How and why racial isolation affects education costs and the provision of equal educational opportunity Journal website: http://epaa.asu.edu/ojs/ Manuscript received: 6/8/2024 Facebook: /EPAAA Revisions received: 28/7/2024 Twitter: @epaa_aape Accepted: 8/8/2024 education policy analysis archives A peer-reviewed, independent, open access, multilingual journal Arizona State University Volume 33 Number 55 September 9, 2025 ISSN 1068-2341 How and Why Racial Isolation Affects Education Costs and the Provision of Equal Educational Opportunity Bruce D. Baker University of Miami, Coral Gables United States Citation: Baker, B. D. (2025). How and why racial isolation affects education costs and the provision of equal educational opportunity. Education Policy Analysis Archives, 33(55). https://doi.org/10.14507/epaa.33.8843 Abstract: This article provides a review of prior empirical work exploring whether and to what extent school district racial composition affects the costs associated with providing equal educational opportunity to achieve a common set of outcomes. This prior work mainly involves education cost function modeling on several states and in an earlier version of our national education cost model. Here, I update the national education cost model and apply a series of tests for selecting the optimal cost model and determining a) whether it is necessary to retain measures of racial composition in the model and b) the effect those measures have on the estimated costs to achieve common outcomes. We find that the optimal model includes an interaction term between % enrollment that is Black and population density and that for majority Black enrollment urban districts, the predicted costs per pupil are 20 to 50% higher when using models with this measure than when using models with race neutral alternatives. While changes in cost estimates for these districts are large, aggregate national cost increases from including racial composition are 1.3 to 2.7% in most years. Keywords: education finance; equity; equal opportunity; racial inequality Cómo y por qué el aislamiento racial afecta los costos educativos y la provisión de igualdad de oportunidades educativas Resumen: Este artículo ofrece una revisión de trabajos empíricos previos que exploran si, y en qué medida, la composición racial de los distritos escolares afecta los costos asociados con la http://epaa.asu.edu/ojs/ https://doi.org/10.14507/epaa.33.8843 Education Polic y Analysis Arc hives Vol. 3 3 No. 55 2 provisión de igualdad de oportunidades educativas para alcanzar un conjunto común de resultados. Estos estudios previos se centran principalmente en modelos de función de costos educativos en varios estados y en una versión anterior de nuestro modelo nacio nal de costos educativos. Aquí actualizo el modelo nacional de costos educativos y aplico una serie de pruebas para seleccionar el modelo de costos óptimo y determinar: a) si es necesario mantener medidas de composición racial en el modelo, y b) el efecto que dichas medidas tienen en los costos estimados para lograr resultados comunes. Encontramos que el modelo óptimo incluye un término de interacción entre el porcentaje de matrícula de estudiantes negros y la densidad poblacional, y que en los distritos urbanos con mayoría de matrícula negra, los costos previstos por alumno son entre un 20% y un 50% más altos cuando se utilizan modelos con esta medida que cuando se emplean modelos alternativos neutrales respecto a la raza. Aunque los cambios en las estimaciones de costos para estos distritos son significativos, los incrementos nacionales agregados en costos al incluir la composición racial son de 1.3% a 2.7% en la mayoría de los años. Palabras clave: financiamiento educativo; equidad; igualdad de oportunidades; desigualdad racial Como e por que o isolamento racial afeta os custos educacionais e a provisão de igualdade de oportunidades educacionais Resumo: Este artigo apresenta uma revisão de trabalhos empíricos anteriores que investigam se, e em que medida, a composição racial dos distritos escolares afeta os custos associados à provisão de igualdade de oportunidades educacionais para alcançar um conjunto c omum de resultados. Esses estudos anteriores envolvem principalmente a modelagem de funções de custo educacional em vários estados e em uma versão anterior do nosso modelo nacional de custo educacional. Aqui, atualizo o modelo nacional de custos educacionais e aplico uma série de testes para selecionar o modelo de custos ideal e determinar: a) se é necessário manter medidas de composição racial no modelo e b) o efeito que essas medidas têm sobre os custos estimados para alcançar resultados comuns. Constatamos que o modelo ideal inclui um termo de interação entre a porcentagem de matrículas de estudantes negros e a densidade populacional e que, em distritos urbanos com maioria de matrículas negras, os custos previstos por aluno são de 20% a 50% mais altos quando se utilizam modelos com essa medida do que quando se empregam modelos alternativos neutros em relação à raça. Embora as mudanças nas estimativas de custos para esses distritos sejam expressivas, os aumentos nacionais agregados de custos ao incl uir a composição racial variam de 1,3% a 2,7% na maioria dos anos. Palavras-chave: financiamento educacional; equidade; igualdade de oportunidades; desigualdade racial How and Why Racial Isolation Affects Education Costs and the Provision of Equal Educational Opportunity On February 6, 2007, an Associated Press headline in the St. Louis Post-Dispatch read, “More Should Be Spent on Black Students, Experts Say.” The article was referring to testimony given a day earlier in a case challenging Missouri’s school funding formula, where two separate experts, myself included, had conducted cost modeling to identify the costs of achieving specific outcome goals for Missouri children. In separate, independent reports, William Duncombe and I had found the inclusion of district racial composition to be an inescapable factor in estimating those costs—that is, that costs were necessarily higher in districts serving larger Black student enrollment shares. Rac ial Isolation , Education Costs, and Equal Educ ational Opportunity 3 Researchers have often found racial achievement gaps that persist above and beyond differences in economic status or parental/family educational background (Reardon et al., 2014; Barton & Coley, 2010; Baker et al., 2000). Some have found that specific interventions or reforms, including class size reduction have differential positive effects on student outcomes by their race (Krueger & Whitmore, 2001; Levin et al., 2007). Still others have found that choices by teachers of where they’d rather teach or stay are influenced by the student racial composition of schools, resulting in the need for a wage premium to retain teachers in schools with large Black student populations (Hanushek et al., 2004; Hanushek & Rivkin, 2006). The role of race, racial segregation, isolation, driven by persistent racial discrimination in schooling, housing and beyond creates undeniable racial inequalities throughout American education systems, realized in nearly any or all data and measures on those systems, from outcomes, to contexts and resources (Baker et al., 2022). Thus, one would expect racial segregation and isolation to affect the costs of providing equal educational opportunity through a variety of interrelated mechanisms. It stands to reason, for example, that if it takes a higher wage to recruit and retain teachers of similar qualifications in schools with larger Black enrollment shares, that it would cost more just to provide equal quality inputs to schooling (comparable teachers and class sizes) in majority Black versus majority white schools. Further, it stands to reason that if scholars have found that class size reduction has differential effects by race—yielding larger advantages for Black than white students—and that targeted class size reduction can be an effective strategy for reducing Black-white achievement gaps, that the overall costs (teacher wage x teacher quantities) to achieve common outcome targets may differ in majority Black versus majority white schools, all else equal. On the one hand, eliminating racial segregation and isolation itself can reduce racial inequality in student outcomes, because it mitigates various detrimental effects of racial isolation (Johnson, 2019). Where racial segregation and isolation and their lingering effects do persist—which is nearly everywhere in the United States—other policy leverage is required (Baker et al., 2022). Most often, however, that “other” policy leverage intentionally avoids the role of race, racism and racial discrimination in causing the racial disparities which are deeply intertwined with economic and educational disparities, yielding incomplete, imprecise remedies (Baker & Castillo, 2024). At the height of the school desegregation legal and policy movement in the post-Brown era, there emerged a parallel path toward mitigating schooling inequality—a legal path that took great pains to identify anything but race that might be an objectionable cause of educational inequality. Federal, then state constitutional challenges to the equity and adequacy of school funding rarely made explicit mention of racial disparities, often leaning in to alternative measures and explanations for the disparities including differences in taxable property wealth and income of households and asserting those disparities should receive the same heightened scrutiny as racial disparities (Heise, 1995; Ryan, 1999). Wealth and income related school funding disparities were and still are highly racially correlated, because in many cases they were caused by racial discrimination regarding