This report is part of a series, Understanding and Improving Title I of ESEA. Nora Gordon is Professor at Georgetown University’s McCourt School of Public Policy, and Sarah Reber is the Joseph A. Pechman Senior Fellow in Economic Studies at the Brookings Institution.
Introduction
The Title I, Part A program (more commonly known as just “Title I”) of the Elementary and Secondary Education Act of 1965 (ESEA) directs funds to local school districts as a function of the number or percentage of disadvantaged children living in the district. In fiscal year (FY) 2021, Congress appropriated a total of $16.5 billion through Title I. Congress also relied on the distribution of Title I funding from earlier years to determine the amounts of COVID relief districts received from nearly $200 billion in Elementary and Secondary School Emergency Relief (ESSER) funding. The use of Title I allocations to distribute so much money through ESSER shone a light on the substantial differences in allocation amounts across and within states.
School districts receive widely varying amounts of Title I funding per formula child—essentially, per child living in poverty—from as low as a few hundred dollars in many small districts to more than $5,000 (again, in very small districts). These differences flow from the design of the law, particularly the four Title I grant formulas and the rules ensuring minimum distributions for states and districts. This report explains these formulas and how they influence the distribution of Title I funds across school districts.
Title I began with ESEA’s passage in 1965 during President Lyndon B. Johnson’s War on Poverty, shortly after the Civil Rights Act of 1964. Although Title I is primarily a grantmaking program to distribute funding to school districts, Congress can condition receipt of Title I funds on other state and district policies or programs, providing incentives for them to take actions that Congress could not otherwise mandate. For example, in the 1960s, districts had to comply with the Civil Rights Act by desegregating their schools to receive Title I funds. In more recent years, states were required to adopt test-based accountability systems under the No Child Left Behind Act (NCLB), the reauthorization of ESEA enacted in 2001. While the antipoverty motivation for Title I suggests a highly redistributive formula that directs funds disproportionately to high-poverty districts, the ability of Congress to condition funding on other policies creates an argument for a program that directs at least modest amounts of funding to all or most states and districts. Political considerations may also undergird decisions to design a program where participation is broad-based.
What is Title I?
Need a refresher on all things Title I? Check out All4Ed’s explainer on the Title I program and why it matters for students and families.
¿Qué es el Título I?
¿Necesita un repaso de todo relacionado con el Título I? Consulte el explicador de All4Ed sobre el programa de Título I y por qué es importante para los estudiantes y las familias.
Figure 1 shows the relationship between the percentage of the school-aged population (5- to 17-year-olds) that meets the Title I formula definition on the horizontal axis and the Title I grant per formula child on the vertical axis. The percentage of the school-aged population that meets the formula definition is close to a child poverty rate in practice; we refer to this as the formula child percentage throughout for precision. Each school district in the United States is represented with a single point. The figure shows a general upward slope, as Title I grants per formula child tend to increase with the formula child percentage. However, the figure also reveals a great deal of variation: districts with similar formula child percentages receive a wide range of Title I funds per formula child. For example, Teague Independent School District (TX) and Winooski School District (VT) each have about one-quarter of its children who are formula eligible, but Teague gets $1,393 per formula child while Winooski gets $5,434 per formula child.^{1}The handful of districts with 25% of formula-eligible children that receive no Title I funds all have school-aged populations below 40. The median child population in districts receiving zero Title I funding is 34; these districts likely choose not to participate due to the administrative costs associated with the program.
Figure 1. District-level Formula Child Percentage vs. Title I Allocation per Formula Child, United States, FY 2021
How does the law produce this type of variation in allocations per formula child? At its inception, the Title I program used a single, straightforward formula to allocate funding, but changes to the Basic Grant formula and the addition of three new formulas over the years have led to a more complicated distribution of federal funds that can be challenging to understand.
Title I funds are now distributed through four separate formulas: (1) Basic Grants, (2) Concentration Grants, (3) Targeted Grants, and (4) Education Finance Incentive Grants (EFIG). All four Title I formulas share two key factors:
- The formulas distribute funds to school districts based on the number of formula children in the district. The formula definition includes children living in households with income below the poverty line (who account for the bulk of formula children by far), as well as children whose families participate in Temporary Assistance for Needy Families (TANF), neglected and delinquent children living in state-run institutions, foster children, and children enrolled in Bureau of Indian Affairs schools.
- The formulas send larger Title I allocations per formula child to school districts in states with higher spending from state and local revenue per pupil (i.e., excluding federal funds).
The Title I formulas share other factors, including minimum allocations for states and hold harmless rules, discussed further below. The Basic Grant is based on the original Title I formula: the incremental funding a district receives per formula child does not depend on how poor the district is, and nearly all districts are eligible. By contrast, each of the other three formulas directs more funds per formula child to districts with more formula children or higher formula child percentages.^{2}Technically, this is not exactly the share of children who meet the formula count definition because a child can be counted in more than one category, e.g., a child could be both living in poverty and a foster child, in which case, they would count as two in the formula count. Concentration Grants do this by setting a meaningful threshold for eligibility based on the number or percentage of formula children; only about half of districts are eligible for Concentration Grant funding. The formulas for Targeted Grants and EFIG use weighting schemes (which differ slightly between the two formulas) whereby funding per formula child increases with the number or percentage of formula children. This report describes how Title I funding is distributed to local school districts, provides an overview of each of the four Title I formulas, and shows how funding per formula child varies across districts with different child poverty rates and other characteristics.
How Are School Districts’ Grants Determined?
Before turning to the details of each of the four formulas, we begin with an overview of the process by which districts’ Title I awards are determined and an introduction to key terminology.^{3}This is intended as an overview rather than a comprehensive description of the funds allocation process and the formulas. Readers seeking complete information should consult the most recent federal law (currently, the Every Student Succeeds Act) and search for sections on “Title I formula,” “formula grant,” and “improving basic programs.” See also Sonnenberg 2016.
How Title I Dollars Add Up: Appropriations, Authorized Amounts, Iterative Federal Allocations, and District Awards
The statutory formulas determine the amount each district is authorized to receive. However, each year, Congress appropriates Title I funds separately for each of the four formulas. In practice, the sum of authorized amounts nationally has exceeded the funds appropriated in every year after 1965, the program’s first year. In other words, Title I is not fully funded; the amount allocated by the U.S. Department of Education to each district is ultimately less than its authorized amount.
State minimum requirements (also known as small state minimums (SSM)) ensure that each state receives a minimum level of total funding from each formula; the method of determining state minimums is different for each formula. The state minimums mean that allocations per formula child are notably higher in low-population states.
To make the allocations sum to the amount Congress appropriated, the authorized amounts are ratably reduced. Broadly, this means each district’s authorized amount is multiplied by a fraction between zero and one. The exact fraction is determined by the amount Congress appropriated divided by how much it would cost to fully fund Title I. For example, fully funding the Basic Grant in FY 2021 would have cost almost seven times as much as Congress appropriated. Ratable reduction is an iterative process, continuing until no allocations violate Title I’s hold harmless or state minimum rules, which apply separately to each of the four formulas. This means the allocation is ultimately a larger share of the authorization for some districts than others.
Hold harmless rules mean that when a district’s formula child count declines rapidly, Title I allocations decline more slowly, protecting districts from sharp reductions in Title I funding due to declines in the number of formula children. The level at which districts are held harmless has varied over time, across the four formulas, and as a function of district formula child percentage. Current hold harmless levels range from 85% to 95% of the previous year’s total (not per formula child) Basic Grant allocation, with higher hold harmless rates in that range for districts with higher percentages of formula children.
All four Title I formulas, in different ways, rely on the counts and percentages of formula children in a district to determine whether, and how much, Title I funding a district is authorized to receive. The U.S. Department of Education uses that information, in conjunction with average education spending levels in each state, to determine allocations.
