Immigration and Spending on Public Education: California,

Immigration and Spending on Public Education: California, 1970 2000 Daniele Coen-Pirani University of Pittsburgh This version: May 2011. Abstract The evolution of education spending in California has received plenty of attention from both academics and practitioners after this state s education finance reform in the 1970 s. This paper quantifies the contribution of immigration to the relative decline in elementary and secondary public education spending per student in California in the period 1970 2000. A quantitative model of school choice and voting over public education is used to perform the counterfactual experiments of interest. The model predicts that education spending per student in California would have been 24 percent higher in the year 2000 if U.S. immigration had been restricted to its 1970 level. Keywords: Immigration, Public Education, Private Education, Education Finance Reform, California. JEL Classification: D7, F22, H52, H75, I22. Thanks to seminar participants at Carnegie Mellon, Notre Dame, Cleveland Fed, Federal Reserve Board, University of Pittsburgh, University of Montreal, McGill, RAND, West Virginia University, Econometric Society Meetings 2009 in San Francisco for useful comments. Special thanks, without implication, to two anonymous referees, Dennis Epple, Holger Sieg, Maria Ferreyra, Krishna Kumar, Steven Lugauer, Randy Walsh, Jon Sonstelie, and Chris Sleet for useful comments. 1

1 Introduction In this paper I study the impact of immigration on spending on elementary and secondary public education in California over the period 1970-2000. In doing so the paper contributes to the debate on two important issues that have attracted much attention from policy makers and academics alike. The first debate concerns the effects of immigration on the wellbeing and economic outcomes of natives. While the literature has focused on the labor market impact of immigrants, less attention has been devoted to the interaction between immigrants and natives that occurs through government spending and taxes. 1 In particular, spending on public education is one of the most important items on the budget of state and local governments. The second debate concerns the significant decline in public education spending per student that occurred in California - the main immigrant-receiving state in the U.S. - relative to the rest of the country since the early 1970 s. While the economics literature has emphasized the role played by education finance reform from a foundation system to a state system, little attention has been paid to the underlying demographic trends over this period. 2 According to U.S. Census data, school-age children from households whose head had immigrated to the U.S. after 1970 accounted for about 40 percent of California s total enrollment in elementary and secondary school in 2000 relative to 8 percent in 1970. The corresponding figure for the rest of the U.S. in 2000 was 13 percent. In all Census years, California households whose head had immigrated to the U.S. after 1970 had, on average, more school-age children than native households, and more than twice as many in 1990 and 2000. Immigrant-headed households accounted for about 30 percent of all households in California in 2000, while the corresponding figure for the rest of the U.S. was only 8 percent. 3 1 See Borjas (2003) and Ottaviano and Peri (2008) for different views on the effect of immigration on the wages of native workers. Borjas (1999) reviews the literature on immigration, and Borjas (1994) contains a review of the literature on immigration and government outlays and taxes. 2 See Silva and Sonstelie (1995) and Fernandez and Rogerson (1999) for analysis of education finance reform in California. 3 In the rest of the paper I refer to an immigrant-headed or simply immigrant household as a household headed by an immigrant who immigrated to the U.S. after 1970 and to a native-headed or simply native 2

The paper develops a quantitative political-economy model of education spending to answer the following counterfactual question: what would have been the level of education spending per student in California in 1980 2000 if U.S. immigration had been restricted to its 1970 level? The main result is that immigration has played a quantitatively important role in the decline in education spending per student. Specifically, I find that in the academic year 1999 2000 education spending per student in California was about $1,482 (in 1999 dollars) lower than it would have been if U.S. immigration had been restricted to its 1970 level. This represents about 24 percent of actual education spending per student in California in 2000. For sake of comparison, education finance reform is estimated to have reduced education spending per student in California by 10 15 percent (Fernandez and Rogerson, 1999 and Hoxby, 2001). In order to answer the counterfactual question above, I employ a political-economy model where California households vote over expenditures on public education in a state-wide voting round. The latter setting is consistent with the institutional setup of education finance in California where since the early 1980 s current spending for elementary and secondary public education has been largely equalized across students and spending decisions are centralized at the state-level. 4 In the model, households are assumed to be heterogeneous with respect to their income, number of school-age children, immigration status, and the weight they attach to education relative to consumption in their utility function. Households with school-age children choose between private and public education. household as a household headed by either a native or a pre-1970 immigrant. According to the 2000 Census, each immigrant-headed household in California had on average 1 school-age child while a native household had 0.45 school-age children. Out of native households only 26 percent had school-age children in 2000, against 52 percent among immigrant-headed households. Conditional on having at least a school-age child, immigrant-headed households had on average 1.93 school-age children against 1.70 among native households. The fertility differential between natives and immigrants is partly due to demographic differences such as age between the two populations. The argument in the paper does not hinge on the specific reason for the observed difference in fertility. 4 See Sonstelie et al. (2000) for a thorough account of education finance reform in California. As discussed by these authors there are components of education spending such as categorical aid that, although determined at the state level, are not by their nature equalized across students. Thus, more precisely equalization refers to regular per pupil spending, which represents 70-75 percent of education spending. In the rest of the paper I ignore this distinction. 3

