage points more likely than private to have some post-secondary education). Public and private primary school teachers are equally educated. On all other dimensions, private schools outperform public schools, and the differences are statistically significant at the 0.01 level. Public schools have 5.5 more pre-primary students and 22.4 more primary students per teacher. Indoor bathrooms are present in 80% of public pre-primary schools and 76% of public primary schools, but in 96% of each of their private counterparts. A library is present in 20% of public pre-primary schools and 33% of public primary schools, but in 62% of private pre-primary schools and 80% of private primary schools. Given high correlations among the infrastructure quality variables, I use principal components analysis to combine them into an index and use the first principal component. For public pre-primary (primary) schools, the first principal component explains 60% (67%) of the variation in the infrastructure quality variables, with an eigenvalue of 3.01 (3.33). The Ministry of Education also provides municipality-level average math and Portuguese test scores of 4th grade students in municipal public primary schools for 2005, 2007, and 2009. These come from the Prova Brasil National Assessment of Educational Achievement. Assuming educational investments (inputs) have a lagged impact on education outputs, I measure test scores at time t + 1 and thus merge these data onto revenues data from 2004, 2006, and 2008. These data are only available for public schools. 4.4. Demographic, political, and economic trends One potential concern is possible correlation between simulated revenue and demographic, political, or economic trends that affect public investment. I thus include total population, age 0–6 population, and age 7–15 population (all in 100,000 s) in Xit—the vector of control variables for municipality i. I also include gross municipal product (GMP) per capita (in 10,000 s of 2005 R$), as this affects the tax base. As a robustness check, I also show specifications controlling for three time-varying political factors, measured using municipal elections data from the Superior Electoral Court (TSE) for 1996, 2000, 2004, and 2008. They include three features of the last mayoral election: the mayor's vote share, the number of political parties competing, and an HHI of between-party competition. 21 These might influence the quality of policies or the level of corruption. As many 17 Population by age data from IBGE are available for 1991, 1996, 2000, and 2007. I compute annual estimates by linear interpolation. 18 This includes any post-high school education, whether or not a degree was obtained. 19 Some schools report using a teacher's house, church, community center, business, barn, or shed to carry out classes. 20 Infrastructure data come from an average across all schools. Teacher education data come from an average across all teachers. Students per teacher data come from an average across municipalities. 21 I compute the standard Herfindahl–Hirschman Index typically used to measure competition among firms in an industry. A market is a municipality, a firm is a political party, and its market share is its share of votes during the last election.

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municipalities are rural, I also take into account shifts in the world prices of three important agricultural products: coffee, cocoa, and bananas. I multiply the current year world price of each (from the International Monetary Fund's International Financial Statistics) by total hectares of it in the municipality in 1994 (from the Institute of Applied Economics Research). This allows the severity of a price shock for a municipality to be determined by the intensity with which it grows the commodity.

4.5. Controlling for another government program: PMAT In 1998—the same year FUNDEF was launched—the Brazilian Development Bank (BNDES) initiated a new program targeting municipal governments: the Tax Administration Modernization Program (PMAT). PMAT was available to all municipalities, providing applicants with subsidized loans to invest in modernizing their tax administration. About 6% of Brazil's municipalities (331 in total, covering about 40% of the Brazilian population) elected to take out a PMAT loan at some point during 1998–2008. Exploiting exogenous variation in the time between application to the program and receipt of funds, Gadenne (2012) estimates that an increase in local tax revenues (which PMAT delivers) boosts investment in municipal public education more than does an equivalent increase in transfer revenue. One may worry that time-variation in the rules governing FUNDEF is somehow correlated with receipts from PMAT. As a robustness check, I estimate specifications that take into account the effect of PMAT, to ensure that such a correlation does not drive my results. I try: a) controlling for a dummy for participation in PMAT by municipality i in year t; b) controlling for the PMAT loan amount per capita in municipality i in year t;22 and c) omitting the roughly 6% of municipalities that had a PMAT program sometime during 1998–2008. None of these has an appreciable impact on my results. Data on participation in PMAT are those collected by Gadenne (2012) through interviews with BNDES.

5. Results 5.1. First stage results Table 4 presents estimates of the first-stage regressions. Actual municipal revenue is robustly positively correlated with simulated revenue. Column (1) indicates that a 10% increase in simulated revenue is associated with a 4.6% increase in revenue.23 The F-statistic on the excluded instrument is 1566. In these and all specifications, I cluster standard errors at the municipality level since revenue and public investments vary at this level. Column (2) explicitly allows municipalities to convert revenue shocks from FUNDEF/B into revenue differently, according to their year 2000 levels of inequality and median income. An increase in simulated revenue increases revenue more in higher-income municipalities (significant at the 0.01 level). However, there is little evidence that the effects of simulated revenue vary with the 2000 Gini. Column (3) estimates an alternative specification, interacting simulated revenue with the time-varying, predicted Gini and median income values (described in Section 4.3.1). I find that municipalities predicted to become richer over the sample period become more likely to convert simulated revenue into revenue. Further, municipalities predicted to become more unequal over the sample period become less likely to convert simulated revenue into revenue. The F-statistic on the joint significance of the excluded 22 Since a PMAT program is six years long, I take the total amount loaned divided by six to be the annual loan amount during each of the six years of the loan (in all other years, it is 0). 23 Several factors can explain why this coefficient is not equal to 1.0. First, municipalities can reduce collections of tax revenue in response to an influx of money from FUNDEF/B. Second, the panel is rather long; changes in the political and economic landscape of a municipality over time may drive the coefficient up or down.

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Table 4 IV First stage results, showing the effect of simulated revenue from the law change on actual revenue. Dependent variable:

Log (simulated revenue)

Log (municipal per capita revenue)

Revenue × Gini Revenue × median Revenue × predicted Revenue × predicted income Gini median income

(1)

(2)

(3)

(4)

(5)

(6)

(7)

0.459*** (0.012)

0.839*** (0.087) 0.145 (0.206) 0.213*** (0.013)

0.784*** (0.029)

0.515*** (0.179) −0.457 (0.422) 0.830*** (0.027)

−0.226*** (0.036) 1.513*** (0.087) 0.091*** (0.005)

−0.044 (0.044)

−0.251*** (0.016)

0.522*** (0.034) 0.791*** (0.022) 0.978*** (0.031) −0.137*** (0.035) −0.342*** (0.040) −0.148*** (0.009) 51,172 0.799 3918 1579.81

1.274*** (0.013) 0.093*** (0.007) −0.333*** (0.009) 0.028*** (0.011) 0.145*** (0.012) 0.043*** (0.003) 51,172 0.836 3918 3690.32

Log (simulated revenue) × Gini Log (simulated revenue) × log (median income)

−0.132*** (0.019) Log (simulated revenue) × log (predicted median inc) 0.140*** (0.014) Log (population) −0.654*** −0.635*** −0.647*** (0.017) (0.017) (0.017) Log (0–6 population) 0.038* 0.053*** 0.046** (0.020) (0.020) (0.020) Log (7–15 population) 0.281*** 0.260*** 0.278*** (0.023) (0.023) (0.023) Log (GMP per capita) 0.079*** 0.081*** 0.080*** (0.006) (0.006) (0.006) Observations 51,212 51,159 51,172 R-squared 0.848 0.850 0.849 Number of municipalities 3919 3915 3918 F Stat, excluded instruments 1565.72 665.3 584.66 Log (simulated revenue) × predicted Gini

1.064*** (0.034) −0.155*** (0.040) −0.341*** (0.047) −0.174*** (0.011) 51,159 0.836 3915 1321.01

−0.245*** (0.007) 0.031*** (0.008) 0.096*** (0.009) 0.032*** (0.002) 51,159 0.848 3915 735.83

Notes: An observation is a municipality - year. Robust standard errors are in parentheses, and clustered at the municipality level. All specifications include municipality and year fixed effects, as well as a linear time trend interacted with the pre-reform, 1997 levels of log(per capita revenue), log(per capita transfer revenue), log(public pre-primary enrollment rate), log(public primary enrollment rate), and log(share of primary school students in state or federally-run schools). ***indicates p b .01; **indicates p b .05; *indicates p b .10. Population is measured in 100,000 s. The mean Gini coefficient in 2000 is 0.39, the mean value of median income per capita (as of the 2000 Census, measured in 10,000 s of 2005 Reais) is 0.23, and mean revenue per capita (in 100 s 2005 Reais) is 9.84. The mean predicted Gini coefficient during 1995–2008 is 0.53 and the mean predicted median income per capita during 1995–2008 is 0.25 (measured in 10,000 s of 2005 Reais). Sources: Author's calculations based on data from IBGE, Ministry of Education, and Tesouro Nacional.

instruments is over 580 in each first stage specification, leaving no concerns of weak instruments. 5.2. Effects of a revenue shock on public investment Table 5 presents OLS and IV estimates of the effect of revenue on various measures of municipal investment, with and without population and GMP controls. These include education and infrastructure spending per capita, the per capita budget surplus, the enrollment rate in public pre-primary schools (municipal public pre-primary students per population of 0–6 year olds), and the enrollment rate in public primary schools (municipal public primary students per population of 7–15 year olds). In every specification—unsurprisingly—revenue is positively correlated with the investment measure. Further, adding controls has little impact on the point estimates. The IV estimates suggest that a 10% increase in revenue induced by the FUNDEF/B reforms is associated with an 11% increase in education spending per capita (Column 2) and a 5% increase in infrastructure spending per capita (Column 4). It is also associated with a 12% increase in the per capita budget surplus (Column 6). The increase in education spending does impact public school enrollment rates, though its effects are much more dramatic in the area of pre-primary education than primary education. A 10% increase in revenue is associated with a 5% increase in the public pre-primary enrollment rate (significant at the 0.01 level), but with a meager 0.09% increase in the public primary enrollment rate (a result which is further statistically insignificant at conventional levels). This latter result suggests that municipal public primary education is not a level for which enrollment levels are constrained by revenue. This may be in part due to the fact that public primary education must be provided to any child whose parents demand it, while municipalities have nearly complete discretion in providing public pre-primary education.24 24 While age 4–6 education is now a legal requirement, it was not so during the sample period.

