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School Districts and Spending in the Schools

Amy Ellen Schwartz
New York University

About the Author

Contents


Introduction

While recent school reform movements have embraced a wide range of policies and programs, an important feature of many of the proposed reforms is decreasing the control wielded by school districts over the level and pattern of spending by individual schools. Hill et al. 1997; and Odden and Busch 1997, are among those who argue forcefully for financing education through a system in which schools operate under contracts with districts and funding comes in the form of block grants based upon the number and characteristics of students the school enrolled. At the extreme, it has been suggested that schools should receive funding and contracts directly from the state, and school districts should be relegated to performing oversight functions. Such a "block grant" system would result in a different distribution of spending in either (or both) of the following ways. First, a state-wide formula would eliminate (or ameliorate) the differences in per pupil spending across school districts. Second, to the extent that the state's allocation formula differs from the de facto formulae now used by individual districts, a statewide program would lead to changes in resource allocation across schools within districts. While there is much research into the interdistrict variation in spending (see, for example, Berne and Stiefel 1984), there is relatively little research into the intradistrict variation in spending across schools. The emerging research in this area—such as Stiefel et al. 1998—has focused, to some extent, on measuring equity, rather than on investigating the factors driving the intradistrict variations. This paper evaluates the distribution of spending across schools using 1995-96 school and district level data for Ohio to analyze the distribution of spending across public schools. The de facto formulae describing this distribution are estimated and the differences in these formulae across school districts are investigated. Thus, this analysis provides insight into the impact of a change to block grant funding on the distribution of spending across schools in Ohio.

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Background

The public finance theories of fiscal federalism and public expenditure determination indicate that school districts play an important role in determining the level of spending by school districts. According to this view, school district budgets reflect the demands of voters within the jurisdiction; demand, in turn, depends on the income, wealth, demographics and preferences of the voters, on the cost of providing education and, of course, on the state and federal funding they receive. The implication is that we should expect there to be variations in spending across districts which reflect the variations in these fundamentals. The much-lamented inequity in education spending across school districts in the United States is, to a large degree, a reflection of local control.1

Although the public finance models described above provide a strong theoretical foundation for understanding district level expenditures, and there has been much work investigating the determinants of expenditures, the empirical literature has been relatively silent about the determination of spending on schools within districts—reflecting, in large part, the scarcity of school-level spending data. As has been well documented and described by a variety of authors (see, for example, Rubenstein 1997; or Cooper 1993), resource allocations within districts derive from the interplay of myriad political, economic, and institutional factors. The patterns of spending that emerge from such a process (in which individual districts allocate spending to their own schools) are likely to be quite different than the pattern that would emerge from the sort of block grant funding that has been proposed. According to the proposed method, a block grant would be awarded by the state directly to schools in an amount which would be determined by some relatively straightforward formula based on enrollment, the level of the school (elementary, middle, high) and including, perhaps, some "weighted per-student formulas providing extra funding for disadvantaged pupils." (Hill et al. 1997, 4.) To the extent that district formulae would differ from an adopted state-wide formula in the relative weights assigned to various factors, the move to a statewide formula would involve changes in the distribution of resources within districts. For example, while some districts may allocate greater funding to high schools relative to elementary schools, others may direct greater resources to elementary schools. Thus, if resources are allocated using a statewide formula, the distribution of spending within some districts will change significantly.

Interestingly, there has been relatively little research in the United States into the distribution of spending across schools within their districts and the positive and normative impacts on school spending, performance, and educational outcomes. With the exception of the recently published Clark and Toenjes 1997, there is a dearth of research into the factors underlying the distribution of resources between schools within their districts. This gap is due, at least in part, to the scarcity of good school-level resource data. Relatively recent data collected for Ohio schools for the 1995-96 school year will allow us to address some of these lacunae. The objective of this study is to investigate the factors that determine school level spending, the differences (or similarities) in the importance of these factors across school districts in order to gain insight into the likelihood and impact of adopting a statewide block grant finance formula.

More specifically, the objective of this research is to develop and empirically investigate the de facto "formulae" by which spending is allocated across school districts in Ohio and the factors determining the differences in these formulae. Specific research questions that are addressed include: Are allocations relatively constant across schools within districts , adjusting for enrollment, school organization or a set of characteristics of the students? To the extent that there are differences across districts, can they be explained by differences in the size of the school district or its urbanization? As an example, are the urban school district formulae different than those characterizing spending in suburban districts? The purpose of these analyses will be to draw lessons from the varied experience of the Ohio schools about the role of school districts in determining school level resources. The paper begins by exploring de facto spending formulae characterizing spending in all schools, then turns to a more detailed analysis of the formulae for a sample of the largest school districts. Finally, the impact of the adoption of a hypothetical state-wide formula is simulated.