The model s parameters are calibrated using micro data from the 1980 U.S. Census and data on public education spending from the National Center for Education Statistics (NCES). The model accounts relatively well for the evolution of education spending in California in the subsequent Census years 1990 and 2000. The model is then used to compute counterfactual tax rates and private school enrollment rates for 1980, 1990, and 2000 by excluding from the economy households whose head immigrated to the U.S. after 1970. The model predicts increasingly higher levels of spending per student from 1980 to 2000 in the counterfactual economy, culminating with the gain of about $1,482 per student cited above. This paper is related to both the literature on the fiscal impact of immigration and the literature on education finance reform. The former line of research takes an accounting perspective by computing the fiscal costs and benefits of immigration given the existing system of transfers, government spending, and taxes (see Borjas and Hilton, 1996, Clune, 1998 and Garvey and Espenshade, 1998). As argued by the National Research Council (1997 page 259) panel: The assumption of exogenous fiscal policies provides useful shortterm estimates for state and local government effects. Future work in this area could examine how much immigration affects fiscal policies... and incorporate such endogenous effects into the modeling exercise. This paper represents a first step in this direction. 5 California represents the most prominent example of an education finance reform that shifted education funding from the local to the state level. This shift, which began in 1971 with the first Serrano ruling, led to the near-equalization of education spending per student by the early 1980 s. 6 Silva and Sonstelie (1995), Fernandez and Rogerson (1999), Sonstelie et al. (2000), and Hoxby (2001) point to this reform as the main reason for the observed decline 5 An exception is Dottori and Shen (2009) who model the impact of low-skill immigration on public education spending. In their model, as in mine, low-skill immigration reduces the average tax base from which public schools are founded and leads to lower support for public education and increased private school attendance by high-income natives. Differently from their theoretical paper I use the model to quantitatively assess these channels. 6 When the Serrano plaintiffs returned to court in 1983, the judge wrote, rejecting their case, that It is this court s view that the proper standard for testing compliance with the judgement is whether the Legislature has done all that is reasonably feasible to reduce disparities in per-pupil expenditures to insignificant differences. As is discussed, the state has met this standard and surpassed it. (cited by Sonstelie et al., 2000, page 55). 4

in education spending per pupil in California in the 1980 s and early 1990 s. Murray et al. (1998), instead, estimate a positive effect of education finance reform on average spending per pupil using panel data on U.S. states. By focusing on the post-1980 period this paper eschews this debate. Instead, it argues that by the year 2000 immigration had become a more important factor than education finance reform in accounting for the relative drop in spending per student in California. The quantitative results of this paper are consistent with the empirical evidence in Poterba (1997) and Fernandez and Rogerson (2001). Using panel data on U.S. states these authors show that for given level of aggregate income, and controlling for state fixed-effects, the elasticity of education spending per student with respect to changes in the number of students enrolled in school is equal to about minus one. Differently from this exclusively empirical work, I endogenize the choice of education spending and school choice and I focus on a specific demographic shock - immigration. The advantage of the structural model adopted here is that it can be used to evaluate the roles of immigrants political power and of private school choice in performing the counterfactual experiments of interest. The rest of the paper is organized as follows. Section 2 presents the basic trends about education spending in California and the rest of the U.S. Section 3 describes the model economy. Section 4 discusses the calibration of the model s parameters. Section 5 performs the counterfactual exercise. Section 6 considers a number of extensions of the basic framework of Sections 3 5. Last, Section 7 concludes. A description of the data is contained in the Appendix. 5

2 Empirical Evidence 2.1 The Evolution of Spending per Pupil over Time The key variable of interest in this study is current education spending per student enrolled in public elementary and secondary school in California. 7 In this section I consider the evolution of this variable over time in California relative to the rest of the U.S. and analyze its components. To fix ideas, it is convenient to denote aggregate nominal spending for public elementary and secondary education in location k at time t by Ek t, where the index k equals CA (California) or US (the U.S. excluding California). Let H t k denote the total number of households in k at time t, and let N t k stand for enrollment in public schools. Last, Y t k is a measure of total nominal income in k at time t. By definition, log spending per student in CA relative to the rest of the US at time t can be decomposed in the following way: log Et CA /N t CA E t US /N t US = log Et CA /Y t CA E t US /Y t US + log Y t CA /Ht CA Y t US /H t US + log Ht CA /N t CA H t US /N t US, (1) or, in words, as the sum of log relative education spending per unit of income, log relative income per household, and log relative number of households per student enrolled in public schools. I analyze the evolution of these variables starting from a given point in time, the school year 1969 70. 8 This initial date works well because the resurgence of large-scale immigration to the U.S. dates back to the Immigration and Nationality Act Amendments of 1965 which facilitated immigration for family unification purposes. Also, the major education reform that equalized spending per student in California occurred in the 1970 s. Table 1 represents the levels of the main statistics about education spending, household income, and public school enrollment of children from native and immigrant households in the different 7 The NCES defines current expenditures as The expenditures for operating local public schools, excluding capital outlay and interest on school debt. These expenditures include such items as salaries for school personnel, fixed charges, student transportation, school books and materials, and energy costs. 8 As a convention, in what follows I refer to the school year 1969-70 as 1970. 6