The OLS and IV estimates are sufficiently different to suggest bias. For education spending and pre-primary enrollment, the OLS estimates are smaller in magnitude than the IV estimates, consistent with the previously-described channels of downward bias. For example, if revenue is higher precisely where there are fewer children, then OLS might downward-bias the effects of revenue on education spending and pre-primary enrollment. In the case of infrastructure spending and the budget surplus, the OLS estimates are larger in magnitude than the IV estimates. This might be due to reverse causality, whereby more public infrastructure and a larger budget surplus tend to support the business climate and thereby raise revenues.25 5.3. The distribution of income and government spending The levels of inequality and median income in a municipality moderate the effects of a revenue shock on government spending, as shown in Table 6. Panel A estimates the coefficients on revenue and its interactions with inequality and median income from Eq. (1). Panel B interacts revenue with terciles of inequality and median income, thus allowing the effects of revenue to vary by inequality and income categories. More unequal and higher-income municipalities are less likely to spend a revenue shock on education, as seen in Panel A. This is true whether we use the 2000 levels of inequality and median income (strategy 1) or use time-varying, predicted values based on national patterns of income growth (strategy 2)—seen in Columns (1) and (2), respectively. The interaction between revenue and the Gini is always negative and significant at the 0.01 level, as is the interaction between revenue and median income. This suggests two things: a) more unequal and richer places (as measured in year 2000) are 25 A budget surplus increases the supply of loans available to private borrowers, pushing down the interest rate (Ball and Mankiw, 1995). Further, DeLong and Summers (1991) suggest that the accumulation of capital stimulates technological change and increases economy-wide productivity.

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Table 5 OLS and IV results, showing the effects of revenue on several measures of government investment. Dependent Variable:

Log (education spending per capita)

Log (infrastructure spending per capita)

Log (budget surplus per capita)

Log (public pre-primary school students per age 0-6 pop.)

Log (public primary school students per age 7-15 pop.)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

0.695*** (0.010)

0.655*** (0.011) −0.212*** (0.020) 0.083*** (0.023) 0.123*** (0.026) 0.035*** (0.006) 50,714 0.786 3919

1.112*** (0.034)

1.132*** (0.038) 0.244*** (0.086) −0.452*** (0.101) 0.443*** (0.114) 0.074*** (0.027) 46,257 0.158 3918

3.105*** (0.055)

3.462*** (0.059) 1.654*** (0.113) −0.532*** (0.132) −0.172 (0.150) −0.257*** (0.037) 33,788 0.269 3918

0.065*** (0.015)

0.083*** (0.015) 0.346*** (0.040) −0.329*** (0.050) −0.203*** (0.054) 0.048*** (0.013) 49,456 0.566 3919

0.117*** (0.012)

0.198*** (0.013) 0.477*** (0.031) 0.161*** (0.047) −0.386*** (0.049) 0.008 (0.011) 48,877 0.538 3919

Panel A: OLS results Log (revenue) Log (population) Log (0–6 population) Log (7–15 population) Log (GMP per capita) Observations R-squared Number of municipalities

50,714 0.784 3919

46,257 0.157 3918

33,788 0.258 3918

49,456 0.563 3919

48,877 0.531 3919

Panel B: IV results Log (revenue)

1.067*** (0.025)

Log (population) Log (0–6 population) Log (7–15 population) Log (GMP per capita) Observations R-squared Number of municipalities

50,713 0.760 3918

1.131*** (0.033) 0.148*** (0.032) 0.023 (0.025) 0.019 (0.027) −0.008 (0.007) 50,713 0.753 3918

0.396** (0.167)

46,256 0.137 3917

0.450*** (0.174) −0.227 (0.153) −0.383*** (0.104) 0.594*** (0.125) 0.149*** (0.033) 46,256 0.143 3917

1.160*** (0.196)

33,777 0.201 3907

1.245*** (0.239) 0.041 (0.201) −0.262* (0.140) 0.335** (0.163) −0.041 (0.043) 33,777 0.206 3907

0.360*** (0.056)

49,455 0.555 3918

0.469*** (0.068) 0.634*** (0.060) −0.375*** (0.051) −0.290*** (0.057) 0.012 (0.015) 49,455 0.556 3918

0.021 (0.047)

48,867 0.530 3909

0.089 (0.058) 0.396*** (0.049) 0.175*** (0.047) −0.362*** (0.051) 0.019 (0.013) 48,867 0.537 3909

Notes: An observation is a municipality - year. I instrument for revenue using simulated revenue. Robust standard errors are in parentheses, and clustered at the municipality level. ***indicates p b .01; **indicates p b .05; *indicates p b .10. Public school refers to municipal public schools, run by the local government. All specifications include municipality and year fixed effects, as well as a linear time trend interacted with the pre-reform, 1997 levels of log(per capita revenue), log(per capita transfer revenue), log(public pre-primary enrollment rate), log(public primary enrollment rate), and log(share of primary school students in state or federally-run schools). Population is measured in 100,000 s and mean per capita income is measured in 10,000 s of 2005 R$. The mean revenue per capita (in 100 s 2005 Reais) is 9.84. Sources: Author's calculations based on data from IBGE, Ministry of Education, and Tesouro Nacional.

less likely to invest an exogenous revenue shock in education, and b) places which we expect to become more unequal and richer due to shifting national income patterns—such as changes in the return to skill and in labor market institutions—become increasingly less likely to invest a revenue shock in education. From Column (1), given a 10% increase in revenue, very equal and very unequal municipalities invest the shock very differently in education. If we set income at its sample median and allow the 2000 Gini to increase from the 10th percentile (0.35) to the 90th (0.44), then the municipality will go from increasing education spending by 8.6% to increasing education spending by only 8.0% (a 0.06/0.86 = 7% decrease in the elasticity).26 Similarly, very poor and very rich municipalities behave differently. If we set the 2000 Gini at its sample median and allow 2000 median income to increase from the 10th percentile (895 $R) to the 90th percentile (4144 $R), then the municipality will go from increasing education spending by 10.2% to increasing education spending by only 7.0% (a 0.32/1.02 = 31% decrease in the elasticity).27 Column (2) shows similar results using the predicted distribution of income. Higher-income municipalities are much more likely than lowincome municipalities to spend a revenue shock on infrastructure, also shown in Panel A. This can be seen in Columns (3) and (4), which use strategy 1 and strategy 2 for measuring the distribution of income, 26 8.6% = 0.774 + (log(0.218) × −0.206) + (0.35 × −0.646), and 8.0% = 0.774 + (log(0.218) × −0.206) + (0.44 × −0.646). 27 10.2% = 0.774 + (log(0.089) × −0.206) + (0.39 × −0.646), and 7.0% = 0.774 + (log(0.414) × −0.206) + (0.39 × −0.646).

respectively. The interaction between revenue and median income is always positive and significant at the 0.01 level. From Column (3), given a 10% increase in revenue, very equal and very unequal municipalities behave similarly in their infrastructure spending. However, very poor and very rich municipalities behave differently. If we set the 2000 Gini at its sample median and allow 2000 median income to increase from the 10th percentile to the 90th, then the municipality will go from increasing infrastructure spending by only 8.3% to increasing infrastructure spending by 12.3% (a 0.40/0.83 = 48% increase in the elasticity). Finally, unequal and higher-income municipalities are both much more likely to save a revenue shock by running a budget surplus— seen in Panel A, Columns (5) and (6) (using strategies 1 and 2, respectively). The interaction between revenue and the Gini is always positive, and it is statistically significant when using strategy 1 (at the 0.05 level). The interaction between revenue and median income is always positive and significant at the 0.01 level. From Column (5), given a 10% increase in revenue, very equal and very unequal municipalities behave differently. If we set income at its sample median and allow the 2000 Gini to increase from the 10th percentile to the 90th, then the municipality will go from increasing its budget surplus by 23.6% to increasing it by 26.0% (a 0.24/2.36 = 10% increase in the elasticity). Similarly, very poor and very rich municipalities behave differently. If we set the 2000 Gini at its sample median and allow 2000 median income to increase from the 10th percentile to the 90th, then the municipality will go from increasing the budget surplus by 19.1% to increasing it by 28.7% (a 0.95/1.91 = 50% increase in the elasticity). From these findings, we see that while higher

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Table 6 IV Results, showing how inequality and median income moderate the effect of revenue on government spending. Dependent variable:

Log (education spending per capita)

Log (infrastructure spending per capita)

Log (budget surplus per capita)

