7

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 were required: (1) estimates of related school-age children (aged 5-17) who were in poor families 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 were needed to implement the allocation formulas for basic and concentration grants; the third set of estimates was needed to determine which school districts have fewer than 20,000 people.2

This chapter considers estimates of poor school-age children for school districts. It reviews the difficulties that confront attempts to develop such estimates; 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. Finally, the chapter discusses the implications of the evaluations for the use of updated school district estimates for Title I allocations. Chapter 8 describes the procedure

1  

See Chapter 1 for the definition of related children.

2  

States, 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.



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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology 7 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 were required: (1) estimates of related school-age children (aged 5-17) who were in poor families 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 were needed to implement the allocation formulas for basic and concentration grants; the third set of estimates was needed to determine which school districts have fewer than 20,000 people.2 This chapter considers estimates of poor school-age children for school districts. It reviews the difficulties that confront attempts to develop such estimates; 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. Finally, the chapter discusses the implications of the evaluations for the use of updated school district estimates for Title I allocations. Chapter 8 describes the procedure 1   See Chapter 1 for the definition of related children. 2   States, 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.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology and evaluations for estimates of the number of all school-age children and of the total population in July 1996 for school districts. ISSUES IN ESTIMATING POVERTY FOR SCHOOL DISTRICTS Developing estimates of the number of poor school-age children (or other characteristics) for school districts presents 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 instances 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. Because 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 can be made by aggregating data for blocks from the decennial census. We briefly review each of these issues in turn. Size Table 7-1 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 households will be very unreliable (i.e., exhibit high sampling variability).3 Even longform census data, as discussed below, are unreliable for many school districts. 3   The American Community Survey that is planned to start in 2003 will collect data from about 3 million housing units each year on an ongoing basis using an unclustered design. It will have sampled households in all school districts, but the sample size will not be large enough to produce sufficiently reliable estimates of poor school-age children for most districts even when the sample is aggregated over 5 years. See National Research Council (2000:Ch.4) for details.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 7-1 Percentage Distribution of School Districts, School Districts Coterminous with Counties, and Counties by Population Size, 1990 Census   All School Districts School Districts Coterminous with Counties   Total Population Districts (1) School-Age Children (2) Districts (3) School-Age Children (4) Counties (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 31.7 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 U.S. Census Bureau. 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).4 In another 17 states, school district boundaries coincide with other political 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). 4   In 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 (see Appendix E).

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology Overall, in 1990, there were 928 districts that comprised an entire county or, in the case of a few districts (e.g., New York City), two or more entire counties. (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 7-1, col. 3)–close to the median population size for all counties (Table 7-1, col. 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 estimates of poor school-age children for districts that serve specific grades is difficult 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 districts, principally because of the lack of administrative data with which to form the predictor variables in a regression model. For example, states do not generally geocode the addresses of Food Stamp Program participants to school districts, 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 students who are approved to receive free meals under 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 are of uncertain quality and applicability (see below, “School Lunch Data ”). In the future, it may be possible to develop appropriate