who could live where, coupled with access to employment (Baker et al., 2022). Only a handful of challenges to school funding formulas have explicitly addressed racial disparities and even fewer included legal claims related to racial disparities.1 As such, little empirical research designed to support school funding remedies and state school finance legislation has directly addressed racial disparities or how to mitigate them. A surprisingly modest body of empirical literature even explores, quantifies and 1 Specifically, Robinson v. Kansas, 295 F.3d 1183 (10th Cir. 2002), Powell v. Ridge, 247 F.3d 520 (3d Cir. 2001) & African American Legal Defense v. New York State, 8 F. Supp. 2d 330 (S.D.N.Y. 1998) in Federal Courts and among the causes of action in Montoy v. State, 279 Kan. 817, 112 P.3d 923 (2005). Education Polic y Analysis Arc hives Vol. 3 3 No. 55 4 decomposes racial disparities in school funding and causes of those disparities (Baker, Srikanth et al., 2020; Bifulco, 2005; Bifulco & Souders, 2023; Sosina & Weathers, 2019; Weathers & Sosina, 2022). Race-avoidant challenges to school funding inequality evolved from the 1970s to present day in state courts, under state constitutional requirements while challenges to racial segregation came and went primarily in federal courts from the immediate post-Brown era through the mid-2000s when the Supreme Court eventually declared that existing within district integration policies (in Seattle and Louisville) could no-longer survive strict scrutiny.2 Even when both types of legal challenges occurred simultaneously in state courts, as in Connecticut, the legal challenges and remedies occurred independent of and without regard for one another, albeit competing for resources.3 Baker, Green and Oluwole (2008) explained that, given what Duncombe (2007) had found in Missouri a year earlier, achieving equal educational opportunity through school finance reform would necessarily require consideration of race. That, if it costs more to achieve state mandated outcome goals as a function of district racial composition, above and beyond other factors including poverty concentration, shares of non-English speaking students and other cost drivers, those costs must be considered in the design of school funding remedies. They must be weighted as a “plus factor” in reform legislation. Not doing so is to knowingly deprive Black students in racially isolated districts of equal educational opportunity. This article explores and expands on the limited literature that attempts to identify and quantify the role that race, racial segregation and racial isolation play in determining the costs of providing equal educational opportunity. Equal educational opportunity, as described by Baker and Green (2012) requires that all children, whatever their own backgrounds or wherever they attend school are provided equal opportunity to achieve common outcome goals. Part of ensuring equal educational opportunity is ensuring that children have access to the resources (class sizes, teacher quality, etc.) needed to have equal opportunity to achieve those outcomes, which in turn requires appropriately calibrated financing. Of particular interest are three major questions, which have only sparsely been addressed in existing literature: 1. What evidence exists that district or school racial composition influences the costs of providing equal educational opportunity? 2. What other research evidence supports causes or reasons why the costs of providing equal educational opportunity vary by school or district racial composition? 3. What empirical evidence exists regarding integration and/or consolidation of school districts by race and effects on costs and costs variation? That is, does integration reduce or otherwise change the distribution of costs associated with racial isolation? We revisit these questions now for a variety of reasons. Baker, Green and colleagues addressed the importance of race in determining education costs and constitutional questions surrounding the use of race factors in state school finance formulas in a series of articles between 2008 and 2011 (Baker, 2011, Baker & Green, 2009; Green et al., 2008). Those articles followed a pair 2 Parents Involved in Community Schools v. Seattle School District, No. 1, 426 F.3d 1162 (9th Cir. 2005) & Meredith v. Jefferson County Board of Education, 548 U.S. 938 (2006). 3 Sheff vs. O’Neill was a desegregation case brought in the 1990s in Connecticut (Sheff v. o'Neill, 238 Conn. 1, 678 A.2d 1267 (1996). That case led to the adoption of interdistrict choice, magnet school programs in Hartford, CT, which was accompanied by significant state funding to support the magnet school program. In the decades that followed, the state’s general school aid formula was challenged separately in CJEFF v. Rell (Connecticut Coalition for Justice v. Rell, 176 A.3d 28, 327 Conn. 650 (2018), where the state’s high court upheld the school aid formula. Rac ial Isolation , Education Costs, and Equal Educ ational Opportunity 5 of U.S. Supreme Court rulings in which the court disallowed consideration of race in school assignment programs (for integration purposes). We argued at that time, that if schools were to remain racially isolated which they likely would, one means of providing equal educational opportunity would be consideration of the costs imposed by racial isolation (Green et al., 2008). I revisit this question now because more recent articles and reports presents the case that such factors can and should play a role in the provision of reparations to Black communities for the educational damages imposed by racial residential housing discrimination (Baker et al., 2022; Green et al., 2020). Further, as illustrated in a more recent article, nationally equated state assessment data from the Stanford Education Data Archive, along with other national data updates and improvements make it possible for us to estimate a National Education Cost Model (Baker et al., 2021). In the article that follows, I review the literature on these questions herein, and address implications for policy and future empirical research. Next, I conduct a series of empirical tests using the National Education Cost Model to identify the optimal cost model, with respect to race sensitive and race neutral alternative cost factors. The analyses herein add to the previous literature in that they use the national cost model (NECM), first reported in 2021, as opposed to state specific models used in earlier work which proposed use of race factors in cost modeling (Baker, 2011; Baker et al., 2021). Additionally, because the emphasis here is on selecting an optimal model, I apply a systematic model-selection method not used previously with the NECM, testing additional specifications and resulting in models with preferable diagnostics over prior NECM estimates. Race & The Estimation of Costs of Equal Educational Opportunity School finance formulas are broadly designed to promote equal educational opportunity, but rarely sufficiently calibrated to accomplish that goal. That is, they include basic funding levels (foundation levels) and cost adjustments or weights related to student needs and other factors, but the basic funding level is rarely if ever set based on the costs for students to meet a specific outcome standard. Similarly, the various weights and cost factors are rarely calibrated according to how much more it might cost to achieve the same outcomes, for some children than others, in one setting versus another. School finance formulas include a relatively standard set of student need and cost factors: • All 50 states provide some adjustment or supplemental aid for children with disabilities; • 44 states provide some adjustment or supplemental aid for children from economically disadvantaged backgrounds, with 26 providing a single weight and 13 providing multiple weights; • 48 states provide some adjustment or supplemental aid for children for whom English is a second language with 27 states including single weights and 10 including multiple weights (Atchison et al., 2023). Additionally, states allocate specific resources or provide block grants targeted toward serving specific student populations. None include weights, resource allocations or targeted grants based on student race or school or district racial composition. In the 1990s and early- to mid-2000s, several states engaged in analyses of the costs of programs and services needed to achieve existing state standards, mostly using panels of experts and practitioners to prescribe the programs and services needed (Baker, 2005, 2006). None of these analyses suggested different resources (smaller classes or different competitive wages) in relation to student enrollment racial composition. More recently, several states have engaged in statistical Education Polic y Analysis Arc hives Vol. 3 3 No. 55 6 modeling to identify costs to achieve desired outcome goals, and how those costs vary by setting, location and students served (Atchison et al., 2023; Atchison et al., 2024; Baker, Atchison et al., 2020; Brooks et al., 2025; Duncombe & Yinger, 2006; Kolbe et al. 2019; Taylor et al., 2018). Among these, recent studies in Delaware, Colorado and Oregon include school racial composition (% Black) as a factor (Atchison et al., 2023; Atchison et al., 2024; Brooks et al., 2025). Among recent peer reviewed applications using education cost modeling, only those by Baker and colleagues, using a recent National Education Cost Model (NECM) include the role of race, with some comparing model estimate differences between models including and those not including racial composition (Baker et al., 2021; Kolbe et al., 2021; Levin et al., 2022; Gronberg et al., 2017; Zhao, 