(1)

(2)

(3)

(4)

(5)

(6)

0.748*** (0.054)

1.540*** (0.379) −0.196 (0.744) 0.262*** (0.055)

1.370*** (0.234)

2.382*** (0.548) 2.647** (1.091) 0.622*** (0.084)

2.395*** (0.391)

Panel A: interactions of revenue with inequality and median income Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income)

0.774*** (0.081) −0.646*** (0.165) −0.206*** (0.013)

Log (revenue) × predicted Gini Log (revenue) × log (predicted median income) R-squared Kleibergen-Paap rk Wald F statistic

0.782 640.41

−0.220*** (0.060) −0.186*** (0.015) 0.778 645.04

0.158 336.81

−0.066 (0.253) 0.227*** (0.064) 0.158 350.37

0.255 235.65

0.614 (0.422) 0.455*** (0.103) 0.243 234.60

Panel B: interactions of revenue with terciles of inequality and median income Distribution of income used:

Actual (year 2000)

Predicted (time-varying)

Actual (year 2000)

Predicted (time-varying)

Actual (year 2000)

Predicted (time-varying)

Log (revenue)

0.880*** (0.031) 0.006 (0.011) −0.027** (0.012) 0.158*** (0.013) −0.096*** (0.016) 0.779 50,660 3914 398.52

0.973*** (0.031) 0.013 (0.009) −0.027*** (0.008) 0.127*** (0.012) −0.025** (0.011) 0.771 50,674 3917 346.96

1.058*** (0.142) 0.026 (0.055) 0.020 (0.054) −0.242*** (0.054) 0.148** (0.067) 0.159 46,218 3913 225.47

0.811*** (0.148) −0.026 (0.041) −0.007 (0.032) −0.116** (0.047) 0.063 (0.042) 0.156 46,223 3915 171.34

2.338*** (0.223) −0.186** (0.085) 0.002 (0.085) −0.365*** (0.085) 0.529*** (0.102) 0.252 33,745 3903 183.51

1.924*** (0.236) −0.104 (0.066) −0.024 (0.055) −0.374*** (0.081) 0.050 (0.072) 0.233 33,758 3906 136.31

Log (revenue) × Gini bottom third Log (revenue) × Gini top third Log (revenue) × Median income bottom third Log (revenue) × Median income top third R-squared Observations Number of municipalities Kleibergen-Paap rk Wald F statistic

Notes: An observation is a municipality - year. I instrument for revenue using simulated revenue. Robust standard errors are in parentheses, and clustered at the municipality level. ***indicates p b .01; **indicates p b .05; *indicates p b .10. All specifications include municipality and year fixed effects, controls for population, age 0–6 population, and age 7–15 population, a control for gross municipal product (GMP), and a linear time trend interacted with the pre-reform, 1997 levels of log(per capita revenue), log(per capita transfer revenue), log(public pre-primary enrollment rate), log(public primary enrollment rate), and log(share of primary school students in state or federally-run schools). The mean Gini coefficient in 2000 is 0.39, the mean value of median income per capita (as of the 2000 Census, measured in 10,000 s of 2005 Reais) is 0.23, and mean revenue per capita (in 100 s 2005 Reais) is 9.84. The mean predicted Gini coefficient during 1995–2008 is 0.53 and the mean predicted median income per capita during 1995–2008 is 0.25 (measured in 10,000 s of 2005 Reais). Sources: Author's calculations based on data from IBGE, Ministry of Education, and Tesouro Nacional.

median income and higher income inequality tend to reduce the amount of a revenue shock allocated to education, an important alternate use of that revenue is the generation of a budget surplus (which can help increase access to credit and lower future taxes). In Panel B, I interact tercile dummies of inequality and median income with revenue to see whether it is particularly high or particularly low inequality and income that drive the results. A few results are interesting and worth noting. Column (1) shows that when a municipality in the middle third on both inequality and median income is given a 10% increase in revenue, it spends 8.8% more on education. If this municipality were instead in the bottom third on inequality, it would spend similarly. It is being in the top third of inequality that has an especially large, negative effect on education spending. That is, the effect of inequality on education investment comes mainly from very unequal areas being less likely to invest a shock in education. Column (3) shows that when a municipality in the middle third on both inequality and median income is given a 10% increase in revenue, it spends 10.6% more on infrastructure. Both being in the bottom and being in the top third on median income significantly affect infrastructure spending, though the negative effect of being in the bottom third is larger in magnitude than the positive effect of being in the top third. That is, the effect of median income on infrastructure investment comes mainly from very poor areas being less likely to invest a shock in infrastructure. Finally, Column (5) shows that when a municipality in the middle third on both inequality and median income is given

a 10% increase in revenue, it increases its budget surplus by 23.4%. If this municipality were instead in the top third on inequality, it would spend similarly. However, being in the bottom third on inequality has a strong, negative impact on the propensity to save a revenue shock. That is, the effect of inequality on the budget surplus seems to come mainly from very equal areas being less likely to save. The results strongly suggest that municipalities at different levels of inequality and median income spend the same revenue shock differently. Unequal and higher-income municipalities are significantly less likely to invest a shock in education. They are more likely to invest it in infrastructure or a budget surplus. That inequality leads to less investment in education fails to support the predictions of Meltzer and Richard (1981). However, it is in keeping with a class of models predicting that the existence of private substitutes means inequality reduces public education investment. That higher income leads to less investment in education supports the model of Suárez Serrato and Wingender (2011), under which poor and unskilled workers value such government services more than richer, skilled workers. Interestingly, the findings on education do not hold for public infrastructure investment, which is broadly enjoyed by most citizens and does not target the poor. Unequal areas are no less likely to spend a revenue shock on infrastructure, and highincome areas are much more likely to spend it on infrastructure. This provides evidence that the distribution of income affects not only the size of government, but also the composition (or type) of government

K. Kosec / Journal of Development Economics 107 (2014) 320–342

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Table 7 IV Results, showing how inequality and median income moderate the effect of revenue on school enrollment. Dependent Variable:

Log (public pre-primary school students per age 0–6 pop.)

Log (public primary school students per age 7–15 pop.)

Log (private preprimary students per age 0–6 pop.)

Log (private primary students per age 7–15 pop.)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

−0.590*** (0.110)

−0.577*** (0.159) −0.841*** (0.270) −0.325*** (0.024)

−0.514*** (0.107)

0.019 (0.180)

−0.487 (0.430) 1.228 (0.886) 0.001 (0.072)

−0.514*** (0.157)

0.540 (0.470) −0.051 (0.999) 0.324*** (0.063)

0.244 581.37 27,414

0.245 280.24 27,386

0.084 580.71 25,081

0.104 298.23 25,053

Panel A: interactions with inequality and median income Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income)

−0.028 (0.164) −0.737** (0.324) −0.257*** (0.026)

−0.031 (0.118) −0.390*** (0.032) 0.559 610.72 49,427

0.494 579.18 48,822

−0.284*** (0.085) −0.284*** (0.029) 0.514 577.77 48,839

Actual (year 2000)

Predicted (time-varying)

Actual (year 2000)

Predicted (time-varying)

Actual (year 2000)

Actual (year 2000)

0.079 (0.066) 0.049** (0.025) −0.009 (0.024) 0.228*** (0.025) −0.102*** (0.032) 0.562 49,410 3914 376.44

0.106* (0.063) 0.015 (0.019) −0.015 (0.014) 0.222*** (0.022) −0.055*** (0.020) 0.564 49,427 3916 321.85

−0.361*** (0.069) 0.021 (0.017) −0.021 (0.019) 0.308*** (0.021) −0.022 (0.035) 0.513 48,822 3905 358.45

−0.182*** (0.064) 0.026* (0.014) −0.034*** (0.012) 0.216*** (0.018) −0.000 (0.019) 0.528 48,839 3907 307.74

−0.142 (0.156) −0.091 (0.082) 0.027 (0.059) 0.169*** (0.065) 0.146* (0.074) 0.247 27,386 2768 175.31

−0.128 (0.135) −0.144 (0.088) −0.091* (0.054) −0.078 (0.061) 0.317*** (0.066) 0.104 25,053 2629 183.57

Log (revenue) × predicted Gini Log (revenue) × log (predicted income) R-squared F Stat, excluded instruments Observations

0.561 612.54 49,410

Panel B: interactions with terciles of inequality and median income

Log (revenue) Log (revenue) × Gini bottom third Log (revenue) × Gini top third Log (revenue) × Median income bottom third Log (revenue) × Median income top third R-squared Observations Number of municipalities Kleibergen-Paap rk Wald F statistic

Notes: An observation is a municipality - year. I instrument for revenue using simulated revenue. Robust standard errors are in parentheses, and clustered at the municipality level. ***indicates p b .01; **indicates p b .05; *indicates p b .10. All specifications include municipality and year fixed effects, controls for population, age 0–6 population, and age 7–15 population, a control for gross municipal product (GMP), and a linear time trend interacted with the pre-reform, 1997 levels of log(per capita revenue), log(per capita transfer revenue), log(public pre-primary enrollment rate), log(public primary enrollment rate), and log(share of primary school students in state or federally-run schools). The mean Gini coefficient in2000 is 0.39, the mean value of median income per capita (as of the 2000 Census, measured in 10,000 s of 2005 Reais) is 0.23, and mean revenue per capita (in 100 s 2005 Reais) is 9.84. The mean predicted Gini coefficient during 1995–2008 is 0.53 and the mean predicted median income per capita during 1995–2008 is 0.25 (measured in 10,000 s of 2005 Reais). Sources: Author's calculations based on data from IBGE, Ministry of Education, and Tesouro Nacional.