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Data

Defining the Sample

We use data from 3,284 schools and 586 districts operating in Ohio during the 1995-96 school year. These include financial data from the Ohio Department of Education "Expenditure Flow Model" (EFM) and Educational Management Information System (EMIS) and data on test scores, inputs (such as numbers of teachers, teacher experience, etc.), enrollment and demographic and socioeconomic characteristics from EMIS. All data are for the academic year 1995-96. (See table 1 for brief descriptions of the variables and table 2 for descriptive statistics.)

The Expenditure Flow Model records expenditures in five categories for 4,169 buildings in 654 districts. Our analysis excludes 802 buildings because they are vocational schools (69), special needs schools (25), "other facilities" (70), and central offices (638).2 The remaining school buildings were matched to data from the EMIS system, which provides a broader range of information about Ohio school districts and school buildings. District information includes revenues by source, degree of urbanization (rural, small town, urban, major urban, and suburban), and some socioeconomic variables describing the characteristics of the population and the students. Building level files include information on student performance on various tests, enrollment and attendance, teacher experience, salary and certification data, school organization (elementary, middle, or high school) and grade span, and some demographic and socioeconomic characteristics describing the students and the staff in the school. While EMIS files provided data for 612 districts and 4,245 buildings, matching the EFM spending data to them resulted in the exclusion of an additional 83 buildings for which EMIS data were unavailable. The implication of this procedure is that 68 districts were excluded from the analysis—generally because they were one building districts providing special needs/vocational education.

The resulting analysis sample contains 586 districts and 3,284 buildings: 2,058 elementary schools (62.7 percent), 569 middle schools (17.3 percent) and 657 high schools (20 percent). Elementary school enrollment totals 785,913, while middle school enrollment is 310,776, and high school enrollment is 503,159.3

A Statistical Portrait of Ohio Schools

As shown in table 2, while total per pupil spending averages $4,936 (BTOTPUP), it spans a wide range in Ohio. The least amount spent was only $2,346 while the most spent was $13,622—almost six times more. Per pupil expenditures for instruction (BINSPUP) averaged roughly $3,127 in 1995-96, ranging from a low of $1,443 to a high of $8,848.

Additional analyses reveal that, on average, elementary schools spent roughly $4,750 per student during the 1995-96 school year of which about $3,095 (65 percent) per student was instructional spending. At an average $5,185 per student, middle school spending exceeds elementary school spending by about $435; total spending in high schools, at $5,304, is higher than in middle schools.

Interestingly, although in Ohio there are far more elementary than high schools, the variation in spending is greatest across high schools. (As an example, the coefficient of variation (CV) is 24.04 for per pupil spending in all categories for high schools, compared to a CV of 19.75 for elementary schools.) Although difficult to interpret, greater homogeneity in elementary school spending may reflect a broader social consensus about elementary school education and a greater attention to ameliorating inequities in elementary schools than in high schools.

There are relatively few variables describing the socioeconomic characteristics of the student and parent bodies used in the analysis, largely due to limitations in data availability. At the building level, only student ethnicity is reported and there are limited data available on the percentage of students who are free lunch eligible (PFLCHP); approximately 56 percent of the schools in the sample reported data on the percentage of students who are eligible for free lunch. On average, 15 percent of the students in a school building are non-white (NONW), and, for those schools reporting, approximately 32 percent of the students are eligible to receive free lunch. There is, of course, substantial variation in the characteristics of the student body across schools and districts. While some schools have virtually no low-income children, in some schools, almost all of the children are poor.

We utilize information on the "urbanization" and the size of the school district in which each school operates. Three dummy variables describe urbanization. Forty percent of the schools are in small town or rural districts (STRUR), 22 percent in suburban districts (SUB) and 38 percent in urban districts (URB). Three dummy variables distinguish districts by size: 29 percent of schools are in very small districts with fewer than 5 schools, 41 percent of the schools are in small districts (SMDIST) which have 5 to 9 schools; and the remaining 30 percent of the schools are in medium to large districts (MLDIST) with 10 or more schools.

It should be noted that the unit of analysis for this study is the building and not the district. The district level data have been merged into the building level file and the district level variables are used to characterize the district in which the school operates. For example, the SMDIST average shows that 41 percent of the schools in the state operate in a school district which has 5 to 9 schools and not that 41 percent of the school districts have 5 to 9 schools. In fact, the average school district in Ohio has about 6 schools.