2022). Similarly, among older peer-reviewed education cost modeling literature, only a handful of papers by Baker and colleagues addressed the role of race in affecting the costs of providing equal educational opportunity (Baker, 2011; Duncombe & Yinger, 1997, 1998; Gronberg et al., 2011, 2012; Imazeki & Reschovsky, 2006). This includes a 2011 article by Baker in which he tests the effectiveness of race-neutral alternatives, including an interaction between poverty and population density to determine whether those race neutral alternatives are sufficient substitutes for including race directly in the model. This particular piece draws on related work by Duncombe (2007) and Duncombe and Yinger (2006). As noted at the outset of this article, William Duncombe (2007), while working on expert testimony on behalf of intervenor district St. Louis City, in a case on Missouri school funding, found it inescapable to include the district’s racial composition in his cost estimates. A year earlier, Duncombe and colleague John Yinger (2006) had been contracted to conduct similar analyses for the State of Kansas to inform reforms of that state’s school funding formula, which was under judicial oversight at the time. In that study, Duncombe and Yinger found their way around using district racial composition by instead including an interaction between poverty and population density to capture the higher costs in the state’s more densely populated larger urban centers and towns which also served larger student minority populations. As a result of that analysis, the Kansas legislature adopted a special weight on child poverty in higher population density districts (Baker, 2022). The modern era of statistical modeling of education costs traces back to the early 1990s, when Downes and Pogue estimated cost models on Arizona school districts to determine the additional costs of serving children from economically disadvantaged backgrounds. But long before that, Garms and Smith, in 1970 sought to identify the additional costs of mitigating racial and economic disparities in children’s outcomes that had been identified in the Coleman Report a few years earlier (Garms & Smith, 1970). While not directly estimating a cost model by modern specifications, Garms and Smith did infer from analyses of the relationship between population characteristics and student outcomes, the weights that should be assigned to school funding in order to close achievement gaps—that is, provide equal educational opportunity. Garms and Smith modeled data on elementary school students in New York state. Among other things, they found: “We immediately found that it was necessary to keep the variables representing ethnic status (N and PR) in spite of the fact that they do not completely meet the criteria for a variable” (Garms & Smith, 1970, p. 313) That is, it didn’t seem conceptually appropriate that race should be a determinant of cost, but it was statistically unavoidably so. State Specific Cost Modeling & the Role of Race There exist a handful of studies that have tested the role of race in education cost models— most specifically testing whether Black enrollment shares in schools or districts affect the costs of Rac ial Isolation , Education Costs, and Equal Educ ational Opportunity 7 achieving any specific aggregate outcome(s). These studies test the importance of including racial composition by applying a handful of analytic techniques, asking: 1. Is school or district racial composition a statistically significant predictor of spending associated with achieving a specific outcome? 2. How does including district racial composition affect cost predictions for districts of varying racial composition? That is, are the difference of policy relevant, important magnitude? 3. Does omitting racial composition create omitted variables bias observable in model residuals? 4. Does omitting racial composition compromise model predictive validity? 5. Are race neutral alternatives, such as Duncombe and Yinger’s “poverty x density” interaction term sufficient substitutes? On the first point, Baker and Green (2009) and Baker (2011) run a series of cost models in which they compare model estimates and results applying a) models excluding racial composition, b) models including racial composition (% Black, % Hispanic, % Black and Hispanic) and c) models including a race neutral alternative (Poverty x Population Density). In the first of these studies, modeling data from Arizona, New Jersey, and Missouri, Baker and Green find: “In short, it costs more to achieve desired educational outcomes in school districts where larger shares of the student population are Black.” But “such findings appear less consequential in states such as Arizona with no majority Black school districts, failing to alter predictive validity of models” (p. 323) And finally, that different models worked better in different states, including whether interacting Black populations with population density improved model performance. In a related paper, focusing specifically on Missouri, Baker (2011) also found some conflicting evidence as to whether a race neutral model, interacting poverty and population density, was sufficient or whether inclusion of race was necessary, using the same, limited set of tests of out-of-sample model predictive validity (p. 58) In each case, cost predictions were significantly affected for majority Black districts when including Black enrollment shares, but improvements to model predictive validity were varied, as noted above. A more recent book chapter by Baker and Castillo (2024) used an updated version of the national cost model estimated by Baker, Weber and Srikanth (2021). Baker (2011) used data from 2001 to 2008 on Missouri school districts, with most data coming from Missouri Department of Elementary and Secondary Education sources. Baker and Castillo (2024) rely on a version of the National Education Cost Model using data from 2009 to 2019. Both sets of estimates find that when race is included in the model, cost predictions for these majority Black Missouri school districts go up by 20 to 37%. As such, failing to address racial difference would understate their costs by that amount. Baker and Castillo (2024) also explore the question of omitted variables bias in the national cost model by way of analyzing residual bias from race sensitive versus race neutral models in the relationship between funding gaps and outcome gaps. In a thoroughly estimated cost model—one that minimizes the omission of relevant cost factors—there should exist a reasonably strong relationship between estimated funding gaps and outcome gaps. Residual variation might, in part, reflect differences in efficiency in the production of outcomes. In Race neutral model, majority Black districts in particular appear less efficient (race predicts the residuals), having larger negative residuals for the input-outcome relationship. Baker and Castillo (2024) provide illustrations of this problem, which I replicate and expand upon herein. Baker and Castillo (2024) did not test whether race neutral alternatives could sufficiently resolve the omitted variables bias problem and Baker Education Polic y Analysis Arc hives Vol. 3 3 No. 55 8 (2011) did not report a similar residual bias test but did show that predictive validity improvements (using split sample methods) were mixed. Atchison and colleagues’ (2023) school level model of costs to achieve state outcome standards in Delaware takes a different approach at testing and applying race neutral alternatives. Atchison and colleagues estimate a school level cost model using data provided by the state of Delaware. The cost predictions from this model across Delaware districts are correlated at 0.89 with adapted estimates from the National Education Cost Model, estimated with district level, national data. Atchison and colleagues employ a two-step process to get from their cost model to a weighted formula proposal. The cost model itself includes racial composition (% Black) as a factor. But in the second step, the authors test whether a parsimonious set of measures can be used to predict sufficiently the cost model predictions from the first step. They find that the race sensitive cost predictions can be accurately proxied with a race neutral model, predicting 98.1% of the variation in the cost estimates. Including race in the weights model increase the variance explained only marginally to 98.5% (See Table A1, Appendix A). Similar approaches were taken more recently in studies in Colorado and Oregon (Atchison et al., 2024; Brooks et al., 2025). Finally, Di Carlo and Edmond (2024) provide a useful illustration of whether reducing school district fragmentation and racial isolation would alter cost variation across districts, using estimates from the National Education Cost Model for New Jersey school districts and simulating the effects of consolidating districts to the county level. They find: “If we hypothetically consolidated all the state’s districts into their home counties, this would reduce racial/ethnic gaps in school funding adequacy by 75-80 percent;” and “The reduction is primarily due to the sharing of costs between districts serving vastly different student populations than their counterparts in the same counties.” This simulation cannot reveal whether aggregate costs would change, or be reduced by smoothing those costs out across districts within counties. Given the available data, the aggregate costs would stay the same because the cost model includes only a linear direct effect of racial composition on costs, as do other cost models discussed herein. Total costs are only reduced by defragmenting if costs escalate non-linearly with Black enrollments, or by interaction