spending. Unequal and high-income areas tend to invest more heavily in goods that broadly benefit all citizens rather than those that target the poor. Ball and Mankiw (1995) provide insight into why unequal and higher-income areas are more likely to save a revenue shock as a budget surplus. Equal and low-income municipalities may have greater popular pressure for raising consumption in the short run given the decreasing marginal utility of consumption. Individuals in such municipalities may also have a higher discount rate, or expect to catch-up and become richer in the future—thus wanting to consume today and pay the tax bill later.28 More unequal and high-income municipalities, on the other hand, may wish to improve the business climate by running a budget surplus. 5.4. School enrollment rates Municipalities increasing education spending may increase public school enrollment—either by attracting children not yet in school (more 28 Ball and Mankiw (1995) note: “Because of technological progress, the income and consumption of a typical individual in the economy rises over time. Because budget deficits shift taxes forward in time, they benefit relatively poor current taxpayers at the expense of relatively rich future taxpayers.”

likely among 0–6 year olds who are not legally required to attend school) or by drawing children from private schools to public. Table 5 provided evidence of an expansion in enrollment due to a revenue shock that is particularly large and statistically significant in the case of pre-primary (age 0–6) education. In this section, I consider how inequality and median income moderate the effects of a revenue shock on school enrollment. In the next section, I turn to the average quality of educational inputs and outcomes following enrollment expansions. Unequal and high-income municipalities are less likely than their more equal and low-income counterparts to raise public school enrollment following a revenue shock, as shown in Table 7. This is true for both public pre-primary education (Columns 1 and 2) and public primary education (Columns 3 and 4), and results using the 2000 levels of inequality and median income are similar to those using time-varying, predicted values. From Panel A, the interaction between revenue and the Gini is negative and significant at the 0.05 level in the case of public pre-primary education and at the 0.01 level in the case of primary education. The interaction between revenue and median income is negative and significant at the 0.01 level in all specifications. While a revenue shock tends to expand public school enrollment (Table 5), the impact of the shock on enrollment varies significantly according to the levels of median income and inequality when we flexibly allow its impact to do so (Table 7).

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Table 8 IV Results, showing how inequality and median income moderate the effect of revenue on the quality of education inputs and outputs. Dependent Variable:

Infrastructure quality index (5 components)

Share of teachers w/some post-secondary education

Log (students per teacher)

Log (Prova Brasil 4th grade test score)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Pre-primary

Primary

Pre-primary

Primary

Pre-primary

Primary

Portuguese

Math

−0.424* (0.249) 1.896*** (0.508) 0.313*** (0.038) 0.899 49,393 3914

−1.132*** (0.376) 2.248*** (0.739) 0.352*** (0.062) 0.876 41,866 3904

−0.108 (0.086) 0.816*** (0.174) 0.120*** (0.013) 0.379 45,485 3913

−0.372*** (0.096) 1.435*** (0.207) 0.129*** (0.013) 0.651 44,876 3904

−0.709*** (0.182) 0.343 (0.378) −0.542*** (0.027) 0.315 45,401 3913

−1.361*** (0.180) 1.519*** (0.370) −0.618*** (0.029) 0.249 44,778 3904

0.081 (0.151) 0.109 (0.139) 0.033*** (0.009) 0.285 11,152 3981

−0.265 (0.187) 0.435** (0.170) 0.066*** (0.011) 0.456 11,152 3981

Pre-primary

Primary

Pre-primary

Primary

Pre-primary

Primary

0.078 (0.362) 0.193 (0.747) −0.070 (0.055) 0.894 26,605 2538

−0.033 (0.388) 0.386 (0.817) 0.068 (0.055) 0.936 20,408 2214

0.127 (0.130) 0.227 (0.255) 0.087*** (0.020) 0.212 25,124 2659

−0.257* (0.149) 0.905*** (0.303) 0.033 (0.022) 0.405 22,837 2472

−0.742*** (0.259) 0.643 (0.527) −0.462*** (0.043) 0.264 25,017 2650

0.334 (0.297) −1.871*** (0.627) −0.315*** (0.043) 0.551 22,604 2464

Panel A: public schools

Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) R-squared Observations Number of municipalities Panel B: private schools

Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) R-squared Observations Number of municipalities

Notes: An observation is a municipality - year. I instrument for revenue using simulated revenue. Robust standard errors are in parentheses, and clustered at the municipality level. ***indicates p b .01; **indicates p b .05; *indicates p b .10. All specifications include municipality and year fixed effects, controls for population, age 0–6 population, and age 7–15 population, a control for gross municipal product (GMP), and a linear time trend interacted with the pre-reform, 1997 levels of log(per capita revenue), log(per capita transfer revenue), log(public pre-primary enrollment rate), log(public primary enrollment rate), and log(share of primary school students in state or federally-run schools). Pre-primary education is age 0–6 education, and primary education is age 7–15 education. Measures of the quality of educational inputs (Columns 1–6) are measured at time t. Test scores (Columns 7–8) are measured at time t + 1. The mean Gini coefficient in 2000 is 0.39, the mean value of median income per capita (as of the 2000 Census, measured in 10,000 s of 2005 Reais) is 0.23, and mean revenue per capita (in 100 s 2005 Reais) is 9.84. Sources: Author's calculations based on data from IBGE, Ministry of Education, and Tesouro Nacional.

To interpret the magnitudes of the effects, it is again helpful to compare a municipality in the middle third on both inequality and income with others, as shown in Panel B. Column (1) shows that if one doubled its revenue, this municipality would increase its public pre-primary enrollment rate by 7.9%. If this municipality were instead in the top third on inequality, it would behave similarly. However, if it were instead in the bottom third on inequality, it would increase preprimary enrollment by a substantially larger 12.8% (7.9 + 4.9)—a difference statistically significant at the 0.05 level. Similarly, if this municipality in the middle third of both inequality and income (which expands pre-primary enrollment by 7.9% following a doubling of revenues) were instead in the bottom third on income, it would increase its pre-primary enrollment rate by a substantially larger 30.8% (7.9 + 22.8) in response to the shock. Were it in the top third on income, it would actual reduce its public pre-primary enrollment rate by 2.1% (7.9–10.0) in response to the shock. Column (2) shows similar results using the predicted distribution of income. These differences by income are statistically significant at the 0.01 level. Results for primary education (Columns 3 and 4) similarly suggest that the distribution of income importantly moderates the effect of a revenue shock on public school enrollment, with municipalities with a Gini coefficient and median income in the bottom third being most likely to expand primary enrollment. One might expect changes in public education investments to negatively impact enrollment in private schools. From Panel A, Columns (5) and (7), we see that a revenue increase has no significant impact on enrollment in private pre-primary. However, a 10% increase in revenue is associated with a 5.1% decrease in the private primary school enrollment rate. Column (8), Panels A and B show that this reduction in private schooling in response to more public sector revenue is much larger in magnitude in municipalities with lower median income. The effects do not vary consistently with the level of inequality.

5.5. Quality of education inputs and outputs Municipalities increasing education spending may increase or decrease the quality of educational inputs and outputs, depending on whether enrollment expansions outpace the additional investments. We have already seen that higher inequality and median income tend to raise the amount of a revenue shock invested in education, as well as raise the public school enrollment rate; a natural question is what these effects imply for educational quality. Conceivably, they may raise or lower the quality of factors including infrastructure, teachers, and learning. In this section, I consider how inequality and median income moderate the effects of a revenue shock on educational quality. I measure educational quality using both educational inputs and a measure of educational outputs: standardized test scores. I consider both public and private school quality, at the pre-primary and primary levels. Public school quality should be directly affected by the investment decisions of local governments. Private school quality may be indirectly affected through changes in demand for private schools. Despite their lower propensity to invest a revenue shock in education or expand public school enrollment, more unequal and higher-income municipalities are more likely to raise the average quality of public education following a revenue shock, as shown in Table 8. Panel A presents results for public schools on three indicators of educational input quality and two indicators of output quality. Panel B presents the same results for private schools. Indicators of input quality include the school infrastructure quality index described in Section 4.3.4,29 the share of teachers 29 Recall that the index is the first principal component of a principal components analysis using five variables: the share of municipal schools with their own building, electricity, indoor toilet, library, and computer. Table C.1 presents results for the five individual infrastructure quality variables.