Census years for California and the rest of the U.S. Taking the difference between equation (1) in year t and its equivalent in 1970 provides the basis for the analysis of the determinants of the evolution of spending per student in California relative to the rest of the U.S. and relative to the year 1970. I implement this decomposition empirically using both yearly data for the period 1970 2005 (Figure 1) and decennial data for the period 1970 2000 (Figure 2). According to both figures California s relative spending per student declines by more than 20 percent between 1970 and 2005, reaching a low point in the mid-1990 s. These figures also suggest that this drop cannot be accounted for by a decline in the fraction of income spent on public education in California relative to the rest of the U.S. 9 The reason why per student spending exhibits such a large decline, instead, is mainly the increase in the student to household ratio in California relative to the rest of the U.S. For example, in 1970 there were 1.40 and 1.35 households in California and in the rest of the U.S., respectively, for each student enrolled in public school. In 2005, there were 2.34 households per student in the rest of the U.S., but only 1.97 in California. Notice how the cumulative change in the relative ratio E/N between 1970 and 2005 is almost identical to the cumulative trend followed by the relative ratio H/N. Note that the demographic shift that led to lower relative H/N ratios in California in 2005 did not start until about 1980. Figure 1 also shows how the ratio of education spending to income declined quickly in California between the mid-1970 s and the early 1980 s, remaining constant until the mid 1990 s and then exhibiting an upward trend. Figure 2, which uses income data from the U.S. Census, shows a further decline in spending relative to income for California until 1990. However, this decline is simply the counterpart of faster growth in income per household in the 1980 s in California than in the rest of the U.S. as recorded by the Census, suggesting that education spending per household was actually fairly constant 9 According to Figure 1, in 2005 California was spending almost the same fraction of its income on public education relative to the rest of the U.S. as in 1970. Figure 2 instead shows a small decline in this indicator. However, the reason for this decline is the fact that relative income per household in California grew faster according to the U.S. Census measure of income than according to the CPS measure of income. In fact, when considering education spending per household, as opposed to per student enrolled, California does not seem to gain or lose relative to the rest of the U.S. between 1970 and 2005. 7

during the 1980 s also according to the Census data (see footnote 9). It is fair to interpret these trends as suggesting that the effect of the Serrano ruling on education spending relative to income emphasized by Fernandez and Rogerson (1999) had already fully taken place by the early 1980 s. 10 How did the relative decline in education spending affect the education sector in California? Data on pupil-teacher ratios show a dramatic increase in average class size in California relative to the rest of the U.S. during the 1980 s and up to the early 1990 s when this figure stabilizes. Schrag (1998, page 15) describes informally some of the consequences of the relative decline in spending: the unmaintained buildings with leaking roofs, falling ceiling tiles, and unusable toilets; the layoffs of school counselors, librarians and nurses; and the reductions in course offerings in everything from art to zoology. Writer Jonathan Kozol found rotting school facilities in the inner cities; California has them in the suburbs as well. 11 2.2 Immigration In this section I present results from a simple statistical counterfactual exercise in order to begin assessing the role played by immigration in generating the trends in Figures 1 and 2. Specifically, I generate a new series for the logarithm of relative (California vs the rest of the U.S.) spending per capita in public education replacing the term Hk t/n k t in equation (1) with the ratio of the number of households headed by a U.S. native individual to the number of children living in such households and enrolled in elementary and secondary public schools. Figure 3 reports the actual data series (solid line) of relative spending in public education per school-age child and the corresponding counterfactual series (dashed line). As the figure shows, relative education spending per student in California would have been about the same 10 Interestingly, during the period under consideration California did not experience a relative reduction in non-education spending per capita by state and local governments (Sonstelie et al., 2000, Figure 5.6). 11 The available empirical evidence on educational outcomes in California also suggests a decline. A study by the Rand Corporation (Carroll et al., 2005) shows that California students taking national achievement tests in the period 1990 2003 scored worse than students from all other U.S. states except Louisiana and Mississippi. These relatively poor results could not be explained by students family characteristics. Sonstelie et al. (2000) show that California s students performed better than average in earlier - although different - standardized tests administered between 1972 and 1980. 8

