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Appendix Use of School Lunch Data in New York State for the Estimation of School-Age Children in Poverty: An Analysis James H. Wyckoff and Frank Papa This analysis uses data from the National School Lunch Program in New York State as an alternative to census data in estimating the number of poor children (age 5-17) for use in the allocation of Title I funds to school districts. This analysis considers two uses of poverty estimates in the Title I allocations. First, for the purpose of estimating the number of school-age children who are in poor families in 1989, we compare estimates from using school lunch data for 1990 with estimates from the Census Bureau's synthetic or constant-share method that is based on 1980 census data. Second, we examine the sensitivity of various methods in estimating the 15 percent threshold for concentration grants. In conclusion, we examine some of the difficulties we encountered in attempting to use school lunch data for this purpose. Although this analysis may provide some interesting insights to some evaluation questions, it only reflects the experience in one state; other states may well differ in critical ways that would lead outcomes to change as well. The data for this analysis cover public schools and come from the New York State Education Department Report 325 for February 1990, printed on July 10, 1992. The 325 Report is an accounting of the number of eligible applicants for free and reduced-price school lunches by school. Our data include all public school reports.1 1Some of the state's 3,279 public schools did not send reports to the New York State Education Department: most of those 389 schools did not operate a school lunch program. Those observations are treated as zeros in the analysis. Reports from private schools are also available but they have not been included in this analysis: 804 private schools reported 42,828 free and reduced-price school lunch applicants in February 1990. This number represents about 12 percent of all school lunch applicants. 97

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98 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY ESTIMATES OF POOR CHILDREN The school lunch method for estimating the number of poor children in each school district is conceptually similar to the census constant-share method. County totals of poor children are allocated to specific school districts on the basis of an estimate of the ratio of poor children in the district to the county total. The school lunch ratio is computed by the ratio of free (or free and reduced-price) school lunch applicants in a school district to those in the county. This ratio is then multiplied by the total number of poor school-age children in the county (from the 1990 census) to arrive at the school district estimate. When districts cross county boundaries, the district is assigned to the county in which the school district administrative office is located.2 In summary: S. go Yip'=-trio Cent, where: J. 1990, (1) yj'is the school lunch estimate of poor school-age children in school district SLi9j0 is the number of school lunch applicants in county i, school district j in Is the number of school lunch applicants in county i in 1990, and CENi90iS the 1990 census estimate of poor school-age children in county i. The evaluation below compares these estimates of poor school-age children to those estimated using the census constant-share method, which applies 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 (synthetic method (2) in Chapter 3~. Mean algebraic and absolute percentage errors are estimated for each method by using the 1990 census totals for school districts as "truth." Tables A-1 to A-3 summarize these results. Table A-1 illustrates the distribution of the algebraic percentage errors, unweighted and when each district is weighted by the number of school-age 2We also computed estimates by employing school-level data to form county pieces when schools of a district are located in more than one county. Roughly 35 percent of the districts cross county boundaries. This estimation method produces estimates that are very close to the method that does not account for the county pieces. As a result, we present only the results that assign a whole district to the county of the district's administrative of lice.

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APPENDIX 99 TABLE A-1 Distribution of Algebraic Percentage Errors for Children Age 5 17 in Families in Poverty, Various Models, Unweighted and Weighted, New York State School Districts in Evaluation Universe, 1990 (N = 623), in percent Census Free and Distribution of AlgebraicConstant Reduced-Price Percentage Errors1980 Share Free Lunch Lunch Unweighted Mean31.2 7.1 14.0 Less than-40.0%10.3 20.4 17.7 -40.0 to -20.0%11.4 12.4 12.8 -19.9 to-10.0%10.6 9.5 9.1 -9.9 to-0.1%9.0 9.5 10.1 0.0to 9.9%10.6 12.0 9.8 10.0to 19.9%7.7 6.6 7.5 20.0 to 39.9%11.9 11.9 10.3 40.0% and more28.6 17.8 22.6 Weighted by Related Children Age 5-17 in Poverty, 1990 Census Mean0.8 1.6 1.3 Less than -40.0%5.0 8.1 6.8 -40.0 to -20.0%16.0 11.0 13.7 -19.9 to-10.0%17.0 10.0 12.1 -9.9 to-0.1%28.6 10.8 29.8 0.0 to 9.9%7.2 33.8 11.8 10.0 to 19.9%8.1 8.1 5.0 20.0to 39.9%8.1 7.9 8.9 40% and more10.1 10.3 11.9 NOTES: The census constant 1980 share estimates are calculated as described in Chapter 3 (syn- thetic method (2)). The school lunch estimates are formed by multiplying the 1990 census estimates of related children age 5-17 in families in poverty for the county by the school district's share of the county's free (free and reduced-price) lunch participants. The mean unweighted algebraic percent- age error is the sum over all school districts of the algebraic difference between the estimate of poor school-age children from a model and the 1990 census estimate as a proportion of the census esti- mate for each district, divided by the number of districts. The weighted mean weights each differ- ence by the census number of poor school-age children in the district.