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Table 9 IV Results, showing how the pre-reform supply of private education moderates the effects of a revenue shock. (1)

(2)

(3)

(4)

0.906*** (0.122) −1.022*** (0.237) −0.223*** (0.020)

0.833*** (0.125) −0.743*** (0.257) −0.215*** (0.020) −0.021*** (0.008)

0.854*** (0.123) −0.726*** (0.259) −0.212*** (0.020)

0.891*** (0.122) −0.696*** (0.255) −0.213*** (0.020)

Dependent variable: log (education spending per capita) Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Log (revenue) × log (No. private primary schools in 1997)

−0.016*** (0.006)

Log (revenue) × log (No. private primary classrooms in 1997) Log (revenue) × log (No. private primary students in 1997) Log(population) Log(0–6 population) Log(7–15 population) Log(GMP per capita) Observations R-squared Number of municipalities Kleibergen-Paap rk Wald F statistic

−0.068* (0.040) −0.023 (0.044) 0.127*** (0.047) −0.001 (0.010) 22,453 0.803 1732 344.00

−0.066* (0.040) −0.008 (0.044) 0.122*** (0.047) −0.002 (0.010) 22,453 0.804 1732 257.16

−0.065* (0.040) −0.011 (0.044) 0.123*** (0.047) −0.002 (0.010) 22,453 0.804 1732 256.55

−0.020*** (0.006) −0.063 (0.040) −0.007 (0.044) 0.123*** (0.047) −0.003 (0.010) 22,453 0.804 1732 256.61

Notes: An observation is a municipality - year. I instrument for revenue using simulated revenue. Robust standard errors are in parentheses, and clustered at the municipality level. ***indicates p b .01; **indicates p b .05; *indicates p b .10. All specifications include municipality and year fixed effects, controls for population, age 0–6 population, and age 7–15 population, a control for gross municipal product (GMP), and a linear time trend interacted with the pre-reform, 1997 levels of log(per capita revenue), log(per capita transfer revenue), log(public pre-primary enrollment rate), log(public primary enrollment rate), and log(share of primary school students in state or federally-run schools). The mean Gini coefficient in2000 is 0.39, the mean value of median income per capita (as of the 2000 Census, measured in 10,000 s of 2005 Reais) is 0.23, and mean revenue per capita (in 100 s 2005 Reais) is 9.84. Sources: Author's calculations based on data from IBGE, Ministry of Education, and Tesouro Nacional.

with at least some post-secondary education, and students per teacher, all measured in period t. Indicators of the quality of educational outputs are the municipality's public school average 4th grade Portuguese and math test scores in year t + 1 (not available for private schools). For public schools, the interaction between revenue and the Gini is positive and statistically significant at the 0.01 level in all specifications except pre-primary students per teacher and 4th grade Portuguese test scores, where it is insignificant at conventional levels. More unequal municipalities are more likely to improve pre-primary and primary school infrastructure quality and also more likely to employ pre-primary and primary teachers with at least some post-secondary education. They are also more likely to raise 4th grade math test scores (though no more likely to raise 4th grade Portuguese test scores). One caveat is that more unequal municipalities are more likely to raise primary school class sizes (though not pre-primary class sizes). Overall, however, inequality makes a municipality more likely to use a revenue shock to increase the average quality of educational inputs, and this further translates into a greater likelihood of raising math test scores.30 Thus, we find no evidence that a lower propensity of unequal areas to invest additional revenue in publicly-provided goods like education compromises the quality of such goods; if anything, unequal areas are more likely to use a revenue shock to raise the average quality of public education. The interaction between revenue and median income is positive and statistically significant at the 0.01 level in all specifications except students per teacher, where it is negative and statistically significant at the 0.01 level. Higher-income municipalities are significantly more likely to improve education along all of the input and output measures of quality. At both the pre-primary and primary school levels, they are more likely to improve school infrastructure quality, more likely to employ teachers with at least some postsecondary education, more likely to reduce class sizes, and more 30 Math test scores may be inherently easier to raise through changes in education inputs than language test scores; this is consistent, for example, with Muralidharan and Sundararaman (2011).

likely to raise 4th grade Portuguese and math test scores. Results instead using a predicted Gini and median income are similar, and available upon request. Panel B of Table 8 presents evidence on the impact of an exogenous public sector revenue shock on the average quality of private school inputs. Recall from Table 7 that a 10% increase in municipal revenue does not affect enrollment in public pre-primary school, but leads to a 5.1% decrease in private primary school enrollment. Now, we see that the revenue increase has no impact on private school infrastructure (either at the pre- primary or primary level). Fixed private school assets remain unchanged—perhaps because they are fixed. However, we do observe changes in the supply and education levels of private school teachers—mostly in more unequal and high-income municipalities. In more unequal municipalities, a revenue increase is far more likely to increase the share of private school teachers with some post-secondary education and to reduce the number of private primary school students per teacher (though similar results are not found for private pre-primary). In higher-income municipalities, a revenue increase is far more likely to increase the share of private pre-primary teachers with some post-secondary education, and to reduce the number of private school students per teacher in both pre-primary and primary schools. Given relatively greater improvements in public school quality in such municipalities, this is consistent with private schools being pressured to increase their quality along flexible dimensions like teacher inputs.

5.6. Mechanisms analysis: initial supply of private schools Thus far, we've seen evidence that municipalities with higher income inequality are less likely to allocate a revenue shock to education. This is consistent with a class of theoretical models predicting that the existence of private substitutes for education makes unequal municipalities relatively less likely to invest in public education. As inequality increases, the share of the population sending children to

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public schools declines, leading to less demand for public education under majority voting. However, a natural question is whether this lower propensity to invest in education is in part due mechanically to the large initial supply of private schools in unequal municipalities. In 1997—a year before the FUNDEF/B reform—the Gini coefficient was positively correlated with a number of indicators of the supply of private primary education: the number of schools (correlation coefficient 0.17), the number of classrooms (0.14), and the number of students (0.16). While the supply of private schools may contract in response to greater public education investment, it may be slow to do so in the short-run. Parents may hesitate to pull children out of their current private schools, and private schools may thus be slow to reduce their capacity or close. I explore the extent to which the supply of private schooling drives the results on inequality by including an interaction between revenue and the 1997 (i.e. initial) supply of private education in Eq. (1). Doing so provides insight into roughly what share of the impact of the Gini was due to its correlation with the private schooling supply. Table 9 presents these results.31 Column (1) is the baseline specification (Eq. (1)). Columns (2)–(4) each add to the baseline specification a control for logged revenue interacted with a logged 1997 measure of the supply of private primary schooling. Column (2) uses the number of schools, Column (3) uses the number of classrooms, and Column (4) uses the number of students. In all three specifications, the interaction between revenues and the 1997 measure of private education supply is negative and statistically significant at the 0.01 level. In municipalities with a larger initial supply of private schooling, a revenue shock is less likely to be spent on education. However, what is particularly interesting is how the coefficient on revenue interacted with the Gini (δ) changes once these new controls are added. Compared with Column (1), δ is 27% smaller in Column (2), 29% smaller in Column (3), and 32% smaller in Column (4). This provides suggestive evidence that an increase in revenue available to local governments interacts with the availability of private schooling to affect government choices regarding education spending. Some 30% of the effect of inequality on education spending may be due to the greater initial supply of private schools in more unequal municipalities. However, the remaining 70% of the effect may be due to other factors—such as a lower demand for public education and less political influence of the poor. 5.7. Robustness 5.7.1. Controlling for PMAT and political and economic trends If time variation in simulated revenue is somehow correlated with other government programs or with political and economic trends that impact public investment, the estimates would be biased due to omitted variables. (Sections 4.4 and 4.5 describe these potential concerns in detail). Table C.2 accordingly examines the sensitivity of the results to a number of alternative specifications. I first take into account the effects of PMAT (a federal program initiated in 1998 which provides subsidized loans to municipalities to improve their tax administration) in several ways. Next, I try controlling for a vector of time-varying political and economic controls: the mayor's vote share, the number of political parties competing for mayor, an HHI of between-party competition for mayor, and the current year world prices of coffee, cocoa, and bananas—each weighted by the 1994 hectares of each crop in the municipality. Column (1) presents the baseline results for the effects of revenue and its interactions with inequality and median income on all of the main public expenditure and enrollment variables (education spending, infrastructure spending, budget surplus, pre-primary enrollment, and primary enrollment). Column (2) omits the 6% of municipalities that had a PMAT program sometime during 1998–2008; Column (3) adds a dummy for participation in PMAT by municipality i in year t; Column (4) controls 31 The sample size is now somewhat smaller, reflecting the fact that many municipalities have no private education at any point during the sample period.

for the PMAT loan amount per capita in municipality i in year t; and Column (5) controls for both the PMAT loan amount per capita and a vector of time-varying political and economic controls (described in Section 4.4). As Table 2 shows, the addition of controls for PMAT and for political and economic shocks has virtually no effect on the coefficients interpreted in this analysis, or their standard errors. That is, the effects of the revenue shocks seem to be due to exogenous changes in the rules governing the FUNDEF/B program and not somehow due to their correlations with these time-varying variables.

