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~2 School District Estimates For Title I fund allocations to be made in spring 1999 for the 1999-2000 school year, the Census Bureau was charged to produce updated estimates of the number of poor school-age children at the school district level. Three sets of school district estimates are required: (1) estimates of school-age children (aged 5-17) who were living in and related to a family in poverty in the preceding calendar year;1 (2) estimates of all school-age children; and (3) estimates of the total population of the district. The first two sets of estimates are needed to implement the allocation formulas for both basic and concentration grants; the third set of estimates is needed to determine which school districts have fewer than 20,000 people.2 This chapter first considers estimates of poor school-age children for school districts. It reviews the difficulties that confront attempts to develop such esti- mates; describes the procedure that the Census Bureau used to develop district- level estimates of school-age children in July 1996 who were in poor families in 1995; and assesses the limited evaluations that are possible of these estimates. The chapter then describes the procedure and evaluations for estimates of the number of all school-age children and of the total population in July 1996 for school districts (see also Bureau of the Census, 1999, which describes the estima 1See Chapter 1, footnote 5, for the definition of "related children." 2States, at their discretion, may aggregate the fund allocations for districts with less than 20,000 population and redistribute the funds by using another method that is approved by the Department of Education. 39

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40 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY lion procedures and evaluations for the 1995 school district estimates). Finally, the chapter discusses the implications of the evaluations for the use of updated school district estimates for Title I allocations. SCHOOL-AGE CHILDREN IN POVERTY issues in Estimating Poverty for School Districts Developing estimates of the number of poor school-age children (or other characteristics) for school districts presents a number of difficult problems. These problems include the small population size of most districts and several other features of their boundaries and scope: school district boundaries in many in- stances cross county lines; they can and often do change over time; and some school districts cover specific grade levels, such as kindergarten-8 or 9-12. Be- cause of these problems, there are no data sources now available for developing updated school district estimates of poor school-age children by using the type of model-based approach that was used for county estimates. These problems also compromise the quality of the estimates for school districts that are available by aggregating data for blocks from the decennial census. We briefly review each of these issues in turn. Size Table 3-1 shows the distribution of total school districts, school districts coterminous with counties, and total counties by population size from the 1990 census. Of 15,226 districts, 49 percent had fewer than 5,000 people, and fully 82 percent had fewer than 20,000 people, while only 9 percent had 40,000 or more people; the median population size was about 5,250. By comparison, of 3,141 counties, 10 percent had fewer than 5,000 people, and 32 percent had 40,000 or more people; the median population size was about 23,000. Small districts, while numerous, accounted for small proportions of school-age children: districts with fewer than 5,000 people included only 6 percent of all school-age children, and districts with fewer than 20,000 people included only 27 percent of all school-age children; in contrast, districts with more than 40,000 people included 58 percent of all school-age children. Such uses as Title I fund allocations, however, require estimates for all school districts, no matter how small. Yet it is not possible to obtain direct estimates for school districts from national surveys, such as the March CPS. Many school districts will have no sampled households in national surveys, and the estimates for all but the largest districts with sampled house- holds will be very unreliable (i.e., exhibit high sampling variability). Even cen- sus data, as discussed below, are unreliable for many school districts.

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SCHOOL DISTRICT ESTIMATES TABLE 3-1 Percentage Distribution of School Districts, School Districts Coterminous with Counties, and Counties by Population Size, 1990 Census 41 All School Districts School Districts coterminous with counties Total Districts School-Age Districts School-Age counties Population (l) Children (2) (3) Children (4) (5) Under 5,000 49.2 6.0 9.3 0.4 9.5 5,000-9,999 17.0 7.7 17.4 2.4 14.5 10,000-19,999 15.6 13.4 27.3 7.1 22.5 20,000-39,999 9.7 15.4 22.4 11.3 21.7 40,000 or more 8.5 57.6 23.7 78.8 Total (Number) 15,226 45.3 million 928 10.1 million 3,141 NOTE: School districts are defined as of 1989-1990. SOURCE: Data from Bureau of the census. Boundaries School district boundaries are, in general, determined by state regulations and practices. In seven states and the District of Columbia, school districts are coterminous with counties; these states included 370 districts in 1990 (2% of the total).3 In another 17 states, school district boundaries coincide with other politi- cal units, such as townships. The boundaries of most, but not all, of the school districts in these states respect county lines. These states included 3,344 districts in 1990 (22% of the total), of which 190 crossed county lines. In the remaining 26 states, school district boundaries are unique to districts and often cross county lines. These states included 11,563 districts in 1990 (76% of the total), of which 3,931 crossed county lines. In all, 4,121 school districts (27% of the total) crossed county lines. It is relatively easy to develop updated estimates of poor school-age children for districts that are coterminous with counties because county boundaries are generally stable over time, counties are relatively large areas, and data sources are available for counties (e.g., the data used to estimate the county model). Overall, in 1990, there were 928 districts that comprised an entire county or, in 3In some other states, some school districts are coterminous with counties; see below. Puerto Rico is treated as a single county and (coterminous) school district for purposes of Title I allocations.

