Is School Funding Fair? A National Report Card Technical Report Data and Methods for Estimating Indicators Bruce Baker Rutgers University Danielle Farrie Education Law Center

Data Table 1 provides a summary of the data sources and availability for our indicators. Most data sources used in the analysis are either U.S. Census sources or National Center for Education Statistics Sources and in most cases the primary sampling unit is the Local Education Agency or School District. In some cases, school level data were aggregated to the school district level. School district characteristics were obtained through the NCES Common Core of Data, Local Education Agency Universe Survey. This survey also provided the data on unified district, elementary district or secondary district status and data on enrollment. The primary source of financial data for the analysis is the U.S. Census Bureau F-33 survey, or survey of local government finances for elementary and secondary education. Though somewhat delayed during the summer of 2009, the 2006-07 school year data were eventually released in late July. One problematic aspect of using these data is that they are, and will be for the foreseeable future, lagged by two full years. This report will be accompanied by additional state followup analyses which account for substantive changes to state school finance systems which may have occurred in more recent years. In any case, the three year analysis of national financial data provides a useful baseline for comparison. The poverty measure used is the U.S. Census Bureau measure of the percent of 5 to 17 year olds falling below the federal poverty threshold (100% poverty threshold). Since Census 2000, the census bureau has been providing annual updates of Small Area Income and Poverty Estimates (SAIPE) for resident populations of geographic areas including public school districts. Census poverty data are used in place of school level tabulations of students qualifying for subsidized lunch in part because of missing data on the latter measure. Nonetheless, the two are highly correlated across states and across districts within states (about .8 weighted by district enrollment and dropping missing values for subsidized lunch rates). One concern is that resident enrollments (the basis of Census estimates) may not precisely represent school enrollments where inter-district choice plans exist. But again, the two measures are highly correlated. Second, it is relevant to evaluate the funding levels of districts where children reside, as those funding levels may be a factor influencing inter-district choices. 1

A second concern is that readers of the public consumption information generated from this report may be more familiar with shares of children qualifying for subsidized lunch, which are much higher than shares of children in poverty, because the income thresholds for qualifying for reduced lunch or free lunch are much higher than the income threshold for poverty (185% poverty for reduced lunch and 130% poverty for free lunch). As such, we present in our report a bridge between census poverty rates and subsidized lunch rates within each state. To compensate for geographic variation in competitive wages, we use the NCES Education Comparable Wage Index (ECWI) estimated by Lori Taylor of Texas A&M University and documented by Taylor and Glander (2006). Unfortunately, the most recent available ECWI is for 2005. For the analyses herein, we lag the ECWI by applying the 2005 ECWI to 2006-07 state and local revenues, 2004 to 2005-06 revenues and so on. Our primary objective in using the ECWI is to adjust for regional variations in competitive wages. While lagging the wage index may alter how the ECWI adjusts our model for inflation (because the index accommodates both inflationary change in wages and regional variation), lagging should have minimal effect on regional variation. However, if NCES fails to update the ECWI in future years, we may be forced to construct our own updates via the method provided by Taylor and Glander (2006). In order to account for the ways in which economies of scale related revenue differences interact with geographic sparsity we include a measure of county level population density accessed from the U.S. Census Bureau, updated annually with model based projections of county level population growth. In order to estimate our effort measure, we rely on Bureau of Economic Analysis estimates of Gross Domestic Product by state. In order to estimate our coverage indicator, we use data from the American Community Survey for the most recent three years, matched to the most recent three years of fiscal survey data. Specifically, we use the “Age” and “School Type” variables. As noted previously, we focus on the narrowed range of 6 to 16 year olds because of variation in the provision of early childhood programs, including the aggressive use of state subsidies for private programs in some states, which might be fairly considered as expanded coverage. We truncate the upper end of the distribution at age 16 because of rates of 17 year olds attending college.

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Table 1 Data Sources Data Type

Primary Sampling Unit District (enrolled population)

Sample Breadth/ Completeness Universe of Local Education Agencies

Key Variables

Data Source

Years Available

CBSA Location, grade range

NCES Common Core of Data - Local Education Agency Universe Survey

Through 2006-07

Demographics/ Enrollment

District (enrolled population)

Universe of Local Education Agencies

ELL, IEP, migrant, enrollment

NCES Common Core of Data - Local Education Agency Universe Survey

Through 2006-07

Demographics/ Enrollment

School (can be aggregated to District) (enrolled population)

Universe of Public Schools

% Free (130% poverty)/ Reduced Lunch (185% poverty) Racial Composition

NCES Common Core of Data - Public School Universe Survey

Through 2006-07

Demographics/ Population

District (resident population)

Universe of Local Education Agencies

U.S. Census Bureau - Small Area Income and Poverty Estimates (SAIPE)

Through 2007

Geographic Variation in Wages

District (Labor Market or CBSA & PUMA mapped to District)

Universe of Local Education Agencies

% 5 to 15 year olds below 100% poverty Education Comparable Wage Index.

NCES Education Comparable Wage Index

1999 to 2005 (updated annually with ~2yr lag)

District Finances

District

Universe of Local Education Agencies

Current operating expenditure s and/or state and local revenues per enrolled pupil

U.S. Census Bureau - Fiscal Survey of Local Governments, Public Elementary and Secondary Finances

Through 2007

Population Density

County

District Characteristics

http://www.census.gov/popest/gallery/map s/maps-county2007.xls (county level) http://www.census.gov/popest/gallery/map s/maps-state2007.xls (state average)

Economic Context

State

All States

Gross State Product

Bureau of Economic Analysis http://www.bea.gov/regional/gsp/

Through 2007

Public School Enrollment Share of Population

State

All States

% of 6 to 16 year olds in public schools

American Community Survey accessed through Integrated Public Use Micro Data System www.ipums.org

