Premature celebrations : The persistence of inter-district funding disparities

Two interlocking claims are being increasingly made around school finance: that states have largely met their obligations to resolve disparities between local public school districts and that the bulk of remaining disparities are those that persist within school districts. These local decisions are described as irrational and unfair school district practices in the allocation of resources between individual schools. In this article, we accept the basic contention of within-district inequities. But we offer a critique of the empirical basis for the claims that within-district gaps are the dominant form of persistent disparities in school finance, finding instead that claims to this effect are largely based on one or a handful of deeply flawed analyses. Next, we present an empirical analysis, using national data, of 16-year trends (1990 to 2005) and recent patterns (2005 to 2007) of between-district disparities, finding that state efforts to resolve between-district disparities are generally incomplete and inadequate and that in some states between-district disparities have actually increased over time.


Introduction
An increasing volume of rhetoric around school finance rests on claims that states have largely met their obligations to resolve disparities between local public school districts.This premise is then extended to the contention that the bulk of remaining disparities are those that persist within school districts, due to irrational and unfair school district resource allocation practices between individual schools (see, for example, McClure, Wiener, Roza, and Hill, 2008; Public Impact, et al.,  2008).In short, since states have done their job to promote equity and adequacy of school funding, school district officials must now meet their corresponding obligations.This argument is also often attached to the remedy of weighted student funding (see Roza, 2006, pointing readers to the Fordham Institute's "Fund the Child" campaign).
Notably, no leading researchers in economics and school finance have joined this overwhelming shift in emphasis away from state-level concerns.Many have opted instead for a broad description of the funding problem that encompasses both within-district and betweendistrict resource disparities (see, e.g., Bifulco, 2005; Burke, 1999; Duncombe and Johnston, 2004;  Downes, 2004; Imazeki and Reschovsky, 2004; Stiefel, Rubenstein & Berne, 1998; Rubenstein et al.,  2007).Nonetheless, arguments favoring a devolution in focus from states to school districts have gained significant traction in policy debates, and they have the rhetorical advantage of providing state policymakers with an enticing, revenue-neutral policy solution (see Public Impact, et al., 2008).If states have done their job, no more money is needed, nor must these policymakers consider painful movement of limited funding away from wealthier districts.Rather, districts must simply reshuffle what they have, in order to achieve optimal distribution.But, as discussed below, the increase in popularity of these political arguments is backed by little or no empirical evidence for the premise that states have already met their end of the bargain (Baker, 2007). 1 This article explores the extent that states have actually resolved substantial disparities in available resources between local public school districts.Although we review recent literature on within-district disparities and their relation to between-district disparities, we do not separately estimate the relative disparities within and between districts.Rather, we remain focused on the single question of whether and to what extent states have substantially resolved past between-district disparities such that it really is time to check that box and move on to other policy concerns.In short, this article begins with a critique of the within-district comparative claims and then examines between-district disparities in state and local revenues per pupil across all states-over the 16-year period from 1990 to 2005 across all states, and with more fine-grained detail for the years 2005 to 2007.