The Big Nine School Districts

As described in greater detail below, some of the analyses—the estimation of district-specific formulae—are performed using a smaller sample of schools, specifically, the 494 in the largest nine school districts reporting data—Akron, Canton, Cleveland, Columbus, Dayton, Parma City, Southwestern, Springfield and Toledo. Total enrollment is 276,855 representing roughly 17 percent of the children in the sample. The largest of these is Columbus, with 131 schools; the smallest is Springfield with only 20 schools. District specific formulae are estimated only for these nine districts for the following reason. While in principle a de facto spending formula could be estimated for every school district in the state, in practice, it is neither feasible nor reasonable. Most of the school districts in Ohio are very small. As shown in table 3, almost 56 percent of the school districts in the analysis sample have four schools or fewer. Another 36 percent have between 5 and 9 schools; 38 districts, representing 6.5 percent of the sample have between 10 and 19 schools and only 9 districts have at least 20. As expected, these 9 districts are all urban districts and differ significantly from the other 577 districts in the sample. Spending in the "big nine" is higher, averaging approximately $800 more than the average district in the state. Big nine schools have a higher percentage of non-white and poor children—more than 50 percent of the children in the average big nine school are non-white and more than 50 percent are eligible for free lunch.

The policy implication of the preponderance of small districts is that in small districts, district administrators could easily design a formula for allocating spending across their schools that mirrors or re-creates the current distribution of spending, should they so desire. Using relatively simple computations, a formula based on a small number of factors could be derived by "working backward" from the allocation the district prefers. Specifically, the number of factors that a district would need would be exactly equal to one less than the number of schools. For example, a district with four schools could derive a formula to allocate spending in any pattern they prefer by appropriately choosing an intercept and coefficients on three factors. While it is also possible to do so in larger districts, the number of factors required increases with the number of schools in the district, increasing both the computational difficulty and the difficulty of designing a credible formula. (Although it seems plausible that a formula based on ten factors describing the characteristics of a school and its student body could potentially be implemented, a formula based upon, say, the fifty or sixty factors that would be necessary for a larger district seems considerably less plausible.)

To the extent that districts are small enough to design formulae to maintain the status quo, a move to formula or block grant funding would affect spending and performance only if (1) the current distribution of spending is not, in fact, what they prefer but is a perverse result of the system, (2) the overall level of spending of the districts is changed, or (3) the schools have been operating inefficiently because the district policies are misconceived— that is, districts have been misallocating resources within schools because, for example, they have inferior information. (Of course, a move to formula funding could affect spending in larger districts for these same reasons as well.) While it is entirely possible that districts would prefer a different distribution than they have, the magnitude of this problem is unknown and answering it would require an analysis that is beyond the scope of this paper. (There are important conceptual and practical difficulties posed by addressing these types of questions.) On the other hand, it seems less likely that districts would choose a higher spending level for their schools if the only change is to formula funding within an individual school district. If the state were to run a block grant system of equal financing across the state, however, we might expect this effect to be fairly important.

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De Facto Spending Formula

A Statewide Formula

The centerpiece of the empirical work is a de facto resource allocation formula that is estimated for schools across Ohio. The underlying notion is that this formula captures the "strategy" or "formula" by which, intentionally or otherwise, resources are allocated across schools. More specifically, de facto resource allocation formulas are estimated in which the amount of spending per pupil in schooliin district j(Yij) in various categories will be "explained" by the available school level data Xij. These are: enrollment (EFMADM), the square of enrollment (EFMSQ) included to allow for returns to scale, dummy variables distinguishing elementary (ES) and middle schools (MS) from high schools (HS), the percentage of the students who are non-white (NONW) and the percentage of the students who are eligible for free or reduced-price lunches (PFLCHP), as a measure of poverty. Since this last variable is only available for 56 percent of the schools in the analysis, a dummy variable, DUMFLE, is also used, indicating whether or not the free lunch eligibility data are available. (Although it would be preferable to include variables describing the population of disadvantaged students in that school—such as percentage with limited English proficiency—Ohio does not report these at the school level, only at the district level.) Brief definitions of the variables used are shown in table 1 and descriptive statistics for these variables are presented in table 2.

Mathematically, the de facto spending formula may be written as:

(1) Yij= a + b Xij+ eij.

where a and b represent parameters to be estimated and e is a standard error term.4 The coefficients can be interpreted as indicating the increase in per pupil spending in school i that is due to a one unit increase inXij. For example, the coefficient on PFLCHP would indicate the increase in school per pupil spending that would accrue due to a one percentage point increase in the percentage of a school's students that are eligible for free lunch. These regressions are estimated for both instructional spending only and for total spending. The first set of regressions provides a description of the pattern of school-level spending across the state of Ohio, ignoring any district level variables. Thus, these might be viewed as capturing the extent to which school spending now conforms to a parsimonious statewide "formula."5

Notice that the de facto spending formula is not a cost function, nor is it an expenditure function. The estimation of a cost function would require data on the prices of inputs, adjust for the quality and characteristics of output, and rely on an assumption that observed spending reflects cost-minimizing behavior. An expenditure function, on the other hand, would include variables that determine the demand for public spending on education—such as income, intergovernmental aid, and the costs of providing education, etc.