2005 to 2007

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Data and Measures for Fairness Models Table 2 presents the variables used in the pooled cross-state and within state regression models. The dependent variable of interest is the Natural Log of State and Local Revenues per Pupil, including all sources of state and local revenues and including revenues that might be used for capital expenses. Federal revenues are generally not included except for those federal revenues which are used as replacement revenues for local funding or state aid under special circumstances (such as impact aid 1 or when 2009-10 data become available, ARRA Stabilization Funds). We focus on State and Local Revenue per pupil as an indicator of the resources delivered to local public school districts or education agencies through the various components of state aid programs in combination with local resources raised. Parsing state aid consistently across states is infeasible, since state general aid programs in some states include adjustments for special student populations and transportation and because parsing local revenues across states and across districts within states is even more complex. All state and local resources associated with the special needs of student populations must be included in our analyses. Focusing on state general formula aid would treat these populations differently across states, depending on which populations are addressed within the general formula. The total of state and local revenue per pupil includes revenues intended for capital expenses, which can be large and lumpy over time. This is one reason for using three year averaging in our analysis. One might argue that states with fast growing affluent suburban districts that are spending large sums on capital to meet growth projections will be unfairly targeted in our analysis as regressive and unfair. We note that the unevenness of capital investment between suburbs and urban core or population stagnant poor rural districts is an important equity concern which we believe should be (and is) included in our analysis. This is especially true where low income rural and urban communities face substantial unmet infrastructure needs and costs. States that provide substantial support for urban infrastructure renewal will likely tilt their profiles favorably with respect to our fairness indicators, as they should.

1

F-33 variables: B10 Direct federal revenue - Impact aid (P.L. 815 and 874), and B12 Direct federal revenue Native American (Indian) education. These revenues are not counted toward a state’s educational effort.

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Table 2 Pooled Cross State and Within State Regression Model Variables Variable Role Dependent Variable Independent District Cost

Variable Measurement State & Local Revenues per Pupil (Total), Natural Log NCES ECWI Scale Categories Population Density (County Level)

Student Need Cost

Census Poverty Rate (SAIPE)

Rationale

State and local revenues at the local district level are the best indicator of how the state school finance system works to deliver resources to school districts. To account for broad, labor market level variations in competitive wages across districts within states and across states To account for differences in state and local revenue associated with pooled cross state differences in spending by size group. As direct effect and by interaction with economies of scale categories, the reason for including the density measure is to create a measure or adjustment for the pooled cross state differences in size and density (sparsity) related costs. To account for student need related costs.

In our regression model, we adopt a strategy for addressing school district size related differences in spending similar to that used by Duncombe and Yinger (2009). While others (Gronberg, Jansen, Taylor and Booker, 2004) adopt polynomial functional forms to account for the declining costs associated with increasing scale, we use the categorical variable approach because of problems that occur at the tails of the polynomial functional form and how those problems may affect coefficient estimates on our primary measure of interest - poverty. For example, if we apply a second order polynomial term in our model it will generate a U-shaped relationship between poverty and spending across districts, implying that costs per pupil - or at least cost-related spending per pupil - increases both for very small districts and for very large ones. However, the increases for the largest urban districts may be associated with elevated and concentrated poverty in those districts. If very large districts have systematically higher poverty rates within a state, the upward curve of the enrollment term polynomial may inappropriately reduce the coefficient magnitude on the poverty measure - our primary coefficient of interest in this analysis. A categorical variable step function, leveling off rather than curving upward, resolves this concern and is standard practice in education cost modeling. In our pooled cross-state models we interact the economies-of-scale dummy variables with a county level measure of population density. We include this Scale by Density interaction to account for the ways in which school district size and density combine to affect uncontrollable differences in education costs. Remoteness factors associated with population density may influence transportation revenues (which are included in our dependent variable) and, by interaction with the scale variable, may influence necessary underlying staffing ratios where schools are necessarily small and where shared services are infeasible.

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Characteristics of the Data Table 3 shows the distribution of districts by state for the three years of data used in the pooled cross-state models. The total numbers of districts vary slightly from year to year. A handful of states have very few local education agencies, leading to less reliable state and local revenue profile predictions. Table 3 Districts per State per Year in Data Set

State Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee

2005 130 53 218 250 972 178 166 16 1 67 180 1 114 864 292 362 300 176 68 221 24 299 552 341 149 522 426 455 17 162 551 89 683 115 199 613 539 194 500 36 85 167 135

2006 131 53 216 250 971 178 166 16 1 67 180 1 114 867 292 363 293 176 68 221 24 299 552 341 149 522 425 454 17 162 551 89 681 115 195 612 539 194 500 36 85 164 135

2007 131 53 207 244 967 178 166 16 1 67 180 1 113 858 292 362 293 174 68 220 24 299 551 336 149 522 419 246 17 161 551 89 682 115 184 612 538 194 501 36 85 158 135

Total 392 159 641 744 2,910 534 498 48 3 201 540 3 341 2,589 876 1,087 886 526 204 662 72 897 1,655 1,018 447 1,566 1,270 1,155 51 485 1,653 267 2,046 345 578 1,837 1,616 582 1,501 108 255 489 405

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Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Total

1,033 40 240 133 296 55 426 48 13,753

1,033 40 236 133 296 55 426 48 13,732

1,030 40 236 132 295 55 424 48 13,455

3,096 120 712 398 887 165 1,276 144 40,940

Figure 1 shows the geographic distribution of school districts by enrollment size and of non-unified school districts. Areas shown with red diagonal slash marks are those areas covered by a mix of non-unified elementary and secondary school districts. These include areas throughout central California, Arizona, western Nebraska and Montana and large sections of northern New England. Large areas of New Jersey and the suburbs around Chicago also fall into this group. Regarding school district enrollment size, very small school districts are shown in brighter shades of red. On average, the smallest school districts appear where we would expect them to, running north to south across the sparsely populated high plains from the Dakotas and Montana down through west Texas. Eastern Washington and Oregon also maintain several small school districts. Few low enrollment school districts exist in southern states, even in rural regions, due largely to county level organization of school districts.

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Figure 1 Geographic distribution of small and non-unified districts

Figure 2 displays the geographic distribution of the National Center for Education Statistics Education Comparable Wage Index. Areas in brighter red are areas of higher competitive wages and areas in green are areas of lower competitive wages. One can see that higher competitive wages are particularly concentrated along the northeast corridor from Washington, DC to Boston and along the west coast. But, higher competitive wages also exist around major metropolitan areas throughout the middle of the country. One can also see that the same areas of the country where the smallest school districts are most common - the high plains from the Dakotas to west Texas are areas with the lowest average competitive wages. As such, in the regression model, these two factors have some counterbalancing effects. While economies of scale related spending may be higher in sparsely populated plains states, competitive wages are consistently lower.