5.7.2. Heterogeneous expenditure constraints Starting in 1998, FUNDEF provided municipalities with revenue shocks that had to be spent on education; this was true for all municipalities—unequal and equal, rich and poor. However, municipalities already accustomed to spending beyond the minimum on education (nearly 2/3 as of 1997) could simply reduce their voluntary (above the minimum, 25% of revenue) education spending in response to a windfall. Doing so effectively allowed them to use some of the windfall on any spending priority (not just education). For municipalities: a) with a higher share of revenue going to education in 1997, or b) with a smaller expected windfall from FUNDEF, these new funds were especially fungible. An example is helpful. Suppose a municipality receives a 5% increase in net revenue in 1998. This money must go into education. If the municipality spent at least 30% of revenue on education in 1997 (5% more than it was required to!), then it could simply reduce this voluntary (above minimal) education spending from 30% in 1997 to 25% in 1998. With the 5% revenue shock plus this 25%, the municipality would continue to spend what it did on education in 1997, and yet would also be able to put 5% more revenue into any other spending priority. If the same municipality received any smaller revenue shock, it would also be able to invest the full shock into any spending priority of its choosing. If this municipality received a shock larger than 5%, however, it would need to spend some part of the shock on education. For example, with a 10% revenue shock, it would have to spend half of the shock on education in order to continue to spend 30% on education (though it would have an additional 5% of revenue to put into another spending priority). However, a municipality with 1997 education spending of 35% or higher would be able to spend the full 10% revenue shock on any spending priority by simply allowing the new revenue to crowd out all voluntary education spending. This implies that FUNDEF/B receipts are more fungible (less constrained in how they are to be used) for two types of municipalities: a) those spending far beyond the minimum on education in 1997, and b) those receiving small amounts from FUNDEF. Education investment is effectively more expensive for a less-constrained municipality, as there are more potential uses of the money. That is, there is a price effect. While less-constrained municipalities include equal and unequal, high and low income municipalities, a potential concern is that the intensity of the price effect is correlated with inequality or median income. To show that such a correlation between the distribution of income and the intensity of the price effect is not driving the results, I estimate Eq. (1) for sub-samples of municipalities that we expect to be among the least constrained to spend a revenue shock on education: a) those in the top third of 1997 education spending as a share of revenue, and b) those in the bottom third of net FUNDEF receipts as a share of revenue.32 In these municipalities, the price effects should be muted, allowing us to more clearly observe the effects of inequality and median income on spending. 32 Since municipalities may have changed their revenue levels and school enrollment in response to the reform, here I simulate what 1997 FUNDEF receipts would be (as a share of 1997 revenue) if FUNDEF were already in place in 1997 (using the 1998 rules for redistribution).

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Table C.3 presents these results. The dependent variable is logged education spending per capita, and I first use actual 2000 inequality and median income, and then use the time-varying, predicted measures of inequality and median income. I find that both inequality and median income still have a strong and statistically significant negative impact on the propensity to invest revenue in education. If anything, the interaction between revenue and inequality is now larger in magnitude—whether we use the 2000 or the predicted measures of the distribution of income. The effects of median income interacted with revenue are quite similar to the baseline estimates. A correlation between the distribution of income and how constrained a municipality is to spend revenue on education does not appear to be driving the results. 5.7.3. Correlates of inequality and income I treat inequality and median income as broad concepts summarizing important dimensions of society. However, my findings may be less interesting if they are simply picking up the effect of some variable correlated with them that also conditions how revenue is spent. For example, it may be more expensive and complicated to provide public education in more urbanized places or in those with extensive racial and social heterogeneity. To explore this possibility, I individually add three interactions with revenue to the model: the year 2000 fraction of the municipality that was urban, the labor force participation rate, and an index of racial fractionalization.33 If the effects of inequality and median income in moderating a revenue shock were to vanish when including these controls, then these effects would seem rather mechanical rather than due to the mechanisms hypothesized in the theoretical models presented. As Appendix Table C.4 shows, inclusion of these interactions with revenue does not significantly affect the magnitude of the main findings or their statistical significance. More heavily urbanized municipalities are less likely to invest a revenue shock in education or to expand public primary enrollment. Municipalities with greater labor force participation are more likely to expand public pre-primary and primary enrollment rates. Finally, municipalities with greater racial fractionalization are more likely to expand public pre-primary enrollment. That the effects of inequality and median income are similar despite the inclusion of these controls is consistent with the political economy mechanisms proposed. That is, inequality and median income seem to be capturing differences in the policy preferences of citizens, or in the influence wielded by relatively poor citizens (who most support public education). 6. Conclusions A long-standing debate in the theory literature concerns how the distribution of income affects the size of government and its propensity to invest in publicly-provided goods. The models of Barzel (1973), Besley and Coate (1991), Epple and Romano (1996), Glomm and Ravikumar (1998), and de la Croix and Doepke (2009) suggest that greater inequality leads to less redistribution, while Meltzer and Richard (1981, 1983), Alesina and Rodrik (1994) and Persson and Tabellini (1994) predict that it leads to more redistribution. This paper partly reconciles these models by focusing on the type of public sector investment. I use credibly exogenous shocks to Brazilian municipalities' revenue during 1995–2008 generated by non-linearities in federal transfer laws to examine the effects of the distribution of income on goods with vs. without private sector substitutes. This reveals an interesting distinction between the two types of goods. Municipalities with higher income inequality or higher median income allocate less of a revenue shock to education (a publicly-provided good that predominantly benefits the poor) and are less likely to expand public school enrollment. 33 Urbanization is as classified by IBGE for the 2000 Census. Labor force participation is the fraction of the adult population that is economically active. Racial fractionalization is an HHI computed using data on the population in each of four categories: black or brown, white, Asian, and indigenous.

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However, they are more likely to invest in public infrastructure, like parks and roads, which is enjoyed by everyone. They are also more likely to save a revenue shock, running a budget surplus. Yet I find no evidence that the quality of public education suffers due to this lower propensity to invest. If anything, unequal and high-income areas are more likely to use a revenue shock to improve public school inputs and test scores. These findings have at least three policy implications. First, revenue transfers that target the poorest local governments and those with the lowest income inequality are likely to be most effective in expanding public education investment and public school enrollment. Policymakers in those municipalities already have a relatively strong desire to spend their next R$ on these uses, and national policymakers should take this into account. In the Brazilian case, a nation-wide education finance equalization reform would boost education spending in uniformly poor municipalities better than a within-state distribution like FUNDEF/B, as there is substantial cross-state revenue inequality. Second, the existence of a vibrant private education sector is important. By absorbing many richer students, it can ensure that limited education resources are not spread too thinly, and quality remains high—especially in highly unequal and high-income areas that are relatively less likely to invest a revenue shock in education. Finally, the steady decline in inequality taking place in Brazil has real implications for public investments—as do changes in inequality in other parts of the world. In particular, one can expect local governments to become increasingly more likely to invest a revenue shock from FUNDEF/B into education and to expand public school enrollment. One could imagine that this would make it increasingly less necessary to mandate minimum expenditures on education. Acknowledgments This research was supported by a National Science Foundation Graduate Research Fellowship and a Stanford Institute for Economic Policy Research Dissertation Fellowship. I am incredibly grateful to my dissertation committee for excellent advising: Caroline Hoxby, Seema Jayachandran, Saumitra Jha, and Romain Wacziarg. I thank Michael Boskin, David Evans, Fernando Ferreira, Maria Fitzpatrick, Claudio Ferraz, Alex Frankel, David Laitin, Darío Maldonado, Karthik Muralidharan, Kathryn Shaw, Ken Shotts, Fabián Valencia, Emiliana Vegas, Scott Wallsten, Joel Wiles, and two anonymous referees for helpful comments. I also thank Érica Amorim, Leonardo Bursztyn, Flavio Cunha, Fernanda Estevan, Pedro Maciel, Guilherme Lichand, David Plank, Joseph Sands, Pedro Silva, and Brian Wampler for data and useful discussions about local government policy in Brazil. Remaining errors are my own. Appendix A. Institutional detail: public education in Brazil, FUNDEF, and FUNDEB In 1985, Brazil began a process of re-democratization following military dictatorship. The constitution of 1988 decentralized substantial power to state and municipal governments. As of 2000, Brazil had 5507 municipalities. Municipal governments are led by an elected mayor and an elected city council comprised of a minimum of nine and a maximum of 55 councilmen, according to population size. Local elections are competitive and held every four years, and voting is compulsory for those over 17. Everyone 16 and older can vote. The mayoral candidate with the largest vote share is elected (with runoff elections in municipalities with populations over 200,000 if no candidate wins at least 50% of the vote). City council seats are filled by a system of open-list proportional representation. Legislative, budgetary, and administrative authority are concentrated in the mayor's office, and the city council is largely responsible for approving mayoral directives (Couto and Abrucio, 1995; Wampler, 2007). The federal government has placed much emphasis on pre-primary education over the last two decades. The 1988 constitution formally recognized age 0–6 education as the right of every child and the responsibility of municipal governments. The 1996 National Education Guidelines