The results of estimating equation (1) for per pupil instructional spending and total spending are shown in the first two columns of table 4. The regressions indicate that a relatively modest share of the variation in spending is explained by the observed variables describing differences in the schools. Approximately 28 percent of the variation in per pupil instructional spending and 30 percent of per pupil total spending is explained by variation in the included variables.

Overall, Ohio elementary schools receive less per pupil than high schools—$126 less on instructional purposes and $838 dollars less overall. While middle schools spend more on instruction (approximately $94 more) they spend less overall, indicating non-instructional spending is significantly lower in middle schools relative to high schools.

The negative coefficient on enrollment in both the instructional and total spending regressions indicates that per pupil spending declines with the size of the student body, reflecting, perhaps, the economies of scale that accrue as, for example, the salary of the principal is spread out over a larger student body. The positive coefficients on the square of enrollment (EFMSQ) indicates that the magnitude of this effect declines somewhat as school size increases. Notice, however, that although these coefficients are statistically significant, their magnitudes are quite small. Thus, while gaining more students may decrease per pupil spending, the effect is likely to be on the order of a few dollars per student. Similarly, while school funding increases significantly with the percentage of non-white students, the effect of a one percentage point increase in non-white students would only increase per pupil spending by $24.

The coefficient on DUMFLE, the dummy variable denoting whether free lunch eligibility data are available, is positive, significant, large, and generally consistent across schools in a district. The obvious implication is that the availability of data is not random—it is systematically related to higher spending. In fact, the schools for which free lunch data are available are quite different from those for which data are unavailable. They are larger, have more non-white students, and are more frequently found in larger, urban districts. Schools with free lunch data available average 523 students, approximately 24 percent of whom are non-white; their districts average 28 schools, 59 percent of which are in urban areas. Schools for which the data were unavailable average 442 students, approximately 4 percent of whom are non-white, have an average district size of 5 schools, only 11 percent of which are urban. Thus, DUMFLE acts, at least in part, as a proxy for large urban school districts, which have a higher percentage of students in poverty. Consequently, the coefficient on FLCHP should be interpreted with caution. Given the availability of the free lunch data—that is, conditional on DUMFLE=1—the coefficient on PFLCHP indicates that spending decreases with the percentage of students who are poor, as indicated by their eligibility for free lunch. That is, spending is higher in schools reporting free lunch eligibility data, however, the magnitude of the premium decreases with the percentage of students who are eligible. Clearly, better, more comprehensive data are required to fully understand or satisfactorily describe the relationship between spending and poverty at the school level in Ohio.

An implication of this analysis is that, when viewed from a state perspective, spending in the schools reflects a considerable variation that is not explained by simple school characteristics. This is, of course, to be expected. Since school spending is largely determined by districts, much of the variation in spending reflects differences in the overall spending level across districts.

Controlling for Interdistrict Differences in Spending

The analysis proceeds by controlling for these district-specific effects to focus on the factors explaining the intradistrict variation in spending. The simple de facto spending formula in equation (1) is augmented to allow each district its own intercept term—that is, allowing a to vary across districts—in order to control for the interdistrict variation in overall spending. More specifically, equation (1) is augmented by a series of district-specific dummy variables,aj:

(2)Yij= aj+ b Xij+ eij.

Notice that the inclusion of the district effects in (2) effectively controls for any district-specific characteristics—including but not limited to overall district spending—that do not vary across schools within a single district. Thus, the estimates tell us about the impact of theXijcontrolling for district differences in policies, revenues, demographics, location, etc. The result of the estimation of equation (2) is a de facto spending formula that controls for the interdistrict variation in school spending, etc.

Parameter estimates for equation (2) for both instructional and total spending, reported in columns (3) and (4) of table 4, indicate that the district dummies are important. The spending regressions with the district dummies explain a much larger share of the variation in spending—R2 s are 0.68 and 0.74—although roughly one-third of the variation in instructional spending and a quarter of the variation in total spending remains unexplained. (An F-test indicates the district dummies are jointly significant at the 1 percent level.) Further, the inclusion of the district dummies has important effects on the coefficients of the other explanatory variables.

As before, elementary schools are seen to receive less money than high schools, but here, the magnitude of the effect is larger—per pupil spending for elementary schools trails high school spending by $1,115 overall, $291 of which is instructional spending. While the regressions again indicate that middle schools receive less money than high schools, instructional spending is now shown to be insignificantly different in middle schools compared to high schools.