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology data sources for a model-based approach to estimating poor school-age children for school districts (see Chapter 9; see also National Research Council, 2000: Ch.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 within-county shares approach to estimate poor school-age children by school districts for 1995. The approach involved seven steps: A survey was conducted in which officials in every state were asked to provide school district boundaries for the 1995-1996 school year. Each 1990 census block was assigned to a school district, as defined for 1995-1996.5 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. 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 of poor school-age children 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 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. 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%.) 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 4) to obtain 1995 estimates of poor school-age children for school districts or school district parts. The 1995 school district estimates of poor school-age children were 5   When 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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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology 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. As an example of the within-county shares 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 districts 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 proportionate 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. For the 1997-1998 school year, 18 states used a similar procedure for allocating their Title I county funds to school districts, in that they made 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 used 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 of poor school-age children 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 also had to 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 delinquent children, and in families with income above the poverty line who receive welfare assistance);6 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 also had to be adjusted to reflect school district boundary changes between 1995-1996 and 1998-1999; the department left it to the states to make appropriate adjustments. 6   Poor school-age children estimated by the Census Bureau were 96.2 percent of the total number of formula-eligible children counted in the Title I allocations for the 1998-1999 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 0.1 percent, respectively, of the total number of formula-eligible children.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology 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 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 shares procedure. This high variability is also a problem for evaluations that use the 1990 census estimates 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 shares procedure 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 within-county shares procedure for school district estimates of the number of poor school-age children are the county model estimates for the target year, which have been extensively evaluated (see Chapter 6), 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 7-2 shows the mean and median coefficient of variation (in percent) for the estimated number of poor school-age children from the 1990 census longform sample, obtained as a simple inflation estimate, for school districts distributed 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 districts in the smallest size category (1-185 students) to 14 percent for districts in the largest size category (3,770 or more students). 7 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 7   The districts in the largest size category have about 20,000 or more total population.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 7-2 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 Long-Form Census Sample (in percent) Estimate Ratio-Adjusted from Long Form and Short Form (in percent) Number of School-Age Children in District Number of Districts Mean C.V. Median C.V. Mean C.V. Median 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 U.S. Census Bureau. 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 7-2 also shows the mean and median coefficient of variation for school district estimates of poor school-age children that were constructed by ratio estimation. In this approach, the proportion of poor school-age children is computed from the long-form sample data and that proportion is then applied to the estimated 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 variation 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. One possible line of research is to use other short-form data

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology (such as race and ethnicity, tenure, family type) as auxiliary information in the estimation of poor school-age children. Another line of research is to smooth the 1990 census school district estimates with the 1990 census county estimates, which would reduce the variability for smaller size districts (see Chapter 9). 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: One 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 within-county shares procedure is analogous to that used by the Census Bureau to produce the 1995 school district estimates from 1990 census within-county 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 1989 estimates, while the 1990 census estimates for 1989 are 6 years out of date for 1995 estimates.) A second method used 1990 census county estimates to construct 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. 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 within-county shares 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

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology 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. 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 had no counterpart in 1980. The resulting evaluation file contains 9,243 districts, which are 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 8   Another assumption for using the evaluation file is that school districts for which the boundaries did not change from 1980 to 1990 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 within-county 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 1990.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology same districts and that their boundaries have not changed.8 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. 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 boundaries. 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 7-3 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 between each set of estimates and the 1990 census estimates. For comparison purposes, the last row of the table provides the same statistics for county estimates of poor school-age children in 1989 from the Census Bureau's county model. The first measure in Table 7-3 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 (see Chapter 6). 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 discussed below, all three 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 proportional errors, which are reflected in the average proportional absolute difference mea-

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology boundaries.14 In addition, the ratio-adjustment procedure employed by the Census Bureau to estimate census shares somewhat reduces their variability. For the six states in this group that used 1990 census data to make direct allocations of basic grants to school districts without regard to the county allocation amounts, the use of the Bureau's 1990 census shares-based estimates has the advantage that they reflect the updated county estimates from the Bureau's county model. Twenty-five states used data sources other than the census, or in combination with the census, to suballocate county Title I funds to school districts. (Three of these states made direct allocations of basic grants to districts.) It was not possible to evaluate the accuracy of such sources as school lunch data across states. The analysis that was conducted for New York (and the preliminary analysis for Indiana, see above) suggests that there are only marginal gains in accuracy from use of school lunch data. Moreover, it is not likely that the use of a shares approach based on school lunch data would produce results that are as consistent across states as the use of a shares approach based on census data: in some states, school lunch shares might be better than census shares; in other states, they might be worse. This inconsistency could be a problem for direct allocation of concentration grants. Overall, the panel found 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 could likely produce; and the absence of strong evidence that there are other, better data sources available for estimation. For the rest of the panel's assessment, it considered more carefully the features of the basic grant and concentration grant allocation formulas and how they might 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 two-stage allocation process, basic grants were 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 remained as specified by the Department of Education. The exception is that the department allowed nine states in which school district boundaries bear little correspon- 14   The Census Bureau provided the Department of Education with a file of 1990 census data for school districts defined according to 1995-1996 boundaries, to which the states can have access.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology dence 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, reflected (approximately) the Census Bureau's updated estimates from its county model, were maintained.15 Direct allocation of basic grants to school districts by using the Census Bureau's within-county shares estimates has 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 (about 10-12%) do not receive basic grants: although there was 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 under direct allocations to school districts are likely to be fairly similar to what the allocations would be under the two-stage procedure. However, when states choose the option in the legislation to redistribute 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 sum of the amounts for the districts in a county may not be similar to what the county amount would be under the two-stage process. The panel was concerned about this possible outcome: the county allocations that were made under the two-stage process reflected (approximately) 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.16 Direct allocations that use the Census Bureau's within-county shares estimates for school districts 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. 15   The county allocations under the two-stage allocation process corresponded only approximately to the county model estimates because of other factors in the allocation formula, such as hold-harmless provisions. 16   For example, the county estimates of poor school-age children developed from the county model are much more reliable than county estimates developed by such methods 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 Chapter 6).