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42 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY the case of a few districts (e.g., New York City), more than one entire county. (The 928 districts include the districts in the seven states and the District of Columbia in which all school districts are counties together with selected districts in other states.) These districts accounted for 6 percent of all districts and 22 percent of all school-age children in 1990. Their median population size in 1990 was about 18,500 (Table 3-1, colt 3) not far from the median population size for all counties (Table 3- 1, colt 5~. Most of the remaining districts, whether or not they cross county lines, present more or less serious problems for updating: they are small, with a median population size of less than 5,000; their boundaries can and often do change; and few data are available for estimating poverty. These districts accounted for 94 percent of districts and 78 percent of all school-age children in 1990. Grade Levels In 1990, 11,284 school districts (74% of the total) served all grades pre- kindergarten, kindergarten, or 1st grade through 12th grade. The remaining 3,942 districts (26% of the total) served a subset of grades, such as elementary grades, high school grades, or middle school grades. Developing updated esti- mates of poor school-age children for districts that serve specific grades is diffi- cult because a method must be devised to allocate the limited available data on school-age poverty to the age range that is appropriate to the grade range of the school district. Data Sources The Census Bureau' s county model can readily provide updated estimates of the number of poor school-age children for the small subset of school districts that comprise entire counties. However, as noted above, a model similar to the county model cannot be developed for the remaining 94 percent of school dis- tricts, principally because of the lack of administrative data with which to form the predictor variables in a regression model. For example, states do not gener- ally geocode the addresses of Food Stamp Program participants to school dis- tricts, so there are no counts of food stamp participants for school districts. Similarly, a substantial proportion of addresses on federal income tax returns cannot be geocoded to census blocks, so it is not possible to estimate the number of poor children reported by families on tax returns for school districts. Finally, data from school districts on participation in the National School Lunch Program (requested from the states by the National Center for Education Statistics in its Common Core of Data Program) are far from complete, and they are of uncertain quality and applicability (see below, "School Lunch Datable. In the future, it may be possible to develop appropriate data sources for a model-based approach to

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SCHOOL DISTRICT ESTIMATES 43 estimating poor school-age children for school districts (see Chapter 5), but such data are not now available. Estimation Procedure In the absence of data with which to develop a school district model similar to the county model, the Census Bureau used a simple synthetic approach to estimate poor school-age children by school districts for 1995. The approach involved seven steps: (1) A survey was conducted to ascertain school district boundaries for the 1995-1996 school year. (2) Each 1990 census block was assigned to a school district, as defined for 1995-1996.4 (3) The 1990 census data were aggregated for the blocks (or fractions of blocks) in each school district or part of a school district that lay wholly within a county. (4) The 1990 census data for each school district or school district part were tabulated to form a ratio estimate of the number of poor school-age children: the ratio estimate was obtained by applying the proportion poor of school-age chil- dren from the census long-form sample data to the short-form complete-count estimate of all school-age children. The ratio estimate was used because it reduced somewhat the high sampling variability in the census estimates for school districts in comparison with estimates formed by simply inflating the long-form number of poor school-age children by the sampling weight. (5) For the school districts or school district parts in a county, the share (proportion) for each school district or school district part of the 1990 census county total of poor school-age children was calculated from the ratio estimates. (For districts that are coterminous with a county, the share was 100%.) (6) The 1990 census shares from step (5) were applied to the updated 1995 county estimates of poor school-age children produced by the county model (see Chapter 2) to obtain 1995 estimates of poor school-age children for school dis- tricts or school district parts. (7) The 1995 school district estimates of poor school-age children were the estimates from step (6) for school districts wholly within a county and the sum of the estimates of school district parts for school districts that crossed county lines. 4When school district boundaries crossed census block boundaries, the poor school-age children in such a block were assigned to the appropriate school districts in proportion to the area of each district included in the block. When two or more school districts included a block because the districts covered selected grades (e.g., kindergarten-8 and 9- 12), the poor children in the block in the relevant age ranges were assigned to the appropriate district on the basis of an analysis of the relationship of age to grade.

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44 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY As an example of the procedure, take a county with 1,600 poor school-age children in 1989 (1990 census data) of whom 1,200 (75%) resided in school district A, 240 in school district B (15%), and 160 in school district C (10%~. If the 1995 county model estimated that the county had only 1,200 poor school-age children, then the estimates of poor school-age children in 1995 for school dis- tricts A, B. and C are 900, 180, and 120, respectively. The estimation method assumes that all three school districts in the county experienced the same propor- tionate decrease in the number of poor school-age children 25 percent as the county as a whole. If this assumption is incorrect (e.g., because the decrease in poverty in the county was concentrated in one of the districts, perhaps because of changes in the housing stock), then the estimates for the three school districts will be incorrect. At present, l 8 states use a similar procedure for allocating their Title I county funds to school districts, in that they make within-county allocations on the basis of 1990 census school district shares of poor school-age children, either solely or in combination with estimates of the other categories of formula-eligible children (e.g., foster children). Another nine states use 1990 census data together with other data sources, such as school lunch data, to allocate Title I county funds to school districts (according to the U.S. Department of Education). The Census Bureau's 1995 school district estimates are not the only input to the Title I allocation formula. To make direct allocations to school districts for the 1999-2000 school year, the Department of Education must also obtain several other data elements for school districts, most of which have not been previously available at the district level: counts of the other categories of formula-eligible children (children in foster homes, in local institutions for neglected and delin- quent children, and in families with income above the poverty line who receive welfare assistance);5 and the dollar amounts of Title I allocations that school districts received for the 1998-1999 school year (to use in the hold-harmless computations). The Census Bureau's estimates of poor school-age children must also be adjusted to reflect school district boundary changes between 1995-1996 and 1998-1999 (although the department may leave it to the states to make appropriate adjustments). Evaluations To evaluate the Census Bureau's 1995 estimates of poor school-age children for school districts, the panel and the Census Bureau first assessed the 1990 spoor school-age children as estimated by the census Bureau were 96.2 percent of the total num- ber of formula-eligible children counted in the Title I allocations for the 1998-lg99 school year. Foster children, children in local institutions for neglected and delinquent children, and children in families with income above the poverty line receiving welfare assistance were 2.6 percent, 1.1 percent, and o.1 percent, respectively, of the total number of formula-eligible children.