The coefficients on enrollment are also of the same signs, and, although they are of a somewhat larger magnitude, they remain small. In contrast, the coefficients on the percentage of non-white students are substantially smaller, suggesting that within individual districts the percentage of non-white students is less important in determining spending than it is in determining overall district spending. One reason may be that there is less variation in the representation of non-white students within school districts than between school districts.

As expected, the coefficient on DUMFLE is insignificant in the presence of the district- specific dummies. This reflects the fact that, for the most part, the availability of the free lunch data is determined by the district. Thus, the district dummies capture most of the variation in DUMFLE. However, the dummy is not perfectly collinear with the district dummies because there are some districts for which free lunch eligibility data are only available for some of the schools.

Particularly interesting in these estimates is that the coefficient on the percentage of free lunch eligible students has a positive, rather than a negative sign. The implication is that, controlling for the differences between districts, greater spending is directed at schools with more poor children, although the magnitude of the effect is fairly small. Here, spending per pupil increases by less than $6 for a one percentage point increase in poor students.

Spending Formulae for the Big Nine Districts

Given the importance of the district in allocating spending, we then turn to estimating spending regressions for individual districts. Unfortunately, as described above, most of the school districts in Ohio are quite small, which precludes the estimation of the de facto spending formulae, for the following reason.

In a district with a very small number of schools any distribution of spending can be perfectly characterized by a de facto spending formula based on the explanatory variables used in this analysis.6 Mechanically, this is a familiar result from statistics. If the number of observations equals the number of independent variables, then the R2 equals 1. Although it is possible—mechanically—to estimate these equations in small districts, it is not particularly meaningful. Thus, we estimate these equations for only the largest districts.

Before estimating district specific regressions, we estimate equations (1) and (2) using only data on the big nine districts. Since almost all of the schools in these districts had data on free lunch eligibility, DUMFLE is not included in the regression. The results of the estimation, shown in table 5, indicate some important differences between the pattern of spending in all of the districts and the pattern of spending in only these districts. First, as previously shown in table 2, overall spending is higher in the larger districts. Second, the disparities in spending between elementary and high schools and also between middle schools and high schools is much larger. All things being equal, high schools receive more than $3,000 in per pupil spending than elementary schools in the big nine districts. As in the previous regressions, these estimates indicate that spending decreases with size of the student body, and increases with the representation of poor children. Finally, the results indicate that school level spending is only partially explained by these variables. R2 s indicate that only about one-third of the variation in instructional spending is explained by these variables, and even in the "best performing" model of total spending that includes the district effects, the regressors explain only 57 percent of the school spending. These suggest that there are substantial differences in these formulae across the big nine districts, even after controlling for the overall level of spending and other common district effects. That is, much of the variation in spending is not explained by the variation in the regressors in a model that constrains the coefficients on all of the regressors (except the intercept) to be the same across districts. Thus, we turn to estimating district-specific spending formula.

District Specific Spending Formulae

Table 6 presents the results of estimating spending formulae for the nine districts in the sample having at least twenty schools—Akron, Canton, Cleveland, Columbus, Dayton, Parma City, Southwestern, Springfield and Toledo. The largest is Columbus, with 130 schools, and the smallest is Springfield, with only 20. Overall, total spending per pupil is better explained than instructional spending (that is, R2 s are higher). The results indicate that, despite important differences in the magnitudes of the coefficients of the variables in these formulae, there is some agreement on the signs of these formulas. That is, policymakers in these districts seem to share some degree of agreement about which of these factors should lead to more generous funding of the schools and which should lead to less generous funding. For example, in all of these districts, elementary schools receive significantly less funding than high schools, and middle schools are either somewhere in between or insignificantly different from high schools. In general, per pupil resources decrease as enrollment increases, as fixed expenses are spread over larger numbers of pupils. In all districts except Akron (in which spending is lower in schools with more non-white students) the representation of non-white students did not have a significant impact on spending. Finally, to the extent that poverty matters, districts direct greater resources toward schools with a greater representation of poor children. This agreement provides some encouragement that a consensus might be reached about a statewide formula.

An important implication of these regressions is that in some districts, school spending conforms fairly closely to what might be a spending formula. In Canton, with 24 schools, for example, almost 90 percent of the variation in total spending is explained by the regression. In Parma with 21 schools or Southwestern with 23 schools, the formula explains roughly 80 percent of the variation in total spending. Even Columbus, with its 130 schools, and Toledo with 60 schools, shows a de facto spending formula that explains about 70 percent of the variation in total spending. Of course, in other districts, spending is quite poorly explained by these school level variables. In Cleveland and Dayton, the de facto spending formulae explain only about one-third of total spending and even less of the instructional spending.