Recent Evidence on Between-district Disparities and State School Finance Policies
In the late 1990's through early 2000's a handful of rigorous studies evaluated changes to the distribution of school funding within and across states.Related studies examined those changes in connection with the existence of judicial mandates for reform in a given state, ultimately looking at the relationship between funding changes and student outcomes.Notable examples include Murray,  Evans and Schwab's (1998) evaluation of the effect of judicial mandates on the level and distribution of funding and Card and Payne's (2002) evaluation of the link between judicial mandates, school finance reforms, changes in the level and distribution of resources, and student outcomes.These teams of authors found that state school finance lawsuits-specifically high court rulings in favor of 1 A secondary current rhetorical argument against increased funding, or school finance reform more generally, rests on the related contention that no substantial improvements to student outcomes or closure of achievement gaps have followed from a purported dramatic increase in state-level funding and improved funding equity over time.Moreover, the argument continues, given the absence of outcome improvements, the asserted major increases to funding have proven ineffective and the fault lies with the policies of local districts or others, rather than with the state funding formulas.This argument as well hinges on whether there really have been substantive and sustained improvements across states in school funding equity and adequacy, and whether school finance reforms have improved student outcomes or reduce achievement gaps.The contention that there have not been improvements is woven throughout the recent work of Hanushek and  Lindseth (2009) and Hill, Roza and Harvey (2008).
plaintiffs-tend to lead to positive changes in the level and distribution of funding.Card and Payne found as well that those changes lead to improvements to the distribution of outcomes.Other recent studies on improvements to equity or adequacy of funding over time have focused longitudinally on specific states and reached similar conclusions (see, for example, Downes, Zabel &  Ansel, 2009 [Massachusetts]: Downes, 2004 [Vermont]; Deke, 2003 [Kansas]).
In addition, a handful of relatively recent publications have described disparities-absolute as well as changes-in school funding by race and/or poverty across states.For example, Bifulco  (2005) conducted a longitudinal analysis of racial disparities in school funding, looking at data from the late 1980s through 2002 across all states.He found that in 2002 the average black student's funding was approximately 8.5% higher than the average white student's funding, with no adjustments applied.However, when resources are adjusted for well-documented factors affecting the costs of producing comparable student outcomes (including student need factors such as poverty and limited English language proficiency), as well as economies of scale and regional labor market variation, he found that the average black student's district had from 3.2% to 15.8% less funding than the average white student's district.
Similarly, intermittent reporting by the Education Trust has noted persistent funding gaps between school districts with high and low poverty rates and high and low enrollment concentrations of students of color. 2 These reports show that some states have relatively small gaps, while others provide greater amounts of funding to higher poverty, higher minority districts.But the reports also identify states that provide much lower levels of funding to higher poverty and higher minority districts.On net, Education Trust finds that higher poverty and higher minority concentration school districts continue to receive relatively less funding from their states.
Taken together, these findings suggest that states have not yet fully met their end of the bargain and that significant work remains to be done at the state policy level before turning attention entirely to within-district resource disparities.That said, the Bifulco analysis leaves off eight years ago, and the Education Trust analysis of funding gaps has methodological and data limitations that prevent readers from making accurate judgments in this regard. 3It also does not address progressor lack thereof-over time.
separate-but-equal policies leading up to Brown v. Board of Education (1954) concerned the fact that districts' separate schools for blacks were resourced at levels below those for whites.
An issue raised by the Los Angeles Unified School District Rodriguez litigation is the degree to which intra-district funding disparities are linked to teacher seniority and transfer policies.Because teachers with more experience tend to transfer to schools serving fewer low-income students of color, and because those teachers are paid more than beginning teachers (Lankford,  Loeb, & Wyckoff, 2002), the salary resources devoted to more advantaged schools tend to be higher.While this can be disregarded as not really about district allocation of funding, we should keep in mind that teacher experience is associated with teacher quality-at least in the early career yearsand that teacher quality is generally regarded as the most important resource a school can provide to its students (see Clotfelter, Ladd & Vigdor, 2005; Rivken, Hanushek & Kain, 2005).Nothing in the analysis that follows should be understood as suggesting that this is not an important issue; our intent is merely to question the associated argument that disparities between districts are no longer of major importance.
Research over the past fifteen years has started to tease out the nature of intra-district spending patterns.These studies are largely limited to a few states or individual districts where school-site expenditure data have been available, including California, Ohio and Texas, as well as select cities in New York State and the city of Chicago.In one early study, for instance, Hertert  (1995) simultaneously evaluated variations in California between-school spending both across districts and within districts, using data from 1990-91.She found generally that between-school disparities across districts were greater than the average district-level spending disparities across districts.Moreover, in some cases between-school disparities within districts were greater than between-school disparities across districts.Hertert accounted for district size and district type to correct for some explainable differences in spending across districts, and she found that accounting for school type did mitigate (but did not completely explain) between-school differences.In another such study, Burke (1999) estimated resource distributions at the school level rather than the district level-revealing significant intra-district disparities that in some states (Illinois and New York) exceeded inter-district disparities. 4Burke's and Hertert's studies represent the most direct test of the relative magnitude of within-and between-district resource variations, but both overlook a number of factors addressed in more recent studies, including differences in costs from one district to the next and one school to the next (see Baker, 2009).
A related body of relevant research looks in isolation at within-district spending (that is, it does not compare these spending patterns to between-district patterns).Steifel, Rubenstein and  Berne (1998) analyzed school-level data from four large urban districts (Chicago, Fort Worth, New York City and Rochester) in an effort to measure within-district disparities in resources.They asked two basic questions.First, how much variation exists across school-level budgets within the districts?Second, to what extent is that variation associated with factors that may affect the costs of providing equal educational opportunity across those schools-most notably, rates of children in poverty? 5 Like Hertert (1995) and Burke (1999), they found significant variation in resources across schools within districts.But they also looked more closely and found that some of that variation was positively associated with poverty rates across schools. 6exas' within-district patterns appear to also show such variation.Ajwad (2006) used data on Texas school-level expenditures for elementary schools to evaluate whether districts have targeted greater resources toward schools in higher-poverty neighborhoods.Using fixed effects expenditure regressions and neighborhood resident population characteristics rather than school enrollments, he shows that Texas school districts, on average, target additional resources toward elementary schools in higher-poverty neighborhoods.Ajwad also finds, however, that the average dollar differences in targeted funding are relatively small.Baker (2009) also focuses on within-district disparities, but-adding an important contextual element to the approaches used in above-discussed studies-he applies school-level cost function modeling 7 to estimate adjustments for costs, and he places disparities in the context of other districts sharing the same labor market.He finds that "in some cases, resource levels in urban core elementary schools are relatively insufficient for competing with schools in neighboring districts to achieve comparable outcomes" (p. 1).That is, between-district disparities may constrain the ability of some districts to resolve within-district disparities, at least for the Ohio and Texas school districts he examined.
But the most prominent work in this area has been conducted by Marguerite Roza and her colleagues, and those studies therefore deserve a close look.As with several of the above-discussed analyses, Roza, Guin, Gross and Deburgomaster (2007) use Texas school-level expenditure data.They examine changes in internal resource allocation from 1994 to 2003.Rather than estimating the statistical relationship between school-level expenditures and cost factors-as did Ajwad (2006), Baker (2009), and Rubenstein, Schwartz, Stiefel and Bel Hadj Amor (2007)-Roza and her colleagues adopt an approach that involves calculating a Weighted Student Index (WSI) to track equity levels and changes over time.A significant shortcoming of the WSI approach, however, is that it fails to measure differences in resources with respect to student population variation across schools.It instead measures whether a child in poverty in one school receives the same level of resources as a child in poverty in another school (even if that level is $0, or 0% more than the nonpoor child). 8The extent to which resources are targeted on the basis of poverty or other costs and 6 Interestingly, this finding was not systematic across settings or school types (e.g., Rochester middle schools showed stronger positive relationships between poverty and resources than Rochester elementary or high schools). 7Cost modeling is commonly used to determine the additional costs of achieving constant outcome targets.It has been used primarily in district-level analyses like those conducted by Imazeki and Reschovsky (2004) and Duncombe and Johnston (2004).The approach involves estimation of econometric models (regression equations) to determine specifically the additional costs associated with student poverty, competitive wages, economies of scale and other uncontrollable factors. 8Roza and her colleagues also test whether variations in their WSI are a function of four different factors: (a) school grade level, (b) percent white in the school, (c) teacher experience, and (d) the academic rank of the school in the state.The authors suggest that this analysis is undertaken with the goal of determining whether observed resource variation (as measured by the WSI) is a function of "intentional" and "unintentional" factors.It is difficult to interpret, however, how this ad hoc mix of outcome measures, organizational features and racial composition relates to more common sets of "cost" factors, or factors outside the control of local school officials that influence the costs of achieving any given level of outcomes (see Duncombe and Yinger,  2008).The dependent variable (WSI) measures resource variation in terms of differences across schools between student subgroups, rather than aggregate resource differences across schools with respect to population differences across schools.A more straightforward interpretation (at least with respect to whether resource variation is a function of uncontrollable cost factors) would be possible from an analysis that used needs is not addressed or accounted for in the study.That is, if every school serving low-income students were funded regressively, this would not be addressed; but if some schools serving lowincome students were regressive and some were progressive, the study would highlight that difference.Those questions are certainly of some import, but they do not get at core equity concerns.Roza, Guin, Gross and Deburgomaster (2007) begin with a quick comparison of withindistrict and between-district disparities in Texas and then jump quickly to their case that "At least in Texas, funding decisions within districts currently have a greater impact on a school's resources than inequalities in access to resources across school districts" (p.70).The first section of their article reports that variations in spending between Texas districts tend to fall within 5% to 10% of mean spending statewide, compared to disparities within large Texas districts (again, disparities in funding of similar students at different schools, as explained above) that tend to be on the order of 15%.Unfortunately, documentation is largely absent concerning the method for calculating the coefficients of variation presented by the authors. 9 There is a bit of a tautology at work here, slightly under the surface.If a researcher were to use the pupil weights and cost factors adopted in the Texas funding formula itself, or weights derived from the implementation of that formula (as is the case with the WSI approach used by Roza and her colleagues) 10 as a basis for accounting for need and cost variation, the result would almost by definition show little disparity between districts funded under that formula.But such an analysis would be based on a deeply flawed assumption-that the state school finance formula itself represents true costs.Categorical weights and other distributional criteria included in state formulas tend to be the result of political wrangling as much as they are reflections of empirical determinations of need.In reality, what an analysis like Roza's effectively shows is only that the state school finance formula does what the state school finance formula does.It is not surprising, then, that others such as Reschovsky and Imazki (2004, showing about a 25% coefficient of variation) report much greater between-district disparities in Texas, both in raw unadjusted spending and in spending adjusted for need and cost. 11nterestingly, Roza, Guin, Gross and Deburgomaster's use of formula-induced spending variation as a proxy for cost and need variation conflicts with the concurrent work of Roza and Guin themselves.In What is the Sum of the Parts?, also released in 2007, Roza, Guin and Davis calculate 'implicit weights' of district spending on specific populations of students for multiple per pupil expenditures as the dependent variable and identified standard cost factors as independent variables in an expenditure function framework. 9Roza, Guin, Gross and Deburgomaster (2007) explain that the WSI is "a ratio … of the actual funding received by each school to the funding we would expect if schools received the district's average allocation for its particular mix of students" (p.78).This calculation is made without judgment regarding whether the estimated average differences relate either logically or empirically to needs or costs.As such, there are clear limitations to the usefulness of an estimate of between-school differences in district-level budgets by factors such as student poverty rates, limited English proficiency rates, and disability rates.This estimate would merely reflect the average effect of the state distribution formula with respect to these factors.The estimate tells us nothing about whether the state weights can rationally be used for cost or need adjustment. 11In addition, Baker (forthcoming), in a study of large urban Texas districts in their labor market context, applies cost-adjusted equity analysis for schools within the large urban core and then across all schools within the labor market for each large urban core.Baker finds that in Dallas the within-Dallas variation is greater than variation across schools throughout the labor market, but that in Houston, San Antonio, Austin and Fort Worth, the labor-market wide variation is greater than the within-urban-core variation.
states.That is, their analysis is based on a calculation of how much is spent on a specific student population in a school district compared to how much is spent on the average student in the same district.They explain that these weights represent budgeting priorities or the "relative investment in each student type" (p.16).The authors show that the budgeting priorities (implicit weights) for different student types vary from one district to the next, pointing out that such variation is problematic.
In contrast, Roza, Guin, Gross and Deburgomaster, in the above-discussed Do Districts Fund Fairly? (2007) article, calculate separate implicit WSIs for each district as a basis for estimating within-district disparities adjusted for student characteristics, across multiple districts.That is, the analysis highlights only funding variations within each district, not allowing for identification of funding variation for similar students between districts, and not allowing for judgments about whether weights are linked to need.Such application of within-district implicit weights is thus deeply problematic at two levels.
First, this approach determines within-district inequities by interpreting or-more accurately-defining the variation in district-level spending priorities as variation in cost and need. 12econd, this approach creates illogical apples-to-bratwurst comparisons by applying different sets of implicit weights across schools for each different district and then, by aggregating the results across districts, mashing together the apples and bratwurst into an unwholesome smoothie.For example, if the child in poverty in school S1 in district D1 receives 20% more than the average child in district D1, then district D1 will be considered equitable if the child in poverty in all schools in that district receive 20% more than average funding.But a second district (D2) would be considered comparably equitable to district D1 if each child in poverty in each school received 10% less than average funding-because D2 disadvantaged poor children as systematically as D1 advantaged them.D2 simply had different "spending priorities" which were equitably applied.Averaging D1's equity with D2's equity, we would find the system to be extremely equitable, despite D2's systematic disadvantaging of poor children.Such a finding masks real inequities that would be revealed by the more standard methods applied by Ajwad (2006), Baker (2009) or Rubenstein, Schwartz, Stiefel and  Bel Hadj Amor (2007).
Simply put, Roza, Guin, Gross and Deburgomaster (2007) fail to acknowledge that Roza, Guin and Davis (2007) severely undermines their findings at these two levels: (a) that the implicitweight-driven WSI reflects spending priorities that cannot reasonably be used as an independent determination of equity that adjusts for student characteristics, and (b) that allowing implicit weights to vary by district in a school-level equity analysis-for which findings are eventually aggregated across districts-produces findings that are difficult to interpret at best, and entirely meaningless at worst.Yet this Education Next study has arguably become the most frequently cited basis for the broader assertion that within-district inequity should supplant between-district inequity as the funding policy concern du jour.