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SCHOOL DISTRICT ESTIMATES 45 census estimates that are used to form school district shares of poor school-age children within counties. The 1990 census estimates are subject to high sampling variability, which is a problem for the Bureau's synthetic shares model. This high variability is also a problem for evaluations that use the 1990 census esti- mates as the standard of comparison. Opportunities to evaluate the school district estimates are constrained by the limitations of available data. The panel and the Census Bureau used a 1980-1990 school district census file to evaluate a few variations of the Bureau's synthetic model for a subset of districts. The panel also evaluated the use of National School Lunch Program data as an alternative method for constructing updated school district estimates of poor school-age children in New York State. Variability in Census Estimates The two inputs to the Census Bureau's synthetic model for school district estimates of the number of poor school-age children are the county model esti- mates for the target year, which have been extensively evaluated (see Chapter 2), and the 1990 census estimates for determining school district shares, which are discussed in this section. The income data that are used to determine poverty status in the census are collected on the long-form questionnaire, which was administered to an average of about one-sixth of households in 1990. The long- form sample size is orders of magnitude larger than the sample size of such household surveys as the CPS, but for small areas, the long-form estimates can exhibit high sampling variability. Table 3-2 shows the mean and median coefficient of variation (in percent) for the estimated number of poor school-age children from the 1990 census long- form sample, obtained as a simple inflation estimate, for school districts distrib- uted into groups categorized by number of school-age children, with each group containing approximately the same number of districts. The mean coefficient of variation is 32 percent for all school districts, varying from 64 percent for dis- tricts in the smallest size category (1-185 students) to 14 percent for districts in the largest size category (3,770 or more students).6 This degree of variability is high. For example, if a typical school district has about 200 poor school-age children, the long-form sample might give estimates anywhere from about 70 to about 330 poor school-age children. (This range is from 200 minus twice the coefficient of variation of 32% for the typical district to 200 plus twice that coefficient of variation.) By comparison, a common design goal for estimates that are published from a survey is a coefficient of variation of 10 percent or less. Table 3-2 also shows the mean and median coefficient of variation for school district estimates of poor school-age children that were constructed by ratio esti 6The districts in the largest size category have about 20,000 or more total population.

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46 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY TABLE 3-2 Average Coefficients of Variation (C.V.) for Two Estimates of Number of Poor School-Age Children for School Districts by Number of School-Age Children, 1990 Census Estimate from Estimate Ratio-Adjusted Long-Form from Long Form and Census Sample Short Form Number of (in percent) (in percent) School-Age Children in Number of Mean Median Mean Median District Districts C.V. C.V. C.V. C.V. Total 14,328 32 23 30 22 1 to 185 1,858 64 54 57 47 186 to 462 2,446 39 30 36 28 463 to 946 2,480 32 24 30 22 947 to 1,811 2,505 28 22 26 21 1,812 to 3,769 2,519 23 19 22 18 3,770 or more 2,520 14 11 13 11 NOTES: Excludes school districts for which the estimated number of poor school-age children is zero. School districts are defined as of 1988-1990. The coefficient of variation is the standard error of the estimate divided by the estimate. SOURCE: Data from Bureau of the Census. mation. In this approach, the proportion poor of school-age children is computed from the long-form sample data and that proportion is then applied to the esti- mated total number of school-age children from the short-form or complete- count census data, which are not subject to sampling variability. This procedure somewhat reduces the variability of the estimates: the mean coefficient of varia- tion of the ratio-adjusted estimates is 30 percent, compared with 32 percent for the long-form estimates, a reduction of 7 percent. The Census Bureau used the ratio-adjusted 1990 census estimates of poor school-age children to construct the 1995 school district estimates but, given time constraints, did not conduct research on ways to further reduce the variability of the census estimates. Such research should be a high priority. One possible approach is to use other short-form data (such as race and ethnicity, tenure, family type) as auxiliary information in the estimation of poor school-age chil- dren. Another approach is to smooth the 1990 census school district estimates

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SCHOOL DISTRICT ESTIMATES 47 with the 1990 census county estimates, which would reduce the variability for smaller size districts (see Chapter 5~. Census Data Evaluations The Census Bureau constructed a file of 1980 and 1990 census data for selected school districts, which was used to compare three sets of estimates of poor school-age children in 1989 with estimates from the 1990 census. In each instance, the 1980 census data that are used in the estimation are solely from the long form, while the 1990 census data are ratio adjusted. Three methods were used for the estimates: (1) One synthetic method used county model estimates to construct school district estimates: method (1) applied the 1980 census shares of poor school-age children for school districts (or parts of school districts) within counties in 1979 to the Census Bureau's 1989 estimates of poor school-age children from its county model, with the county estimates controlled to the national estimate of poor school-age children in 1989 (from the 1990 census). This procedure is analogous to that used by the Census Bureau to produce the 1995 school district estimates from 1990 census shares applied to 1995 county model estimates, except that the 1980 census data are not ratio adjusted. (Also, the 1980 census estimates for 1979 are 10 years out of date for the 1989 estimates, while the 1990 census estimates for 1989 are 6 years out of date for the 1995 estimates.) (2) A second synthetic method used 1990 census county estimates to con- struct school district estimates: method (2) applied the 1980 census shares of poor school-age children for school districts (or parts of school districts) within counties to the 1990 census county estimates of poor school-age children. This procedure eliminates the error in method (1) that is due to the county model. (3) The third method was a national stable shares procedure: method (3) applied the 1980 census shares of poor school-age children for school districts within the nation as a whole to the national estimate of poor school-age children in 1989 from the 1990 census. This procedure assumes no change whatsoever in the relative shares of poor school-age children among school districts from the previous census, not even the change that occurs in methods (1) and (2) because of changes in the relative shares of poor school-age children among counties. For several reasons, these comparisons provide only limited information with which to evaluate the Census Bureau's synthetic model for school district estimates. First, the alternative models are not very different from the Census Bureau's model. Second, the 1990 census estimates that are the standard of comparison are subject to high sampling variability even after ratio estimation. Finally, the evaluation file, of necessity, contains only a subset of school districts.