Throughout this report, we use data from the U.S. Department of Education on federal allocations at the school district level for FY 2021 (i.e., the 2020–21 school year), because these allocations are what the formulas determine.^{4}Some funding is reallocated from regular school districts to charter schools that operate (for federal purposes) as school districts. We do not have data on Title I funding for charter school districts, so they are excluded from this analysis. Puerto Rico is also excluded from the analysis because it is treated separately under the law. The amounts districts ultimately receive (and keep) vary from the federally allocated amount for several reasons.^{5}For instance, states must set aside a share of district allocations for school improvement activities (roughly 7%), provided this set-aside does not decrease district-level awards relative to the previous year. States may also set aside an additional 3% of district allocations to provide direct student services, as well as a 1% set-aside for state administration. What matters for this report’s purposes is that the patterns in allocations per formula child for different types of districts are similar to those for actual funding per formula child.
Formula Children
The counts and percentages of formula children used in the Title I formulas are determined by children who live in the geographic boundaries of the district, whether or not they are enrolled in public schools operated by the district. The definition includes children living in households with income below the poverty line (who account for the bulk of formula children by far), as well as children whose families participate in TANF, neglected and delinquent children living in state-run institutions, foster children, and children enrolled in Bureau of Indian Affairs schools.
Each of the four formulas considers either the district’s percentage or count of formula children (sometimes weighted) as a key input in calculating district allocations. A district’s formula child percentage is the number of formula children divided by the number of 5- to 17-year-old children who live in the district (multiplied by 100).
Adjusted State Per-Pupil Expenditure
The amount of Title I funds allocated to school districts per formula child is, for each formula, based on adjusted state per-pupil expenditure (SPPE). Adjusted SPPE is calculated as a ratio at the state level. Both the numerator (expenditures) and denominator (student count) are constructed as averages over a three-year period, with a lag. For example, the FY 2022 Title I allocations would be based on adjusted SPPE calculated with data from FY 2018, FY 2019, and FY 2020. Expenditures (the numerator) exclude major federal revenue sources, including Title I and funding for school meals. The denominator in adjusted SPPE (student count) is average daily attendance. The resulting ratio is then adjusted by multiplying it by a factor of 0.4 for most states; this factor is greater for the lowest-spending states and smaller for the highest-spending states.^{6}For Basic, Concentration, and Targeted Grants, high-spending states have their SPPE adjusted downward to a maximum of 120% of the national average (40% of 120% of the national average is 48% of the national average, as described in the law), and low-spending states get their adjusted SPPE bumped up to a minimum of 80% of the national average (40% of 80% of the national average is 32% of the national average, as described in the law). For EFIG state-level allocations, the floor is 34% of the national average, and the ceiling is 46% of the national average.
Expenditures depend on what types and quantities of goods and services school districts buy, and the prices of those goods and services. Although adjusted SPPE was included in the formula to account for differences in the price of educational inputs (primarily wages for staff) across places, it captures more than geographic variation in salaries—it also reflects the quantities of staff and other inputs states and school districts choose to fund. Overall, adjusted SPPE is negatively correlated with state-level formula child percentages. In other words, poorer states have lower per-pupil expenditure and thus, lower adjusted SPPE; all else equal, this yields lower Title I allocations in those states. However, because adjusted SPPE incorporates a floor and a ceiling,^{7}For Basic, Concentration, and Targeted Grants, high-spending states have their SPPE adjusted downward to a maximum of 120% of the national average (40% of 120% of the national average is 48% of the national average, as described in the law), and low-spending states get their adjusted SPPE bumped up to a minimum of 80% of the national average (40% of 80% of the national average is 32% of the national average, as described in the law). For EFIG state-level allocations, the floor is 34% of the national average, and the ceiling is 46% of the national average. the negative correlation between state formula child percentages and adjusted SPPE is reduced.
The EFIG formula uses two other metrics derived from education spending in addition to adjusted SPPE. The “Effort Factor” measures how high a state’s unadjusted SPPE is relative to its per capita income, as compared with the national average. The “Equity Factor” is a complicated measure of how much spending varies across school districts within each state. As discussed further below, even large changes in the Equity or Effort Factors typically would not change Title I allocations very much. Therefore, the actual incentive effects of EFIG are quite weak. For more information, see Title I’s Education Finance Incentive Grant Program Is Unlikely to Increase Effort and Equity in State Policy.
Putting It Together: Inputs and Rules by Formula
Table 1 summarizes the requirements for districts to receive each type of Title I grant (eligibility) and the factors that enter the calculation of the allocation amount for school districts under each of the four Title I formulas. For Basic, Concentration, and Targeted Grants, the allocations are calculated for each district, and a state’s allocation is simply the sum of the allocations for its districts. For EFIG, allocations are first made to states and then the state-level allocation is divided among districts according to the formula. Table 2 shows the percentage of all school districts eligible for each of the four grants and the percentage of formula children residing in those districts.
Table 1. Inputs and Rules for How the Four Title I Formulas Allocate Funding to School Districts
Basic Grant | Concentration Grant | Targeted Grant | Education Finance Incentive Grant^{a} | |
Eligibility^{b} | At least 10 formula children and at least 2% formula children | More than 6,500 formula children or at least 15% formula children | At least 10 formula children and at least 5% formula children | At least 10 formula children and at least 5% formula children |
Count of Formula-Eligible Children (Unweighted) | x | x | ||
Adjusted Version of State Per-pupil Expenditure | x | x | x | x |
Small State Minimum | x | x | x | x |
Hold Harmless | x | x | x | x |
Number or Percentage Weighted Count of Formula-Eligible Children (Nonlinear) | x | x | ||
State Equity Factor | Affects state- and district-level allocations | |||
State Effort Factor | Affects state-level allocations but not how those are distributed to districts | |||
Notes: |
Table 2. District Eligibility by Grant, FY 2021
Grant Type | Percentage of Districts Eligible | Percentage of Formula Children in Eligible Districts |
Basic | 95.0% | 99.9% |
Concentration | 46.4% | 76.3% |
Targeted | 87.9% | 98.2% |
EFIG | 87.9% | 98.2% |
Basic Grants
Nearly all school districts are eligible for the Basic Grant, which requires at least 10 formula children and a formula child percentage of at least 2% in the school district. In FY 2021, 95% of districts were eligible for the Basic Grant.^{8}Eligible districts can elect not to participate in Title I.
The Basic Grant formula authorizes eligible districts to receive an amount equal to 40% of the adjusted SPPE for each formula child. Because Title I is not fully funded, however, districts receive less. Fully funding the Basic Grant would have required Congress to appropriate about $44 billion to the Basic Grant alone for FY 2021, compared to the actual Basic Grant appropriation of about $6.4 billion (U.S. Department of Education 2021). None of the formulas have been fully funded since 1965, but the current under-funding of the Basic Grant is partially by design. Since 2001, Congress has directed all “new” funding for Title I to the Targeted Grant and EFIG formulas, holding nominal appropriations for Basic and Concentration Grants constant.
To illustrate how elements of the Basic Grant formula influence the allocation of funds, we show how the per–formula child Basic Grant allocation varies, first looking at state-level averages, then at the distribution across districts within a state.
Figure 2 shows the average Basic Grant allocation per formula child in each state in FY 2021. States that benefit from the small state minimum provisions are colored in gray; this explains why some states get such high average allocations per formula child. Vermont and Wyoming are clear outliers, but Alaska, the District of Columbia, Montana, New Hampshire, North Dakota, and South Dakota also benefited from the SSM for Basic Grants.^{9}States that are bound by the small state minimum vary by formula and over time. Although these states have high levels of funding per formula child, financing the small state minimum requirement does not divert a major share of the total funds appropriated for Basic Grants, because the states benefiting from this provision, by definition, have few formula children relative to the national total.