The Missing Link and Misguided Assumptions
12 Recall that Roza and her colleagues explain that the WSI is a ratio of actual funding received relative to expected funding if the school received the district average for its mix of students.Though this approach has little to do with adjustment for "costs" or "needs," Roza, Guin, Gross and Deburgomaster (2007) state: "The WSI allows us to compare per-pupil funding in schools while accounting for the types of students a school serves."( p. 71) None of the above-discussed studies addresses more broadly the level of between-district disparities across all states and school districts.This is important because the recent policy arguments directly implicate the relationship between within-district and between-district disparities.That is, some researchers and advocates have begun to contend that within-district disparities are more important than any remaining between-district disparities.
Carr, Gray and Holley (2007), for example, contend that average per pupil spending in higher-poverty districts in Ohio has increased over time at a rate faster than in lower-poverty districts.They also contend that this spending has reached an average level higher than for lowerpoverty districts (Chart 2, page 3).The authors present cursory analyses to support these contentions, failing to explore in any depth whether these differences are systematic across districts.That is, are there significant inequities between districts among higher-and lower-poverty districts?Instead, they move quickly from their broad findings to the argument that the state of Ohio has met its state obligation and that the remaining focus should be on within-district inequities.
To the authors' credit, as we discuss later herein, it turns out that Ohio does indeed have a progressive distribution of fiscal resources across school districts-more resources targeted to higher-poverty districts-on average. 13Whether Ohio has met its obligation as a state is a separate question.Also to their credit, the authors do not attempt to extrapolate their Ohio-based claims to other states or to the nation as a whole.
More troublesome claims are presented in a recent highly publicized report on school finance reform from the Center for Reinventing Public Education (Hill, Roza and Harvey, 2009).The report states that recent "intradistrict or subdistrict studies have questioned the importance of district-level spending differences, showing that there is more variation in per-pupil spending within than between districts" (p.18).The authors' only citation for the presumption that within-district inequity is a greater national problem than between-district inequity is to the study of Texas large districts by Roza, Guin, Gross and Deburgomaster (2007) noted above.That is, the authors make a nationwide policy argument on the basis that prior research has documented within-district inequity as the greater problem.The flaw here is two-fold.First, Hill, Roza and Harvey cite only a piece coauthored by Roza which considers only Texas data, not national data or data on any state other than Texas.Second, as we have discussed above, the analysis of Texas data itself is extremely problematic.
In the same report, Hill, Roza and Harvey cite the findings of Rose, Sonstelie and Reinhard (2006) on within-district teacher salary disparities in California.Again, they extend these findings to the rest of the country but offer no evidence to support their key contention that "What is true in California happens to some degree in every other state and every large district" (p.10). 14n other occasions, Roza and Hill have argued that persistent between-district disparities may exist but are relatively unimportant.Following a state high court decision in New York mandating increased funding to New York City schools, Roza and Hill (2005) opined: "So, the real problem is not that New York City spends some $4,000 less per pupil than Westchester County, but that some schools in New York [City] spend $10,000 more per pupil than others in the same city."That is, the state has fixed its end of the system enough.
This statement by Roza and Hill is even more problematic when one dissects it more carefully.What they are saying is that the average of per pupil spending in suburban districts is only $4,000 greater than spending per pupil in New York City but that the difference between maximum and minimum spending across schools in New York City is about $10,000 per pupil.Note the rather misleading apples-and-oranges issue.They are comparing the average in one case to the extremes in another.
In fact, among downstate suburban15 New York State districts, the range of between-district differences in 2005 was an astounding $50,000 per pupil (between the small, wealthy Bridgehampton district at $69,772 and Franklin Square at $13,979).In that same year, New York City as a district spent $16,616 per pupil, while nine downstate suburban districts spent more than $26,616 (that is, more than $10,000 beyond the average for New York City).Pocantico Hills and Greenburgh, both in Westchester County (the comparison County used by Roza and Hill), spent over $30,000 per pupil in 2005. 16These numbers dwarf even the purported $10,000 range within New York City (a range that we agree is presumptively problematic); our conclusion based on this cursory analysis is that the bigger problem likely remains the between-district disparity in funding.
That said, these are anecdotal comparisons between values not adjusted for variations in costs. 17What these examples and the above review do highlight is the very shallow depth of the current research base that might be used to tease out the relative sources of school-level funding disparities.Studies of within-district disparities are largely confined to a few states or individual districts where school-site expenditure data have been available.Yet, notwithstanding the fact that state school finance policies are idiosyncratic, studies having oft-suspect validity from select locations have been extrapolated by prominent researchers and advocates to have broader implications for within-and between-district disparities in other states. 18here are, by our count, five inter-connected issues swimming around in this soup: 1.The existence of within-district funding disparities.2. The extent of any such within-district disparities.3. The continuing existence of between-district disparities.4. The extent of any such between-district disparities.5.The relative causal importance of within-and between-district disparities.Our best reading of the extant literature tells us that numbers (1) and ( 3) should be noncontroversial: disparities do exist, but they vary tremendously by jurisdiction.As discussed above, the evidence regarding number (2) is very limited, which also means we can provide no answers regarding number (5).But it is number (4) that is most interestingly implicated by the recent policy push-the contention that we as a nation have made such progress on addressing between-district disparities that we can now turn our attention elsewhere.As such, a fifty state analysis of the current status of between-district funding inequities is warranted.