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology Analysis with 1989 school lunch data for New York State districts with fewer than 20,000 people (476 districts, see Appendix D, Table D-9) did not find evidence of this problem. The average absolute and average proportional absolute 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 believed it to be 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 another data source. The Department of Education can achieve this outcome by 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, were never allocated as shares of the county totals under the two-stage procedure because only a fraction (less than half) of jurisdictions was eligible.17 Under the two-stage process, concentration grants were allocated to those counties that had more than 6,500 or more than 15 percent of formula-eligible school-age children. In turn, states allocated county concentration grants to those districts in eligible counties that exceeded the threshold number or percentage of formula-eligible children: most districts that qualified for concentration grants presumably did so on the basis of exceeding the percentage threshold; few presumably did 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 two-stage allocation process.18 Eligible districts under the two-stage process were 65 percent of the total districts in eligible counties. (In states that used another data source, such as free lunch counts, to distribute county concentration amounts to districts, a higher percentage of school districts in eligible counties were likely classified as eligible for concentration grants; see below.) 17   In contrast, all counties and almost 90 percent of school districts were eligible for basic grants. 18   The tabulations were limited to districts in the 1980-1990 evaluation file for which the boundaries did not cross county lines, totaling 6,434 districts, or 70 percent of the districts in the evaluation file.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology The census tabulations showed that an additional 9 percent of school districts, containing 14 percent of poor school-age children, would be eligible for concentration grants except that they are located in a county that is not eligible. Under the two-stage procedure, states could reserve up to 2 percent of their concentration grant funds to allocate to eligible districts that were not in eligible counties, but these amounts were probably not adequate for the children in those districts. The panel noted 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, 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.) 19 Evaluation One of the reasons for the legislation mandating direct allocations to school districts was to target concentration grants to all eligible school districts, including those in ineligible counties. To assess the appropriateness and reliability of the Census Bureau's updated school district estimates of poor school-age children for direct allocation of concentration grants, the panel first examined the rate of agreement between the Census Bureau's within-county 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 threshold: 0 to 15 percent and 15 percent or higher; see Table 7-5. The tabulations were prepared from the 1980-1990 evaluation file for districts that did not cross county lines. The 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 method (1) school district estimates and the 1990 census ratio-adjusted estimates was least for school districts with fewer than 5,000 people: 64 19   For a discussion of issues in the relationship of funding formulas and data sources, see National Research Council (2000:App.).

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 7-5 Agreement Between Within-County Shares Method (1) Estimates and 1990 Census School District Estimates for Proportions of School-Age Children in Poverty in 1989 Method of Estimate Percentage of School Districts Percentage of Poor School-Age 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 U.S. Census Bureau; see Chapter 6, Table 6-5 (model b) for county model comparisons. percent agreement for districts and 65 percent agreement for poor school-age children. 20 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 20   At least part of the explanation is that the census comparison estimates are subject to particularly high sampling variability for the smallest districts (see Table 7-2).