in 2000 as it was in 1970 if the ratio of households per public-school student in California had been equal to the value computed for native households only. 2.3 Private Schools Downes and Schoeman (1998) have argued that California s school finance reform of the 1970 s has led to a significant increase in enrollment into private schools. A similar argument can be made regarding the reaction of native households to California s immigration wave. Betts and Fairlie (2003) use Census data to document the existence of a negative relationship between immigrant inflow in a metropolitan area and enrollment rates in private schools. In a recent empirical paper on California, Cascio and Lewis (2010) show using district-level data that native households with children respond to an inflow of Hispanic households with low English proficiency in their school district by relocating to other areas or enrolling their children in private school. Specifically, they find that between 1970 and 2000, the average metropolitan school district in California lost about two children to private schools within the district for every ten additional low-english Hispanic arrivals in its public schools. Figure 4 plots the evolution of private school enrollment rates by children from native households in California and in the rest of the U.S. Notice that in 1980 California had approximately the same private school enrollment rate among native households as the rest of the U.S. In the following 20 years California experienced an increase in private school attendance relative to the rest of the U.S., with the gap in enrollment rates being slightly smaller than one percentage point in 2000. The quantitative predictions of the model introduced in the next section are consistent with these trends. 3 Model In this section I introduce a simple political-economy model of spending on public education and household choice of public vs private education. The model is then calibrated to 9

the data and used to interpret the trends in public education spending per student. The economy (California) is populated by a measure one of households with preferences defined over a composite private good different from education, denoted by c, public education services per student, denoted by e, and private education services per student, z. A household cannot consume both public and private education services. Define an indicator variable I(z) = 1 if z > 0 and I(z) = 0 if z = 0. A household s utility function takes the following form: 12 u(c, e, z; λ, m) = cα α + γ m (1 I (z)) eα α + γ mλi (z) zα α, (2) where α < 1, γ m > 0, and λ > 0 are parameters. The functional form in equation (2) represents a generalization of the one adopted by Fernandez and Rogerson (1999, 2003) along two dimensions. First, the weight γ m on education might differ between immigrant (m = 0) and native (m = 1) households. Second, households with children choose between private and public education. There is unobserved heterogeneity about the intensity of preferences for private education, captured by the household-specific parameter λ. The parameter λ is distributed independently of any other observable household characteristic such as income, etc. Its unconditional mean in the population is set equal to one so that a-priori the average household does not prefer one type of education service over the other keeping quality constant (i.e. for e = z). Differently from most public finance models of education spending (see e.g. Epple and Nechyba, 2004 for a review of the literature), I also explicitly consider heterogeneity among households with respect to their number of school-age children, denoted by n. Households for whom n > 0 can choose between public and private schools. Households with n = 0 are assumed to care about public education. The rationale for this assumption is that according 12 This class of preferences exhibits a unit elasticity of education spending relative to income. This is consistent with the empirical evidence in Fernandez and Rogerson (2001). In assuming that households care about public education spending per student, I am implicitly postulating a constant returns to scale technology in the provision of education, in which marginal and average production costs coincide. 10

to the Census data, in any given year, about 70 percent of households have no children enrolled in primary or secondary school, both in California and in the rest of the U.S. A household without school-age children is still likely to care about public education either because its grown-up children have attended public schools or because its pre-school children will attend public schools when they reach the appropriate age. Public school enrollment rates are about 90 percent in the sample period. External effects associated with a more educated population such as lower crime, productivity spillovers, a more educated electorate, etc. (e.g., Lochner and Moretti, 2004) could also rationalize support for public education among households without school-age children. 13 Spending on public education is financed through a linear tax s on household income y. 14 A household that chooses public education receives utility: U (y (1 s), e, m) u(y(1 s), e, 0; 0, m). A household with school-age children can also opt for private education (Epple and Romano, 1996). In this case, its consumption is equal to its after-tax income minus any spending on private education. The relative price of education is denoted by p m and is allowed to differ between children of native and immigrant households: c = y(1 s) p m nzi (z). 13 The argument that households without school-age children care about public education spending because it is capitalized into housing values is less suitable to post-serrano California where per student spending is equalized across school districts. As in Epple and Romano (1996) households with private school children do not support public education. Given that they represent only about 3 percent of all households, the fact that they are assumed not to care about public education is unlikely to play a quantitatively important role. 14 I focus on a linear tax for simplicity and to maintain comparison with the existing literature (e.g. Fernandez and Rogerson, 1999), despite the fact that California s income tax is progressive. It is not a-priori clear how progressivity of the tax system might affect the results of the counterfactual experiment, in light of the fact that marginal tax rates are endogenous. 11