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and Frameworks Law emphasized the educational value of pre-primary education by integrating crèches (age 0–3) and preschools (age 0–6, and 0–5 starting in 2007) as the domain of the Ministry of Education. National enthusiasm for pre-primary education has been spurred on by an alarming rate of failure out of first grade: 29.3% as of 2001 (UNESCO, 2006). This compares unfavorably even with most Sub-Saharan African countries, which have the world's highest regional average failure rate. Additionally, Brazil performs far below peers with similar per capita GDP on Program for International Student Assessment (PISA) tests. With a lot of studies emerging saying that early childhood education can equip children with the cognitive and non-cognitive skills required for success in primary school and beyond, the Brazilian federal government has been keen to capitalize on this. Souza (2005), Minister of Education during 1995–2002, describes the federal government's motivations for greater education investment and monitoring of performance indicators. Despite this rhetoric, however, the federal government has largely recused itself from pre-primary and primary education policy. Part of this is an artifact of the 1988 Constitution, which gave considerable policy autonomy to municipal governments. As Plank (1996) notes: “The Constitution's concession of independence to municipalities significantly reduces the power both of the Ministry of Education and state governments, while greatly expanding opportunities for administrative and policy innovation.” Political pressure for municipal autonomy had been building during the 20 years of military rule preceding the 1988 Constitution. About 54% of the congressmen drafting the 1988 Constitution had been previously involved in local politics as mayors or city councilmen, and they wanted to financially weaken the federal government. The federal government has interfered in municipal education policy by imposing an education spending floor: at least 25% of municipal revenue from any source—local or transfer revenue. The federal government has also passed several education finance reform laws. In 1998, the government implemented the “Fund for the Development of Elementary Education and Teachers” (Fundo de Manutenção e Desenvolvimento do Ensino Fundamental e de Valorização do Magistério), or FUNDEF. This policy was expanded in the 2007 “Fund for the Development and Maintenance of Basic Education” (Fundo de Manutenção e Desenvolvimento da Educação Básica), or FUNDEB. FUNDEF obligated each of Brazil's state and municipal governments to pay 15% of each of four intergovernmental transfers into a state-level education fund. These four transfer receipts were typically the largest four sources of transfer revenue for municipal governments, and included: transfers from the municipal participation fund (FPM), the tax on goods and services (ICMS), the tax on industrialized products (IPI), and transfers under the complementary law. In Portuguese, these are the Fundo de Compensacao dos Estados Exportadores (IPI), the Imposto Sobre Circulacao de Mercadorias e Servicos (ICMS), the Parte do Fundo de Participacao dos Municipios (FPM), and the Lei Complementar (LC 87/ 96) transfer. The federal government sets IPI tax rates and the state government sets ICMS tax rates subject to federal minima and maxima. FPM is the “Revenue Sharing Fund of the Municipalities.” Of the federal government's proceeds from the collection of taxes on income and earnings and on industrialized products, 22.5% is given to Brazil's municipalities as an FPM transfer. Usually, these four transfers form the majority of the municipal revenue base. They are in some sense local taxes; the state and federal governments set the rates and bases, and collect the taxes, but they then transfer the revenue to municipalities on the basis of its municipality of origin. These payments into the school fund did count toward the 25% of revenue that must be spent on education, but municipalities also had to spend 25% of all other revenue (from sources other than these four transfers), and an additional 10% of these four transfers, on education. For more details, see Gordon and Vegas (2005), Estevan (2007), and UNESCO (2007). FUNDEF generated 27 education funds: one for each state, and one for the Federal District. Fund receipts were redistributed back to

municipalities within each state so that each government's share of the pie was equal to its share of the state's total enrolled primary school children. The state government itself also paid into the fund by the same set of rules, and also claimed a share of the pie equal to its share of students (although state governments are generally less involved in primary education, and almost entirely uninvolved in pre-primary education). All fund receipts had to be spent on education. Additionally, 60% of fund receipts had to be spent exclusively on teacher compensation. Each municipality was also required to establish a council that would oversee expenditures (Sands, 2008). If gross fund receipts alone were not enough to achieve a federal minimum investment level per primary school child (set annually), the federal government would ‘top off’ the fund to ensure minimal primary school expenditure per child. Importantly, this federal ‘top-off’ ensured that primary education was already universal and of minimal required quality before the municipality spent the 10% or more of additional revenue mandated by the 1988 Constitution's 25% spending floor on education. As UNESCO (2007) notes, the intention was that states would spend this additional (non-school fund) money on secondary education, and municipalities would spend it on pre-primary education and other education-related expenditures. On December 23, 1997, President Fernando Henrique Cardoso and Minister of Education Paulo Renato Souza announced the size of the federal top-off policy that would be put into effect for 1998 (and would be revised periodically). FUNDEF was implemented at the start of the new school year in 1998, with municipal receipts from the fund based on the 1997 Census of Schools (Censo Escolar) enrollments data. In 2007, FUNDEB increased the fraction of transfer revenue to be contributed to the state education fund: from 15% in 2006 to 16.67% in 2007, 18.33% in 2008, and 20% in 2009 onward. Also, while FUNDEF only considered primary school students in assigning capitation grants, FUNDEB gradually expanded this to include pre-primary, primary, and secondary school students. Appendix B. Construction of simulated instruments The construction of the simulated revenue variable follows techniques standard in the public finance literature. The exact redistribution algorithms defined by the FUNDEF (1998) and FUNDEB (2007) education finance reform laws provide me with an exogenous source of variation in municipal per capita revenue during 1998–2008. This variation is exogenous since these federal laws were enacted without regard for any specific municipality or state's revenue or education policies. The FUNDEF law defined how revenue would be redistributed within states in a very careful algorithm, detailed in Ministério da Educação (2006). For 1998–1999, having data on the following variables allows one to determine how each municipality will fare under FUNDEF: total revenue of each municipality in the state, total revenue of the state government itself, total children enrolled in municipal primary schools in each municipality in the state, total children enrolled in state primary schools in the state, and the annually-set federal ‘minimum expenditure per primary school student’ amount. Given these variables alone, one can determine exactly which municipalities will be net winners, which will be net losers, and by how much. During 2000–2004, the algorithm began to make the federal top-off amount vary based on the primary school level of students. Children in grades 1–4 of primary school were weighted differently than children in grades 5–8. During 2005–2006, the algorithm began to make federal top-off depend not only on the primary school level, but also on urbanization status. Thus, one would additionally need to know how many children were enrolled in grades 1–4 of urban primary schools, how many were enrolled in grades 1–4 of rural primary schools, how many were enrolled in grades 5–8 of urban primary schools, and how many were enrolled in grade 5–8 of rural primary schools. Beginning in 2007, under FUNDEB, the algorithm was complicated even more, to depend (in addition to all these previous factors) on the number of children enrolled in urban vs.

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Appendix C. Appendix tables

Table C.1 IV Results, showing how inequality and median income moderate the effect of revenue on school infrastructure quality. Dependent variable is share of schools with:

Own building

Electricity

Indoor bathroom

Library

Computer

(1)

(2)

(3)

(4)

(5)

0.006 (0.043) −0.087 (0.093) −0.005 (0.007) 49,393

−0.267*** (0.053) 0.490*** (0.117) −0.031*** (0.008) 49,393

−0.211*** (0.066) 0.709*** (0.148) 0.045*** (0.010) 49,393

0.064 (0.073) −0.011 (0.125) 0.062*** (0.011) 49,393

0.233** (0.091) 0.273 (0.177) 0.255*** (0.014) 49,393

−0.062 (0.042) 0.077 (0.090) −0.001 (0.008) 41,866

−0.691*** (0.092) 1.156*** (0.190) −0.043*** (0.014) 41,866

−0.479*** (0.096) 0.920*** (0.209) 0.028* (0.015) 41,866

0.077 (0.103) −0.214 (0.178) 0.095*** (0.017) 41,866

0.371*** (0.109) −0.309 (0.204) 0.235*** (0.017) 41,866

0.105 (0.112) −0.034 (0.240) 0.015 (0.018) 26,605

0.009 (0.026) −0.030 (0.055) −0.003 (0.005) 26,605

−0.020 (0.063) 0.087 (0.140) −0.000 (0.011) 26,605

0.097 (0.176) −0.078 (0.362) −0.031 (0.026) 26,605

−0.132 (0.154) 0.241 (0.322) −0.057** (0.024) 26,605

0.100 (0.109) −0.138 (0.247) 0.004 (0.016) 20,408

−0.033 (0.036) 0.043 (0.077) −0.014** (0.006) 20,408

0.037 (0.066) −0.110 (0.144) −0.008 (0.010) 20,408

−0.019 (0.185) 0.197 (0.394) 0.048* (0.027) 20,408

−0.147 (0.182) 0.477 (0.386) 0.050* (0.028) 20,408

Panel A: public pre-primary schools Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Observations Panel B: public primary schools Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Observations Panel C: private pre-primary schools Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Observations Panel D: private primary schools Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Observations

Notes: An observation is a municipality - year. I instrument for revenue using simulated revenue. Robust standard errors are in parentheses, and clustered at the municipality level. ***indicates p b .01; **indicates p b .05; *indicates p b .10. All specifications include municipality and year fixed effects, controls for population, age 0–6 population, and age 7–15 population, a control for gross municipal product (GMP), and a linear time trend interacted with the pre-reform, 1997 levels of log(per capita revenue), log(per capita transfer revenue), log(public pre-primary enrollment rate), log(public primary enrollment rate), and log(share of primary school students in state or federally-run schools). The mean Gini coefficient in2000 is 0.39, the mean value of median income per capita (as of the 2000 Census, measured in 10,000 s of 2005 Reais) is 0.23, and mean revenue per capita (in 100 s 2005 Reais) is 9.84. Sources: Author's calculations based on data from IBGE, Ministry of Education, and Tesouro Nacional.