with other terms such as poverty. That said, balancing costs across jurisdictions itself is sufficient reason to pursue integration and district defragmentation. Next Steps & Future Empirical Questions The above studies and reports provide a patchwork of evidence regarding the importance of considering school or district racial composition in determining the costs associated with providing equal educational opportunity and in translating those costs into school funding formulas. The National Education Cost Model, and underlying data, along with the increased number of state specific analyses recently released and ongoing provide opportunities to fill in this patchwork and address some key remaining questions. First, drawing on what has already been produced, both in terms of findings and methods/applications, further evidence on the extent to which school district racial composition affects costs of providing equal educational opportunity is warranted, including: a) Whether different measures of racial composition, racial groups and subgroups matter and differ by state and regional policy context? b) Whether non-linear relationships and interactions exist wherein reduction of racial isolation would lead to lower overall costs? c) Whether and to what extent race-neutral alternatives are sufficient substitutes in state school finance policies? Rac ial Isolation , Education Costs, and Equal Educ ational Opportunity 9 Future empirical analyses addressing these questions should include all of the above methods for evaluating reliability and validity, including: 1) Predictive validity tests of models using split-cross validation techniques (training set, test set) as used by Baker (2011) wherein optimal model identification is based on maximizing prediction accuracy and minimizing prediction bias; 2) Residual bias checks for omitted variables bias as used by Baker and Castillo (2024); 3) Inter-model correlations between models estimated with alternative sources of data (federal vs state), alternative breadth of samples (single stage versus national or regional) and alternative units of analysis (district vs school); 4) Tests of race-neutral proxies using a second stage analysis for translation to policy: a. tests of “weights” models for explaining cost variation, and evaluation of residual bias; b. tests of predictive accuracy of “weights” models. Perhaps the most effective test of whether consolidation and integration, or racially integrative defragmentation can affect overall costs is to estimate continuously updated cost models through a period of reform involving either fragmentation or defragmentation resulting in increased or decreased racial isolation. Repeated model estimation and updating may pick up changes to overall costs of meeting common outcome goals that cannot be picked up by way of modeling non- linearities and interaction terms with models for fixed time periods on systems experiencing minimal structural or demographic shift. Empirical Tests of a National Education Cost Model Here, I provide a limited series of empirical tests and illustrations using the National Education Cost Model, first published in 2021 (Baker et al., 2021). The model has since been updated with additional years of expenditure and outcome data. As described in our 2021 article, the model combines data from the School Finance Indicators Database, which includes district level financial data from the Census Fiscal Survey of Local Governments (F-33), demographic and economic context data from the EDGE data system of the National Center for Education Statistics, as well as the more recently developed Neighborhood Poverty Index, and our own extended version of the Education Comparable Wage Index. Our outcome measures are an overall outcome index, nationally normed and mean centered from the Stanford Education Data Archive, v5.0 (Reardon et al., 2024b). These are the data sources that have only recently enabled estimation of a national cost model, and while imperfect (neither spending data nor outcome data, in my opinion, are perfectly, precisely equated across state boundaries), they provide a unique opportunity for multistate, interstate comparisons. Baker (2025) provides a comprehensive deep dive into the theoretical basis and empirical specification of the education cost function. First, that the education cost function predicts spending variation as a function of a) student outcomes, b) student characteristics, c) school context and structure (size and location), d) input prices (competitive wages for teachers), and e) factors that may explain spending variation unrelated to outcome variation (inefficiency/efficiency) factors. Efficiency factors fall into three categories: 1) Competitive pressures (competition density, as measured by a Herfindahl index), 2) Public monitoring measures, and 3) Fiscal capacity measures. Public monitoring measures typically include measures of shares of children in public schooling or of school age on the premise is that publics with more or less direct stake in local public schools place varied pressure on their spending behavior. Fiscal capacity measures may include measures of local family income. Put bluntly, those with the capacity to spend more on programs and services Education Polic y Analysis Arc hives Vol. 3 3 No. 55 10 which may not contribute directly to our measured outcomes are more likely to do so. Further, the broadly accepted specification of the model is that outcomes and spending are considered endogenous and thus outcomes are instrumented in a two-stage least squares model. Typical instruments for such models include demographics and outcomes of neighboring school districts, which may put pressure on outcomes of the observed district. Baker (2025) also provides a discussion of district versus school level cost modeling. Importantly, the local public school district is the fiscal agent where to which state aid is allocated, where local tax and revenue decisions are made and where budgets are adopted for schools. Districts also may assign specific programs to specific schools under their oversight, and districts determine attendance boundaries for schools, both affecting student sorting. So, in general, districts are the most relevant unit for such cost analyses, especially for informing state aid distribution. But school models can be used to reveal important variation across schools within districts, including whether district choices regarding attendance boundaries and program assignment create inefficient or inequitable variation across schools. Baker (2025) lists specific measures used in recent studies, across each of these categories. Traditionally, student need measures reflect those used in state school finance policies, such as a) a measure of child poverty or low income status, b) measures of shares of children who are English learners, and d) measures that capture shares of children by disability classification. Herein lies the potential role for racial composition, which until recently had not been included with regularity. Baker (2025) explains the approach commonly used for selecting the relevant measure for each construct, for example—whether to use census poverty rates or rates of children qualified for free or reduced lunch for cost modeling? For uniformity of measurement purposes herein, and having tested a variety of alternatives over time, we select the U.S. Census Bureau’s measure of child poverty. Note that I also test as an alternative, the Stanford Education Data Archive’s more comprehensive measure of Socioeconomic Status (SES Composite) and report the results in Appendix Table A4 (Fahl et al., 2024). I expected that this more comprehensive measure might reduce the marginal contribution of race in the models, because Reardon at al. (2024a) using similar data note “The association of racial segregation with achievement-gap growth is completely accounted for by racial differences in school poverty.” But in tests with the models herein, results changed only slightly and other model diagnostics failed (Appendix Tabe A4). Like Baker and Green (2009), I test a set of models that include and exclude race variables: 1) race sensitive model including % Black enrollment; 2) race neutral model; 3) race neutral model with poverty rates interacted with population density; 4) race sensitive model interacting % Black with population density. Earlier publications had not previously tested the fourth of these models. Of primary interest is whether the third model sufficiently captures the higher costs associated with racially isolated, often inner urban fringe or urban core districts, when compared with the race sensitive models. Here, I test the above measures using a conventional 2-stage least squares (Instrumental Variables) education cost function, following our previous work and that of Duncombe and Yinger (Baker, 2006; Duncombe & Yinger, 2011; Kolbe et al., 2021). The model includes per pupil spending as the dependent variable, includes a handful of indirect controls for inefficiency, and treats the outcome measure as endogenous, using as (exogenous) instruments, the demographic characteristics of surrounding school districts (other than the observed). Rac ial Isolation , Education Costs, and Equal Educ ational Opportunity 11 I evaluate the four models above across four categories to identify the optimal model and then compare cost predictions from the models, specifically for districts whose enrollments are majority Black. These tests draw on the work of Baker (2006) and Duncombe (2006), where both laid out frameworks for evaluating the reliability, validity and usefulness of education cost analyses. Category 1: Model Estimates & Diagnostics First, the models must meet