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Figure 2 Geographic distribution of the NCES Education Comparable Wage Index (2004)

Figure 3 displays the geographic distribution of Census Poverty rates which play somewhat of a counterbalancing role with competitive wages in some regions. Poverty rates are relatively low in the northern high plains (with a few exceptions, including very high poverty Indian reservations in South Dakota), but higher in the southern plains. On average, poverty rates are higher in southern states, in Appalachia and north to south along the Mississippi delta. Poverty rates are generally lower in the northeast, where competitive wages are also higher. Competitive wages, however, are sensitive to regional economic differences, whereas poverty shares are based on poverty thresholds that are not sensitive to regional differences. As such, some might argue that poverty in lower “cost” regions of the country is overstated relative to poverty in higher cost regions. Inclusion of both the NCES ECWI and census poverty rates in our regression models corrects for this problem because we estimate the extent to which state and local revenues are sensitive to variations in census poverty rates, controlling for regional wage variation.

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Figure 3 Distribution of U.S. Census Small Area Income and Poverty Estimates - Percent 5 to 17 in Poverty

Estimating Models To generate projections of state profiles, we estimate a three year regression model using a pooled cross-state universe of local public school districts and local education agencies. That model is specified: lnSLOCREVPPd,t = b0 + b1ECWId,t-2 + b2SCALEd,t + b3lnDENSITYc + b4(SCALEd,t x lnDENSITYc) + b5STATEd+ b6YEARd,t + b7(STATEd,t x YEARd,t) + b8POVERTYd,t + b9(POVERTYd,t x STATEd) + e Where lnSLOCREVPP is the natural logarithm of state and local revenue per pupil for district “d” at time “t”, ECWI is the comparable wage index for district “d” at time “t-2” (lagged primarily due to lack of updated index), SCALE is a series of categorical dummy variables indicating district enrollment size for district “d” at time “t” and SCALE is interacted with DENSITY which is the 2007 population density (natural log) for the primary county “c” of location for district. This

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interaction term is included to capture the national average spending differences associated with economies of scale given population density. STATE is the state of district “d” which is interacted with two year dummy variables (for 2005-06 and 2006-07, with base year 2004-05) in order to generate a coefficient of state specific state and local revenue per pupil increases. POVERTY is the U.S. census poverty rate for resident 5 to 17 year olds in district “d” at time “t” which is then interacted with STATE. It is this last interaction in the model that is of primary interest to us in evaluating the fairness of state school finance systems. That is, how do state and local revenues per pupil vary by poverty, within states? Models are weighted for district enrollment. The reason for choosing to weight by enrollment in this analysis is that the ultimate goal of analyses of this type is to evaluate how the state school finance system treats children in school districts. As such, it makes little sense to identify a state as fair if that state has a large number of very small high poverty school districts that are well funded, but a handful of large districts which are poorly funded serving many more children than the aggregate of the small districts. With the estimated regression equation we then predict for each state the expected state and local revenues per pupil for a district with 0% poverty, 10% poverty, 20% poverty and 30% poverty holding constant at national average the NCES ECWI and density, setting the economies of scale dummies to zero (such that the hypothetical district represents a scale efficient district of over 2,000 students) and setting the year to 2006-07. Generating Predicted Values & Profiles Once the regression model is fit to the three years of data, we use the various pieces of that regression model, “coefficients” or multipliers, as a basis for adjusting state and local revenue estimates for districts of specific characteristics within and across states. For example, the regression model finds, as we would expect, that state and local revenues per pupil tend to be higher as district enrollments decrease below 2000 students. Similarly, as we would expect, our model estimates show that within any smaller size category, state and local revenues increase as density decreases. Ideally, we would want to know that these are the differences in state and local revenue by size and density that are necessary for producing constant outcome levels. Such a more refined measure would represent a true cost differential, rather than a simple revenue variation. Sadly, common outcome measures required for conducting such analyses are unavailable (across all districts). These caveats in mind, Figure 4 displays the average national variation in state and local revenues associated with economies of scale, holding all other factors constant including population density. Figure 5 shows the economies of scale effects at two different density levels – a population of 460 per square mile and a population of 20 per square mile. At 460 per square mile, a district enrolling under

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100 students has state and local revenue per pupil nearly 43% above that of a district with 1501 to 2000 students. For low population density districts (20 per sq. mile), the difference climbs to nearly 70%. These become the rates at which our projections correct for economies of scale and density and the interaction between the two. Figure 4 Economies of Scale and Density Adjustments from Model $14,000 State & Local Rev. PP

$13,000 $12,000 $11,000 $10,000 $9,000 $8,000 $7,000

o 15 01 t

20 00

15 00 o 12 01 t

12 00 60 1

to

60 0 to 30 1

30 0 to 10 1

Un de r1 00

$6,000

Enrollment Group

Below, we provide two examples of how profile projections are carried out for states based on our models. First, we look at New Jersey, a relatively high funding state that targets substantially greater resources to higher poverty districts. Our regression model tells us that for every one unit change there is in the national wage index (NCES ECWI), state and local revenues change in the same direction by about ¼ that amount (.242). For example, holding other variables constant, a district in a labor market that has 30% higher private sector wages than a district in another labor market is expected to have about 7.5% higher state and local revenue per pupil. Were we instead to adjust our state and local revenues for the full value of the ECWI, we would be significantly overcompensating for private sector wages. Bear in mind though, that we are simultaneously compensative for poverty and population density, which also relate to the ECWI. Our model also tells us that aside from density related size effects, population density is also slightly positively associated with costs. This likely occurs because of the relationship between regional wage variation and high density regions. On