Goals of this Analysis
The following analyses are focused only on the question of between-district disparities.That is, we are investigating the sometimes-explicit, sometimes-implicit argument that states have fulfilled their equity obligations, allowing a narrowed focus on district-level resource distribution policies.Our analyses are in two parts.First, we evaluate changes in the income-revenue relationship across school districts within states from 1990 to 2005.That is, we evaluate the extent to which combined state and local revenues per pupil are associated with median household income at the school district level.We apply Census 1990 income estimates for data from 1990 to 1995 and Census 2000 income estimates for data from 1996 to 2005.The goal of these analyses is to identify the extent to which state and local revenues across all states and within each state are linked to local differences in income.We characterize state school finance systems where state and local revenues are positively associated with income as regressive, meaning that wealthier districts receive more revenues.Similarly, we characterize state school finance systems where state and local revenues are negatively associated with income as progressive.This approach is similar to that used by Card and Payne (2002).
Second, using the most recent three years of federal data on local school district finances, we generate-for each state-predicted values of state and local revenue per pupil at 0% poverty, 10% poverty, 20% poverty and 30% poverty (based on U.S. Census Poverty Rates), 19 holding constant district economies of scale, population density, regional variations in competitive wages, and year.This approach allows us to construct a more complex and thorough model of state and local expenditures and also allows us to evaluate the extent to which states are providing predictably progressive (systematically supporting poor districts and the children they serve) resources across all districts within the state.