Interestingly, as mentioned above, total spending conforms more closely to a formula than does instructional spending. If, in fact, school districts rely on formulas only to allocate teachers, as is sometimes claimed, one would expect that it would be the reverse—instructional spending should be better explained by student counts. Of course, the factors included in these regressions may be different from those used by the schools in practice and/or the regressions may be misspecified in some other way.

Extending the Statewide Formula

The results of estimating the district specific regressions provide evidence that the formula describing the allocation of resources differs across districts—even across these relatively similar districts—thus suggesting that additional exploration into the differences in the formula is warranted. To fully investigate the interdistrict differences in formulae and the factors driving those differences would require a sophisticated behavioral model that explicitly models the determinants of the formula at the district level. Unfortunately, the data are insufficiently rich (in particular, there is an insufficient number of schools in many of the districts) to allow the use of the more sophisticated techniques.7

Instead, we employ a fairly simple method to investigate the extent to which the coefficients of the formula differ across types of districts—we interact each of the variables in the formula with dummy variables indicating whether a school is in an urban (URBAN) school district, whether the school is in a small town or rural district (STRUR), whether it is in a medium- to large-size district (MLDIST), having 10 schools or more, or a small district (SMDIST), having 5 to 9 schools. The omitted categories are suburban districts and very small districts.

The results of these regressions are shown in table 7. (An F-test of the joint significance of the interaction effects indicates significance at the one percent level.) The first two columns report the results of estimating the formula including the four dummies and interacting them with the model variables. In the second two columns, only the interactions are included because the included district effects are collinear with the dummies.

These regressions describe significant differences in the formulae across different district types. Urban, suburban, and small town/rural districts differ from one another—as indicated by the significance of the coefficients on the URBAN and STRUR variables—and small and very small districts seem to be characterized by different formulae than medium to large districts—as suggested by the significance of the coefficients on MLDIST. Overall, suburban districts spend the most, urban districts spend less, and small town/rural districts spend the least. Conditional on urbanization, however, it is the largest districts that spend the most, small districts spend the least, with the very smallest districts in between.

Interestingly, the other coefficients in the formula also differ by district type. Although all district types direct greater spending to schools with a higher percentage of non-white students, the increment is least in urban districts—the coefficient on URBAN is significant and negative. At the same time, all districts spending less money per pupil in larger schools—the effect is somewhat more modest in urban and small town/rural districts. Larger enrollment does not lead to a significant increase in spending in small town/rural districts, although this may be due to the limited variation in school sizes within these districts.

As before, spending is lower in elementary schools than middle schools and, in turn, lower in middle schools than high schools. Overall, however, this differential is greatest in medium- to large-size suburban districts, more modest in urban districts, and fairly small in small town/rural districts with fewer than 10 schools. Finally, the estimates of the coefficients on PFLCHP indicate that, on average, schools with a higher proportion of poor children receive less money in all but the medium to large districts.

Regressions were also run including district effects, and the results are reported in columns (3) and (4) of table 7. Recall that including the district effects precludes the inclusion of other district characteristics directly. Thus, the dummy variables for urbanization and district size are only included as interactions with the other included variables. As seen previously, these regressions summarize the factors explaining the intradistrict variations in spending since the district effects control for the interdistrict variations.

Again, the regressions reveal some systematic differences in spending patterns. Both medium- to large-size and small-size districts direct more resources to schools with a greater proportion of non-white students. Also, larger schools receive fewer resources per pupil than smaller schools, but there is no significant difference in the magnitude of the effect across district types. The same general pattern holds for elementary, middle, and high schools, although there are some differences in magnitudes. There are, however, significant differences in the estimated effect of increased poverty among the students. These regressions indicate that, holding the district characteristics constant, schools with a greater proportion of poor children receive greater spending. The magnitude of the impact is greatest in suburban districts (approximately $27 more in per pupil spending for every one percentage point increase in the percentage of students free lunch eligible) but still significant in urban districts ($13) and small town/rural districts (approximately $11). The coefficient does not vary significantly with the size of the district.

Simulating a Statewide Spending Formula

Although the spending formulas estimated above are clearly simplistic—a more realistic formula would include additional variables describing the special educational needs of students, the relative costs of purchased inputs, etc.—these estimates can be used to gain insight into the impact of allocating spending according to a statewide formula. Thus, we use the parsimonious spending regression in column (2) of table 4 to estimate the total spending per pupil that would be allocated to each of the 3,284 schools in Ohio.