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average, we also see that higher poverty areas, which also tend to be lower private sector wage areas, have lower state and local revenue per pupil. Now to focus on New Jersey: our model tells us that, on average, NJ State and local revenue per pupil is significantly higher than the baseline state in the model, Alabama, even after accounting for regional private sector wages. Our NJ State Dummy variable is assigned a multiplier of .449. But, that margin drops slightly for the most recent year of the data, so the NJ 2007 adjustment multiplier is -.097. The multiplier of interest for our within state fairness models is the NJ by Poverty multiplier which is 1.505, a very large positive value indicating that within NJ higher poverty districts receive a substantial boost to their state and local revenues per pupil. On the one hand, we can use these multipliers to project what a New Jersey school district would be likely to have in state and local revenues under actual New Jersey conditions – high regional labor costs, high density and moderate poverty. The first equation below does just that. Complicating the interpretation of our models is that we use the Natural Logarithm of state and local revenue per pupil as our “dependent variable” (predicted measure). In the first equation that value is 9.620 for New Jersey and is associated with state and local revenue per pupil of $16,683 in 2006-07. We arrive at that number by multiplying the wage multiplier times the average New Jersey NCES wage index of 1.441, the density multiplier of .020 times the average New Jersey school district population density (by county) of 7.509 (also natural log, associated with about 1,800 persons per sq. mile) and so on. In some cases a “1” is included simply to indicate that the state being projected is New Jersey, in this case. The effect multipliers are unique to each state in the model.

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New Jersey District at New Jersey Average Poverty & Density 9.620 = (.242 x 1.441cwi) + (.020 x 7.509dens) + (.449nj_effect x 1) + (.1702007_effect x 1) - (.097nj07_effect x 1) - (.385 x .976pov) + (1.505njpov_effect x .976pov) + 8.587 $16,683 = exp(9.722) If we wanted to predict what a New Jersey district at a fixed poverty level would likely have in state and local revenues, if that district was a) in an average wage labor market rather than NJ, and b) in an average population density county rather than NJ average, we just change key numbers in the equation, and get a somewhat different predicted value. The next equation sets the poverty rate to 10% (slight change over 9.67%) and reduces the wage index to national average and reduces the density to national average for districts linked to county density data. Here, we find that the NJ district placed in national average labor market and density conditions and having 10% poverty would have about $15,060. This is our corrected state and local revenue figure. To generate the remaining profile projections, we simply replace the 10% poverty values with 20%, 30% and so on. New Jersey Cost and Need Adjusted at 10% Poverty 9.620 = (.242 x 1.124cwi) + (.020 x 6.133dens) + (.449nj_effect x 1) + (.1702007_effect x 1) - (.097nj07_effect x 1) - (.385 x .10pov) + (1.505 njpov_effect x .10pov) + 8.587 $15,060 = exp(9.620) In our next example, we apply the same strategy to Arizona based on Arizona specific multipliers and Arizona specific characteristics. The first difference we see is that Arizona is in a somewhat lower wage area, with an average CWI for districts in the state at 1.155 rather than New Jersey’s 1.441. However, the 1.155 is still higher than the national mean value of 1.124. We also see that Arizona on average has lower population density at 5.171, which is lower than the national mean figure of 6.133. The “Arizona” effect is actually negative, meaning that on average, controlling for other factors, Arizona state and local revenue per pupil is lower than that of the baseline state Alabama. Like New Jersey, the Arizona by year factor is also negative meaning that state and local revenue growth lagged in 2007. Where New Jersey had a large within state multiplier times poverty, Arizona’s is modest at .518, but is positive and larger than the negative baseline (Alabama) effect (-.385) indicating that overall, higher poverty districts in Arizona have marginally higher

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state and local revenues per pupil (almost entirely as a function of impact aid to Indian districts). Poverty levels on average are much higher in Arizona districts at 17.4%. Multiplying and summing, we get a predicted natural log of state and local revenue for an Arizona district in Arizona’s average context of 8.973 which is $7,889 per pupil. Arizona District at Arizona Average Poverty & Density 8.973 = (.242 x 1.155cwi) + (.020 x 5.171dens) - (.104az_effect x 1) + (.1702007_effect x 1) - (.089az07_effect x 1) - (.385 x .174pov) + (.518azpov_effect x .174pov) + 8.587 $7,889 = exp(8.973) What happens when we place Arizona into the national average context and set poverty rates to 10%? Replacing the 1.155 ECWI with the 1.124 average, and the low density of 5.171 to the higher average of 6.133 and then setting poverty rates to 10% brings Arizona roughly back to the same value of about $7,900 per pupil. This occurs because the lowered poverty rate and CWI lower the projected revenue figure, but the density is raised, counterbalancing these effects (in this case, the density factor picking up some of the wage difference associated with more densely populated metropolitan areas). Arizona Cost and Need Adjusted at 10% Poverty 8.975 = (.242 x 1.124cwi) + (.020 x 6.133dens) - (.104az_effect x 1) + (.1702007_effect x 1) - (.089az07_effect x 1) - (.385 x .10pov) + (.518azpov_effect x .10pov) + 8.587 $7,906 = exp(8.975) Comparison of Complexity to Other Methods While this new approach seems complicated, expressed in similar form, typical approaches to generated “need” adjusted revenue or expenditure measures are only marginally simpler, but include numerous arbitrary assumptions and exclude major cost factors. For example, if we wanted to compute a “cost” adjusted expenditure or state and local revenue figure by methods similar to those used by Education Trust and Education Week, we would begin by calculating a Weighted

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Full Time Equivalent Enrollment (WFTE) count. We would create this count by adding to the actual enrollment, additional weighted enrollments by poverty, limited English proficiency and special education. We would have to pick a student poverty count method for determining the number of students who should be weighted and we would have to pick a weight for those children, which would likely range from .2 to .5. Ideally, we would pick our weight based on empirical literature on costs and our weight would be chosen based on the count method we chose for identifying students who should receive the weight (see Duncombe and Yinger, 2005, who find a weight of 1.09 per child qualifying for subsidized lunch and 1.49 per child under the census poverty threshold). Similar choices would be made for count methods and weighting factors for limited English proficient students and children with disabilities. Economies of scale and density are neglected entirely. WFTE = ENROLL + (%POV x ENROLL x .4) + (%LEP x ENROLL x .6) + (%SPED x ENROLL x .9) Next, the resource figure – state and local revenues or current expenditures – is divided by the weighted FTE enrollment to generate a dollars-per-weighted-pupil figure. Then that figure is divided by the full value of the NCES Education Comparable Wage Index to create a regionally cost adjusted, dollars-per-weightedpupil figure. Adj. $$ Per Pupil = (Actual Total $$/ WFTE)/ECWI By contrast, the approach we take herein evaluates statistically the actual relationship between the poverty count method chosen and state and local revenues (thus it would differ by count method) and includes statistically estimated adjustments for scale and sparsity. Finally, instead of assuming that aggregate education resources are 100% sensitive to regional wage variation, our analyses estimate the statistical relationship between the ECWI and state and local revenues per pupil (albeit, it may be the case that state and local revenues are not sufficiently sensitive to regional wage variation). Correlations among Context Measures Figure 5 displays the relationship across states between state average poverty rates and the effort index asking whether effort may be hampered by poverty or whether effort is higher where incomes are lower. There exists little relationship across states between effort as we have measured it herein, and state level poverty rates.