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48 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY Scope of Evaluation File The 1980-1990 evaluation file was constructed from school district data sets that were prepared after each census. It was not possible to retabulate the individual block records from the 1980 census to match the 1990 census school district boundaries; instead, the goal was to identify a set of school districts in the data set for each year that could reasonably be assumed to have retained the same boundaries and grade ranges. The 1980 and 1990 census school district files were matched, using their identification numbers and other characteristics, and the following kinds of 1990 districts were dropped from the evaluation file: 928 districts or district parts for which the district or part was coterminous with a county and, hence, for which the county model would provide estimates; 4,108 districts that were not "unified," that is, that covered a limited grade range, such as Kindergarten-8 or 9-12; 416 districts that were newly formed and had no counterpart in 1980; 12 districts in counties that changed boundaries between 1980 and 1990; . and 609 districts that crossed county lines and for which one or more of the county pieces in one year had no counterpart in the other year. The resulting evaluation file contains 9,243 districts, which represent 61 percent of the 15,226 school districts that were included in the 1990 census school district file and 56 percent of school-age children. The subset of school districts in the evaluation file closely resembles the entire set of 1990 school districts in terms of the distribution of total population and total number of school-age children in 1990. For example, the subset of districts in the evaluation file includes 47 percent with fewer than 5,000 people and 8 percent with more than 40,000 people; the corresponding figures for the entire set of 1990 school districts are 49 percent and 9 percent, respectively. A key assumption for using the evaluation file is that the 9,243 districts in the file, which had the same identification numbers in both 1980 and 1990, are the same districts and that their boundaries have not changed.7 This assumption could be incorrect in some instances. For example, if a school district follows township boundaries and the township annexed land from another town between 1980 and 1990, it is likely that the school district identification number was the same in both 1980 and 1990 even though the boundaries changed. 7Another assumption for using the evaluation file is that school districts for which the boundaries did not change from 1980 to 1sso represent the behavior of districts for which the boundaries did change. To the extent that changes in boundaries are associated with changes in population, the synthetic shares approach may work less well for districts for which boundary changes occurred. However, these districts were less than 7 percent of the districts in 1sso.

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SCHOOL DISTRICT ESTIMATES 49 To investigate this assumption, the Census Bureau looked at unified school districts, not coterminous with counties, that had the same identification numbers in 1990 and in the 1995-1996 school district boundary survey. For 6 percent of these districts, which accounted for 2 percent of school-age children, the total number of school-age children originally tabulated in the 1990 census differed by 5 percent or more from the number retabulated according to the 1995- 1996 bound- aries. For the remaining 94 percent of districts, the two tabulations were exactly the same or differed by less than 5 percent, indicating that the same identification number is a reasonably good indicator of stability in school district boundaries. Summary of Evaluation Results: Absolute Differences Table 3-3 provides summary statistics for the three sets of school district estimates of poor school- age children in 1989 in comparison with the 1990 census estimates. The statistics provided are the average absolute difference between the estimates from a model or method and the census, as a percentage of the average number of poor school- age children in the census, and the average proportional absolute difference be- tween each set of estimates and the 1990 census estimates. For comparison purposes, the last row of the table provides the same statistics for county esti- mates of poor school-age children in 1989 from the Census Bureau's county model. The first measure in Table 3-3 assesses the absolute difference between estimates from a method and the 1990 census in terms of numbers of poor children, while the second measure assesses the absolute difference in terms of proportional errors for school districts. From a national perspective, it can be argued that the absolute differences in terms of numbers are more important for effective Title I allocations because, with direct allocation, Title I funds are primarily distributed in proportion to the number of children in a school district. Therefore, the amount of funds that are misallocated depends primarily on the number of children rather than on the percentages by district. For example, an error of 5 percent in the number of school-age children in poverty in a large district could correspond to many thousands of children and have more impact on the allocation of funds than errors of 5 percent (or greater) in several smaller districts. However, from the district perspective, the proportional error for a district's allocation is also important. Ideally, a method will perform well on both types of measures, but, as dis- cussed below, all three synthetic shares methods perform much worse on the average proportional absolute difference measure overall than on the average absolute difference measure. The reason for this consistent finding is that there are many small school districts that tend to have much larger-than-average pro- portional errors, which are reflected in the average proportional absolute differ- ence measure. However, the much larger proportional errors for small districts do not represent many poor school-age children and so do not contribute as much to the absolute difference measure.