More specifically, "formula spending" is found as the amount of spending predicted by the regression for each school. Next, we compute the change in spending that would result as the difference between predicted and actual spending. Since this change is, in fact, the prediction error or residual of the regression, the changes in spending average to zero across schools, by construction.8 That is, the average school should neither gain nor lose money if spending was allocated according to this formula. Of course, there are significant changes in the distribution of spending. Perhaps most important, although disparities in spending would not disappear, they would be significantly ameliorated. As an example, while current spending ranges from a low of $2,346 per pupil to a high of $13,622, formula spending would be significantly more compressed—the lowest spending school would spend $3,820 and the highest spending school would spend $7,637. (The standard deviation would shrink from 1,089 to 599.)

As shown in table 8, under such a formula, most schools would see relatively modest changes in spending. Roughly half would see spending changes of less than 10 percent and roughly 80 percent will see changes less than 20 percent. Measured in dollar terms, roughly half will see changes in per pupil spending of less than $500 and roughly 80 percent will experience changes of less than $1,000 per pupil. Of course, a significant number of schools would see large spending changes. Most of those will be increases; however, there are those that would see significant decreases. For example, 65 schools would be allocated more than 30 percent less money than they currently spend. As expected, these are the schools that currently spend substantially more than most of the schools in the state.

Notice that this simulation suggests that there would be substantial opposition to the adoption of such a statewide formula. Although high spending school communities may be willing to accept some redistribution in order to achieve greater equity across schools and districts within the state, it seems unlikely that they would support a formula such as this that would substantially change their own spending. At the same time, those who would gain money are quite likely to support finance reform and the frequencies in table 8 indicate that they are in the majority—almost 55 percent of the schools in the sample (enrolling roughly 55 percent of the students) experience gains, rather than losses.

Thus far, this paper has considered a radical change in the financing of public schools—the move from district control of the distribution of spending to state control. Although this has considerable appeal, the political obstacles to enacting such a reform are unlikely to be overcome quickly. A more realistic policy would be to reallocate the state funding currently provided to schools in order to effect a distribution of spending that most closely approximated the preferred distribution. That is, reduce or eliminate state aid to schools identified as spending "too much" by the formula and increase state aid to those spending "too little." For 1,351 of the 1,486 schools that would lose money in formula financing, the necessary cutback could be accomplished by reducing or eliminating state aid currently received. However, the incentive implications for local revenue raising by schools are serious and problematic. Given these limitations, adopting such a modified formula system would lead to a substantial reduction in disparities in spending overall—the standard deviation for the modified formula approach is 700, which is higher than the 598 of formula spending, but still quite a bit lower than the 1,089 of the current system. (Since mean spending is roughly the same for all three distributions, the coefficients of variation would show the same pattern.) The reduction in the range of spending would not, however, shrink as significantly as under formula financing. Again, the "bottom" is brought up—from $2,346 to $3,820—but, since the highest spending schools received little state funding to begin with, spending at the top is relatively unchanged—the new maximum of $12,829 is only marginally lower than the current $13,621 and nowhere near the $7,636 recommended by the formula.

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Conclusions

This paper uses school and district level data from Ohio for 1995-96 to analyze the distribution of spending across schools and districts to inform the policy debate regarding block grant funding for public schools. The results have indicated that the patterns of spending across and within school districts in the state of Ohio vary substantially. These differences are driven by both differences in the schools and by differences in the districts in which these schools operate. Districts differ not only in their average spending, but also in the way that they distribute spending between elementary, middle and high schools, for example. There appears, however, to be some modicum of agreement across districts about which of these factors ought to trigger greater spending and which should trigger less spending. At the same time, the regressions reveal a fair amount of diversity in the size of the response—whether due to differences in enrollment, student poverty, etc.

As noted above, the regressions indicate that the combination of interdistrict variation in the overall level of spending and the intradistrict variation in the allocation across schools results in a spending system in which only about 30 percent of the variation in spending is explained by a set of factors that should play an important role in any spending formula that might be adopted—enrollment, the grade level served by the school (elementary, middle or high school), and the percentage of non-white students or those eligible for free lunch. Thus, a move to any statewide formula based upon these characteristics would be likely to produce significant changes in the pattern of spending across Ohio public schools. Clearly, there are variables not included in this formula (due to limitations in data availability) that could be expected to be included in any adopted formula—such as those describing the special educational needs of students or describing the costs of purchased inputs, etc. Thus, while moving to a system of state-level block grant funding might have an intuitive appeal, such a system would differ substantially from the current system, in that it would likely standardize both the level and distribution of spending across districts. A straightforward simulation indicates that a shift to allocating spending according to a statewide spending formula would significantly reduce the disparities in spending between the highest and lowest spending schools and much of the redistribution could be accomplished by re-allocating state aid money. While such a policy change would likely be opposed by schools experiencing spending declines, simulations suggest that since more schools (enrolling more students) gain, there may be sufficient political will to adopt such broad finance reforms. An intermediate plan, that would redistribute only state funding now allocated to public schools according to the formula, might be more politically palatable to those who favor local control. Such a program would still direct substantial cuts to a large number of schools, but would not constrain schools in their locally financed spending, offering school districts the opportunity to offset the loss of state aid with additional local tax revenue.