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Figure 5 Relationship between State Average Poverty Rates and Effort

Effort Index[1] .04 .05

.06

Vermont

New Jersey Maine

.03

West Virginia Wyoming Michigan New York South Carolina New Hampshire Maryland Wisconsin Rhode OhioIsland Georgia Arkansas KansasPennsylvania Mississippi Connecticut Alabama Indiana New Mexico Massachusetts Montana Iowa Kentucky Florida Nebraska Minnesota Texas IdahoIllinois Missouri Virginia Alaska California Oklahoma Utah Arizona Washington North Carolina Colorado Oregon North Dakota Nevada Tennessee Louisiana South Dakota

.02

Delaware

.05

R-squared

.1

.2 .15 Census SAIPE Poverty Rate

.25

= 0.0202

Figure 6 displays the relationship between effort and the coverage measure. Here too there exists little relationship, even though one might expect effort to be systematically lower in states with lower rates of coverage. Anecdotally, this assumption appears only to hold true for Delaware and Louisiana, but is not a pattern across all states.

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Figure 6 Relationship between Coverage and Effort

Effort Index[1] .04 .05

.06

Vermont

New Jersey Maine

.03

Maryland

Louisiana

West Virginia Wyoming Michigan New YorkSouth New Carolina Hampshire Ohio Rhode Island Georgia Wisconsin Arkansas Pennsylvania Kansas Mississippi Alabama IndianaConnecticut New Mexico Massachusetts Montana Iowa Kentucky Florida Nebraska Minnesota Texas Idaho Missouri Illinois Virginia Alaska California Oklahoma Utah Arizona Washington NorthColorado Carolina Oregon North Dakota Nevada Tennessee South Dakota

.02

Delaware

.75

R-squared

.8 .85 .9 % 6 to 16 yr Olds in Public Schools [2]

.95

= 0.0001

Figure 7 displays the relationship between organization and effort, on the assumption that states with less organized school systems might require higher rates of effort to keep those systems financial viable. Again, the relationship between these factors is not strong, but anecdotal cases like Vermont do stand out. Vermont despite its relatively small geographic size, has very few children in organized scale efficient school districts and Vermont has by far the highest level of effort to support its public school system.

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1

Figure 7 Relationship between Effort and Organization

% Organized [2] .4 .6

.8

Maryland Florida North Nevada Louisiana UtahCarolina Delaware Virginia South Carolina Georgia Alabama Virginia Tennessee RhodeWest Island Colorado Washington New Mexico Connecticut Oregon Texas Kentucky Pennsylvania Massachusetts New York Mississippi Alaska Indiana Michigan Idaho Ohio Minnesota Missouri California Wisconsin New Jersey KansasWyoming Nebraska Arkansas Oklahoma Arizona New Hampshire Maine

.2

North Dakota Iowa South Dakota Illinois

0

Vermont

Montana

.02

R-squared

.03

.04 Effort Index[1]

.05

.06

= 0.1216

Correlations between Context and Fairness Measures Figure 8 displays the cross state relationship between Per Capita GDP (State) and expected state and local revenues per pupil at 0% poverty. Here, there exists a reasonably strong relationship, where states having greater economic productivity tend to be spending more on public education.

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20000

R-squared

New York

Wyoming

Delaware

Vermont Pennsylvania Maryland Rhode Island New Hampshire Maine

New Jersey

Connecticut

Massachusetts

Virginia Florida Wisconsin Nevada Kansas Louisiana Illinois Georgia AlabamaMichigan West Virginia North Carolina South Carolina Iowa NebraskaMinnesota OhioNorth DakotaColorado Washington Kentucky Indiana California Texas Missouri New Mexico Alaska Oregon Arkansas Mississippi Montana Arizona Idaho South Dakota

6000

State&Local at 0% Pov 8000 10000 12000 14000

16000

Figure 8 Relationship between Per Capita GDP (State) and Per Pupil Revenues

Tennessee Oklahoma Utah

30000 40000 50000 Per capita real GDP by state (chained 2000 dollars)

60000

= 0.2936

The relationship between our effort measure and state and local revenues at 0% poverty is comparable to the relationship between economic capacity and state and local revenues. That is, our revenue projections are not likely driven by state economic capacity alone.

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16000

Figure 9 Relationship between Effort and Per Pupil Revenues

State&Local at 0% Pov 8000 10000 12000 14000

New York Wyoming

Delaware

Vermont Connecticut Pennsylvania Maryland

New Jersey Rhode Island New Hampshire Massachusetts Maine Virginia Florida

6000

Wisconsin Nevada KansasMichigan Louisiana Illinois Alabama Georgia West Virginia North CarolinaIowa South Carolina Nebraska Minnesota Colorado Ohio North Dakota Washington Kentucky Indiana California Texas Missouri New Mexico Oregon Alaska Arkansas Mississippi Montana Arizona Idaho South Dakota Tennessee Oklahoma Utah

.02

R-squared

.03

.04 Effort Index[1]

.05

.06

= 0.2384

Across states, economic capacity as measured by GDP coupled with effort as measured by state and local revenue per pupil as a share of GDP explain the majority of differences in state and local revenue projections for districts with fixed characteristics and specific poverty levels. To some extent, this finding is a given, since the effort measure is based on cumulative state and local revenues with each state. The combination of Effort and GDP per Capita explain 66% of the differences in state and local revenue at 0% poverty. Correlations between Fairness Measures and Other Equity Indicators We conclude with selective comparisons between our fairness indicators and indicators frequently used by Education Week for rating state school finance systems. Figure 10 compares our “fairness” high/low ratio with the Coefficient of Variation estimated by Education Week for 2006, which includes weights for children in poverty or with disabilities and applies the NCES wage index. 2 2