Figure 2. Average Basic Grant Allocations per Formula Child by State, FY 2021
The Basic Grant formula is designed to allocate roughly the same amount of funding per formula child to each district within a state, regardless of its formula child percentage. Figure 3 presents the same average Basic Grant allocation per formula child as in Figure 2 but with the formula child percentage on the horizontal axis. States with higher formula child percentages, i.e., poorer states, generally receive smaller Basic Grant allocations per formula child. This is for two reasons. First, states that benefit from the SSM (shown in gray) tend to have lower formula child percentages. In addition, the adjusted SPPE is negatively correlated with the state-level formula child percentage (poorer states spend less), and the formula sends larger allocations per formula child to states with higher adjusted SPPE.^{10}Appendix Table 1 shows the adjusted SPPE and the formula child share for each state, as well as information about whether the state benefits from SSM for each of the four formulas.
Figure 3. Formula Child Percentage vs. Basic Grant Allocation per Formula Child by State, FY 2021
These state-level factors—the SSM provisions and adjusted SPPE—explain most of the variation in average Basic Grant allocations per formula child between states. However, two districts in the same state with the same number of formula children, can also receive different Basic Grant allocations. That is because of the law’s hold harmless rules, which limit the amount a district’s total allocation can fall each year.^{11}Held harmless districts help explain why two states with identical adjusted SPPE and formula shares could receive different Basic Grant amounts per formula child; states where more districts (weighted by the number of formula children) are being held harmless will have larger Basic Grant allocations per formula child, all else equal.
As an example, Figure 4 shows the Basic Grant allocation per formula child received by each district in Pennsylvania on the vertical axis in relation to the formula child percentage for the district on the horizontal axis (recall that the formula child percentage is almost the same as the child poverty rate).
Figure 4. Basic Grant Allocations per Formula Child, Pennsylvania, FY 2021
The vast majority of districts in Pennsylvania are allocated $904 per formula child from the Basic Grant in FY 2021. The districts represented with gray dots in Figure 4 receive somewhat more; this is because they experienced recent declines in the number of formula children, so benefited from Title I’s hold harmless provisions.^{12}Districts could benefit from the hold harmless provisions even without experiencing absolute declines in the number of formula children (and therefore in their authorized amounts before ratable reduction). If a district’s authorized amount grows less quickly than those of other districts, and appropriations do not keep up with national growth, its allocation could be held harmless. For example, Lakeview School District (labeled in Figure 4) was allocated $1,147 per formula child from the Basic Grant. The number of formula children in the district declined substantially, from 312 for FY 2018 to 219 for FY 2021, as a result of declining child population and enrollment (which fell by about a quarter in the last 10 years).
To summarize, the Basic Grant is the most straightforward of the four Title I formulas, yet hold harmless and state minimum provisions and the use of adjusted SPPE create departures from a constant grant amount per formula child:
- Small state minimums: Districts in low-population states have larger grants per formula child than they otherwise would.
- Hold harmless provisions: Districts where the number of formula children has declined rapidly in recent years have larger grants per formula child than they otherwise would.
- Adjusted SPPE in the formula: Grants per formula child are higher in districts in states where average spending per pupil from state and local sources is higher, all else equal.
While these provisions create some variation in per–formula child grants, overall, the Basic Grant formula is designed to send roughly similar amounts per formula child to all districts regardless of how many or what percentage of children are Title I eligible. Over time, Congress added additional Title I formulas (with their own dedicated appropriations), with the goal of sending more Title I funding per formula child to districts with greater concentrations of poverty. The other three formulas, which target more money to districts with concentrations of poverty, as described below, share the features described above for the Basic Grant formula.
Concentration Grants
The first effort to direct more funds per formula child to districts with greater concentrations of poverty came with the Concentration Grant formula, which entered the law as part of the Education Amendments of 1974.
The idea that communities with concentrated poverty face particular challenges—and so need extra funding—is intuitive, but defining concentrated poverty and choosing the best way to direct additional funds is not necessarily straightforward (see “Why Target Funds to Places with Concentrated Poverty?”). Should concentration of poverty be measured at the school or district levels? Should it be based on the number of children living in poverty, or the percentage of children living in poverty?
Policymakers may wish to target additional funding to places with concentrated poverty for two broad reasons. First, concentrated poverty may be associated with smaller (per pupil) local tax bases and, therefore, these areas have difficulty raising sufficient funds for schools locally. If this is the concern, targeting school districts with high poverty rates makes sense because in most states, school districts, unlike individual public schools, bear substantial responsibility for raising revenue.^{13}There are important caveats to this reasoning: (1) in many states, state governments are more important sources of revenue for schools than local districts; (2) poverty is imperfectly correlated with property wealth, which typically is the relevant tax base for local revenue.
More importantly, concentrated poverty may be associated with higher costs of delivering an adequate education. For example, students who live in neighborhoods with concentrated poverty need additional academic, social, and emotional support to succeed in the classroom and graduate from high school. This concern points to a need to target additional funds to schools serving those students. However, Title I formulas determine allocations to districts, and while there are federal ranking and serving constraints on how districts can distribute Title I funds to schools, districts retain considerable discretion over distribution of Title I funds to the schools they serve (for more information, see “Every Student Succeeds Act Primer: Title I Funding for High Schools” (Alliance for Excellent Education 2017) and Title I of ESEA: Targeting Funds to High-Poverty Schools and Districts.
The Concentration Grant takes a hybrid approach to identifying districts with concentrations of poverty. Districts are eligible if they exceed a threshold for either the percentage or number of formula children. Thus, Concentration Grants function like Basic Grants but with stricter eligibility requirements: a district must have more than 6,500 or 15% formula children. Districts with large child populations can qualify to receive Concentration Grants with formula child percentages less than 15% by meeting the 6,500 formula child threshold. Nationally, about 180 districts have at least 6,500 formula children. Of these, about 80% meet the at-least-15% criterion as well; the rest qualify for Concentration Grants with formula child percentages below 15%.
Allowing districts to qualify for Concentration Grants based on the number of formula children even if the percentage of formula children is low may make sense if the goal is reaching students in schools with high concentrations of poverty. Schools with high formula child percentages in some large districts would not be able to access Concentration Grant funds if district-level formula child percentages alone determined eligibility. At the same time, allowing districts to qualify for additional funds based on counts of formula children without regard to formula child percentages preferences larger districts, all else equal (see “Tradeoffs of Allocating Funds Based on District Formula Child Percentages vs. Counts” for more information).
The extent to which high-poverty schools are located in high-poverty districts depends on how large districts are and how economically segregated districts are. Both of these vary considerably across states.^{14}While district boundaries can change over time, district size is in large part historically determined, with some states having school districts that coincide with city/town, county, or other jurisdictional boundaries and other states having more fragmented school districts.
For example, Maryland has 24 countywide school districts, while neighboring Pennsylvania has about 500 school districts of varying size. In both states, the distribution of the percentage of students who are free or reduced-price lunch eligible (FRPLE)^{15}Note that FRPLE is correlated with, but not the same as, the poverty rate. Students with incomes up to 185% of the poverty line are FRPLE, so FRPLE rates are higher than poverty rates. FRPLE is used in this example because data on poverty rates is not available at the school level. These calculations are based on data from the 2019–20 school year (Reardon et al. 2021). across schools overall is quite similar. However, the average high-FRPLE school (defined arbitrarily here as having FRPLE population above 75% of enrollment) is in a school district with a higher percentage of FRPLE students in Pennsylvania (about 78%) than in Maryland (67%). This is in large part because Maryland has large countywide school districts, leading to less between-district economic segregation.
If Title I funds were targeted to areas of concentrated poverty based solely on the district-level formula child percentage, schools with similar formula child percentages would, all else equal, get more Title I funds in smaller districts than larger ones. That is because each school matters more for the district average poverty rate when there are fewer schools in the district. Targeting extra Title I funding for concentrations of poverty based on the district-level formula child percentage alone would reward states like Pennsylvania with greater between-district economic segregation, while penalizing states like Maryland with more economic segregation within districts than between them.