Clearly, these results are only suggestive and much additional work is warranted to inform the policy community. As the push to school-level financing and control continues, it is advantageous to look to the lessons offered by the varied actual experiences of school districts within an individual state to guide these policy decisions. This paper offers progress in that direction.

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Footnotes

1 At the same time, local control may contribute to greater efficiency. To the extent that families are mobile and can choose between school districts competing for their children, local control may put pressure on schools to operate more efficiently. Further, it may result in the efficient "matching" of families into districts offering the kinds of schools they prefer and are willing to pay for. Of course, this efficiency "gain" comes at a price: local control as practiced in most of the United States has generally entailed considerable inequity.

2 Note that the Cincinnati school district and the 79 schools within it are not included in the analysis because EFM spending data were unavailable. According to correspondence with Dr. Matthew Cohen at the Ohio Department of Education, Cincinnati data were prorated, so that all 79 buildings were shown to have identical spending. Thus, the district total was the only entry included in the file for this district.

3 The analysis sample was constructed in a fashion similar to that employed by Sherman and Best (1996) in their research on school-level expenditures in Ohio in 1992-93. Sherman and Best's study focuses on approximately 3,600 schools in 607 "regular" K-12 districts in Ohio; for example, "only elementary middle, and secondary schools with an enrollment greater than zero were included in the file for analysis" (page 41).

4 As an alternative, log-linear formula regressions were run. The results were qualitatively similar.

5 In practice, any formula for block grant funding of schools would include more variables describing the particular characteristics of the students, personnel, organization, etc. of individual schools. Clearly, the absence of such data in currently available data sets points to the need to develop accounting and administrative systems before any "direct-to-school" funding formula is implemented.

6 For a regression with an intercept and six explanatory variables it is, of course, impossible to estimate coefficients without at least eight observations—here, given by the number of the schools in the district.

7 In principle, Hierarchical Linear Modeling or a random coefficients specification could be employed to investigate these further. However, the large number of districts for which there are only a small number of schools limits both the power and usefulness of these techniques. These techniques could be usefully employed to an analysis focusing on a larger, perhaps national, sample of large school districts.

8 More important, perhaps, is that overall spending remains relatively constant—in large part because enrollment is included among the regressors.

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References

Berne, Robert and Leanna Stiefel. 1984. The Measurement of Equity in School Finance. Baltimore: Johns Hopkins University Press.

Clark, Catherine and Lawrence Toenjes, 1997. "Exploring Alternatives for Allocating Resources to Individual Schools" (Draft, 1997).

Cooper, Bruce S. 1993. "School-Site Cost Allocations" (paper presented at the annual meeting of the American Education Finance Association, 1993).

Hill, Paul T., James W. Guthrie, and Lawrence C. Pierce. 1997. "Public School Block Grant Funding Under a Contracting Strategy" (Draft, Consortium for Policy Research in Education, University of Wisconsin-Madison, 1997).

Oates, Wallace. 1972. Fiscal Federalism. New York: Harcourt Brace Jovanovich, Inc.

Odden, Allan and Carolyn Busch. 1997. "Funding Schools for High Performance Management: School-Site Based Financing" (Draft, Consortium for Policy Research in Education, University of Wisconsin-Madison, 1997).

Rubenstein, Ross H. 1997. School-Level Budgeting and Resource Allocation in the Chicago Public Schools: Processes and Results. Unpublished Dissertation, 1997. New York University.

Schwartz, Amy E., Leanna Stiefel, and Ross Rubenstein. 1998. "Education Finance." In Handbook of Public Finance, edited by Fred Thompson: 447-482. New York: Marcel-Dekker.

Sherman, Joel and Clayton Best. 1996. "Assessment and Analysis of School-Level Expenditures." (Unpublished paper prepared for the National Center for Education Statistics, 1996).

Stiefel, Leanna, Ross Rubenstein, and Robert Berne. 1998. "Intra-District Equity in Four Large Cities: Data, Methods and Results." Journal of Education Finance 23 (4): 447-467.

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Acknowledgments

Support for this research was graciously provided by the National Center for Education Statistics. Thanks are due to William Fowler for help in formulating the topic and to Matthew Cohen and Leanna Stiefel for useful comments and suggestions, to Hella Bel Hadj Amor for research assistance and to Tania Caceres for her patient and able secretarial assistance.

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