In case the household opts for private education, its indirect utility is defined as: V (y (1 s), n, λ, m) max {u(y(1 s) p m nz, 0, z; λ, m)}. z Conditional on opting for private education, the optimal quantity of private education services chosen by a household is given by: z ((1 s)y, n, λ, m) = (1 s)y p m n + [(p m n) / (γ m λ)] 1 1 α. (3) Notice that the per-child optimal quantity of private education is increasing in the household s after-tax income, and in its preference for private education, and decreasing in the price of education and the household s number of children. A household chooses public over private school if and only if: U (y (1 s), e, m) V (y (1 s), n, λ, m). Denote by ŷ the level of income at which a household is indifferent between private and public schools: ŷ (n, s, e, λ, m) = e 1 s γ 1 α m [ ( 1 + (p m n) α 1 α (γm λ) 1 1 α ) ] 1. (4) 1 α α 1 The income cut-off for attending private school increases with the level of public education services, the tax rate, the household s number of children and the price of education. Moreover, if α < 0, the cut-off decreases with the education preference parameter γ m. Let f(y, n, m, λ) denote the joint density of income, number of children, immigration status, and the parameter λ in the population of households. For given s and e, the per household measure of children attending public school by immigration status is then given 12

by: n m = n ŷ(n,s,e,λ,m) 0 0 n f(y, n, m, λ)dydλ, for m = 0, 1. (5) The government s budget is assumed to be balanced: (p 0 n 0 + p 1 n 1 ) e = sy, (6) where y denotes average household income in the economy. The government s budget allows for the possibility that the cost of educating immigrant children might differ from the cost of educating native ones. Equation (6) assumes that the income of all households is taxed at the same rate s. In particular, the model abstracts from issues of tax evasion and illegal immigration for lack of reliable data. Note, however, that the explicit consideration of tax evasion is likely to generate larger declines in education spending associated with immigration than the numbers reported in this paper. The tax rate s is assumed to be determined by majority voting by all native households. 15 In what follows I focus on a majority-voting equilibrium in which, when voting, native households take as given their own choice of school as well as the choice of all other households. This guarantees that household preferences are single-peaked over tax rates. Formally, a majority-voting equilibrium is comprised of a tax rate s, a level of public school services per student e, private school services per student z ((1 s )y, n, λ, m), and measures of students attending public school (n 0, n 1) by immigration status, such that: 1. Private school services per student, z ((1 s )y, n, λ, m) are given by equation (3) if y > ŷ (n, s, e, λ, m) and zero else; 2. The government s budget constraint, equation (6), is satisfied; 3. Public school attendance by immigration status n m is given by equation (5); 4. The equilibrium tax rate and education services per student (s, e ) are preferred by at least 50 percent of 15 In reality the amount of education spending in California is determined by the interaction of the legislature and the governor. Education spending represents one dimension of the overall budget process. While more sophisticated modelling of the legislative process might be feasible, here I adopt the median voter approach to aggregation of policy preferences to keep comparability with the previous literature which uses the same framework (e.g. Fernandez and Rogerson, 1999). 13

the voters to any alternative (ŝ, ê) such that ê = ŝy/ (p 0 n 0 + p 1 n 1). The majority-voting equilibrium tax rate s is the median tax rate when households preferred rates are sorted from lowest to highest. The equilibrium level of education spending per student, the object of my analysis, is given by sy/ (n 0 + n 1). It is straightforward to show that, at a majority-voting equilibrium, the preferred tax rate by a household characterized by (y, n, λ, m) is given by: { } 1 1 + γ 1 α 1 m [(p 0 n 0 + p 1 n 1) y/y] α 1 α if y ŷ (n, s, e, λ, m) or n = 0 ŝ = 0 if y > ŷ (n, s, e, λ, m) and n > 0 (7) This expression is useful to discuss a couple of important issues. The first concerns the uniqueness of equilibrium in this economy. Multiplicity might in general arise due to the existence of a private school option (Epple and Romano, 1996). While, I cannot prove uniqueness in general, there is an important special case in which this can be done. Specifically, if utility takes the logarithmic form (α = 0) then the preferred tax rate of a native household without children in private school is equal to γ 1 / (1 + γ 1 ). A suffi cient condition for this tax rate to be the unique majority-voting equilibrium is then that native households with n = 0 are a majority of the native population, as it is the case empirically. Since the calibrated value of α is different from zero, I verify numerically that the equilibrium of the model is unique. The second issue is how native households react to an inflow of immigrants. There are two mechanisms. First, an inflow of immigrants tends to increase the tax price of education services, represented by the term [(p 0 n 0 + p 1 n 1) y/y] in equation (7), for all households. This increase might occur for three reasons: immigrant households tend to have lower average income; they tend to have more children per household; the cost of educating immigrant children might be larger than the cost of educating native children. The tax price is the amount by which a household s taxes would have to increase to increase e by one unit. The level 14