Allowing districts to qualify for Title I funding based on the formula child count (rather than the formula child percentage) is one approach to direct more federal resources to large and economically diverse districts that do not have particularly high districtwide formula child percentages but do have high-poverty schools. District size varies across states; therefore, allocating funds based on counts or percentages prevents high-poverty schools in states with large districts from missing out on federal funds.
Each of the four Title I formulas other than the Basic Grant is designed with these tradeoffs in mind: districts can qualify for additional funding if they have high formula counts or high formula child percentages. This means that large districts often get larger grants per formula child than smaller districts with the same formula child percentage. This is horizontally inequitable at the district level. However, the alternative—allocating Title I by using only districts’ formula child percentages to account for concentrated poverty—could produce inequities at the school level. This is because funding for high-poverty schools would depend on the formula child percentage of their district, and schools with similar poverty rates could fare quite differently depending on whether they were located in a state more like Pennsylvania or one more like Maryland. More analysis of school-level data could shed light on this question, but policymakers will continue to face this tradeoff in light of the widely varying sizes and structures of school districts across states.
The Concentration Grant is a relatively blunt way to target funding to places with concentrations of poverty; districts simply are or are not eligible, and the bar for eligibility is set substantially higher than for the other three formulas. Among districts meeting the Concentration Grant eligibility requirements, funding is distributed just like the Basic Grant on a flat per–formula child basis that is a function of adjusted SPPE and subject to hold harmless and state minimum rules.^{16}The states receiving the small state minimum for Concentration Grants are Alaska, Montana, North Dakota, South Dakota, Vermont, and Wyoming. Just under one-half of districts (46%) are eligible for Concentration Grants, but three-quarters of formula children (76%) in the United States live in these districts.
The formulas discussed next—Targeted Grants and EFIG—are both more complex in their structure than Concentration Grants in ways that could permit more refined progressivity and targeting of funds to districts with high concentrations of poverty. However, most districts are eligible for some level of funding from Targeted Grants and EFIG, while many districts are ineligible for Concentration Grants and receive zero such funds. The districts that are ineligible for Concentration Grants free up money for eligible (and poorer) districts given a fixed budget for the program. Ultimately, the distribution of the Concentration Grant is the most progressive of the four types; this is clear from looking at data on district-level poverty and allocations (see Title I of ESEA: How the Formulas Benefit Different Types of School Districts) though not obvious from the formulas themselves.
Figure 5 shows the relationship between the per–formula child Concentration Grant and the formula child percentage for districts in Pennsylvania. Many districts are ineligible for Concentration Grants; all districts with zero Concentration Grants have formula child percentages less than 15%. On the other hand, some districts with formula child percentages below 15% receive funding from the Concentration Grant. There are two possible reasons for this. First, a district can qualify for a Concentration Grant if it has 6,500 formula children even if its formula child percentage is below 15%; no districts in Pennsylvania are in this category.^{17}Nationally, less than 0.5% of districts receiving Concentration Grants fall in this category. These districts account for about 5% of formula children nationally. Second, a district can benefit from hold harmless provisions that allow it to continue to receive Concentration Grant funding even when its number or percentage of formula children falls below the eligibility threshold. The Pennsylvania districts with formula child percentages less than 15% that receive Concentration Grant funding (the gray dots) had higher formula child percentages in the recent past.
Figure 5. Concentration Grant Allocations per Formula Child, Pennsylvania, FY 2021
As Figure 5 demonstrates, the targeting in the Concentration Grant formula operates solely through eligibility. Once districts meet the eligibility criteria, the formula does not distinguish among eligible districts that have higher or lower formula child percentages. Most Pennsylvania districts with a formula child percentage above 15% received the same amount, $230 per formula child. As with the Basic Grant, hold harmless rules mean that some districts receive larger allocations per formula child (the gray dots above $230 on the vertical axis). Hold harmless rules also allow districts no longer eligible to continue receiving Concentration Grant funds, which range in value depending on how long they have been held harmless (the gray dots where the formula child percentage is less than 15%).
Targeted Grants
Targeted grants and EFIG were first introduced into ESEA under the Improving America’s Schools Act in 1994 (IASA) (Snyder et al. 2019). The House Committee on Education and Labor proposed creating the Targeted Grant in addition to the Basic and Concentration Grants, while the Senate Committee on Labor and Human Resources proposed creating EFIG to replace all other Title I grants. Ultimately, Basic and Concentration Grants were retained, and both new grants were added. However, even though all four formulas were authorized into law, funds were not appropriated for either of the two new grant programs until after the passage of NCLB in 2002 (Ibid.). Since NCLB’s enactment, Congress has directed all new Title I funding to be split equally between the Targeted Grants and EFIG and has kept funding for the Basic and Concentration Grants fixed in nominal terms.
Recall that while eligibility for Concentration Grants depends on a district’s number or percentage of formula children, the amount of the Concentration Grant per formula child in eligible districts does not.^{18}In practice, Concentration Grants are quite progressive because just over one-half of districts are ineligible. Across all districts, the amount of Concentration Grant per formula child is positively correlated with district poverty rates. By contrast, the amount of Targeted Grant funding a district receives per formula child varies depending on the number or percentage of formula children living in its boundaries. To be eligible for Targeted Grants, districts need to meet minimal requirements of having (1) at least 10 formula children and (2) at least 5% formula children. Although these eligibility requirements are similar to those for the Basic Grant, the increased progressivity of Targeted Grants comes through the weighting scheme (described below) rather than the eligibility rules; 88% of districts are eligible for Targeted Grants, and 98% of formula children live in a district eligible for Targeted Grants.
The Targeted Grant formula combines key features of Basic and Concentration Grants by offering relatively uniform SPPE-adjusted grants per formula child (like Basic), with additional funds for districts with higher numbers or percentages of formula children (like Concentration). The key feature of the Targeted Grant formula is its weighting scheme, whereby districts with larger numbers or higher percentages of formula children receive more funding per formula child. Rather than each formula child receiving the same weight, as with the Basic and Concentration Grant formulas, the Targeted Grant formula sets out a series of brackets based on the number or percentage of formula children in the district that weight formula children in higher brackets more.
The law defines two sets of brackets and weights for the Targeted Grant. One is based on the percentage of formula children (percentage weighting) and the other on the number of formula children (number weighting) in the district. The U.S. Department of Education calculates both a percentage-weighted and number-weighted count for each district and uses whichever is greater to determine authorized Targeted Grant amounts. See “How Number and Percentage Weighting Work: An Example,” to learn more about how the weighted child count is produced.
The use of both number-weighted and percentage-weighted child counts may advantage certain kinds of districts. Table 3 presents the Targeted Grant brackets and weights and illustrates how the weighted formula count is calculated for the Targeted Grant for a hypothetical district with 5,000 formula count children and a population of 20,000 total school-aged children.