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64 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY be better than census shares; in other states, they might be worse. This inconsis- tency could be a problem for direct allocation of concentration grants. Overall, the panel finds four reasons to support use of the Census Bureau's school district estimates of poor school-age children for direct allocation of Title I allocation funds: the congressional mandate for direct allocations; the use of a uniform procedure to derive the Census Bureau's estimates; the somewhat greater accuracy of the Census Bureau's estimates of 1990 census shares compared with what the states can likely produce; and the absence of strong evidence that there are other, better data sources available for estimation. For the rest of our assess- ment, we consider more carefully the features of the basic grant and concentra- tion grant allocation formulas and how they may interact with the provision in the 1994 legislation that states may redistribute the aggregate allocations for districts with fewer than 20,000 people by some other method that the Department of Education approves. Basic Grants Under the current two-stage allocation process, basic grants are allocated to school districts essentially as shares of the county total amounts. Whatever the data source used by a state to form the within-county shares (e.g., census data, school lunch data, combination of two or more data sources), the county totals remain as specified by the Department of Education. The exception, as noted above, is that the department currently allows nine states in which school district boundaries bear little correspondence to county boundaries to redistribute the total basic grant allocation for the state without regard to the county allocations. For other states, the county totals, which, in turn, reflect (approximately) the Census Bureau's updated estimates from its county model, are maintained.l3 Direct allocation of basic grants to school districts by using the Census Bureau's synthetic shares estimates would have the same property of essentially respecting the county totals because the Census Bureau's estimation procedure controls the school district estimates to county estimates derived separately from its county model. The correspondence between the county totals from the two- stage allocation process and those from the sums of direct allocations to the districts in each county will not be exact for several reasons. One, the hold- harmless provisions applied at the county level will give a somewhat different result from applying the hold-harmless provisions to districts and aggregating the resulting amounts to counties. Also, in contrast to counties, a proportion of school districts (12% in 1995-1996, the most recent year for which the Depart 13The county allocations under the current two-stage allocation process correspond only approxi- mately to the county model estimates because of other factors in the allocation formula, such as hold- harmless provisions.

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SCHOOL DISTRICT ESTIMATES 65 ment of Education has data) do not receive basic grants: although there is no eligibility threshold for counties to qualify for basic grants, school districts must have at least 10 formula-eligible children, and the number of eligible children must exceed 2 percent of the total number of school-age children in the district. Nonetheless, for basic grants, the county totals would likely be fairly similar whether direct allocations are made to school districts or the two-stage process is continued. However, if states choose the option of redistributing the aggregate of the direct allocation amounts for school districts with fewer than 20,000 people by using some other data source (such as school lunch data), then the county totals for these districts may not be similar to the county amounts under the two-stage process.l4 The panel has a concern about this possible outcome: the county allocations that are made under the current two-stage process reflect (approxi- mately) the Census Bureau's county estimates from its county model, and these estimates are the only small-area estimates of poor school-age children that have been thoroughly evaluated and determined to be reasonably reliable.l5 Direct allocations that use the Census Bureau's synthetic shares school district estimates would also reflect (approximately) the Bureau's county estimates, but state plans to redistribute the direct allocation amounts for school districts with fewer than 20,000 people by using some other data source may not have this desirable property. Analysis with 1989 school lunch data for New York State districts with fewer than 20,000 people (476 districts, see the appendix, Table A-9) did not find evidence of this problem. The average absolute and average proportional abso- lute differences from 1990 census school district estimates of poor school-age children were about the same for estimates that were developed by using free lunch counts with and without county controls. However, this analysis pertains to only one alternate data source in only one state. In the absence of a complete analysis of alternate data sources, the panel believes it is desirable, to the extent possible, that the basic grant allocations reflect the county model estimates in all states, including those that choose the option of redistributing the aggregate of the direct allocations for school districts under 20,000 population by using an- other data source. The Department of Education can achieve this outcome by 14Presumably, the states that are more likely to choose this option are the 25 states that, at present, use another data source (e.g., free lunch data, free and reduced-price lunch data, or AFDC data) as the only factor or as one of the factors in allocating county allocations to districts. School districts with fewer than 20,000 people in these 25 states were 46 percent of total districts nationwide in 1990, containing 13 percent of total school-age children. 15For example, the county estimates of poor school-age children developed from the county model are much more reliable than county estimates developed by synthetic methods, such as applying within-state county shares of poor school-age children in the previous census to updated estimates from the Census Bureau's state model (see National Research Council, l998:Table 4-2).

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66 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY approving state reallocation plans that, in general, propose to aggregate the direct allocation amounts for districts under 20,000 population within counties and redistribute the county totals among the districts under 20,000 population in each county. Concentration Grants Concentration grants, in contrast to basic grants, are not allocated as shares of the county totals because only a fraction (less than half) of jurisdictions are eligible.l6 Under the current two-stage process, concentration grants are allo- cated to those counties that have at least 6,500 or more than 15 percent of for- mula-eligible school-age children. In turn, states allocate county concentration grants to those districts in eligible counties that exceed the threshold number or percentage of formula-eligible children: most districts that qualify for concentra- tion grants will do so on the basis of exceeding the percentage threshold; few will do so on the basis of having more than 6,500 formula-eligible children. Tabulations of 1990 census data in the evaluation file identified 30 percent of school districts, containing 60 percent of poor school-age children, as eligible for concentration grants under the current two-stage allocation process.l7 Eligible districts under the two-stage process were 65 percent of the total districts in eligible counties. (In states that use another data source to distribute county concentration amounts to districts, such as free lunch participants, a higher per- centage of school districts in eligible counties may be classified as eligible for concentration grants; see below.) The census tabulations showed that an additional 9 percent of school dis- tricts, containing 14 percent of poor school-age children, would be eligible for concentration grants if they were located in an eligible county. Currently, states may reserve up to 2 percent of their concentration grant funds to allocate to eligible districts that are not in eligible counties, but these amounts are probably not adequate for the children in those districts. We note that the use of fixed thresholds for concentration grants places great demands on the quality of the estimates of those thresholds. An error of only one poor school-age child can make the difference between receiving a grant and not receiving a grant. For school districts that receive concentration grants to which they would not be entitled if true estimates of poor school-age children were available, these errors will be perpetuated through the hold-harmless provisions, In contrast, all counties and almost 90 percent of school districts are eligible for basic grants. 17The tabulations were limited to districts in the 1980-1990 evaluation file for which the bound aries did not cross county lines, totaling 6,434 districts, or 70 percent of the districts in the evaluation file. The classification of counties and school districts as eligible for concentration grants considered only the criterion of having a school-age poverty rate of more than 15 percent.