of public education services per student e preferred by a native household with children in public school and preferred tax rate ŝ can be shown to fall by 1 αŝ 1 α percent for an increase in the tax price by one percent. The magnitude of the decline depends on the elasticity parameter α, with lower values of α associated with a more price-inelastic demand. When α = 0, this elasticity is equal to one, as native households without children in private school prefer to keep the tax rate constant at γ 1 / (1 + γ 1 ) when faced with an inflow of immigrants. When α < 0, instead, as will be assumed in the empirical section of the paper, the increase in the tax price induced by the inflow of immigrants makes all households without private school children increase their support for higher tax rates. The resulting increase in the tax rate partially offsets the direct effect of immigration on e, leading to a less than proportional decline in households preferred amount of education services. Second, the reduction in e that follows an inflow of immigrants induces some native households who previously attended public schools to move to the private system because the quality of the public system declines. Formally, for given tax rate, a one percent increase in the tax price causes the private school cut-off in equation (4) to fall by one percent. The reduction in public school attendance by native households contributes to further reduce political support for the public system. In the following I describe the calibration of the model and use the latter to quantify the magnitude of these effects. 4 Empirical Implementation The model is calibrated to the beginning of the post-education reform period in California, around 1980. To calibrate the economy I need to specify the values of the parameters that are constant over time (α, γ 0, γ 1, p 0, p 1 ) and the joint density f(y, n, m, λ) which varies across Census years. 15

To calibrate the density f(y, n, m, λ), I assume that the taste parameter λ is independent of (y, n, m) in the population. The distribution of λ is taken to be lognormal with constant parameters (µ λ, σ λ ). The parameter µ λ must equal σ 2 λ /2 for the mean of λ to equal one. The joint distribution of (y, n, m) can be written as: g(y, n, m) = g(y n, m)h (n, m), (8) where h (n, m) is the joint density of (n, m). The conditional density g(y n, m) is assumed to be lognormal with parameters µ y (n, m) and σ y (n, m). The latter are estimated by matching the conditional mean (E [y n, m]) and variance (V [y n, m]) of household income in the population: µ y (n, m) = ln E [y n, m] 1 ( )] V [y n, m] [1 2 ln + E [y n, m] 2, (9) { [ ( )]} 1 V [y n, m] 2 σ y (n, m) = ln 1 +. (10) E [y n, m] 2 Immigration status (m) takes two possible values according to whether the household head is a U.S. born individual or a foreign-born person who immigrated to the U.S. before 1970 (m = 1), or alternatively, is a foreign-born individual who immigrated to the U.S. in or after 1970 (m = 0). A household s number of children (n) is assumed to take four possible values: 0, 1, 2, and 3 +, where 3 + equals the average number of children in households with at least 3 children. The density h (n, m) is estimated non-parametrically using the frequency count of each cell (n, m). The relative price of education for a native household p 1 is normalized to one without loss of generality. The relative price of education spending for an immigrant child is set conservatively to p 0 = 1.04 or four percent above the price for native children. I compute this figure using the data on California s categorical aid per student compiled by Sonstelie et al. (2000, table 4.7). Categorical aid represents about 20 percent of spending per student and 16

compensatory education, which covers students with limited English proficiency, represents about 20 percent of categorical aid over the sample period. I calibrate the remaining four parameters (α, γ 0, γ 1, σ λ ) to match four key moments in the data reported in Table 3. The first two moments are the per household number of native and immigrant children enrolled in public school in 1980. Higher values of γ 1 and γ 0 are associated with lower public school attendance by native and immigrant children respectively if α < 0 (see equation 4). The third targeted moment is the share of income spent on public primary and secondary education in California in 1980, s = 0.0494. The elasticity parameter α contributes to determine the share of income devoted to education spending. To see this, it is convenient to consider a representative-agent version of the model in which all households have the same preferences, income, and number of children. In this ) setting it is straightforward to check that the equilibrium tax rate is s = ((γ/n) 1 1 1 α + 1 (see equation 7). Given γ/n, the elasticity parameter α determines s uniquely. Specifically, if γ/n < 1, as is the case empirically, smaller values of α map into smaller equilibrium tax rates. The fourth and last moment is the ratio between the average incomes of households with children in public and private schools in 1980. The parameter σ λ determines the degree of income mixing in private schools, with higher levels of σ λ associated with a higher ratio of average income in public relative to private schools. Table 2 reports the calibrated values of the parameters. The calibrated value of the parameter α is 0.34. This is very close to the value of 0.25 preferred by Fernandez and Rogerson (1999) in their study of education finance reform in California. 16 The tax price elasticity of the demand for education for the median voter implied by α = 0.34 is equal to 0.76. This value is slightly higher in absolute value than the range ( 0.25, 0.5) reported by Bergstrom et al. (1982) in their survey of the literature, but smaller than the value implied by Fernandez and Rogerson (1999) s calibration. A second feature of the calibration is that immigrant households place a smaller weight on education relative to native households. 16 Their preferred value is such that their model generates the best fit for the observed distribution of spending per student across students in California before education finance reform. 17