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology better than the rate of agreement for counties. For districts and poor school-age children for which the method (1) and 1990 census estimates were not in agreement, method (1) classified a higher percentage in the under 15 percent school-age poverty rate category. To focus on the issue of concentration grant eligibility for school districts with direct allocations versus the two-stage process, the panel examined the correspondence between the method (1) estimates and the 1990 census estimates for cross-classifications of 1989 school district and county school-age poverty rate categories; see Table 7-6 and Table 7-7. 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, Table 7-6 and Table 7-7), and that another 10 percent of districts, containing 12 percent of poor school-age children would be eligible for a concentration 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 Table 7-6 and Table 7-7), but method (1) 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, 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 method (1). There are also districts and poor school-age children that would be eligible under the two-stage process according to 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 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%), method (1) 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 method (1). There are also additional districts and poor school-age children that would be eligible according to method (1) but ineligible according to the 1990 census: they comprise 49 percent of the additional districts and 10 percent of the additional poor school-age children that are eligible according to method (1) (cell m divided by cell o). Overall, the classification differences between the 1990 census estimates and the 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 children). However, the classification differences are relatively small for the additional poor school-age children that would be eligible under direct allocations. In particular, the

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 7-6 Comparison of Within-County Shares 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 (l) 15% or more 4.9 (m) 5.0 (n) 9.9 (o) Subtotal 43.8 (p) 9.4 (q) 53.2 (r) Total 60.4 39.6 100.0 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 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 discusion. SOURCE: Data from U.S. Census Bureau.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 7-7 Comparison of Within-County Shares 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 (l) 15% or more 1.2 (m) 10.7 (n) 11.9 (o) Subtotal 18.5 (p) 14.0 (q) 32.5 (r) Total 26.0 74.0 100.0 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 U.S. Census Bureau.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology percentage of poor school-age children in the additional districts that would be eligible for concentration grants according to the within-county shares method (1) estimates but would not be eligible according to the 1990 census estimates is relatively 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 evaluations of the Census Bureau 's school district estimates, they are based on a single comparison point. 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. Understanding the limits of the evaluations and the alternatives available, the panel concluded, 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 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 raised several issues for the panel to consider. States could propose to use another method, not only to redistribute the allocations among the districts that the Department of Education determined to be eligible for concentration grants on the basis of the Census Bureau's estimates, but also to redetermine eligibility. Under the previous two-stage procedure, the states that distributed county concentration grant allocations to districts on the basis of some other data source than the census used the alternate data source for both eligibility and amounts. The use of free lunch or free and reduced-price lunch data in place of estimates of poor school-age children to redetermine eligibility as well as to redistribute allocation amounts likely has the effect that more districts receive concentration grants than would be the case 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. Consequently, more children fall below 130 percent of poverty (the threshold for free lunches) or below 185 percent of poverty (the threshold for reduced-price lunches) than fall below 100 percent of poverty.21 (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 21   However, not all eligible children apply for reduced-price lunches.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology poverty threshold and about 38% are in families with incomes below 185% of the poverty threshold.)22 For this same reason, it is likely that proportionately more districts received concentration grants under the two-stage process in states that used school lunch data to determine eligibility than in states that used 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 Appendix D, Table D-5, Table D-6, Table D-7 through Table D-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 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 method (2) 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 method (2) estimates (115 districts according to the 1990 census). As noted above, 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 reached 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 occurred under the two-stage allocation process, in which school district concentration grants were allotted from county totals.23 However, such situations may be somewhat more likely to occur under direct allocations, which 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 22   Data from panel tabulations of the March CPS for income years 1994-1996. 23   The 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 method (2) estimates, suggests that such situations occurred in the past.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology Census Bureau's estimates of school-age poverty rates. Analysis conducted for New York State confirmed this outcome (see Appendix D, Table D-7, Table D-8): 127 school districts with fewer than 20,000 people would be eligible for concentration 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 method (2) estimates. Study of the Allocation Process Overall, by applying a relative standard for evaluation, the panel found reasons 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 concluded that, in general, it is desirable for both basic grant and concentration grant allocations 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 recognized 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 approximates the allocations that would result for counties under the 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 controls. For this reason, the panel believed it to be critically important for the Department 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.