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SCHOOL DISTRICT ESTIMATES 67 particularly if the hold-harmless rate is retained at 100 percent. (There are also fixed thresholds for school districts to receive basic grants, although they are low, as noted above.)l8 Evaluation One of the reasons for the legislation mandating direct allocations to school districts was to target concentration grants to all eligible school districts, includ- ing those in ineligible counties. To assess the appropriateness and reliability of the Census Bureau's updated school district estimates of poor school-age chil- dren for direct allocation of concentration grants, the panel first examined the rate of agreement between the Census Bureau's synthetic shares method (1) and the 1990 census in classifying school districts into one of two poverty rate categories for school-age children in 1989 that correspond to the concentration grant thresh- old: 0 to 15 percent and 15 percent or higher; see Table 3-7. The tabulations were prepared from the 1980-1990 evaluation file for districts that did not cross county lines. The synthetic method (1) school district estimates and the 1990 census ratio- adjusted estimates for 1989 assigned the same poverty rate category (0 to 15% or 15% or higher) to 76 percent of school districts and 87 percent of poor school-age children. By comparison, the county model estimates and the 1990 census county estimates for 1989 assigned the same poverty rate category to 88 percent of counties and 92 percent of poor school-age children. The rate of agreement between the synthetic method (1) school district estimates and the 1990 census ratio-adjusted estimates was least for school districts with fewer than 5,000 people: 64 percent agreement for districts and 65 percent agreement for poor school-age children.l9 The rate of agreement was highest for school districts with 40,000 or more people: 92 percent for both districts and poor school-age children, slightly better than the rate of agreement for counties. For school districts for which the synthetic method and the 1990 census estimates were not in agreement (24% in terms of districts and 13% in terms of poor school-age children), the synthetic method classified a much higher percentage as having a school-age poverty rate of under 15 percent than did the census estimates. To focus on the issue of concentration grant eligibility for school districts with direct allocations versus the current two-stage process, the panel examined the correspondence between the synthetic method (1) estimates and the 1990 18For a discussion of issues in the relationship of funding formulas and data sources; see Zaslavsky and Schirm, 1998. 19At least part of the explanation is that the census comparison estimates are subject to particularly high sampling variability for the smallest districts (see Table 3-2).

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68 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY TABLE 3-7 Agreement Between Synthetic Method (1) Estimates and 1990 Census School District Estimates for Proportions of School-Age Children in Poverty in 1989 Method of Estimate Percentage of Percentage of Poor School-Age School Districts Children Method (1) and Census Estimate, All Districts Both under 15% 50.0 25.6 Both 15% or more 25.7 60.9 (Total in agreement) (75.7) (86.5) Census under 15%, method (1) 15% or more 8.8 2.5 Census 15% or more, method (1) under 15% 15.6 11.0 Method (1) and Census Estimate, Districts Under 5,000 Population Both under 15% 37.6 20.2 Both 15% or more 26.6 44.9 (Total in agreement) (64.2) (65.1) Census under 15%, method (1) 15% or more 14.1 6.4 Census 15% or more, method (1) Under 15% 21.6 28.5 Method (1) and Census Estimate, Districts of 40,000 or More Population Both under 15% 59.8 22.0 Both 15% or more 31.8 70.0 (Total in agreement) (91.6) (92.0) Census under 15%, method (1) 15% or more 2.4 1.3 Census 15% or more, method (1) under 15% 6.0 6.8 County Model and Census Estimate, All Counties Both under 15% 30.5 40.9 Both 15% or more 57.1 50.7 (Total in agreement) (87.6) (91.6) NOTES: School district estimates are based on 9,243 districts in the 1980-1990 evaluation file. The 1990 census estimates for school districts are the ratio-adjusted estimates (see text). The method (1) school district estimates are produced by applying 1980 census within-county school district shares of poor school-age children to the county model estimates for 1989 and controlling to the 1990 census national estimate of poor school-age children in 1989. SOURCE: Data from Bureau of the Census; see National Research Council (1988:Table 4-4 [model b]) for county model comparisons. census estimates for cross-classifications of 1989 school district and county school-age poverty rate categories; see Tables 3-8 and 3-9. The synthetic method (1) estimated that 32 percent of districts, containing 59 percent of poor school- age children, would be eligible for a concentration grant under the two-stage process (cell f, Tables 3-8 and 3-9~. Another 10 percent of districts, containing 12 percent of poor school-age children, would be eligible for a concentration