This is an implication of the fact that immigrant households are less likely to have children in private school conditional on income and number of students. 17 The calibration procedure then accounts for the observed enrollment of immigrant children in public school by selecting a value for γ 0 smaller than the corresponding one for γ 1. The calibrated model can be used to predict the income share of spending in education, enrollment in public schools, and other moments of interest for the Census years 1990 and 2000. In using the model to predict outcomes for 1990 and 2000, I keep the same parameters (α, γ 0, γ 1, σ λ, µ λ, p 0 ) from Table 2, and re-calibrate the density g(y, n, m) for 1990 and 2000 along the lines described above for 1980. Table 3 summarizes the moments predicted by the model and presents them together with the actual data for California. Notice that the model accounts reasonably well for the evolution of the triple (s, n 0, n 1 ) observed in California in 1990 and 2000. Specifically, the model correctly predicts the reduction in the share of income devoted to public education between 1980 and 1990 and the subsequent rise between 1990 and 2000. As discussed at the end of Section 3, there are two main forces that drive the dynamics of s in the model. The first one is the variation over time in the tax price of public education services. The tax price of public education services declined in the 1980 s and increased in the 1990 s, as the ratio y/ (p 0 n 0 + p 1 n 1) went from $97,050 in 1980 to $131,500 in 1990 and subsequently fell to $123,040 in 2000. The model correctly predicts that, following this variation in the tax price, the income share of education spending (i.e. s) should have decreased in the 1980 s and increased in the 1990 s. The second major force that determines the dynamics of s is private school attendance. Higher private school attendance reduces the support for public education and tends to lower the equilibrium tax rate. Notice that the model correctly predicts higher private school enrollment by native households in 2000 than in 1980, even if it incorrectly gives rise to a decline in private enrollment between 1980 and 1990. 17 A logistic regression using 1980 Census data for California reveals that an immigrant-headed household is 0.7 percent less likely to have children in private school than a native household with the same income level and number of children. 18

Table 3 contains additional information about the relative incomes of public and private school households and their average number of children. Note that, consistently with the data, the model predicts a decline in public school households income relative to their private school counterpart in the 1980 s and 1990 s. Also, the model correctly predicts that public school households have, on average, more school-age children than private school ones. 5 Counterfactual Exercise In this section I use the model developed so far to provide an answer to the following question: what would have been the level of education spending per student in California in 1980 2000 if U.S. immigration had been restricted to its 1970 level? The model can be used to compute counterfactual enrollment rates in private school and education spending relative to income. To perform such exercise a stand has to be taken about the effect of restricted immigration on the income of native households residing in California. Ignoring this general equilibrium effect might lead one to either under or overstate the negative impact of immigrants on relative spending per student in California. The effect of immigration on the labor income of natives and previous cohorts of immigrants is the subject of some controversy in the literature (see e.g., Borjas, 2003 and Card, 2001). Recent research by Ottaviano and Peri (2008) points to a possible positive effect of immigrants on the average wages of natives, but their finding has been challenged by Borjas, Grogger, and Hanson (2008). In light of the uncertainty about the effect of immigration on the wages of natives, I take as a benchmark the case in which the income of natives and pre-1970 immigrants is unaffected by restrictions to immigration. Section 6.2 of the paper discusses the consequences of relaxing this assumption. 5.1 Counterfactual The model is used to compute the counterfactual level of spending per child and other indicators of interest in 1980, 1990, and 2000 in a version of the economy without households 19

whose head immigrated to the U.S. in or after 1970, according to the U.S. Census. Formally, the following density: g(y, n, m m = 1) = g(y, n, 1) n h (n, 1) (11) is used in the counterfactual exercise, instead of the one in equation (8). Table 4 contains the results of this exercise. A comparison of Tables 3 and 4 reveals that in the economy with post-1970 immigration restrictions public education spending per student in California is 3, 15, and 24 percent higher than in the benchmark in 1980, 1990, and 2000 respectively. In the year 2000, in the economy with immigration restrictions spending per student would have been $1,482 higher than in the benchmark economy and $1,295 higher than in reality. 18 5.2 Decomposition The reduction in spending per student associated with immigration can be attributed to differences between natives and immigrants in: 1) the number of school-age children per household; 2) average income; 3) cost of education; 4) preferences for education. Table 5 presents the results of a decomposition of the overall change in spending per student moving from the benchmark economy to the counterfactual one into these different components. In this table I also evaluate the consequences of relaxing the assumption that immigrant households do not vote in the benchmark version of the model. The second and last columns of Table 5 present the level of spending per student in the benchmark and counterfactual economies respectively. The middle columns of Table 5, instead, present the level of spending per student in economies that might be thought of as alternative benchmarks against which to compare the level of spending in the counterfactual economy. For example, column A in Table 5 represents spending per student corresponding to an economy identical to the benchmark one except for the fact that immigrants are allowed to vote on education spending. This economy is characterized by a lower level of 18 Recall that the model underpredicts education spending per student in California in the year 2000 by about $187. 20