the basic statistical tests for model coefficients and tests that the instruments are valid (Partial F >10) and pass tests for overidentification (p-value of Hansen J>.05). Category 2: Out of Sample Prediction For this test, I split our modeling data set into an 80% sample and 20% sample, using a random seed. We fit models to the 80% sample (parameters reported in Appendix A, Table A2) and then use those models to predict the spending per pupil of the 20% extract. We compare both the absolute percent error (average forecast accuracy error) and the average percent error (which picks up over or under prediction bias) for the four models. Error rates in a national model of school district spending are expected to be quite high because I have tried to identify a sufficiently generalizable cost model (cost factors related to spending) and have not removed state specific effects. The question at hand is which model best predicts (lowest error) spending variation in an out of sample test. Category 3: Model Validity – Input Gap to Outcome Gap A basic validity check on cost estimates is to compare the funding gap—current spending to cost estimate for a given outcome—to the actual outcome gaps with respect to that same outcome. That is, do districts that spend more than needed to achieve a given outcome, also achieve more, and vice versa. More importantly, how strong is this correlation between funding gaps and outcome gaps. We compare our models on this basis (see Table A3, Appendix A). Category 4: Omitted Variables Bias From the previous analysis one can also check whether certain subsets of districts or whether districts on certain dimensions fall out of line from the average trend for the relationship between funding gaps and outcome gaps. For example, do I find that districts with majority Black enrollments on average have larger outcome gaps than expected, given the estimated size of their funding gaps? If so, our models may negatively bias the spending predictions for these districts. For this analysis, I estimate a model of the residuals from the relationship in Category 3—the residuals of the relationship between funding gaps and outcome gaps—to determine whether those residuals are biased by district racial composition, and which among our four models yields the least residual bias of this type? Findings Table 1 shows the estimates and diagnostics for the four models. The vast majority of estimates are statistically significant and in the expected direction. The poverty by density, percent Black enrollment, and Black by density coefficients are all significant. Models where percent Black is in the second stage, use percent Hispanic of surrounding districts as an instrument, while models that exclude percent Black in the second stage include percent Black or Hispanic of surrounding districts as an instrument. Partial F statistic indicating instrument validity (that they predict variation in the outcome in the first stage model) are all sufficiently high (over 150). Overidentification may be an issue in the third model—poverty by density—which has a Hansen J p-value of <.05. Education Polic y Analysis Arc hives Vol. 3 3 No. 55 12 Table 1 Alternative Cost Model Estimates IV Reg Grade 3-8 Black IV Reg Grade 3-8 Neutral IV Reg Grade 3-8 Pov x Dens IV Reg Grade 3-8 Black x Dens coef R.S.E coef R.S.E coef R.S.E coef R.S.E Outcome Index 1.841*** 0.114 1.956*** 0.127 1.935*** 0.129 1.783*** 0.106 Labor Cost Index 0.478*** 0.035 0.573*** 0.036 0.633*** 0.037 0.499*** 0.034 Student Needs Child Poverty Rate 2.260*** 0.164 3.312*** 0.227 2.312*** 0.215 2.219*** 0.155 Disability Rate (state ctr) 3.002*** 0.148 2.957*** 0.157 2.932*** 0.158 2.929*** 0.141 % ELL 1.938*** 0.136 1.700*** 0.133 1.622*** 0.133 1.846*** 0.126 % Black 1.034*** 0.061 0.399*** 0.069 %Poverty x Pop Density 0.217*** 0.038 %Black x Pop Density 0.115*** 0.012 Grade Range Distribution % Pre-k 0.011 0.144 0.173 0.153 0.129 0.152 -0.007 0.140 % 9 to 12 0.507*** 0.041 0.499*** 0.044 0.498*** 0.044 0.491*** 0.040 Economies of Scale Less than 100 Students 0.573*** 0.080 0.545*** 0.082 0.551*** 0.081 0.557*** 0.079 101 to 300 Students 0.385*** 0.022 0.367*** 0.022 0.366*** 0.021 0.371*** 0.021 301 to 600 Students 0.220*** 0.016 0.199*** 0.016 0.199*** 0.016 0.213*** 0.016 601 to 1200 Students 0.141*** 0.013 0.119*** 0.013 0.117*** 0.013 0.140*** 0.012 1201 to 1500 Students 0.109*** 0.014 0.090*** 0.015 0.091*** 0.015 0.112*** 0.014 1501 to 2000 Students 0.100*** 0.013 0.083*** 0.013 0.085*** 0.013 0.104*** 0.012 Population Density (ln) -0.061*** 0.007 -0.036*** 0.006 -0.076*** 0.010 -0.070*** 0.007 Efficiency Measures % Pop 5 to 17 Years Old -1.004*** 0.166 -0.444*** 0.122 -0.429*** 0.122 -0.975*** 0.160 Housing Value Ratio -0.356*** 0.030 -0.409*** 0.034 -0.380*** 0.033 -0.329*** 0.028 Herfindahl Index -0.359 0.475 0.363 0.506 -0.005 0.499 -0.161 0.462 Time Period 0.016*** 0.001 0.016*** 0.001 0.014*** 0.001 0.015*** 0.001 Constant 8.560*** 0.065 8.233*** 0.063 8.314*** 0.064 8.558*** 0.063 Number of observations 147,186 147,186 147,186 147,186 Instrument Diagnostics Partial F (excluded inst) 177.54 160.12 157.19 191.96 Hansen J (p-value) 0.6245 0.3392 0.0406 0.7952 Model Selection Tests Test Set (out of sample) Prediction Correlation (r) with current spending (20% Test Set) .298 .271 .291 .339 MAPE (20% Test Set) 36.2% 38.3% 37.2% 35.1% MPE (20% Test Set) 14.0% 17.6% 18.9% 15.2% FundGap x OutGap Validity Test (rsq) 0.450 0.383 0.391 0.453 Residual Bias (% Black) 0.055*** -0.417*** -0.394*** 0.092*** note: *** p<0.01, ** p<0.05, * p<0.1 Rac ial Isolation , Education Costs, and Equal Educ ational Opportunity 13 Overidentification is a more significant problem in the SES models reported in Appendix A4. Appendix A1 shows the estimates from the same models estimated to 80% of the data (Training Set), revealing consistent findings. Results are similar when selecting a randomized 50% sample. In general, the models work, statistically speaking and are quite robust. Across the models, the rank order of performance on model selection tests is as follows: 1. For correlation between predicted out of sample spending and actual, Black by Density performed best, Black alone second, Poverty by Density third, and Poverty alone last; 2. For overall error rates of prediction of out of sample spending, Black by Density performed best, Black alone second, Poverty by Density third, and Poverty alone last, but for directional bias in out of sample prediction Black alone slightly outperformed Black by Density; 3. For the strength of the relationship between estimated funding gaps and outcome gaps, Black by Density performed best, Black alone second, Poverty by Density third, and Poverty alone last, but for racially correlated residuals (bias) Black alone performed slightly better than Black by Density. That is, across all tests it is clear that racial composition is important to the prediction of costs and estimation of funding gaps, in terms of identifying the best—statistically speaking—model. It also seems relatively clear that interacting race with population density yields marginal improvements to the models. Table 2 shows the differences in per pupil cost predictions (to achieve national average outcomes in reading and math, grades 3 to 8) for the Nation’s majority Black enrollment districts which have over 2,000 enrolled pupils. That is, what is the expected per pupil cost for all children to have equal educational opportunity to achieve the relatively low bar outcome of national mean assessment scores? Many of these districts, like Birmingham City are specifically noted in Baker, Di Carlo and Green’s 2022 report which outlined over a century of residential discrimination, district boundary manipulation and other factors that have made these districts the racially isolated districts they are today. Birmingham City is reported to be 88.7% Black. If I estimate the cost of providing students in Birmingham City to achieve the outcome goal in question, without including racial composition, I estimate that they would need to spend about $27,328 per pupil. If I try the race neutral alternative of interacting their high poverty rate with population density, that figure goes up slightly to $27,857. But, if I account for the share of the student population that is Black the cost estimate rises to nearly $44,000 per pupil, and interacted with density, just over $44,000 per pupil. The difference between the race neutral and race sensitive models is the reparatory margin needed to begin counteracting over a century’s worth of racially discriminatory policies (Baker, Di Carlo & Green, 2022). Reparatory margins are smaller for the other cities in Table 2, but still of importance. Figure 1 provides illustrations for three states that are home to substantial racial segregation due to discriminatory housing polices. Model results in the left-hand panel are from the Poverty by Density, race neutral models and model results in the right-hand panels are from the Black by Density model. National results are in the background (gray dots) and the overall trendline of funding gaps to outcome gaps is included. Districts from the specific state are represented as Black Diamonds in the foreground. The size of the diamonds represents district enrollment. Districts falling below the diagonal are districts that achieve less than expected on the outcome index, given their relative funding. One might label them “inefficient.” Or, as noted previously, one might consider the possibility that the models on the left suffer from omitted variables bias—that I’ve missed an important cost factor. Identifying and including that cost factor might move those districts into line, per se, with average efficiency expectations. Education