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SCHOOL DISTRICT ESTIMATES 69 grant under direct allocations (cell o). These aggregate percentages are similar to those for the 1990 census, noted above (see cells h and q in Tables 3-8 and 3-9), but the synthetic method and the 1990 census classified a number of districts differently. Of the districts and poor school-age children that the 1990 census estimated would be eligible for concentration grants under the two-stage process, the syn- thetic method (1) agreed for 86 percent of districts and 96 percent of poor school- age children (cell e divided by cell h). The other 14 percent of districts and 4 percent of poor school-age children would be ineligible for concentration grants under the two-stage process according to the synthetic method (1~. There are also districts and poor school-age children that would be eligible under the two-stage process according to the synthetic method (1) but ineligible according to the 1990 census: they comprise 18 percent of the districts and 3 percent of the poor school-age children that are eligible according to the synthetic method (1) (cell d divided by cell f). Of the additional districts and poor school-age children that the 1990 census estimated would be eligible for concentration grants under direct allocations (i.e., those in counties with school-age poverty rates under 15%), the synthetic method agreed for 53 percent of districts and 76 percent of poor school-age children (cell n divided by cell q). The other 47 percent of the additional districts and 24 percent of the additional poor school-age children would be ineligible according to the synthetic method (1~. There are also additional districts and poor school- age children that would be eligible according to the synthetic method (1) but ineligible according to the 1990 census: they comprise 49 percent of the addi- tional districts and 10 percent of the additional poor school-age children that are eligible according to the synthetic method (1) (cell m divided by cell o). Overall, the classification differences between the 1990 census estimates and the synthetic method (1) estimates are relatively large for the additional districts that would be eligible under direct allocations (i.e., districts with 15% or more poor school-age children in counties with less than 15% poor school-age chil- dren). However, the classification differences are relatively small for the addi- tional poor school-age children that would be eligible under direct allocations. In particular, the percentage of poor school-age children in the additional districts that would be eligible for concentration grants according to the synthetic esti- mates but would not be eligible according to the 1990 census estimates is rela- tively small (10%~. It should be kept in mind that these evaluations are limited in at least three ways. First, they apply only to a subset of school districts in the evaluation file, which are, themselves, a subset of total districts. Second, like all of the evalua- tions of the Census Bureau's school district estimates, they are based on a single time comparison. Third, the 1990 census estimates that are the standard of comparison are subject to high sampling variability for smaller school districts even with ratio adjustment.

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70 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY TABLE 3-8 Comparison of Synthetic Method (1) and 1990 Census School District Estimates for Proportions of School-Age Children in Poverty in 1989, by 1990 Census County School-Age Poverty Rate: Distribution by Percentage of School Districts CENSUS COUNTY SCHOOL-AGE POVERTY RATE 15% OR MORE Census School District Rate Under 15% 15% or More Total Method (1) School District Rate Under 15% 10.8 (a) 4.3 (b) 15.1 (c) 15% or more 5.7 (d) 25.9 (e) 31.6 (f) Subtotal 16.6 (g) 30.2 (h) 46.8 (i) CENSUS COUNTY SCHOOL-AGE POVERTY RATE UNDER 15% Census School District Rate Under 15% 15% or More Total Method (1) School District Rate Under 15%38.9 (j)4.4 (k)43.3 (1) 15% or more4.9 (m)5.0 (n)9.9 (a) Subtotal43.8 (p)9.4(q)53.2(r) Total60.439.6100.0 NOTES: The two poverty rate categories used are those specified for concentration grants, 0-15 percent and 15 percent or more. Cell entries are percentages of the 6,434 school districts in the 1980-1990 evaluation file for which the boundaries did not cross county lines. The 1990 census county and school district esti- mates are the ratio-adjusted estimates (see text). The method (1) school district estimates are pro- duced by applying 1980 census within-county school district shares of poor school-age children to the county model estimates for 1989 and controlling to the 1990 census national estimate of poor school-age children in 1989. See text for discussion. SOURCE: Data from Bureau of the Census.

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SCHOOL DISTRICT ESTIMATES 7 TABLE 3-9 Comparison of Synthetic Method (1) and 1990 Census School District Estimates for Proportions of School-Age Children in Poverty in 1989, by 1990 Census County School-Age Poverty Rate: Distribution by Percentage of Poor School-Age Children CENSUS COUNTY SCHOOL-AGE POVERTY RATE 15% OR MORE Census School District Rate Under 15% 15% or More Total Method (1) School District Rate Under 15% 6.1 (a) 2.5 (b) 8.6 (c) 15% or more 1.5 (d) 57.5 (e) 59.0 (f) Subtotal 7.5 (g) 60.0 (h) 67.5 (i) CENSUS COUNTY SCHOOL-AGE POVERTY RATE UNDER 15% Census School District Rate Under 15% 15% or More Total Method (1) School District Rate Under 15%17.3 (j)3.3 (k) 20.6 (1) 15% or more1.2 (m)10.7 (n) 11.9 (o) Subtotal18.5 (p)14.0 (q) 32.5 (r) Total26.074.0 100.0 NOTES: The two poverty rate categories used are those specified for concentration grants, 0-15 percent and 15 percent or more. Cell entries are percentages of poor school-age children in 1989 in the 6,434 school districts in the 1980-1990 evaluation file for which the boundaries did not cross county lines. The 1990 census county and school district estimates are the ratio-adjusted estimates (see text). The method (1) school district estimates are produced by applying 1980 census within-county school district shares of poor school-age children to the county model estimates for 1989 and controlling to the 1990 census national estimate of poor school-age children in 1989. See text for discussion. SOURCE: Data from Bureau of the Census.