spending per student than the benchmark for two reasons. First, immigrant households have on average a lower income level than native households, so that, given α < 0, they prefer lower levels of spending. Second, according to the calibrated parameters immigrants are found to care relatively less about education than natives, i.e. γ 0 < γ 1. This experiment also clarifies that the assumption that immigrants do not vote in the benchmark version of the model is conservative in the sense of reducing the magnitude of the spending gains associated with restricting immigration. Column B presents the results for an economy similar to the benchmark except for the fact that both the preference for education and the cost of education are equal for immigrants and natives, i.e. γ 0 = γ 1 and p 0 = p 1. The level of spending per student in this economy is very close to the benchmark. Finally, column C is the same as B except that immigrants income is scaled up to be the same as that of natives, on average. Spending in economy C is higher than in all the other economies, except for the counterfactual, as scaling up immigrants income results in a large tax base. I interpret the comparison of spending per student between economy C and the counterfactual economy with restricted immigration (last column of Table 5) as providing a measure of the contribution of demographic factors to the gain in spending resulting from switching from the benchmark to the counterfactual model. The comparison between these two columns shows how even if immigrants had the same average income, cost of education, and preferences as natives, but kept their own demographic characteristics, spending per student in the year 2000 would still be $1,253 below the counterfactual economy with no immigrants. This is 84 percent of the gap in spending between the benchmark and counterfactual economies. The remaining 16 percent of this gap is attributable to factors different from demographics with a major role attributable to the lower average income of immigrants. The decomposition indicates that the lower average income of immigrants accounts for a drop of $210 in spending per student in the year 2000, or 14 percent of the gap between the benchmark and counterfactual economy. 19 The remaining factors appear to play 19 The $210 figure is obtained by subtracting spending per student in column B from spending per student in column C for the year 2000. 21

relatively negligible roles. 5.3 Private School In the economy with restricted immigration (Table 4), native households increase their public school attendance relative to the benchmark model (Table 3). This switch has in principle an ambiguous effect on education spending. On the one hand, as native households move into the public system they support higher levels of spending per student. One the other hand, as these households move into the public system, their children use some of its resources. In order to assess the contribution of this mechanism to the results of Table 4, I recomputed the majority voting equilibrium in the counterfactual economy keeping native households choice of private vs public schooling constant at what it was in the benchmark model. I find that quantitatively the second effect is larger than the first one, so that education spending per student is higher if households school choice is kept constant in the counterfactual exercise. The net effect is, however, quantitatively small, amounting to $58 additional spending per student in the year 2000. 5.4 Comparison with the Literature The magnitude of the counterfactual results in Table 4 is consistent with Poterba (1997) and Fernandez and Rogerson (2001). Using panel data for U.S. states these authors estimate that the elasticity of public education spending per student in a state with respect to the average number of students per household is equal to 1. In the counterfactual economy (Table 4), the number of students per household is 0.42 in 2000 while the corresponding figure in reality is 0.52 (Table 1), or about 21 percent higher. An elasticity of 1 implies a counterfactual amount of education spending per student of $7,692 in 2000 in California. This is very close to my finding in Table 4. Several authors have estimated (Fernandez and Rogerson, 1999 and Silva and Sonstelie, 1995) that education finance reform reduced education spending per student in California by 10 15 percent. According to my model, 22

in 1990 immigration generates declines (relative to a non-immigration benchmark) in public education spending by 15 percent, a figure comparable to those often attributed to education finance reform. 6 Sensitivity Analysis and Extensions In this section I discuss some of the assumptions of the basic model presented in Sections 3 5, and evaluate the impact of relaxing them on the main results. 6.1 Sensitivity Analysis In this section I explore the sensitivity of the main results in Table 4 to the model s parameters. Specifically, the percentage gain in spending per student associated with restricting immigration is computed by varying one parameter at a time, while keeping the other ones fixed. 20 The results are summarized in Table 6 which contains the results for the year 2000. The top portion of this table focuses on the key elasticity parameter α. A larger (absolute value) value of this parameter implies a more inelastic demand for education, and a smaller counterfactual gain in spending per student. A wide range of values of α is considered, from 0.25, as assumed by Fernandez and Rogerson (1999), to 3.74 corresponding to the smallest tax price elasticity reported by Bergstrom et al. (1982) in their survey of the literature. The top panel of Table 6 shows that the percentage gain in spending per student from restricting immigration decreases proportionately to the size of the tax price elasticity. For example, as this elasticity declines from 0.76 (α = 0.34) to 0.50 (α = 1.11), the counterfactual gain in spending declines by about a third too (from 24 to 16 percent). The bottom portion of Table 6 considers the sensitivity of results to doubling the absolute value of each parameter (other than α) at a time while keeping the other ones constant at their 20 Notice that in order to focus on the effect of changing a single parameter, the parameters of the model that are not subject to sensitivity analysis are not recalibrated to match the moments discussed in Section 4. 23