Table 3. Applying Number and Percentage weighting to calculate Weighted Formula Children for A Targeted Grant For A Distrcit with 5,000 Formula Children and 20,000 Total Children
Number Weighting | |||||
From the law | Example district | ||||
Minimum | Maximum | Weight | Unweighted count in range | Weighted count in range | |
1 | 691 | 1 | 691 | 691 | |
692 | 2,262 | 1.5 | 1,571 | 2,357 | |
2,263 | 7,851 | 2 | 2,738 | 5,476 | |
7,852 | 35,514 | 2.5 | |||
35,515 | 3 | ||||
Sum | 5,000 | 8,524 | |||
Percentage Weighting | |||||
From the law | Example district | ||||
Minimum % | Maximum % | Weight | % of all children in range | Unweighted count in range | Weighted count in range |
0 | 15.58 | 1 | 15.58 | 3,116 | 3,116 |
15.58 | 22.11 | 1.75 | 6.53 | 1,306 | 2,285.5 |
30.16 | 38.24 | 2.5 | |||
30.16 | 38.24 | 3.25 | |||
38,24 | 4 | ||||
Sum | 25 | 5,000 | 6,846.5 |
First, we calculate weighted formula children using the number weighting scheme. The first 691 formula children fall into the first bracket and receive a weight of 1.0, so their weighted count is 691. The 1.5 weighting factor applies to the formula children from 692 to 2,262. These 1,571 unweighted formula children count as 2,356.5 weighted formula children. The 2.0 weighting factor is applied to the remaining 2,738 unweighted formula children, yielding an additional 5,476 weighted eligible children. The 2.5 and 3.0 weighting factors would not apply for this district, because it has fewer than 7,852 formula children. Summing the number-weighted counts yields 8,523.5 weighted formula children.
Next, we calculate the weighted number of formula children applying the percentage weighting scheme. The first 15.58% of all children in the district who are formula children (.1558 × 20,000 = 3,116) are weighted by 1.0. An additional 6.53% of formula children (1,306 unweighted formula children) fall within the next range and are weighted by 1.75, yielding 1,547 additional weighted formula children. The remaining 2.89% of formula children (578 unweighted formula children) fall entirely within the next range and are weighted by 2.5, or 1,445 additional weighted formula children. With 25% of the district’s formula-eligible children, the 3.25 and 4.0 weighting factors are not applicable. The sum of the weighted formula children under the percentage weighting scheme, 6,846.5, is less than the 8,523.5 weighted count produced through number weighting.
Once the weighted count of eligible children is determined, i.e., using the larger of the weighted counts produced by these two methods, Targeted Grants are allocated similarly to Basic and Concentration Grants based on adjusted SPPE and ratably reduced to match the total appropriation with adjustments for state minimum^{19}States receiving the small state minimum for Targeted Grants are Alaska, Delaware, the District of Columbia, Idaho, Maine, Montana, New Hampshire, North Dakota, Rhode Island, South Dakota, Vermont, and Wyoming. and hold harmless provisions. Whether a district benefits from number or percentage weighting depends on its total population of 5- to 17-year-olds and the formula child percentage.
Figure 6 illustrates this relationship. The horizontal axis captures the formula child percentage in the district^{20}Over 98% of districts have formula child shares below 40%, so the figure covers the relevant range. Likewise, about 1% of districts have child populations greater than 50,000, and they all benefit from number weighting. and the vertical axis measures the district’s school-aged population. Whether a district generates a higher weighted count using percentage or number weighting depends on these two factors.^{21}Although the formula does not reference school-aged population specifically, for a given formula child share, differences in the school-aged population correspond to differences in the formula child count, which enters the formulas. Districts in the dark purple region do not qualify for Targeted Grants because they have a formula child percentage less than 5% and/or fewer than 10 formula children. Districts in the magenta region do better with number weighting, and districts in the green region do better with percentage weighting. For districts in the blue region, number and percentage weighting yield the same weighted formula count.
Figure 6. Number vs. Percentage Weighting in the Targeted Grant as a Function
of District School-Aged Population and Formula Share
Weighting Scheme that Yields Max Weight Count
This figure illustrates three key points:
- Holding constant the district’s formula child percentage, larger districts (above some threshold school-aged population) generally benefit from number weighting.^{22}Percentage weighting would be preferred for districts with formula child shares above 77% regardless of population, but in practice, very few districts fall in this range (only two in the most recent data).
- Holding constant the district’s school-aged population, districts with formula child percentages above some threshold will benefit from percentage weighting.
- Districts with formula child percentages below roughly 16% never benefit from percentage weighting. For districts with formula child percentages between 5% and 16%, the two methods either yield the same weighted formula count or, for districts with larger populations, number weighting is preferred.
Nationally, about 10% of districts arrive at a higher weighted count using the number weighting scheme, 39% benefit from percentage weighting, and for 39% of districts, the two methods yield the same weighted formula count. The remaining 12% of districts are not eligible for Targeted Grants. Even though only 10% of districts rely on number weighting, these districts are large and serve about 65% of unweighted formula children. About 23% of formula children live in districts that use percentage weighting, 10% of formula children live in districts where number and percentage weighting produce the same weighted counts, and just under 2% live in districts that are not eligible for the Targeted Grant.^{23}All of the figures in this paragraph are based on analysis of FY 2021 allocations.
Figure 7 shows Targeted Grant allocations per unweighted formula child for districts in Pennsylvania versus the formula child percentage. Districts in magenta use number weighting, districts in green use percentage weighting, and for districts in blue, both methods produce the same outcome. Districts that benefit from hold harmless rules are marked in a darker shade of each respective color. The blue and green circles trace out the relationship between the formula child percentage and the Targeted Grant per formula child for districts that are using percentage weighting. Districts with formula percentages below 5% are not eligible, so the allocations are zero; for those between 5% and 16%, all formula children receive a weight of 1, and districts were allocated about $357 per formula child. As the formula child percentage increases, districts receive larger allocations per formula child.
Figure 7. Targeted Grant Allocations per Formula Child, Pennsylvania, FY 2021
The magenta dots represent districts that benefit from number weighting because they have relatively large school-aged populations. For example, North Penn School District, labeled in Figure 7, has a formula child percentage around 6% and received $408 per formula child (instead of $357). This is because the district has a school-aged population of 15,731, whereas other districts with similar formula child percentages have school-aged populations between 2,000 and 10,000. Very large districts benefit the most from number weighting because a larger share of their formula children get the highest weight of 3. Philadelphia City School District, which has a child population of about 240,000 and is also labeled in Figure 7, was allocated $968 per formula child, compared to $600 to $670 per formula child for other districts with similar formula child percentages whose grants are calculated using percentage weighting.^{24}These numbers represent allocations per formula child living in Philadelphia City School District and may differ from the award per formula child that the district actually received. One reason for this discrepancy is because some of this allocation is directed to charter schools serving formula children who live within the school district boundaries, and Philadelphia has a substantial charter sector. The method of allocating Title I funds to charter schools is complicated and varies by state, and we do not observe the final awards.
Similarly to Basic and Concentration Grants, some districts receive higher Targeted Grant allocations per formula child than they otherwise would because of hold harmless provisions (the circles in the darker shades or magenta, green, and blue on the figure). Smaller districts are more likely to experience a large proportional decline in formula children over a short period, so districts with lower enrollments are most likely to benefit from hold harmless provisions.
Aside from Philadelphia and a few other cities, school districts in Pennsylvania are relatively small; the state has about 500 school districts, with a median child population around 2,300. In states with larger districts, the relationship between allocations per formula child and the formula child percentage depicted in Figure 7 for Pennsylvania can look quite different. For example, Maryland has 24 countywide districts, with a median child population of about 18,600 and six districts with child populations above 50,000, including its highest-poverty district, Baltimore City Public Schools.
Figure 8 shows Targeted Grant allocations per unweighted formula child versus the formula child percentage for districts in Maryland. The relationship between formula child percentage and the allocation per formula child is weak; there is no clear line of districts in the Maryland plot as there is for Pennsylvania because most districts use number weighting (in magenta). Smaller districts with high poverty rates that use percentage weighting (in green), like Dorchester County Public Schools, received smaller Targeted Grant allocations per formula child.
Figure 8. Targeted Grant Allocations per Formula Child, Maryland, FY 2021
As discussed in “Tradeoffs of Allocating Funds Based on District Formula Child Percentages vs. Counts,” the decision to target funding based on numbers versus percentages of formula children relates to important tradeoffs. Typically, in states that have larger school districts, high-poverty schools are less likely to be in high-poverty districts, so they would not benefit as much under percentage weighting. Similarly, percentage weighting rewards economic segregation between districts. On the other hand, number weighting directs disproportionate funding to large districts with low or moderate formula child percentages. In the context of fixed appropriations, this funding comes at the expense of smaller districts with higher formula percentages.