Longitudinal Changes, from 1990 to 2005
The first data set consists of 10,189 unified public school districts matched (the same districts over time) over the 16-year period from 1990 to 2005.The dependent measure of interest is 19 U.S. Census Small Area Income and Poverty Estimates (SAIPE) data are used in this analysis in part due to gaps in reporting of subsidized lunch data across all districts and states.In general, free and reduced price lunch rates run about 2 to 3 times U.S. Census poverty rates because higher-qualifying income thresholds are applied (130% poverty level for free lunch and 185% poverty level for reduced price lunch).Accordingly, the 30 percent poverty category here corresponds to an approximately rate of 90 percent free and reduced price lunch.
the total state and local revenues per pupil at the level of the school districts.Other relevant measures include the National Center for Education Statistics (NCES) Education Comparable Wage Index (available from 1997 to 2005), district enrollments, and data on median household income drawn from the U.S. Census and NCES School District Demographics System.
The objective of the statistical model is to evaluate the relationship between the income measure and state and local revenues per pupil, over time, but conditional on major factors affecting the differential costs of providing education in different settings and under different conditions.As such, the following equation is applied:  Census 1990 and 2000).
State and Local Revenue per Pupil is expressed here as a natural logarithm because it is assumed that marginal increases in state and local revenue diminish at very high levels of median household income, also expressed as a natural logarithm.The ECWI (education comparable wage index) is applied annually from 1997 to 2005, but it is held at 1997 levels back through 1990 (because of its unavailability prior to 1997).Economies of scale are captured with a series of enrollment group variables from less than 100 students up to greater than 2,000 students.
Note that from 1997 to 2005, the ECWI picks up inflationary changes but prior to 1997, the year fixed effect picks up those inflationary changes.Our primary interest is in the income term and that term's interaction with the year term-or the way in which the relationship between income and state and local revenues per pupil changes over time.Below, in the "Findings" section of this article, we plot these elasticities over time to characterize the improvement-or lack thereof-in the distribution of state and local per pupil revenues over time.