The coefficient of variation is a measure of the disparity in funding across school districts in a state. As the coefficient gets lower, it indicates greater equity. Spending figures were adjusted to reflect regional cost differences, using the NCES Geographic Cost of Education Index, and weighted for student needs (students in poverty equal 1.2; students in special education equal 2.3 for data before 2001, and 1.9 for 2001 data and subsequent years). Beginning

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In short, the assumption of the Education Week CV analysis is that states with a larger CV are less equitable states - or less fair. As it turns out, Figure 10 shows that some states that by our measures are the “most fair”, such as New Jersey or Minnesota, are considered much less fair by Education Week. States like Alabama do very well on Education Week’s CV as a measure of fairness, but do very poorly on our measure. In short, the Education Week method of estimating unfair variations in fiscal resources penalizes states which actually target substantial additional resources (more than the 20% weight) to higher poverty districts.

.3

Figure 10 Relationship between Fairness Ratio and Ed Week CV

.25

Montana

Vermont

EW CV 06 .2

North Dakota Idaho New Hampshire

New Mexico

Texas

New Jersey Arizona Massachusetts South Dakota Oklahoma Nebraska Mississippi

.15

Pennsylvania Nevada Kansas Wyoming Missouri California Indiana New York Illinois Maine Colorado Washington Connecticut Delaware Oregon Virginia MichiganSouth Carolina Kentucky NorthMaryland Carolina Georgia Iowa Tennessee Rhode Island Arkansas

Ohio

Minnesota Utah

.1

Wisconsin Alabama Florida West Virginia

.6

R-squared

.8

1 1.2 Fairness Ratio

1.4

1.6

= 0.0236

with 2004 data, the U.S. average is calculated using an average of the states’ averages. For prior years of data, the U.S. average is calculated using a grand mean.

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Education Week uses a separate measure to estimate the relative “adequacy” of state education funding. The measure is called the “Spending Index” and is a measure of the percent of children in a state that are in districts that spend more than the national average. This measure also includes need and regional wage adjustments. 3 Figure 11 relates our measure of the expected state and local revenues at 10% poverty to the Education Week Spending measure. The major problem with the Education Week measure is that it ignores entirely between state spending variations above the national average. For those below the national average, the Education Week measure is reasonably related to our predicted revenue figures.

20000

Figure 11 Relationship between Ed Week Spending Index and Per Pupil Revenues

State&Local at 0% Pov 10000 15000

New York Wyoming Vermont

Delaware New Jersey Connecticut New Hampshire Pennsylvania Maine Maryland Massachusetts Rhode Island

Arizona Idaho

Wisconsin Virginia Illinois Kansas Florida Michigan Nevada Iowa Louisiana Georgia Alabama Nebraska Minnesota North Dakota West Virginia Colorado NorthMissouri Carolina Ohio South Washington Carolina California Texas Indiana Kentucky New Arkansas MexicoOregon Alaska Montana Mississippi South Dakota

OklahomaTennessee

5000

Utah

60

70

80 Ed Week Spending Index '06

90

100

3

Per-pupil spending levels weighted by the degree to which districts meet or approach the national average for expenditures. Figures were adjusted to reflect regional cost differences, using the NCES Geographic Cost of Education Index, and weighted for student needs (students in poverty equal 1.2; students in special education equal 2.3 for data before 2001, and 1.9 for 2001 data and subsequent years). Beginning with 2004 data, the U.S. average is calculated using an average of the states' averages. For prior years of data, the U.S. average is calculated using a grand mean.

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Figure 12 tests the common assumption that an increased state share of funding is associated with improved equity. But, Figure 12 shows no relationship between the extent to which higher poverty districts have more resources than lower poverty districts and the percent of funds that come from state sources. New Jersey provides a particularly striking example of a state with a very high Fairness Ratio coupled with relatively low state share.

1.6

Figure 12 Relationship between State Share and Fairness Ratio

1.4

Utah New Jersey

Minnesota

Ohio

Fairness Ratio 1 1.2

South Dakota Massachusetts Montana Indiana New Mexico Tennessee Oregon Wyoming Oklahoma Iowa Arizona Arkansas Kentucky California Georgia South Carolina Rhode Island West Virginia Nebraska Vermont Washington Mississippi Wisconsin Texas Kansas Michigan Colorado Florida Maryland Alabama Delaware Idaho Missouri Maine Pennsylvania Virginia North Carolina North Dakota New York

.8

Connecticut

Illinois Nevada

.6

New Hampshire

30

R-squared

40

50 60 State Share of Revenue

70

80

= 0.0105

Comparison with Funding Gap Report Unlike Education Week equity indicators, Education Trust adopts the same underlying assumption that we do in this report – that it is incumbent upon state legislatures to target additional resources to school districts with greater poverty rates and that one can at least partially evaluate state school finance systems by measuring the differences in resources between higher and lower poverty school districts. Education Trust constructs their funding gap measures by taking the average spending of high and low poverty (top and bottom quartile) districts and measuring the difference between the two. Three major shortcomings of the approach are that a) Education Trust does not account for whether the pattern is systematic from higher to lower poverty districts, b) Education Trust does not

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include the full range (excludes the middle) of districts in their analysis and c) Education Trust does not account for cost factors such as economies of scale and density. Figure 13 displays the relationship between the Education Trust poverty funding gaps and our high/low fairness ratios within states. There exists a reasonably strong relationship between the two but not a perfectly linear relationship. Utah, South Dakota and Montana perform much better on our fairness index than on the Education Trust funding gap measure, likely because we account for economies of scale and population density. Illinois, dismal by either account, also performs slightly better on our measures because we account for economies of scale and population density.