Figure 9 shows how the average Targeted Grant allocation per formula child at the state level relates to the state-level formula child percentage; states that benefit from the small state minimum allocation are in gray. As with the Basic Grant, some states have much larger allocations per formula child because of the small state minimum; recall that does not redirect substantial funds in total, because those states have small numbers of (weighted) formula children by definition.
States that spend more on K–12 schools, i.e., those with higher adjusted SPPE, have larger Targeted Grants per formula child on average, but the presence of districts with large numbers or percentages of formula children also influences each state’s average grant. As Figures 2 and 3 demonstrate for the Basic Grant, several states are clustered near the lowest allocation per formula child because they have the minimum adjusted SPPE. Likewise, many states with the maximum adjusted SPPE are clustered with similar allocations per formula child. For the Targeted Grant, Figure 9 shows how the average allocation per formula child varies more among states with the minimum or maximum adjusted SPPE depending on whether the districts in that state have high numbers or percentages of formula children. Setting aside the states in gray that benefit from the small state minimum, the relationship between a state’s average Targeted Grant per formula child and the state’s formula count percentage is essentially uncorrelated, whereas it is negatively correlated for the Basic Grant.
Figure 9. Average Targeted Allocation per Formula Child vs. Formula Child Percentage by State, FY 2021
States with many large districts also receive larger average Targeted Grant allocations per formula child. For example, Maryland and Massachusetts have similar formula child percentages and receive similar Basic Grant allocations per formula child because they are both at the maximum adjusted SPPE. But average Targeted Grant allocations per formula child are much higher in Maryland than Massachusetts because Maryland has large, countywide school districts that benefit substantially from number weighting, while Massachusetts has many smaller districts that do not.
Education Finance Incentive Grants (EFIG)
Like Targeted Grants, Education Finance Incentive Grants (EFIG) were first introduced into law with the passage of IASA, but funds were not appropriated for them prior to the passage of NCLB (Snyder et al. 2019). While all Title I funds can serve as an incentive for states and districts to comply with the Title I program requirements (e.g., administering statewide assessments, reporting on state and district report cards, and operating state accountability systems), EFIG aims to create incentives for states to increase their education spending relative to state income (through the Effort Factor) and change their school finance systems to reduce a specific measure of variance (through the Equity Factor).^{25}The same logic would suggest that the use of adjusted SPPE in all four formulas provides an incentive for greater state and local spending on K–12 education, but the use of SPPE traditionally has been framed as a cost adjustment rather than an incentive. Also, the adjusted SPPE in the other three grant formulas is used without reference to state-level income.
The method for allocating EFIG funding differs from the other three Title I formulas in that it uses a two-step approach to determine district allocations: (1) funds are allocated to states based on state-level factors, and then (2) the formula dictates how each state’s allocation is divided among eligible school districts within the state. The EFIG formula directs more funds to states with greater effort and equity (measured in a specific way, described below), but the impact of these incentives is limited both by the amount of funding at stake and the limited range of the measures of effort and equity. Within-state distribution of EFIG funds to districts depends on brackets of formula child counts or percentages and associated weights, similar to Targeted Grants. For EFIG, however, the weighting scheme also depends on the state’s Equity Factor.
EFIG Allocations to States
The EFIG formula allocating funds to states is meant to reward states with higher spending on education per pupil relative to state per-capita income (PCI) (the Effort Factor) and with a more equitable distribution of funding across districts within the state (the Equity Factor). In this section, we describe the first step, in which state-level EFIG allocations are determined and how changes in the inputs to the formula would change states’ EFIG allocations.
When EFIG funds are allocated to states, the unweighted number of formula children in the state is multiplied by its Effort Factor and Equity Factor, and (as with the other formulas) by adjusted SPPE.^{26}The SPPE used for EFIG is slightly different from that used in the other formulas; it is bounded by 34 to 46% of the national average, rather than 32 to 48%. This means that states that do better on one or both of these unique factors get more EFIG funding per formula child. In other words:
The state allotments are then adjusted through ratable reduction to meet the amount appropriated each year, while holding districts harmless and meeting small state minimum requirements.
The Equity and Effort Factors appear to have equal importance in the equation above. However, as discussed below, the Effort Factor ranges from 0.95 to 1.05, while the Equity Factor theoretically may range from 1.0 to 1.3—and, in practice, ranges from about 1.05 to 1.30. This means that the Equity Factor plays a larger role in determining state-level allocations than the Effort Factor, though as we will show, both have quite small impacts on Title I allocations overall.
Figure 10 shows the relationship between a state’s formula child percentage and its EFIG allocation per formula child. The states in gray are subject to EFIG’s small state minimum; because of their low child populations, their relatively higher allocations have limited repercussions for other states. The negative correlation in Figure 10 is similar to that for the Basic Grant, depicted in Figure 3. In both cases, the correlation is negative because states with higher formula child percentages (i.e., poorer states) tend to spend less on K–12 schools; this means all else equal, they have lower adjusted SPPE values, and consequently, lower Title I allocations per formula child.
Figure 10. Average EFIG Allocation per Formula Child vs. Formula Child Percentage by State, FY 2021
Differences at the state level between allocations for the Basic Grants and EFIG per formula child occur because of the use of the Effort and Equity Factors in EFIG’s two-step allocation process. The overall levels of funding for the two also differ, depending on how much Congress appropriates to each formula.
Figure 11 shows the state-level distribution of Basic Grant funds per formula child on the left, and EFIG funds on the right. The differences in the distributions of the data (i.e., when states are no longer listed in rank order from highest to lowest on the right-hand panel) are due to the Effort and Equity Factors in the EFIG formula and differences in which states qualify for the small state minimum. The differences in the levels, or different scales on the horizontal axes, is because of differences in total appropriations for the two formulas. The order of the states is the same in both panels; states are sorted by average Basic Grant allocation per formula child.
Figure 11. Basic vs. EFIG Allocation per Formula Child, FY 2021
As with the Basic Grant, the small state minimum (states with gray bars) is the reason for the highest allocations per formula child under EFIG. The small state minimum is determined separately for each formula, so some states are eligible for the minimum under EFIG but not the Basic Grant. The extent to which the state-level distributions between the Basic Grant and EFIG are similar reveals just how limited the joint impact of the Equity and Effort Factors are in determining state-level allocations.
The most noticeable differences come from states like Illinois and Pennsylvania, which receive a smaller EFIG allocation per formula child than their Basic Grant allocations might suggest. These states have relatively low Equity Factors (indeed, Illinois is an outlier and has the lowest value of any state), but they both have high Effort Factors, somewhat offsetting their low Equity Factors. These factors are discussed next, and their values for each state are listed in Appendix Table 1.
The Effort Factor
The Effort Factor captures the extent to which the average state per-pupil expenditure (SPPE) for schools, compared to per-capita income (PCI), is higher or lower than the average for the United States overall.^{27}The SPPE measure excludes spending from certain federal funding and is not capped at a minimum and maximum value as above. The Effort Factor uses three-year averages in both the numerator and denominator, but that is omitted here for simplicity.
States that have a ratio of SPPE to PCI that is higher than the national average will have an Effort Factor greater than 1. States with a lower-than-average ratio of SPPE to PCI will have an Effort Factor less than 1. Roughly, this means that states that have high education spending relative to average income score higher on effort. The Effort Factor is capped at 0.95 and 1.05, which limits the impact on state EFIG allocations, and by extension, the power of the incentive.
The Effort Factor depends on average SPPE from nonfederal sources in the state; whether that funding comes from state or local sources does not matter. Yet the incentive realistically could only matter for state policymakers. Any one district’s revenue efforts, with few exceptions, will not meaningfully impact the average SPPE for the whole state. Additionally, the Effort Factor influences the EFIG allocation to the state overall, not just to the districts that contributed to the higher average SPPE by increasing funding for schools from local sources.