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Table C.2 IV Results, showing robustness of the results to controls for the PMAT program and time-varying political and economic shocks. Baseline

Exclude PMAT municipalities

Dummy for PMAT

PMAT R$ per capita control

PMAT R$, polit. & econ. controls

(1)

(2)

(3)

(4)

(5)

0.809*** (0.084) −0.687*** (0.170) −0.201*** (0.014) 47,040

0.773*** (0.081) −0.643*** (0.165) −0.206*** (0.013) 50,660

0.775*** (0.081) −0.650*** (0.165) −0.205*** (0.013) 50,546

0.784*** (0.082) −0.663*** (0.167) −0.203*** (0.013) 50,321

1.628*** (0.404) −0.404 (0.789) 0.273*** (0.058) 42,885

1.543*** (0.379) −0.208 (0.744) 0.260*** (0.055) 46,218

1.550*** (0.379) −0.206 (0.745) 0.261*** (0.055) 46,104

1.515*** (0.383) −0.156 (0.754) 0.257*** (0.056) 45,917

2.402*** (0.573) 2.279** (1.124) 0.614*** (0.089) 31,284

2.390*** (0.547) 2.612** (1.089) 0.617*** (0.085) 33,745

2.389*** (0.549) 2.609** (1.091) 0.611*** (0.085) 33,657

2.456*** (0.554) 2.493** (1.106) 0.610*** (0.086) 33,494

−0.035 (0.174) −0.780** (0.341) −0.260*** (0.028) 45,923

−0.027 (0.164) −0.741** (0.324) −0.257*** (0.026) 49,410

−0.028 (0.164) −0.742** (0.325) −0.257*** (0.026) 49,298

−0.041 (0.164) −0.705** (0.326) −0.259*** (0.026) 49,074

−0.623*** (0.163) −0.864*** (0.281) −0.334*** (0.026) 45,393

−0.569*** (0.158) −0.865*** (0.270) −0.328*** (0.024) 48,822

−0.575*** (0.159) −0.852*** (0.270) −0.326*** (0.024) 48,710

−0.566*** (0.160) −0.911*** (0.272) −0.326*** (0.025) 48,486

Dependent variable: Log (education spending per capita) Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Observations

0.774*** (0.081) −0.646*** (0.165) −0.206*** (0.013) 50,660

Dependent variable: Log (infrastructure spending per capita) Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Observations

1.540*** (0.379) −0.196 (0.744) 0.262*** (0.055) 46,218

Dependent variable: Log (budget surplus per capita) Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Observations

2.382*** (0.548) 2.647** (1.091) 0.622*** (0.084) 33,745

Dependent variable: log (public pre-primary enrollment) Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Observations

−0.028 (0.164) −0.737** (0.324) −0.257*** (0.026) 49,410

Dependent variable: log (pubic primary enrollment) Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Observations

−0.577*** (0.159) −0.841*** (0.270) −0.325*** (0.024) 48,822

Notes: An observation is a municipality - year. I instrument for revenue using simulated revenue. Robust standard errors are in parentheses, and clustered at the municipality level. ***indicates p b .01; **indicates p b .05; *indicates p b .10. All specifications include municipality and year fixed effects, controls for population, age 0–6 population, and age 7–15 population, a control for gross municipal product (GMP), and a linear time trend interacted with the pre-reform, 1997 levels of log(per capita revenue), log(per capita transfer revenue), log(public pre-primary enrollment rate), log(public primary enrollment rate), and log(share of primary school students in state or federally-run schools). PMAT is a federal subsidized loan program aimed at improving municipal tax collection. PMAT R$ per capita is positive for the years a municipality had a PMAT program, and is 0 otherwise. Political controls include the mayor's vote share, the number of political parties competing for mayor, and an HHI of between-party competition for mayor. Economic controls include the current year world price multiplied by the 1994 number of hectares for coffee, cocoa, and bananas. The mean Gini coefficient in 2000 is 0.39, the mean value of median income per capita (as of the 2000 Census, measured in 10,000 s of 2005 Reais) is 0.23, and mean revenue per capita (in 100 s 2005 Reais) is 9.84. Sources: Author's calculations based on data from IBGE, Ministry of Education, and Tesouro Nacional.

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Table C.3 IV Results, showing results on education spending for a sub-sample of particularly unconstrained municipalities. All municipalities

Municipalities in top third of 1997 education spending as a share of revenue

Municipalities in bottom third of FUNDEF receipts as a share of revenue

(1)

(2)

(3)

0.774*** (0.081) −0.646*** (0.165) −0.206*** (0.013) 50,660 0.782 3914 640.41

0.939*** (0.110) −1.080*** (0.212) −0.203*** (0.021) 17,207 0.824 1346 219.41

1.033*** (0.207) −0.936* (0.490) −0.160*** (0.038) 14,989 0.673 1134 157.81

0.748*** (0.054) −0.220*** (0.060) −0.186*** (0.015) 50,674 0.778 3917 645.04

0.696*** (0.087) −0.244*** (0.085) −0.198*** (0.026) 17,207 0.823 1346 212.46

0.976*** (0.107) −0.303** (0.143) −0.082* (0.046) 14,991 0.672 1135 172.59

Dependent variable: log (education spending per capita) Panel A: 2000 inequality and income Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Observations R-squared Number of municipalities Kleibergen-Paap rk Wald F statistic Panel B: predicted inequality and income Log (revenue) Log (revenue) × predicted Gini Log (revenue) × log (predicted income) Observations R-squared Number of municipalities Kleibergen-Paap rk Wald F statistic

Notes: An observation is a municipality-year. I instrument for revenue using simulated revenue. Robust standard errors are in parentheses, and clustered at the municipality level. ***indicates p b .01; **indicates p b .05; *indicates p b .10. All specifications include municipality and year fixed effects, controls for population, age 0–6 population, and age 7–15 population, a control for gross municipal product (GMP), and a linear time trend interacted with the pre-reform, 1997 levels of log(per capita revenue), log(per capita transfer revenue), log(public pre-primary enrollment rate), log(public primary enrollment rate), and log(share of primary school students in state or federally-run schools). The mean Gini coefficient in2000 is 0.39, the mean value of median income per capita (as of the 2000 Census, measured in 10,000 s of 2005 Reais) is 0.23, and mean revenue per capita (in 100 s 2005 Reais) is 9.84. The mean predicted Gini coefficient during 1995–2008 is 0.53 and the mean predicted median income per capita during 1995–2008 is 0.25 (measured in 10,000 s of 2005 Reais). Sources: Author's calculations based on data from IBGE, Ministry of Education, and Tesouro Nacional.

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Table C.4 IV Results, showing how the effects of inequality and median income vary when including other socioeconomic variables interacted with revenue. (1)

(2)

(3)

(4)

0.778*** (0.081) −0.654*** (0.165) −0.206*** (0.013)

0.698*** (0.084) −0.458*** (0.173) −0.189*** (0.014) −0.046*** (0.016)

0.782*** (0.082) −0.651*** (0.166) −0.208*** (0.015)

0.748*** (0.090) −0.612*** (0.173) −0.208*** (0.013)

Dependent variable: log (education spending per capita) Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Log (revenue) × log (% urban in 2000) Log (revenue) × log (labor force participation rate in 2000)

0.014 (0.041)

50,449 641.34

50,449 480.73

50,449 481.20

−0.016 (0.014) 50,449 422.11

−0.023 (0.165) −0.750** (0.325) −0.255*** (0.026)

−0.080 (0.168) −0.611* (0.335) −0.243*** (0.028) −0.033 (0.028)

0.032 (0.165) −0.705** (0.326) −0.291*** (0.031)

−0.133 (0.179) −0.593* (0.339) −0.262*** (0.027)

Log (revenue) × log (racial fractionalization index in 2000) Observations Kleibergen-Paap rk Wald F statistic Dependent variable: log (public pre-primary enrollment rate) Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Log (revenue) × log (% urban in 2000) Log (revenue) × log (labor force participation rate in 2000)

0.217** (0.087)

49,221 611.14

49,221 458.61

49,221 458.00

−0.056* (0.029) 49,221 430.86

−0.575*** (0.159) −0.842*** (0.271) −0.325*** (0.024)

−0.665*** (0.164) −0.620** (0.282) −0.305*** (0.025) −0.053** (0.021)

−0.523*** (0.159) −0.801*** (0.271) −0.358*** (0.027)

−0.550*** (0.166) −0.877*** (0.276) −0.323*** (0.025)

Log (revenue) × log (racial fractionalization index in 2000) Observations Kleibergen-Paap rk Wald F statistic Dependent variable: log (public primary enrollment rate) Log (revenue) Log (revenue) × Gini Log (revenue) × log (median income) Log (revenue) × log (% urban in 2000) Log (revenue) × log (labor force participation rate in 2000)

0.204*** (0.060)

Log (revenue) × log (racial fractionalization index in 2000) Observations Kleibergen-Paap rk Wald F statistic

48,634 577.89

48,634 433.82

48,634 432.94

0.012 (0.026) 48,634 408.12

Notes: An observation is a municipality - year. I instrument for revenue using simulated revenue. Robust standard errors are in parentheses, and clustered at the municipality level. ***indicates p b .01; **indicates p b .05; *indicates pc.10. All specifications include municipality and year fixed effects, controls for population, age 0–6 population, and age 7–15 population, a control for gross municipal product (GMP), and a linear time trend interacted with the pre-reform, 1997 levels of log(per capita revenue), log(per capita transfer revenue), log(public pre-primary enrollment rate), log(public primary enrollment rate), and log(share of primary school students in state or federally-run schools). The mean Gini coefficient in 2000 is 0.39, the mean value of median income per capita (as of the 2000 Census, measured in 10,000 s of 2005 Reais) is 0.23, and mean revenue per capita (in 100 s 2005 Reais) is 9.84. Sources: Author's calculations based on data from IBGE, Ministry of Education, and Tesouro Nacional.

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