Current Profiles, from 2005 to 2007
Our second data set consists of over 13,000 local public school districts from 2005 to 2007 and combines data from multiple sources including the following: U.S. Census fiscal survey of local governments (state and local revenues per pupil), U.S. Census small area income and poverty estimates of children between the ages of 5 and 17 in poverty, the NCES Education Comparable Wage Index (ECWI), and a county-level measure (from U.S. Census) of population density.
We use these data to estimate a slightly more complex model than the one estimated for our longitudinal analysis.In this case, our goal is to test the sensitivity of state and local revenues per pupil to student poverty rates across districts.Similar to our approach with the first set of analyses, a regressive state school finance system is one in which state and local revenues per pupil are negatively and systematically associated with poverty rates across districts, a progressive system is one in which state and local revenues per pupil are positively associated with poverty across districts, and a neutral system is one in which no relationship exists between poverty rates and state and local revenues per pupil.We assume a policy objective of progressiveness, where the ultimate objective of state school finance policy is to provide equal educational opportunity to children attending districts in high-poverty settings by providing additional resources in those settings (see Duncombe and  Yinger, 2008).We estimate the elasticities 20 between poverty and state and local revenues, conditional on major factors with demonstrated potential to affect the relative costs of providing educational services in one setting or location versus another.
We estimate a three-year regression model using a pooled cross-state universe of local public school districts and local education agencies.That model is specified as follows: In this model, lnSLOCREVPP is the natural logarithm of state and local revenue per pupil for district "d" at time "t", ECWI is the education comparable wage index for district "d" at time "t-2" (lagged primarily due to lack of an updated index), 21 SCALE is a series of categorical dummy variables indicating district enrollment size for district "d" at time "t", and SCALE is interacted with the natural log of the 2007 population density (DENSITY) for the primary county "c" of the district's location.This interaction term is included to capture the national average spending differences associated with economies of scale given population density.STATE is the state of district "d", which is also included in an interaction term with two year dummy variables (for 2005-06 and 2006-07, with base year 2004-05) in order to generate a coefficient of state-specific revenueper-pupil increases (both state and local).The next term is POVERTY, which is the U.S. census poverty rate for resident 5-to 17-year olds in district "d" at time "t", which is followed by an interaction term between POVERY and STATE.It is this final interaction that is of primary interest to us in evaluating the fairness of state school finance systems.That is, how do state and local revenues per pupil vary by poverty, within states?
This model is weighted for district enrollment because the ultimate goal of analyses of this type is to evaluate how, on average, the state school finance system treats its children.As such, it makes little sense to identify a state as fair if that state has a large number of very small high-poverty school districts that are well funded, but a handful of large districts that are poorly funded serving many more children than the aggregate of the small districts.The same is true of the inverse scenario, where a state does a good job in funding its larger urban districts but neglects poor rural 20 Elasticities are measured on a scale from 1 to -1, where an elasticity of 1.0 would signify a perfect alignment between revenues and median household income, while an elasticity of -1.0 would signify a perfect negative relationship between revenues and median household income.An elasticity of 1.0 would indicate that for a 1% change in income, one would expect a corresponding 1% change in state and local revenue per pupil.An elasticity of .1 would indicate that for a 10% change in income, one could expect a 1% change in state and local revenue.Relationships among variables like income and revenue must be evaluated against "expectations" for relationships among those specific variables, rather than against some more general statistical benchmark.In this case, an elasticity of .20 would be considered high. 21The current NCES ECWI is available for all districts from 1997 to 2005 and accounts for both betweenlabor market differences in competitive wages and inflationary changes in wages over time.Because it is reasonable to assume that most teachers in a school district were hired two or more years ago it is reasonable to account for cost variation across districts by lagging the CWI by two years.Further, we account additionally for inflation by including a year fixed effect in our models which should pick up any differences in the average change in state and local revenue not captured by the inflation component of the CWI (even if we excluded the inflation component).Finally, our use of the ECWI is primarily to account for between-labor market differences which do not change substantively from year to year.ones.In both types of scenarios, the weight remains greater on large districts because of the numbers of children they serve.
With the regression equation estimates, we then predict for each state the expected state and local revenues per pupil for a district with 0% poverty, 10% poverty, 20% poverty and 30% poverty.In doing so, we hold constant at the national average the NCES ECWI, we set the economies of scale dummy indicators to zero and the density to average (such that the hypothetical district represents a district of over 2,000 students, or one operating at the most efficient scale), and we set the year to 2006-07.