To illustrate how the fiscal incentive in the Effort Factor works, we describe how an increase in combined state and local funding for schools would have affected Mississippi’s EFIG allocation.^{28}The numbers we calculated here may be slightly different from those produced by the U.S. Department of Education because of revisions to data or other discrepancies in data sources; these calculations are designed to demonstrate how the incentives in EFIG operate. We use data from FY 2018 for this illustration. Mississippi’s Effort Factor was 0.971, and its districts received about $52 million in EFIG funding. State and local spending in Mississippi was about $4 billion per year for the three years that are averaged for the purposes of calculating the Effort Factor. If annual combined state and local spending in the state had been $200 million higher in each of those three years, that would have increased Mississippi’s Effort Factor to 1.019, which would have increased its EFIG allocation by about $2.5 million. That is, for each additional dollar Mississippi spent, it would get a match of 1.3 cents in additional EFIG money. Further, the additional federal money would be restricted; it must be distributed to districts and spent according to Title I rules. The amount of additional EFIG funding that an increase in state and local spending would produce is also unpredictable and would be experienced with a significant lag.^{29}The amount of additional EFIG funding that an increase in state and local spending would produce also depends on how the change affects the state’s Equity Factor, how much Congress allocates to the program, and what other states are doing since the national average SPPE and PCI enter the formula for the Effort Factor. In addition, the formula uses three-year averages, and the data is available with a lag, so the full increase in EFIG funding would not be felt for at least five years, making it difficult for a state policymaker to take political credit for the additional funding.
For most states, the financial incentive to increase average spending is even weaker because of how the Effort Factor is capped. For states with uncapped Effort Factors less than 0.95 or more than 1.05, the Effort Factor used in the formula is 0.95 and 1.05, respectively. States that are well below or above the cap would have to increase or decrease their average spending substantially to change their EFIG allocation. For example, Idaho had an uncapped Effort Factor of about 0.76. For Idaho, even a 25% increase in spending would not have increased its EFIG allocation, since it would only bring its uncapped Effort Factor to the minimum of 0.95. Only after achieving that increase would Idaho begin to get the small implicit match described for Mississippi above, and the amount would depend on several other factors, including spending and per-capita income in other states.
Figure 12 shows the distribution of states by their uncapped Effort Factor for FY 2020 (the most recent year for which there is relevant data; the capped Equity Factor for FY 2021 is listed in Appendix Table 2). Only 10 states were in the incentivized range for the Effort Factor, meaning additional state and local spending on education would have yielded very small or uncertain increases in EFIG funding as in the Mississippi example. Another 10 states had uncapped Effort Factors within 0.05 of the minimum or maximum, so could have entered the incentivized range with a 5% change in spending. The other 30 states had uncapped Effort Factors quite far from the incentivized range and would need to make large changes in state and local spending before EFIG allocations were affected at all.
Figure 12. Distribution of States by Uncapped EFIG Effort Factor, FY 2020
Altogether, the incentives to increase state and local spending on education to receive additional EFIG funding as a result of the Effort Factor are extraordinarily weak and hard to understand.
The Equity Factor
Determining whether the distribution of school spending across districts in a state is “equitable” is not straightforward, as there are both different conceptions of equity and different ways to measure it. One common approach is to use a measure of inequality or dispersion, which captures the extent to which per-pupil spending varies across districts in the same state. However, the fact that not all districts spend the same amount per pupil does not necessarily mean that higher-poverty districts are losing out. Inequality or dispersion measures do not take account of the characteristics of districts with higher or lower spending; therefore, these measures do not distinguish between spending inequality that is driven by higher spending among low-poverty districts versus spending inequality that is driven by higher spending among high-poverty districts. The EFIG Equity Factor is derived from a weighted coefficient of variation of per-pupil current expenditure, an inequality/dispersion measure.^{30}A typical coefficient of variation captures how much the data is dispersed, as opposed to all having the same value (in this case, for district-level spending per pupil within a state). The coefficient of variation used in the Equity Factor weights formula children additionally (a nonformula child counts as 1.0, while a formula child counts as 1.4) in two ways. First, the denominator in calculating per-pupil expenditure is 0.4 × the number of formula + enrollment. This makes a district with a higher formula child percentage have lower weighted per-pupil spending for purposes of the calculation. Additionally, districts are weighted by 0.4 × the number of formula children + enrollment in calculating the coefficient of variation. This measure is more sensitive to variance generated by districts with more formula children, but it is still a measure of variance rather than progressivity. Districts with enrollment less than 200 are excluded.
The U.S. Department of Education defines the Equity Factor as 1.3 minus this variance measure in producing the data for allocating Title I. We follow that convention in this report to match how the allocations are produced. This definition is also more intuitive than simply calling the Equity Factor a variance measure, because lower variance generates higher Equity Factor values.^{31}Different NCES publications take different approaches, referring to the Equity Factor as the variance measure, or as 1.3 minus the variance measure. This likely stems from the law, which refers to this coefficient of variation itself as the Equity Factor, which would mean states with higher variance in funding have lower Equity Factors. Sonnenberg notes, “See section 1125A(3)(b)(3)(B). Note that there is a typo in this section: the legislation says the Equity Factor (when it means the coefficient of variation) for certain defined states ‘shall not be greater than 0.10.’ Were the Equity Factor and not the coefficient of variation set at 0.10, the EFIG formula would essentially eliminate these states from the allocation process” (2016). The Equity Factors for several states deviate from this formula as set out in federal regulations.^{32}Sonnenberg notes an exception to setting the Equity Factor equal to 1.3 minus the coefficient of variation: “the coefficient of variation for states that (a) meet the disparity standard described in section 222.162 of title 34, Code of Federal Regulations or (b) have only one LEA (e.g., Hawaii and the District of Columbia) shall not be greater than 0.10” (2016, 9). Sonnenberg also notes, “The Equity Factor is fixed by legislation for some states: i. The Equity Factor is fixed at 1.2 for Alaska, Louisiana, and New Mexico. ii. The Equity Factor is fixed at 1.3 for the District of Columbia, Hawaii, and Puerto Rico” (2016, 34).
In states with fewer and larger districts, there will typically be more variance across schools within districts—and less variance between districts—than in states with more and smaller districts. To understand this intuition, think of a large county-level district as an average of many small town-level districts. Much of the variation across the towns will be washed out in county-level data. Figure 13 shows that state Equity Factors are positively correlated with average district size (as measured by enrollment) in the state. States with larger districts also tend to have higher Equity Factors, even though average district size is largely historically determined, rather than a reflection of policymakers’ current actions.
Figure 13. State EFIG Equity Factor vs. Average District Enrollment, FY 2021
In contrast with inequality/dispersion measures, another approach to quantifying within-state equity is to measure the progressivity (or regressivity) of school spending. This approach considers whether higher-poverty districts tend to spend more or less, on average, than lower-poverty districts. States where per-pupil spending is higher in high-poverty districts are said to have a progressive distribution of per-pupil spending. The Urban Institute finds that in most states, per-pupil spending is either flat (unrelated to poverty) or progressive (higher spending for students living in poverty, on average) (Urban Institute 2017). In states where spending is already flat or progressive, an increase in progressivity—which, arguably, increases “equity”—will register as an increase in inequality or dispersion, which may decrease “equity” on measures designed with that purpose in mind.
Figure 14 shows how one measure of progressivity—the difference in per-pupil state and local revenue experienced by students in poverty versus other students^{33}This measure is equal to the average per-pupil state and local revenue, weighted by poor students, less the average per-pupil state and local revenue, weighted by non-poor students —is unrelated to the state’s Equity Factor in EFIG. Consider New York and Ohio, where state and local revenue per pupil in the average poor student’s district is more than $800 per pupil higher than in the average non-poor student’s district. These states have more progressive allocations of state and local funds by this measure than all states but Alaska. Nonetheless, both New York and Ohio are below average according to the EFIG Equity Factor (see Appendix Table 2 for a listing of the Equity Factor and the progressivity measure shown in Figure 14.)