Polic y Analysis Arc hives Vol. 3 3 No. 55 14 Table 2 Differences in Cost Predictions – Majority Black School Districts (>20k enrollment) State District Enrollment % Poverty % Black % Black Neutral Pov x Density Black x Density AL Birmingham City 21,597 41.1% 88.7% $43,960 $27,328 $27,857 $44,216 AL Jefferson County 35,336 22.2% 50.8% $21,235 $15,832 $16,104 $21,441 AL Mobile County 52,460 23.1% 50.6% $20,274 $14,998 $15,211 $20,189 AL Montgomery County 27,399 32.5% 78.5% $31,264 $19,425 $19,540 $30,683 AR Little Rock SD 21,612 26.7% 60.6% $30,482 $20,600 $20,756 $30,269 DC District of Columbia PS 49,896 25.0% 57.7% $28,354 $22,949 $24,062 $31,042 GA Atlanta Public Schools 51,012 26.6% 72.2% $25,524 $16,939 $17,491 $26,948 GA Bibb County 21,373 36.3% 77.7% $31,182 $20,842 $21,270 $31,624 GA Savannah-Chatham County 36,502 23.9% 57.7% $21,700 $16,062 $16,422 $22,051 GA Clayton County 52,149 26.9% 69.2% $28,101 $18,941 $19,431 $29,500 GA DeKalb County 93,470 23.7% 59.3% $26,836 $19,015 $19,422 $28,140 GA Douglas County 25,884 19.5% 54.9% $21,252 $15,466 $15,796 $21,611 GA Henry County 42,388 12.2% 57.6% $16,648 $11,072 $11,323 $17,040 GA Muscogee County 30,757 30.4% 57.2% $25,767 $19,013 $19,427 $26,212 GA Richmond County 29,093 31.5% 74.9% $28,468 $18,508 $18,897 $28,872 LA Caddo Parish 36,153 29.8% 63.2% $23,498 $16,926 $17,128 $23,317 LA East Baton Rouge Parish 40,283 27.7% 71.3% $26,286 $16,772 $17,055 $26,998 MD Baltimore City PS 77,856 31.3% 75.7% $38,322 $25,775 $27,089 $42,404 MD Charles County PS 26,768 8.9% 56.7% $15,764 $11,249 $11,560 $15,945 MD Prince George's County 131,646 14.8% 55.3% $25,800 $18,929 $19,305 $26,790 MI Detroit Public Schools 48,782 40.2% 81.6% $47,270 $31,302 $32,454 $50,440 MS Jackson Public School District 20,401 40.1% 95.0% $37,194 $21,282 $21,408 $36,389 NY Rochester City SD 24,898 38.9% 53.4% $47,071 $39,628 $40,612 $47,326 OH Cincinnati Public Schools 34,635 32.2% 61.7% $34,619 $26,288 $27,229 $36,016 OH Cleveland Municipal 34,941 39.1% 64.0% $47,169 $36,442 $37,953 $49,259 OH Columbus City School District 46,657 29.2% 53.0% $34,343 $26,577 $27,219 $35,337 PA Pittsburgh SD 21,407 24.4% 51.3% $22,171 $16,984 $17,472 $22,979 SC Richland 01 22,202 26.6% 70.3% $24,153 $15,509 $15,758 $24,348 SC Richland 02 27,761 15.3% 61.0% $17,568 $11,034 $11,197 $17,778 VA Newport News PS 27,113 22.7% 54.1% $20,388 $15,179 $15,643 $21,498 VA Norfolk City PS 27,955 21.4% 58.4% $20,397 $14,447 $14,973 $21,941 VA Richmond City PS 28,225 34.1% 55.4% $28,886 $23,756 $24,630 $30,449 WI Milwaukee School District 71,510 30.4% 50.4% $32,899 $27,055 $28,082 $34,411 Rac ial Isolation , Education Costs, and Equal Educ ational Opportunity 15 Figure 1 State Specific Illustrations This is what I see in Figure 1. The larger diamonds in Missouri that fall well below the expected outcomes and have race neutral funding gaps under $10,000 per pupil have much larger funding gaps when considering race, near and exceeding $20,000 per pupil and in the right-hand panel fall right on the average efficiency trajectory. That is, they move to the left (larger funding gap estimate) in the figure. The City of Philadelphia (largest district in Pennsylvania), in the second row, shows a similar yet smaller movement from below the line, to right in line with average efficiency. The case is similar for the City of Baltimore (Diamond furthest to the left in the bottom row). Education Polic y Analysis Arc hives Vol. 3 3 No. 55 16 Conclusions and Policy Implications Prior studies and the analyses presented herein make a compelling case that school district racial composition is an important factor determining the costs of providing equal educational opportunity. First, models including racial composition reduce or eliminate residual bias, indicating that race-neutral models suffer from omitted variables bias. When that bias is reduced, districts with majority Black enrollments fall in line with average efficiency (in the production of outcomes) expectations. We should have no reason, other than perhaps our own racial biases, for hypothesizing differently. Perhaps most importantly, the predicted costs of providing equal educational opportunity, when including racial composition, change substantively for majority Black districts. Those districts, many of which have been created to be and reinforced as economically depressed and racially isolated for over a century, face uniquely higher costs of providing equal educational opportunity. It’s important to understand that, knowing the effects found herein – the magnitudes of the reparatory margins estimated herein – if we continue to ignore those effects and conduct only race avoidant analyses to guide race avoidant policy, we are knowingly depriving students of equal educational opportunity on the basis of their race. Ignoring the above findings deprives Black students in majority Black districts of equal opportunities to achieve common outcome goals – to succeed on state standards – perpetuating racial educational inequality. A next step in this process is to determine whether and to what extent these costs and the total costs to a state of providing equal educational opportunity can be reduced substantively by defragmentation of racially isolated local public school districts to improve racial integration. Much has been made in the literature over the potential cost savings associated with consolidation of local public school districts, with emphasis on achieving economies of scale, especially for highly fragmented districts in close proximity to one another. The racial isolation that persists across many of these same boundaries and its affects on the costs of providing all children equal educational opportunity deserves at least equal attention and can be studied by similar methods. We expect, based on our finding herein that the costs associated with the interaction between racial composition and population density can be disrupted and reduced by district defragmentation and racial integration. If so, the efficient path toward providing racial equal educational opportunity is a both- and path, involving both appropriately calibrated state school finance systems to address all costs and needs and aggressively integrating and defragmenting local public school districts, to more efficiently achieve these ends. Finally, I see these efforts as both required under state constitutions that demand the provision of equal educational opportunity and as reparations for the decades of policies and practices that have inflicted these damages, and high costs on our nation’s majority Black communities in particular. The current political and legal context poses significant challenges for moving this agenda forward. In the current environment, the mere acknowledgment of race has become taboo. The first wave of these studies showing race effects on costs came as the Supreme Court was further limiting consideration of race in student assignment, and the federal legal climate has only further backslid from that moment. But at the same time, the empirical evidence has become even stronger and state courts and advocacy organizations have begun to consider the intersection of racial segregation, isolation and school funding inequality.4 The forces that brought us to the current unfavorable federal policy and legal environment have been at work for at least half a century. Progress back toward real, racial equality—a new reconstruction—will likely take at least equally long. 4 See https://www.brownspromise.org/ Rac ial Isolation , Education Costs, and Equal Educ ational Opportunity 17 References Atchison, D., Baker, B. D., Levin, J., Fatima, S., Trauth, A., Srikanth, A., Herberle, C., Gannon- Slater, N., Junk, L., & Wallace K. (2023). Assessment of Delaware public school funding. https://education.delaware.gov/wp-content/uploads/2023/12/23- 22933_1_Delaware_Full_Report-FMT-ed103023-Version-2.pdf Atchison, D., Levin, S., Levin, J., Kolar, A., Blair, D., Srikanth, A., & Salvato, B. (2024). Equity and adequacy of Colorado school funding: A cost-modeling approach. https://air.org/sites/default/files/2025-04/Colorado-Adequacy-Study-Final-Report- December-2024.pdf. Baker, B. D. (2005). The emerging shape of educational adequacy: From theoretical assumptions to empirical evidence. Journal of Education Finance, 30(3), 259-287. Baker, B. D. (2006). Evaluating the reliability, validity, and usefulness of education cost studies. Journal of Education Finance, 32(2), 170-201. Baker, B. D. (2011). Exploring the sensitivity of education costs to racial composition of schools and race-neutral alternative measures: A cost function application to Missouri. Peabody Journal of Education, 86(1), 58-83. https://doi.org/10.1080/0161956X.2011.539957 Baker, B. D. (2022). School finance and education equity: Lessons from Kansas. Harvard Education Press. Baker, B. D. (2025). Framework for evaluating & reforming education finance systems. (EdWorkingPaper: 25 - 1127). Annenberg Institute at Brown University: https://doi.org/10.26300/pa0r-n548 Baker, B. D., Atchison, D., Levin, J., & Kearns, C. (2020) New Hampshire Commission to Study School Funding, Final Report: https://carsey.unh.edu/sites/default/files/media/2020/09/20- 12685_nh_final_report_version_v5_draft_1.pdf Baker, B. D., & Castillo, W. (2024). Systemic racial disparities in large data on school district finance & housing: Three empirical illustrations. Manuscript submitted for publication. Baker, B. D., Di Carlo, M., & Green III, P. C. (2022). Segregation and school funding: How housing discrimination reproduces unequal opportunity. Albert Shanker Institute. https://www.shankerinstitute.org/sites/default/files/2022-05/SEGmetro_SA.pdf Baker, B. D., Di Carlo, M., & Green