Findings
In this section, we provide national longitudinal findings, as well as current status and longitudinal findings for selected states (by region).Figure 1 presents the national mean elasticity between income and per pupil revenues (state and local) from the models using the data from 10,189 districts.It shows that state and local revenues in 1990 were positively associated in a relatively strong way with median household income (an elasticity of over .20).Since that time, the relationship has moderated, with the income-revenue relationship becoming less positive, meaning that school funding overall has become less regressive.But funding has nevertheless remained positively associated with income as an average across all states.This finding, of course, conceals substantial heterogeneity across states.Figure 2 displays the individual state trends of income-revenue elasticity for three Mid-Atlantic states (Delaware was excluded from this longitudinal analysis due to insufficient data points across districts for all years).
Consistent with the national trend, all of the Mid-Atlantic states have become less regressive over time.Nonetheless, all these states start out highly regressive, and only New Jersey has a negative income-revenue relationship across their school districts at the end of the period.From 1998 through 2005, the relationship between income and state and local revenues in Maryland actually increases.In New York, despite a fairly steady move toward less regressiveness, the relationship between income and state and local revenue in 2005 remains stronger than the national average relationship had been in 1990.Figure 3 presents the profiles of these three states plus Delaware, showing projected state and local revenues at varied poverty levels for 2007 after controlling for regional costs, population density, economies of scale and poverty.As in Figure 2, the New Jersey distribution is progressive while the others are regressive.The additional information provided in Figure 3 is the overall level of funding available across districts at differing levels of poverty.Comparing New York and New Jersey, for example, low-poverty New York districts have more resources than low-poverty New Jersey districts, but for higher-poverty districts the differential is reversed.Both New York and New Jersey districts have more resources than those in Delaware and Maryland.(Vermont is excluded due to data issues including relatively small shares of children attending unified public school districts.)Massachusetts shifted from a positive to negative income-revenue relationship in the mid-1990s and then leveled off at this negative (progressive) relationship.Because two high-poverty districts experienced funding increases (Hartford and New Haven), Connecticut also shifted to a slightly negative income-revenue relationship, albeit not statistically significant.Rhode Island also shifted to a slightly (and non-significant) negative relationship between income and revenue around 2000.By contrast, income-related inequities in state and local revenues per pupil remained sizeable in New Hampshire throughout the period, and inequities in Maine actually increased between 1998 and 2005.Figure 5 shows the 2007 state-level poverty profiles for New England states (including Vermont), again controlling for regional costs, population density, economies of scale and poverty.As revealed in Figure 4, Massachusetts and Connecticut are the only two states in New England where poverty districts have, on average, more resources per pupil, with that relationship being less systematic in Connecticut than in Massachusetts.In Rhode Island, the distribution remains poverty-neutral.Vermont, too, is fairly neutral, but at a higher spending level than the other states.In Maine and especially New Hampshire, higher-poverty districts have significantly less state and local revenue per pupil than lower-poverty districts.
Figure 6 shows the longitudinal trends in income-revenue elasticity for North Central states.As this figure makes clear, Minnesota is the only state in this region that has achieved progressive distribution of resources with respect to income, beginning with a progressive distribution by 1990 and building on that progressiveness during the succeeding years.This pattern is driven largely by elevated levels of funding in Minneapolis and St. Paul.In contrast, Iowa and Wisconsin have maintained relatively neutral funding with respect to income since the mid-1990s.Illinois, similar to Maryland and Maine, has become increasingly regressive since the mid-1990s.By 2004, Illinois had an income-revenue relationship comparable to the national average relationship in 1990.The above graphs are illustrative of the heterogeneity of school funding inequities that persist across states in most regions.Appendix A sets forth a table of projected state and local revenues at varied poverty levels for all states, based on our three-year panel analysis from 2005 to 2007.Notably, some regions-in particular, the Southeast-include only states where the povertyrevenue relationship remains regressive.
Table 1 presents a subset of the data in Appendix A, summarizing spending trends in those states having the most and least progressive distribution of state and local revenues.Alaska 22 and Utah, 23 which lead the pack, are both a bit quirky.Other states with positive systematic relationships between state and local revenues and poverty include New Jersey, Minnesota, Massachusetts, Indiana, and Ohio. 24Despite our efforts to correct as fully as possible for factors such as size and economies of scale, we remain less confident in relationships revealed for South Dakota, Montana and New Mexico because of smaller overall shares of total children attending scale-efficient unified districts, but all three do show statistically significant positive relationships.
Among the bottom ten states are six where the negative relationship between state and local revenue per pupil and poverty is not systematic (labeled with an "N" in the "confidence" column on the right side of the table).These states' school finance systems are certainly still problematic; on average, high-poverty districts receive less than low-poverty districts.But a non-systematic relationship suggests differences in state and local revenues where some poor districts receive more than others and some less than others, even after accounting for a variety of other cost factors.