Figure 14. State EFIG Equity Factor vs. Difference in Per-Pupil State and Local Revenue of Districts Attended by Poor vs. Non-Poor Students
How changes in spending patterns across districts in a state influence a state’s Equity Factor is even more opaque than for the Effort Factor because the formula to determine it is more complicated. To explore this, we simulated a scenario for this report where state and local spending was increased by $4,000 per formula child—with no increase for other children—in all districts.^{34}For simplicity, we use a single year of data from 2018–19, the most recent available, rather than a three-year average, to demonstrate this point. Such a change would be a clear move toward greater equity—at considerable expense. Figure 15 shows the distribution of the simulated percent change in the Equity Factor associated with this hypothetical change, i.e., the percent change in EFIG funding the state would have experienced if state and local spending had been higher by $4,000 per formula child. This move toward a substantially more equitable distribution of spending would produce very small—and sometimes negative—changes in the Equity Factor and therefore to total EFIG allocations to states.
Figure 15. Simulated Percent Change in Equity Factor for $4,000 Increase in State and Local Spending per Formula Child
In Connecticut, for example, increasing current spending by $4,000 per formula child would increase its simulated Equity Factor from 1.154 to 1.166.^{35}By using a single year of data to illustrate the point, the Equity Factor does not correspond to Connecticut’s actual Equity Factor that was actually used in allocations in a specific year. As a result, Connecticut would receive a 1.1% increase in its EFIG allocation.^{36}Because this would also cause an increase in average per-pupil current expenditure, this change could increase the Effort Factor, which interacts with the Equity Factor in the formula. Spending in Connecticut is already high enough to put the state well above the 1.05 maximum for the Effort Factor, so that is irrelevant in this case. Even in states that are in the uncapped zone for the Effort Factor, fairly large changes in spending typically have small effects on both Factors, so the interaction is also small. Changes in state EFIG allocations depend not only on changes in their own authorized amounts, but they also depend on changes in the amount authorized for all other states and the amount appropriated by Congress.^{37}This principle applies to all the grant formulas and makes it impossible for states and districts to understand changes in allocations based solely on changes in their own data. EFIG is equivalent to just 0.3% of total revenue from state and local sources in Connecticut—less than one-half of a percentage point—so this 1.1% increase in its EFIG allocation would represent a 0.0032% increase in the state’s total education revenue. In short, Connecticut would spend an additional $278 million in state and local funding to receive an additional $364,000 in EFIG funds, corresponding to a match of a fraction of a cent (0.13 of a cent) to the dollar. This implicit match rate is low across all states and for many, this increase in progressivity would reduce their EFIG allocations (the negative values in Figure 15).
We also note that designing a policy that increases funding in this way may not be straightforward, depending on the pre-existing state finance program, because local school districts could respond to changes in state aid. In addition, the formulas use three-year averages, and data availability lags several years. This means that a change in funding this year will take more than five years to translate fully to (very small and uncertain) changes in EFIG funding, making the incentives even more opaque.
EFIG Within-State Allocations to School Districts
Both the Effort and Equity Factors determine EFIG allocations to states; the Equity Factor (but not the Effort Factor) is also used to determine how state EFIG allocations are spread across eligible school districts (i.e., those with at least 10 formula children and formula child percentages of at least 5%, the same as the Targeted Grant) within states. In states with lower Equity Factors, the formula directs a larger share of a state’s EFIG allocation to its higher formula child (with number or percentage weighting) districts, relative to lower formula child districts in the same state. The idea is that the allocation of EFIG should be more progressive in states where the allocation of state and local funding is less progressive. The approach is similar to the brackets and weights used in the Targeted Grant formula, i.e., number-weighted and percentage-weighted formula child counts are calculated, and the maximum of the two determines the district’s allocation. The formula child brackets (by count and percentage) are the same for EFIG as for Targeted Grants. With EFIG, however, a state’s weighted coefficient of variation (WCV) determines which weight is applied to a given bracket. As mentioned earlier, the Equity Factor is 1.3 minus the WCV, so the WCV and Equity Factor move in opposite directions. There are three sets of weights, as summarized in Table 4 below.
Table 4. Weighting Eligibility Counts for EFIG
Number Weighting | ||||
Weight if state WCV is: | ||||
Minimum | Maximum | <0.1 | ≥0.1 & <0.2 | 0.2+ |
1 | 691 | 1 | 1 | 1 |
692 | 2,262 | 1.5 | 1.5 | 2 |
2,263 | 7,851 | 2 | 2.25 | 3 |
7,852 | 35,514 | 2.5 | 3.375 | 4.5 |
35,515 | 3 | 4.5 | 6 | |
Percentage Weighting | ||||
Weight if state WCV is: | ||||
Minimum % | Maximum % | <0.1 | ≥0.1 & <0.2 | 0.2+ |
0 | 15.58 | 1 | 1 | 1 |
15.58 | 22.11 | 1.75 | 1.5 | 2 |
22.11 | 30.16 | 2.5 | 3 | 4 |
30.16 | 38.24 | 3.25 | 4.5 | 6 |
38,24 | 4 | 6 | 8 |
The first set of weights applies to districts in states deemed most equitable, with WCVs less than 0.1; these are the same weights and brackets as those used to determine Targeted Grants. The second set of weights is more redistributive than the first because it applies to districts in states whose WCVs are greater than or equal to 0.1 and less than 0.2. The most redistributive is the third set of weights, which applies to districts in states with WCVs of 0.2 or more. For example, the highest bracket in the number-weighted schedule weights each formula child in excess of 35,514 by 3.0 in the states deemed most equitable (according to the Equity Factor metric) but by 6.0 in the least equitable states.
Figure 16 shows the within-state distribution of district-level EFIG allocations per formula child versus the formula child percentage in Pennsylvania.
Figure 16. EFIG Allocations per Formula Child, Pennsylvania, FY 2021
This figure looks similar to that of the Targeted Grant (Figure 7). Pennsylvania has an Equity Factor of 1.1043, meaning its within-state EFIG allocations are determined by the middle set of brackets and weights. The precise brackets and weights are, therefore, different from those used for the state’s Targeted Grant allocations, but the overall pattern is similar. Hold harmless provisions (districts with gray dots) and number weighting play the same role in explaining the pattern of EFIG allocations depicted above as they do for Targeted Grants, but for simplicity, we do not indicate which districts use number weighting versus percentage weighting on the figures showing EFIC allocations.
Unlike Pennsylvania, in states where districts tend to be larger, most districts will use number weighting. Thus, the relationship between district formula child percentage and EFIG allocation per formula child will be weaker, just as it is for Targeted Grants.
Figures 17 and 18 show how district-level Targeted Grant and EFIG allocations differ for Illinois, which has the lowest Equity Factor, and Washington, which has a relatively high Equity Factor. The differences in the levels of the two allocations, as well as their distributions, are informative. In Illinois, the average EFIG allocation is lower than the average Targeted Grant allocation; in Washington, the reverse is true. State-level differences in Targeted Grant and EFIG allocations come from the Effort and Equity Factors (Illinois was rewarded for effort and penalized for equity; Washington was penalized for effort and rewarded for equity), as well as the extent to which formula children are concentrated in districts within the state. The state-level Targeted Grant allocation is the sum of district-level allocations (which depend on weighted formula children), so states with more districts that have high numbers or percentages of formula children will receive more Targeted Grant funding than EFIG funding, all else equal.
Figure 17. EFIG and Targeted Grant Allocations per Formula Child, Illinois, FY 2021