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72 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY Understanding the limits of the evaluations and the alternatives available, the panel concludes, on balance, that the use of the Census Bureau's school district estimates for direct allocations of concentration grants would be an improvement over the current two-stage process. As intended by the 1994 legislation, many of the eligible districts that could not receive concentration grants with a two-stage allocation would receive such grants with direct allocations. Reallocation of Concentration Grants The option for states to redistribute concentration grant direct allocations for school districts with fewer than 20,000 people raises several issues. Presumably, states might propose to use another method to redistribute the allocations among the districts that the Department of Education determined to be eligible for con- centration grants on the basis of the Census Bureau' s estimates. Or, states might propose to use another method to redetermine both eligibility and allocation amounts. (The states that currently distribute county concentration grant alloca- tions to districts on the basis of some other data source than the census use the alternate data source for both eligibility and amounts.) The use of free lunch or free and reduced-price lunch data in place of esti- mates of poor school-age children to redetermine eligibility as well as to redis- tribute allocation amounts would likely have the effect that more districts receive concentration grants than they would with the use of the Census Bureau's school- age poverty estimates. The reason is that the income eligibility thresholds for free or reduced-price school lunches are higher than the poverty threshold. Con- sequently, more children fall below 130 percent of poverty (the threshold for free lunches) or below 185% of poverty (the threshold for reduced-price lunches) than fall below 100% of poverty.20 (About 20% of school-age children nationally are in families with incomes below 100% of the poverty threshold, while about 26% are in families with incomes below 130% of the poverty threshold and about 38% are in families with incomes below 185% of the poverty threshold. For this same reason, it is likely that proportionately more districts are currently receiving concentration grants under the two-stage process in states that use school lunch data to determine eligibility than in states that use 1990 census data. In either case, the effect is to spread concentration grant dollars more thinly. Analysis with 1989 school lunch data for New York State school districts with fewer than 20,000 people (476 districts; see the appendix, Tables A-5 through A-8) provides evidence of the effect of using estimates that reflect higher poverty thresholds. Under the two-stage process, 136 such districts in New York 20However, not all eligible children apply for reduced-price lunches. 2iData from panel tabulations of the March CPS for income years 1994-1996.

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SCHOOL DISTRICT ESTIMATES 73 State would be eligible for concentration grants by using free and reduced-price lunch data and 112 would be eligible by using free lunch data, whereas only 76 districts would be eligible according to the synthetic method (1) estimates (or the 1990 census). Under direct allocations, the effect is much more pronounced: 294 districts with fewer than 20,000 people would be eligible for concentration grants by using free and reduced-price lunch data, and 214 districts would be eligible by using free lunch data, whereas only 109 districts would be eligible according to the synthetic method (1) estimates (115 districts according to the 1990 census). The panel concluded that any redistribution of basic grant direct allocations for districts with fewer than 20,000 people should be performed for such districts within each county to the extent possible, thereby reflecting (approximately) the county estimates of poor school-age children. For concentration grants, the panel reaches the same conclusion, although it should be noted that there may be a problem with this approach when different data are used for reallocation. For example, if a county has two school districts and only one district is eligible for a concentration grant according to the Census Bureau's estimates of poor school- age children, but both districts are eligible by using school lunch data, then the first district will lose some of its dollars to the second district. Presumably, similar situations occur under the current two-stage allocation process, in which school district concentration grants are allotted from county totals.22 However, such situations may be somewhat more likely to occur under direct allocations, which will provide concentration grants to eligible districts in counties that do not meet the concentration grant threshold. One approach that could ameliorate this effect is to adjust school lunch data for school districts in a county to equal the Census Bureau's estimate of total poor school-age children for the county. The use of adjusted school lunch data to determine school-age poverty rates would be less likely to result in a much larger number of school districts qualifying for concentration grants than the use of the Census Bureau's estimates of school-age poverty rates. Analysis conducted for New York State confirmed this outcome (see Appendix, Tables A-7, A-8~: 127 school districts with fewer than 20,000 people would be eligible for concentra- tion grants under direct allocations by using adjusted free and reduced-price lunch data versus 294 districts that would be eligible by using unadjusted data. The corresponding figures are 124 districts and 214 districts by using adjusted and unadjusted free lunch data. By comparison, 109 districts would be eligible by using the synthetic method (1) estimates. 22The New York State analysis, in which more districts were eligible for concentration grants under the two-stage process by using school lunch data than by using the synthetic estimates, sug- gests that such situations currently occur.

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74 SMALL-AREA ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY Study of Allocation Process Overall, by applying a relative standard for evaluation, the panel finds rea- sons to support the use of the Census Bureau's updated estimates of poor school- age children for direct allocation to school districts. Also, the panel concludes that, in general, it is desirable for both basic grant and concentration grant alloca- tions to reflect the county model estimates in all states, including those that choose the option of redistributing the direct allocations for school districts under 20,000 population by using another data source. However, the panel recognizes that there are uncertainties about the operation of the formulas: for example, the extent to which the sum of direct school district allocations for counties will approximate the allocations that would result for counties under the current two- stage process and the extent to which there may be significant reallocations of concentration grant dollars from poorer to less poor districts with county con- trols. For this reason, the panel believes it is critically important for the Depart- ment of Education to undertake a thorough study of the direct allocation process, both the methods used by the states and the results. Simulations of the allocations that would likely have been made under the two-stage process would be very helpful to inform the study.