Conclusions and Policy Implications
Overall, we find that there has been no consistent treatment or resolution of between-district disparities in school revenues.New Hampshire and some other states have made no apparent progress.Illinois is an example of a state that has actually become more regressive over time.Pennsylvania and New York are among those states that, while still highly regressive, may be making recent progress as a result of newly adopted state school finance formulas.And states like New Jersey, Massachusetts and Ohio have made genuine progress in moving toward a progressive system.
This answers an important question: problems with between-district revenue disparities are still not resolved.Some states have made progress, but others have actually regressed.
The above analysis, however, does not attempt to answer a second, related question.Researchers such as Roza have raised comparative issue: which type of disparity-inter-district or intra-district-results in greater inequities.An analysis that would appropriately answer this question concerning relative importance would require more systematic efforts to evaluate simultaneously these disparities and their effects on students in a given area.Such analyses would also require more systematically collected data on school-site expenditures.Only a handful of states, including California, Ohio, Rhode Island and Texas, currently engage in a thorough collection of this type of data across all districts.Further, even among these states, data on school-site expenditures differ from state to state, making difficult any cross-state comparisons of within-district disparities.
For the foreseeable future, therefore, researchers will likely be confined to evaluating withinand between-district equity for specific states, one at a time.This type of focus on individual states is generally most appropriate anyway, given the heterogeneity of state school finance systems.Few generalizations regarding equity of school funding can reasonably be drawn across all states or even among groups of geographically contiguous states; any such generalizations should be greeted with a high degree of skepticism.
We certainly recommend that more states collect and make available school-level spending data.Yet we hasten to add that the comparative question itself is largely misguided.There is no need to rank the two sources of inequity, nor is there a need to address one to the exclusion of the other.Moreover, our inability to draw national conclusions regarding within-or between-district inequities only modestly constrains any policy responses.The role of federal funding is relatively limited, having negligible effects on the overall relationships addressed in the analyses set forth above (Baker, Sciarra and Coley, forthcoming).Instead, each individual state has control over the levels of funding available across its local public school districts.Each state also has control over accountability policies that might push those districts toward greater internal equity in resource distribution.The solutions to these state-level problems lie largely with state governments, in the absence of a dramatically expanded federal role.Downes (2002) similarly explains that: School finance reforms, tax and expenditure limitations, and legislation enabling the creation of charter schools have as many differences across states as they have commonalities.The challenge facing researchers is to determine what lessons can be learned only from national-level analyses and only from state-level case studies and to distill these lessons for policymakers (p.161).
The main lesson to be drawn from the cumulative state-level analyses documented earlier in this article is that it is premature to shift policy attention away from between-district spending disparities.Just to be clear, it is difficult to evaluate the policy impact to date of advocacy in favor of this shift the emphasis.Looking first at litigation, we see little evidence, as of yet, that state courts are willing to emphasize one over the other, or to back off from mandating that states resolve between-district disparities until districts first do their part.Moreover, we expect that state courts will continue to acknowledge that the primary responsibility for ensuring equity across both schools and districts rests with the state, pursuant to language in state constitutions.
But we are less sanguine about the potential emphasis shift in state legislatures.A goal of this article is to head off what we perceive as a growing wave of policy advocacy and punditry seeking to provide ineffective but deceptively convenient revenue-neutral school-finance "solutions" for state legislatures (see Baker and Elmer, 2009).We point to the esteemed list of signatories of the original Fordham Institute Fund the Child advocacy document as evidence that our concerns are not unfounded (Fordham Institute, 2006). 25We also point to proposals from the Center for American Progress for using Title I aid as the carrot for requiring states to fix within-district but not betweendistrict disparities as evidence that influential policy think tanks at least plan to use this argument to influence federal policy (McClure, Wiener, Roza, and Hill, 2008).Such arguments have made their way into congressional hearings in the past year, and we expect increased emphasis on these issues as reauthorization of ESEA moves forward. 26esearch and policy attention to within-district resource allocation should certainly continue, since it appears that this is an important issue as well.But policymakers should be skeptical of claims that the resource needs of high-poverty schools can generally be met merely via a reshuffling of district-level resources.Further, policymakers must be cognizant that persistent between-district disparities may significantly constrain districts' ability to resolve within-district disparities (Baker,  forthcoming).Remedies should consider both simultaneously.While the circumstances of each state and each district will differ, spending patterns in the country as a whole are still far from the progressivity that would be needed to provide equitable and adequate resources to these schools.

Figure 1 :
Figure 1: National Mean Relationship between Income and State and Local Revenue per Pupil over Time

Figure 2 :
Figure 2: Subdivision and State Level Changes in Income-Revenue Relationship in Mid-Atlantic Region

Figure 3 :
Figure 3: State Level Profiles of State and Local Revenue per Pupil for Mid-Atlantic States in 2007

Figure 4
Figure4compares the trends in income-revenue elasticity for states in New England.(Vermont is excluded due to data issues including relatively small shares of children attending unified public school districts.)Massachusetts shifted from a positive to negative income-revenue relationship in the mid-1990s and then leveled off at this negative (progressive) relationship.Because two high-poverty districts experienced funding increases (Hartford and New Haven), Connecticut also shifted to a slightly negative income-revenue relationship, albeit not statistically significant.Rhode Island also shifted to a slightly (and non-significant) negative relationship between income and revenue around 2000.By contrast, income-related inequities in state and local revenues per pupil remained sizeable in New Hampshire throughout the period, and inequities in Maine actually increased between 1998 and 2005.

Figure 4 :
Figure 4: Subdivision State Level Changes in Income-Revenue Relationship in New England Region

Figure 5 :
Figure 5: State Level Profiles of State and Local Revenue per Pupil for New England States in 2007

Figure 6 :
Figure 6: Subdivision and State Level Changes in Income-Revenue Relationship in North Central Region

Figure 7
Figure 7 displays the 2007 poverty profiles for these states.Only Minnesota maintains a poverty-progressive distribution of state and local revenues per pupil.Wisconsin and Iowa maintain

Figure 7 :
Figure 7: State Level Profiles of State and Local Revenue per Pupil for North Central States in 2007 t + b 4 lnINCOME d,t + b 5 (lnINCOME d,t x YEAR d ) + e Where SLOCREVPP is the total of state and local revenue per pupil for each school district, ECWI is the National Center for Education Statistics Education Comparable Wage Index, SCALE is a matrix of dummy variables indicating enrollment size, STATE is a matrix of dummy variables for each state, YEAR is a matrix of dummy variables for each year in the data set, and INCOME is median household income (from U.S.

Table 1 :
Most and least progressive states in 2007 to receive systematically less state and local revenue per pupil than low-poverty districts.Since 2006-07, New York and Pennsylvania have begun implementing changes to their state school finance systems, which may change this distribution.Illinois and New Hampshire, however, have not.
*were expected