4000

Figure 13 Relationship between Fairness Ratio and Ed Trust Poverty Funding Gaps

Ed Trust Pov. Gap '06 -2000 0 2000

New Jersey

Massachusetts

Minnesota

New Mexico Ohio Kentucky Connecticut Oregon Arkansas Wyoming Tennessee Maryland Rhode South Carolina Oklahoma Island Indiana North DakotaMississippi California Iowa Washington Georgia Nebraska West Virginia Florida Missouri Virginia Colorado Arizona Texas Idaho South Dakota Vermont Kansas Maine Alabama Wisconsin Montana North Carolina Nevada Michigan Delaware Pennsylvania New Hampshire

Utah

Illinois

-4000

New York

.6

R-squared

.8

1.2 1 Fairness Ratio

1.4

1.6

= 0.7598

Focusing in Figure 14 on the middle of the distribution where it would appear that there is more agreement between Education Trust and our measures, there actually is less. The R-squared between these two measures for the middle range of districts is only .50. While a strong relationship, these two measures purport to measure the same thing – the extent to which states target additional resources to higher poverty school districts. Thus, the r-squared should be very high. Our fairness ratios and the Education Trust funding gaps differ largely because we account for economies of scale and population density, and because we account for

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wage variation via a regression model rather than using the NCES CWI as a blunt instrument for correcting resource measures. Arizona performs better on our index because of compensation for density by scale. Florida, on the other hand performs better on the Education Trust index having essentially no gap, but is revealed as significantly regressive in our analysis. Kansas is an example where previous Education Trust technical documentation points to high poverty in remote rural districts which have high spending as a potential complicating factor in their analysis.

1000

Figure 14 Relationship between Fairness Ratio and Ed Trust Poverty Funding Gap

Kentucky

Ed Trust Pov. Gap '06 500 -500 0

Oregon Arkansas Wyoming South Carolina Rhode Island

Oklahoma

California Mississippi Washington Georgia Iowa Nebraska West Virginia

Florida Colorado Texas Louisiana Kansas

Arizona Vermont Wisconsin

-1000

Michigan

.9

R-squared

.95

1 Fairness Ratio

1.05

1.1

= 0.5069

Comparison with the Federal Equity Indicator We conclude with a comparison of our fairness index to the Federal Equity Indicator used to guide the distribution of Federal Title I Education Finance Incentive Grants (EFIG). The equity indicator is essentially a pupil weighted (need adjusted) coefficient of variation like the Education Week CV discussed previously. And like the Education Week CV, our fairness index is unrelated to the Federal Equity Indicator. Most problematic is the fact that states with very high fairness values, like New Jersey, Ohio and Massachusetts, would be penalized toward receipt of EFIG funds simply because they are putting fiscal effort into higher

26

poverty districts. Meanwhile, states that we identify as significantly regressive, like Florida, receive very good Federal Equity Ratings.

.25

Figure 15 Relationship between Fairness Ratio and EFIG Equity Index

EFIG Equity Index '07 .15 .2

Illinois

Montana Virginia Missouri Vermont Wyoming New York Pennsylvania Idaho

Massachusetts

Ohio

New Hampshire Michigan

New Jersey

Arizona Minnesota South Dakota

Utah

.1

Indiana Tennessee Dakota Maine NevadaNorth Oklahoma Connecticut Arkansas Kentucky Mississippi MarylandNebraska South Carolina Georgia California Kansas Rhode Oregon Island New Mexico Colorado Alabama Louisiana Texas Wisconsin NorthDelaware Carolina Washington Iowa

.05

Florida West Virginia

.6

R-squared

.8

1 1.2 Fairness Ratio

1.4

1.6

= 0.0017

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Table 4 Model Parameter Estimates DV = State & Local Rev. PP (ln) NCES ECWI Density (ln) Enrollment Enroll Under 100 Enroll 100 to 300 Enroll 301 to 600 Enroll 601 to 1200 Enroll 1201 to 1500 Enroll 1501 to 2000 Enroll over 2000 Density x Enrollment Enroll Under 100 Enroll 100 to 300 Enroll 301 to 600 Enroll 601 to 1200 Enroll 1201 to 1500 Enroll 1501 to 2000 State Fixed Effect Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico

Coefficient 0.242 0.020

Std. Err. 0.010 0.001

P>t 0.000 0.000

0.722 0.473 0.266 0.165 0.087 0.027 0.000

0.045 0.019 0.015 0.011 0.015 0.013 0.000

0.000 0.000 0.000 0.000 0.000 0.030

-0.058 -0.052 -0.030 -0.023 -0.011 -0.003

0.013 0.005 0.004 0.002 0.003 0.002

0.000 0.000 0.000 0.000 0.000 0.260

-0.146 -0.104 -0.044 -0.051 0.073 0.387 0.384 0.614 0.039 0.043 0.367 -0.137 0.195 0.235 0.108 0.075 -0.105 0.002 0.337 0.270 0.323 0.159 0.088 -0.156 0.078 -0.154 0.083 0.117 0.386 0.449 -0.052

0.039 0.022 0.029 0.019 0.023 0.023 0.059 0.036 0.023 0.021 0.024 0.037 0.020 0.022 0.028 0.026 0.025 0.030 0.034 0.022 0.021 0.020 0.022 0.028 0.022 0.041 0.031 0.070 0.033 0.020 0.033

0.000 0.000 0.125 0.007 0.001 0.000 0.000 0.000 0.089 0.043 0.000 0.000 0.000 0.000 0.000 0.004 0.000 0.943 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.007 0.092 0.000 0.000 0.114

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DV = State & Local Rev. PP (ln) New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Year = 2006 State Growth Effect 2006 over 2005 (State x 2006) Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey

Coefficient 0.612 0.024 0.051 0.034 -0.282 -0.069 0.367 0.310 0.019 -0.173 -0.276 -0.020 -0.443 0.527 0.185 0.025 0.108 0.261 0.463 0.063

-0.109 -0.038 -0.031 -0.004 -0.039 0.001 -0.015 -0.024 0.018 -0.003 0.124 -0.040 -0.041 -0.100 -0.031 0.039 0.022 0.066 -0.023 0.010 0.009 -0.035 -0.021 0.022 -0.021 -0.005 -0.001 -0.013 -0.008 -0.049

Std. Err. 0.020 0.023 0.045 0.020 0.025 0.029 0.020 0.033 0.028 0.038 0.024 0.019 0.027 0.044 0.021 0.023 0.039 0.022 0.064 0.014