III, P. C. (2023) Understanding the first, second, and third order effects on disparities in K-12 funding and outcomes. Poverty & Race, 32(2), https://www.prrac.org/understanding-the-first-second-and-third-order-effects-on- disparities-in-k-12-funding-and-outcomes-april-july-2023-pr-journal/ Baker, B. D., & Green III, P. C. (2009). Equal educational opportunity and the distribution of state aid to schools: Can or should school racial composition be a factor? Journal of Education Finance, 289-323. Baker, B. D., & Green III, P. C. (2012). Conceptions of equity and adequacy in school finance. In Handbook of research in education finance and policy (pp. 225-243). Routledge. https://doi.org/10.4324/9780203961063-20 Baker, B. D., Keller-Wolff, C., & Wolf-Wendel, L. (2000). Two steps forward, one step back: Race/ethnicity and student achievement in education policy research. Educational Policy, 14(4), 511-529. https://doi.org/10.1177/0895904800144004 Baker, B. D., Srikanth, A., Cotto Jr, R., & Green III, P. C. (2020). School funding disparities and the plight of Latinx children. Education Policy Analysis Archives, 28(135). https://doi.org/10.14507/epaa.28.5282 Baker, B. D., Weber, M., & Srikanth, A. (2021). Informing federal school finance policy with empirical evidence. Journal of Education Finance, 47(1), 1-25. https://doi.org/10.1353/jef.2021.a806389 https://education.delaware.gov/wp-content/uploads/2023/12/23-22933_1_Delaware_Full_Report-FMT-ed103023-Version-2.pdf https://education.delaware.gov/wp-content/uploads/2023/12/23-22933_1_Delaware_Full_Report-FMT-ed103023-Version-2.pdf https://air.org/sites/default/files/2025-04/Colorado-Adequacy-Study-Final-Report-December-2024.pdf https://air.org/sites/default/files/2025-04/Colorado-Adequacy-Study-Final-Report-December-2024.pdf https://doi.org/10.1080/0161956X.2011.539957 https://doi.org/10.26300/pa0r-n548 https://carsey.unh.edu/sites/default/files/media/2020/09/20-12685_nh_final_report_version_v5_draft_1.pdf https://carsey.unh.edu/sites/default/files/media/2020/09/20-12685_nh_final_report_version_v5_draft_1.pdf https://www.shankerinstitute.org/sites/default/files/2022-05/SEGmetro_SA.pdf https://www.prrac.org/understanding-the-first-second-and-third-order-effects-on-disparities-in-k-12-funding-and-outcomes-april-july-2023-pr-journal/ https://www.prrac.org/understanding-the-first-second-and-third-order-effects-on-disparities-in-k-12-funding-and-outcomes-april-july-2023-pr-journal/ https://doi.org/10.4324/9780203961063-20 https://doi.org/10.1177/0895904800144004 https://doi.org/10.14507/epaa.28.5282 https://doi.org/10.1353/jef.2021.a806389 Education Polic y Analysis Arc hives Vol. 3 3 No. 55 18 Barton, P. E., & Coley, R. J. (2010). The Black-White achievement gap: When progress stopped. Policy Information Report. Educational Testing Service. Bifulco, R. (2005). District-level Black-White funding disparities in the United States, 1987-2002. Journal of Education Finance, 31(2), 172-194. Bifulco, R., & Souders, S. (2023). Racial disparities in school poverty and spending: Examining allocations within and across districts. AERA Open. https://doi.org/10.1177/23328584241293423 Brooks, C. D., Levin, J., Salvato, B., & Baker, B. D. (2025). Understanding the cost of providing adequate educational opportunity in Oregon. https://www.air.org/sites/default/files/2025-02/Task-5- Understanding-the-Cost-of-Providing-Adequate-Educational-Opportunity-in-Oregon-Jan- 2025.pdf Di Carlo, M., & Edmond, A. (2024). School district fragmentation, segregation and funding equity in New Jersey. Shankerblog. https://www.shankerinstitute.org/blog/school-district- fragmentation-segregation-and-funding-equity-new-jersey Downes, T. A., & Pogue, T. F. (1994). Adjusting school aid formulas for the higher cost of educating disadvantaged students. National Tax Journal, 47(1), 89-110. https://doi.org/10.1086/NTJ41789054 Duncombe, W. (2006). Responding to the charge of alchemy: Strategies for evaluating the reliability and validity of costing-out research. Journal of Education Finance, 137-169. Duncombe, W. (2007). Estimating the cost of meeting student performance standards in the St. Louis public schools. Report Prepared for the St. Louis Board of Education. Syracuse University, Center for Policy Research. Duncombe, W., & Yinger, J. (1997). Why is it so hard to help central city schools? Journal of Public Policy Analysis and Management, 16(1), 85-113. https://doi.org/10.1002/(SICI)1520- 6688(199724)16:1<85::AID-PAM5>3.0.CO;2-E Duncombe, W., & Yinger, J. (1998). School finance reform: Aid formulas and equity objectives. National Tax Journal, 51(2), 239-262. https://doi.org/10.1086/NTJ41789325 Duncombe, W., & Yinger, J. (2006). Estimating the costs of meeting student performance outcomes adopted by the Kansas State Board of Education. Prepared for the Kansas Legislative Division of Post Audit. https://www.maxwell.syr.edu/uploadedFiles/cpr/research/cpr_research_education_finance _policy/Kansas_Report.pdf Fahle, E. M., saliba, j., Kalogrides, D., Shear, B. R., Reardon, S. F., & Ho, A. D. (2024). Stanford Education Data Archive: Technical documentation (Version 5.0). Retrieved from https://purl.stanford.edu/cs829jn7849 Garms, W. I., & Smith, M. C. (1970). Educational need and its application to state school finance. Journal of Human Resources, 304-317. https://doi.org/10.2307/144608 Green III, P. C., Baker, B. D., & Oluwole, J. O. (2008). Achieving racial equal educational opportunity through school finance litigation. Stanford Journal of Civil Rights & Civil Liberties, 4, 283. Green III, P. C., Baker, B. D., & Oluwole, J. O. (2020). School finance, race, and reparations. Washington and Lee Journal of Civil Rights and Social Justice, 27, 483. https://doi.org/10.2139/ssrn.3766279 Gronberg, T. J., Jansen, D. W., & Taylor, L. L. (2011). The adequacy of educational cost functions: Lessons from Texas. Peabody Journal of Education, 86(1), 3-27. https://doi.org/10.1080/0161956X.2011.539953 https://doi.org/10.1177/23328584241293423 https://www.air.org/sites/default/files/2025-02/Task-5-Understanding-the-Cost-of-Providing-Adequate-Educational-Opportunity-in-Oregon-Jan-2025.pdf https://www.air.org/sites/default/files/2025-02/Task-5-Understanding-the-Cost-of-Providing-Adequate-Educational-Opportunity-in-Oregon-Jan-2025.pdf https://www.air.org/sites/default/files/2025-02/Task-5-Understanding-the-Cost-of-Providing-Adequate-Educational-Opportunity-in-Oregon-Jan-2025.pdf https://www.shankerinstitute.org/blog/school-district-fragmentation-segregation-and-funding-equity-new-jersey https://www.shankerinstitute.org/blog/school-district-fragmentation-segregation-and-funding-equity-new-jersey https://doi.org/10.1086/NTJ41789054 https://doi.org/10.1002/(SICI)1520-6688(199724)16:1%3C85::AID-PAM5%3E3.0.CO;2-E https://doi.org/10.1002/(SICI)1520-6688(199724)16:1%3C85::AID-PAM5%3E3.0.CO;2-E https://doi.org/10.1086/NTJ41789325 https://www.maxwell.syr.edu/uploadedFiles/cpr/research/cpr_research_education_finance_policy/Kansas_Report.pdf https://www.maxwell.syr.edu/uploadedFiles/cpr/research/cpr_research_education_finance_policy/Kansas_Report.pdf https://purl.stanford.edu/cs829jn7849 https://doi.org/10.2307/144608 https://doi.org/10.2139/ssrn.3766279 https://doi.org/10.1080/0161956X.2011.539953 Rac ial Isolation , Education Costs, and Equal Educ ational Opportunity 19 Gronberg, T. J., Jansen, D. W., & Taylor, L. L. (2012). The relative efficiency of charter schools: A cost frontier approach. Economics of Education Review, 31(2), 302-317. https://doi.org/10.1016/j.econedurev.2011.07.001 Gronberg, T. J., Jansen, D. W., & Taylor, L. L. (2017). Are charters the best alternative? A cost frontier analysis of alternative education campuses in Texas. Southern Economic Journal, 83(3), 721-743. https://doi.org/10.1002/soej.12173 Hanushek, E. A., Kain, J. F., & Rivkin, S. G. (2004). Why public schools lose teachers. Journal of Human Resources, 39(2), 326-354. https://doi.org/10.2307/3559017 Hanushek, E. A., & Rivkin, S. G. (2006). School quality and the Black-White achievement gap (No. 12651). National Bureau of Economic Research. https://doi.org/10.3386/w12651 Heise, M. (1995). State constitutions, school finance litigation, and the third wave: From equity to adequacy. Temple Law Review, 68, 1151. Imazeki, J., & Reschovsky, A. (2006). Does No Child Left Behind place a fiscal burden on states? Evidence from Texas. Education Finance and Policy, 1(2), 217-246. https://doi.org/10.1162/edfp.2006.1.2.217 Johnson, R. C. (2019). Children of the dream: Why school integration works. Basic Books. Kolbe, T., Baker, B. D., Atchison, D., & Levin, J. (2019). Pupil weighting factors report. State of Vermont, House and Senate Committees on Education. https://legislature.vermont.gov/assets/Legislative-Reports/edu-legislative-report-pupil- weighting-factors-2019.pdf Kolbe, T., Baker, B. D., Atchison, D., Levin, J., & Harris, P. (2021). The additional cost of operating rural schools: Evidence from Vermont. AERA Open, 7, https://doi.org/10.1177/2332858420988868 Krueger, A., & Whitmore, D. (2001). Would smaller classes help close the Black-White achievement gap? (No. 830). Princeton University, Department of Economics, Industrial Relations Section. Levin, H. M., Belfield, C., Muennig, P. & Rouse, C. (2007). The public returns to public educational investments in African American males. Economics of Education Review, 26(6) 699-708. https://doi.org/10.1016/j.econedurev.2007.09.004 Levin, J., Baker, B., Lee, J., Atchison, D., & Kelchen, R. (2022). An Examination of the Costs of Texas Community Colleges. REL 2023-142. Regional Educational Laboratory Southwest. Reardon, S. F., Ho, A. D., Shear, B. R., Fahle, E. M., Kalogrides, D., Saliba, J. (2024b). Stanford Education Data Archive (Version 