P>t 0.000 0.298 0.264 0.091 0.000 0.015 0.000 0.000 0.502 0.000 0.000 0.292 0.000 0.000 0.000 0.263 0.005 0.000 0.000 0.000

0.038 0.019 0.023 0.015 0.020 0.022 0.040 0.052 0.016 0.017 0.032 0.028 0.017 0.019 0.023 0.023 0.021 0.021 0.031 0.019 0.019 0.017 0.020 0.022 0.019 0.035 0.027 0.024 0.031 0.018

0.004 0.047 0.182 0.807 0.048 0.957 0.709 0.639 0.258 0.874 0.000 0.155 0.012 0.000 0.170 0.089 0.291 0.001 0.464 0.613 0.641 0.042 0.277 0.332 0.264 0.880 0.979 0.577 0.791 0.006

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DV = State & Local Rev. PP (ln) New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Year = 2007 State Growth Effect 2007 over 2005 (State x 2007) Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire

Coefficient -0.031 -0.004 -0.027 -0.010 -0.024 -0.028 -0.006 -0.011 0.002 -0.006 -0.008 -0.032 -0.020 -0.015 0.003 -0.014 -0.026 -0.035 -0.046 -0.096 0.170

-0.040 -0.089 -0.107 -0.013 -0.107 -0.056 -0.024 -0.053 0.037 -0.034 0.111 -0.099 -0.098 -0.338 -0.081 0.010 0.001 0.008 -0.056 -0.007 -0.074 -0.097 -0.095 -0.063 -0.129 -0.034 -0.065 -0.070 -0.060

Std. Err. 0.026 0.016 0.018 0.041 0.017 0.021 0.022 0.017 0.034 0.020 0.038 0.019 0.015 0.023 0.043 0.018 0.019 0.027 0.019 0.044 0.014

P>t 0.226 0.784 0.125 0.812 0.155 0.182 0.768 0.530 0.946 0.775 0.836 0.092 0.199 0.503 0.942 0.442 0.160 0.206 0.017 0.029 0.000

0.037 0.019 0.023 0.015 0.020 0.022 0.040 0.052 0.016 0.017 0.032 0.028 0.017 0.019 0.023 0.023 0.021 0.021 0.031 0.019 0.019 0.017 0.020 0.023 0.019 0.035 0.027 0.024 0.031

0.288 0.000 0.000 0.388 0.000 0.011 0.543 0.309 0.021 0.046 0.001 0.000 0.000 0.000 0.000 0.665 0.975 0.709 0.071 0.731 0.000 0.000 0.000 0.005 0.000 0.338 0.017 0.003 0.052

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DV = State & Local Rev. PP (ln) New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Census Poverty Rate State Progressiveness Factor (State x Poverty) Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada

Coefficient -0.097 -0.081 -0.026 -0.059 -0.061 -0.078 -0.069 -0.077 -0.071 -0.060 -0.063 -0.064 -0.111 -0.060 -0.064 -0.014 -0.056 -0.067 -0.120 -0.127 0.078 -0.385 0.000 4.334 0.518 0.504 0.491 0.089 0.819 -0.006 (dropped) 0.054 0.468 (dropped) -0.032 -0.456 0.906 0.532 0.112 0.497 0.067 -0.142 0.007 0.971 0.132 1.461 0.248 -0.050 0.919 0.339 -0.599

Std. Err. 0.018 0.026 0.016 0.018 0.042 0.017 0.021 0.022 0.017 0.035 0.020 0.038 0.019 0.015 0.022 0.043 0.018 0.019 0.027 0.019 0.044 0.075

P>t 0.000 0.002 0.111 0.001 0.147 0.000 0.001 0.000 0.000 0.085 0.002 0.091 0.000 0.000 0.005 0.738 0.002 0.000 0.000 0.000 0.080 0.000

0.000 0.239 0.090 0.122 0.079 0.113 0.107 0.454

0.000 0.000 0.000 0.000 0.429 0.000 0.990

0.115 0.089

0.638 0.000

0.233 0.083 0.100 0.173 0.137 0.103 0.116 0.205 0.114 0.095 0.084 0.118 0.101 0.095 0.210 0.195 0.489

0.892 0.000 0.000 0.002 0.414 0.000 0.560 0.488 0.951 0.000 0.114 0.000 0.014 0.596 0.000 0.083 0.221

31

DV = State & Local Rev. PP (ln) New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Constant

Coefficient -1.099 1.505 0.832 -0.271 -0.200 -0.257 1.274 0.604 0.676 -0.178 0.436 0.457 1.156 0.772 0.158 1.759 0.287 -0.190 0.266 0.397 0.244 0.646 8.587

Std. Err. 0.275 0.091 0.130 0.081 0.105 0.307 0.085 0.110 0.152 0.085 0.131 0.124 0.181 0.107 0.078 0.173 0.351 0.100 0.109 0.169 0.096 0.517 0.020

P>t 0.000 0.000 0.000 0.001 0.057 0.402 0.000 0.000 0.000 0.037 0.001 0.000 0.000 0.000 0.043 0.000 0.414 0.057 0.014 0.019 0.011 0.211 0.000

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References Duncombe, W., Yinger, J. (2005) How Much more Does a Disadvantaged Student Cost? Economics of Education Review 24 (5) 513-532 Duncombe, W. and Yinger, J.M. (2008) Measurement of Cost Differentials In H.F. Ladd & E. Fiske (eds) pp. 203-221. Handbook of Research in Education Finance and Policy. New York: Routledge. Duncombe, W., and Yinger, J.M. (2009) State Education Aid, Student Performance and School District Efficiency in New York State. Center for Policy Research. Maxwell School, Syracuse University Gronberg, T., Jansen, D., Taylor, L., Booker, K. (2004) School Outcomes and Schools Costs: The Cost Function Approach. (College Station, TX: Busch School of Government and Public Service, Texas A&M University). Retrieved March 1, 2006 from http://bush.tamu.edu/research/faculty_projects/txschoolfinance/papers/SchoolOut comesAndSchoolCosts.pdf Taylor, L. L., Glander, M. (2006). Documentation for the NCES Comparable Wage Index Data File (EFSC 2006-865). U.S. Department of Education. Washington, DC: National Center for Education Statistics.

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