5.0). Retrieved from https://purl.stanford.edu/cs829jn7849 Reardon, S. F., Robinson-Cimpian, J. P., & Weathers, E. S. (2014). Patterns and trends in racial/ethnic and socioeconomic academic achievement gaps. In Handbook of research in education finance and policy (pp. 491-509). Routledge. Reardon, S. F., Weathers, E. S., Fahle, E. M., Jang, H., & Kalogrides, D. (2024a). Is separate still unequal? New evidence on school segregation and racial academic achievement gaps. American Sociological Review, 89(6), 971-1010. https://doi.org/10.1177/00031224241297263 Ryan, J. E. (1999a). The influence of race in school finance reform. Michigan Law Review, 98(2), 432- 481. https://doi.org/10.2307/1290344 Sosina, V. E., & Weathers, E. S. (2019). Pathways to inequality: Between-district segregation and racial disparities in school district expenditures. AERA Open, 5(3), https://doi.org/10.1177/2332858419872445 Taylor, L., Willis, J., Berg-Jacobson, A., Jaquet, K., & Caparas, R. (2018). Estimating the costs associated with reaching student achievement expectations for Kansas public education students: A cost function approach. WestEd. Retrieved from https://probstforprogress.com/wp- https://doi.org/10.1016/j.econedurev.2011.07.001 https://doi.org/10.1002/soej.12173 https://doi.org/10.2307/3559017 https://doi.org/10.3386/w12651 https://doi.org/10.1162/edfp.2006.1.2.217 https://legislature.vermont.gov/assets/Legislative-Reports/edu-legislative-report-pupil-weighting-factors-2019.pdf https://legislature.vermont.gov/assets/Legislative-Reports/edu-legislative-report-pupil-weighting-factors-2019.pdf https://doi.org/10.1177/2332858420988868 https://doi.org/10.1016/j.econedurev.2007.09.004 https://purl.stanford.edu/cs829jn7849 https://doi.org/10.1177/00031224241297263 https://doi.org/10.2307/1290344 https://doi.org/10.1177/2332858419872445 https://probstforprogress.com/wp-content/uploads/2018/03/kansas_adequacy_study_cost_function_approach_20180315_final.pdf Education Polic y Analysis Arc hives Vol. 3 3 No. 55 20 content/uploads/2018/03/kansas_adequacy_study_cost_function_approach_20180315_fin al.pdf Weathers, E. S., & Sosina, V. E. (2022). Separate remains unequal: Contemporary segregation and racial disparities in school district revenue. American Educational Research Journal, 59(5), 905- 938. https://doi.org/10.3102/00028312221079297 Zhao, B. (2022). Estimating the cost function of Connecticut public K–12 education: Implications for inequity and inadequacy in school spending. Education Economics, 1-32. https://doi.org/10.1080/09645292.2022.2077914 Bruce D. Baker The University of Miami, Coral Gables bdb119@miami.edu Bruce D. Baker is a professor in the Department of Teaching and Learning at the University of Miami in Coral Gables, FL. His research focuses on elementary, secondary and post-secondary education costs, financing of education systems and the economics of education systems. His recent books include His most recent books from Harvard Education Press include Educational Inequality and School Finance: Why Money Matters for America’s Students, and School Finance and Education Equity: Lessons from Kansas. A forthcoming book from Harvard Education Press will focus on housing discrimination and school funding inequality, coauthored with Matt Di Carlo of the Albert Shanker Institute. He is a recently inducted Fellow of the American Educational Research Association and serves in advisory and research fellow roles for the National Education Policy Center, Learning Policy Institute and Brown’s Promise. education policy analysis archives Volume 33 Number 55 September 9, 2025 ISSN 1068-2341 Readers are free to copy, display, distribute, and adapt this article, as long as the work is attributed to the author(s) and Education Policy Analysis Archives, the changes are identified, and the same license applies to the derivative work. More details of this Creative Commons license are available at https://creativecommons.org/licenses/by-sa/4.0/. EPAA is published by the Mary Lou Fulton College for Teaching and Learning Innovation at Arizona State University. Articles are indexed in CIRC (Clasificación Integrada de Revistas Científicas, Spain), DIALNET (Spain), Directory of Open Access Journals, EBSCO Education Research Complete, ERIC, Education Full Text (H.W. Wilson), QUALIS A1 (Brazil), SCImago Journal Rank, SCOPUS, SOCOLAR (China). About the Editorial Team: https://epaa.asu.edu/ojs/index.php/epaa/about/editorialTeam Please send errata notes to Jeanne M. Powers at jeanne.powers@asu.edu https://probstforprogress.com/wp-content/uploads/2018/03/kansas_adequacy_study_cost_function_approach_20180315_final.pdf https://probstforprogress.com/wp-content/uploads/2018/03/kansas_adequacy_study_cost_function_approach_20180315_final.pdf https://doi.org/10.3102/00028312221079297 https://doi.org/10.1080/09645292.2022.2077914 mailto:bdb119@miami.edu https://creativecommons.org/licenses/by-sa/4.0/ http://www.doaj.org/ http://www.doaj.org/ https://epaa.asu.edu/ojs/index.php/epaa/about/editorialTeam mailto:mailtojeanne.powers@asu.edu Rac ial Isolation , Education Costs, and Equal Educ ational Opportunity 21 Appendix A Table A1 Weights models estimated to Delaware Data Student Need Factor Cost Model Coeff. Weights 1 (Race Sensitive) Weights 1 (Race Neutral) Weights 2 (Race Sensitive) Weights 2 (Race Neutral) % Low Income 0.520 * 1.696 * 1.966 * 1.696 * 1.966 * % with Disabilities 1.159 * 3.157 * 3.075 * 3.157 * 3.075 * % Complex/Multiple Disabilities 1.396 * 4.101 * 4.288 4.101 * 4.288 % ELL 0.260 * 1.280 * 1.140 * 1.280 * 1.140 * % Voc Tech 1.535 * 4.620 * 4.594 4.620 * 4.594 % Middle Grades -0.011 0.987 * 0.978 * 0.987 * 0.978 * % Secondary grades 0.038 1.036 * 1.033 * 1.036 * 1.033 * % Black 0.149 * 1.159 * 1.159 * R-Squared 0.9831 0.9791 0.9851 0.9811 *p<.05 Table A2 Training Set Models (80% Sample) IV Reg Grade 3-8 Black IV Reg Grade 3-8 Neutral IV Reg Grade 3-8 Pov x Dens IV Reg Grade 3-8 Black x Dens coef R.S.E coef R.S.E coef R.S.E coef R.S.E Outcome Index 1.866*** 0.118 1.987*** 0.132 1.965*** 0.135 1.808*** 0.110 Education Comparable Wage Index 0.478*** 0.035 0.575*** 0.037 0.636*** 0.037 0.499*** 0.034 Student Needs Child Poverty Rate 2.304*** 0.170 3.377*** 0.237 2.340*** 0.221 2.261*** 0.161 Disability Rate (state ctr) 3.010*** 0.152 2.977*** 0.163 2.949*** 0.163 2.936*** 0.145 % ELL 1.959*** 0.140 1.724*** 0.137 1.643*** 0.137 1.868*** 0.130 % Black 1.046*** 0.063 0.411*** 0.071 %Poverty x Pop Density 0.224*** 0.040 %Black x Pop Density 0.115*** 0.012 Grade Range Distribution % Enrollment in Pre-k -0.012 0.144 0.155 0.155 0.110 0.154 -0.030 0.140 % Enrollment in Secondary Grades 0.500*** 0.042 0.492*** 0.045 0.490*** 0.045 0.484*** 0.041 Economies of Scale Less than 100 Students 0.547*** 0.080 0.518*** 0.081 0.525*** 0.080 0.532*** 0.078 101 to 300 Students 0.382*** 0.022 0.365*** 0.022 0.364*** 0.022 0.368*** 0.021 301 to 600 Students 0.220*** 0.016 0.200*** 0.016 0.200*** 0.016 0.213*** 0.016 601 to 1200 Students 0.142*** 0.013 0.120*** 0.013 0.119*** 0.013 0.141*** 0.012 1201 to 1500 Students 0.112*** 0.014 0.094*** 0.015 0.095*** 0.015 0.115*** 0.014 1501 to 2000 Students 0.098*** 0.013 0.081*** 0.014 0.084*** 0.014 0.103*** 0.013 Log of Population per Square Mile -0.063*** 0.007 -0.037*** 0.006 -0.078*** 0.011 -0.072*** 0.007 Efficiency Measures % Pop 5 to 17 Years Old -1.019*** 0.160 -0.442*** 0.122 -0.428*** 0.122 -0.990*** 0.154 Housing Value Ratio -0.365*** 0.031 -0.420*** 0.036 -0.390*** 0.035 -0.338*** 0.029 Herfindahl Index -0.353 0.480 0.355 0.518 -0.024 0.510 -0.151 0.468 Time Period 0.016*** 0.001 0.016*** 0.001 0.014*** 0.001 0.015*** 0.001 Constant 8.570*** 0.066 8.237*** 0.065 8.322*** 0.066 8.568*** 0.064 Number of observations 117,656 117,656 117,656 117,656 Note: *** p<0.01, ** p<0.05, * p<0.1 Education Polic y Analysis Arc hives Vol. 3 3 No. 55 22 Table A3 Residual Bias Check (with year fixed effect) DV=Model Residuals % Black Neutral Pov x Density Black x Density coef Se coef se coef se coef se % Black 0.055*** 0.004 -0.417*** 0.004 -0.394*** 0.004 0.092*** 0.004 % Hispanic -0.087*** 0.003 -0.037*** 0.003 -0.029*** 0.003 -0.083*** 0.003 Census Poverty Rate 5 to 17 yr Olds -0.820*** 0.008 -0.635*** 0.008 -0.627*** 0.009 -0.851*** 0.008 Constant 0.153*** 0.003 0.188*** 0.003 0.182*** 0.003 0.151*** 0.002 Number of observations 149,224 149,224 149,145 149,145 R2 0.111 0.191 0.179 0.113 Note: *** p<0.01, ** p<0.05, * p<0.1 Table A4 Test of Alternative SES Measure Black Direct Effect with Census Poverty Black Direct Effect with SES Composite coef R.S.E coef se Outcome Index 1.855*** 0.124 1.814*** 0.144 Labor Cost Index 0.381*** 0.037 0.580*** 0.034 Student Needs Child Poverty Rate 2.199*** 0.177 SES Composite (SEDA) -0.310*** 0.030 Disability Rate (state ctr) 2.878*** 0.153 2.597*** 0.142 % ELL 1.924*** 0.145 1.833*** 0.157 % Black 1.062*** 0.067 0.906*** 0.063 Grade Range Distribution % Pre-k 0.064 0.141 0.169 0.134 % 9 to 12 0.540*** 0.042 0.546*** 0.042 Economies of Scale Less than 100 Students 0.554*** 0.079 0.737*** 0.078 101 to 300 Students 0.373*** 0.022 0.474*** 0.024 301 to 600 Students 0.209*** 0.016 0.278*** 0.017 601 to 1200 Students 0.130*** 0.013 0.165*** 0.013 1201 to 1500 Students 0.099*** 0.014 0.115*** 0.014 1501 to 2000 Students 0.091*** 0.013 0.096*** 0.012 Population Density (ln) -0.065*** 0.008 -0.060*** 0.008 Efficiency Measures % Pop 5 to 17 Years Old -0.948*** 0.162 -0.846*** 0.150 Housing Value Ratio -0.459*** 0.036 -0.275*** 0.027 Herfindahl Index -0.672 0.495 -0.759 0.490 Time Period 0.019*** 0.001 0.006*** 0.001 Constant 8.838*** 0.074 8.714*** 0.068 Number of observations 147,183 146,771 Instrument Diagnostics Partial F (excluded inst) 144.32 115.82 Hansen J (p-value) 0.8313 0 Note: *** p<0.01, ** p<0.05, * p<0.1