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100 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY TABLE A-2 Mean Absolute and Algebraic Percentage Errors for Children Age 5-17 in Families in Poverty, Various Methods, New York State School Districts in Evaluation Universe, 1990, Unweighted, in percent Census Constant 1980 Share Percent of Mean Mean Districts Absolute Algebraic Category (N = 623) % Error % Error Total 100.0 53.4 31.2 1990 School District Population Under 2,500 11.9 66.3 34.0 2,500-4,999 14.3 41.2 15.8 5,000-7,499 17.5 57.7 32.6 7,500-9,999 10.8 58.7 28.3 10,000-14,999 12.5 61.3 45.1 15,000-19,999 9.5 43.5 29.8 20,000-29,999 10.8 67.2 55.8 30,000-39,999 5.3 36.5 11.6 40,000-49,999 2.9 42.6 25.1 50,000-99,999 3.9 24.9 10.7 100,000 or more 0.8 12.0 -12.0 1980-1990 Population Growth Decrease of 10.0% or more 3.9 45.5 30.6 Decrease of 5.0-9.9% 12.0 54.7 34.9 Decrease of 0.1 -4.9% 24.4 48.1 27.1 Increase of 0.0-4.9% 21.8 50.6 28.1 Increase of 5.0-9.9% 15.9 58.2 35.8 Increase of 10.0% or more 22.0 59.4 33.4 Percentage Poor School-Age Children, 1990 0.0% 2.3 0.0 0.0 0.1 %-5.9% 34.2 97.7 83.6 6.0-8.9% 16.1 42.1 20.1 9.0- 12.4% 17.0 33.1 8.7 12.5-16.4% 15.1 26.4 3.0 16.5-23.9% 11.9 23.6 -15.6 24.0% or more 3.5 24.6 -20.6

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APPENDIX 10 Free Lunch Mean Absolute % Error Free and Reduced-Price Lunch Mean Algebraic % Error Mean Absolute % Error Mean Algebraic % Error 48.77.1 52.114.0 57.44.6 59.810.1 40.1-0.4 41.94.2 65.830.4 71.238.8 47.2-12.1 45.7-10.1 53.222.1 60.431.3 39.3-6.3 43.11.3 47.314.1 54.327.8 37.2-9.0 38.3-3.3 36.7-14.4 36.9-8.0 24.2-7.0 26.5-2.9 5.15.1 4.7-0.9 23.4-0.9 31.810.0 63.07.0 67.511.0 39.3-10.3 40.4-4.9 47.920.4 51.227.7 43.012.0 47.220.1 60.611.3 64.619.4 0.00.0 0.00.0 81.422.2 90.237.6 41.92.7 44.88.9 41.06.8 41.710.6 22.6-2.0 22.00.8 24.3-10.4 23.4-12.3 24.2-16.3 24.5-21.4

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102 TABLE A-2 Continued SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY Census Constant 1980 Share Percent of Mean Mean Districts Absolute Algebraic Category (N = 623) % Error % Error Change in Poverty Rates for Children, 1980- 1990 Decrease of 10.0% or more 4.5 132.1 129.3 Decrease of 5.0-9.9% 11.9 95.9 93.4 Decrease of 0.1-4.9% 46.1 55.8 50.2 Increase of 0.0-4.9% 29.2 23.9 -18.7 Increase of 5.0-9.9% 7.1 37.6 -37.1 Increase of 10.0% or more 1.3 59.1 -59.1 Percent of Population Black, 1990 0.0-0.9% 15.1 29.9 9.9 1.0-4.9% 36.9 48.6 23.9 5.0-9.9% 34.7 64.5 42.0 10.0-24.9% 13.3 64.5 47.1 Percent of Population Hispanic, 1990 0.0-0.9% 1.0-4.9% 5.0-9.9% 22.6 38.4 16.0 49.3 48.8 28.4 28.1 73.7 48.3 NOTES: The census constant 1980 share estimates are calculated as described in Chapter 3 (syn- thetic method (2)). The school lunch estimates are formed by multiplying the 1990 census estimates of related children age 5-17 in families in poverty for the county by the school district's share of the county's free (free and reduced-price) lunch participants. The mean unweighted absolute (algebraic) children from families in poverty. Each of the methods results in estimates with some very large errors. For example, consider the weighted results. All three methods have at least 15 percent of the districts with errors of at least 40 percent. This pattern is also illustrated in Table A-2, which shows unweighted estimates broken down by various school district characteristics. Regardless of method, the errors are very large on average and in most categories. Weighting by the number of poor school-age children in 1990 substantially reduces the percentage errors across all methods, as shown in Table A-3. This approach yields results that are quite similar across all three models. Mean

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APPENDIX 103 Free Lunch Free and Reduced-Price Lunch Mean Mean Mean Mean Absolute Algebraic Absolute Algebraic % Error % Error % Error % Error 101.8 48.1 103.3 51.8 64.5 47.5 73.4 57.2 53.4 11.5 57.0 20.5 33.8 -13.5 34.5 -8.6 26.4 -23.1 26.1 -21.5 44.2 -36.2 43.9 -42.0 33.3 5.3 34.8 9.8 46.7 17.2 50.0 22.0 54.0 0.2 57.5 8.2 57.8 0.9 64.2 11.7 41.3 13.8 45.3 19.2 40.8 9.9 44.1 18.4 68.5 -3.2 71.5 2.0 percentage error is the sum over all school districts of the absolute (algebraic or signed) difference between the estimate of poor school-age children from a model and the 1990 census estimate as a proportion of the census estimate for each district, divided by the number of districts. algebraic percentage errors are relatively small; however, as one would expect, mean absolute percentage errors are much larger. Most of the patterns of errors with respect to school district attributes are as would be expected. For example, school districts with small total population have larger errors than districts with larger populations. An important result of this analysis is that even after some effort in data preparation, the school lunch method is still not meaningfully better than the census constant-share method. At least in New York State it does not appear that

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104 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY TABLE A-3 Mean Absolute and Algebraic Percentage Errors for Children Age 5-17 in Families in Poverty, Various Methods, New York State School Districts in Evaluation Universe, 1990, Weighted by Children Age 5-17 in Poverty, 1990 Census, in percent Census Constant 1980 Share Category Percent of Districts (N = 623) Mean Absolute % Error Mean Algebraic % Error Total 100.0 23.9 0.8 1990 School District Population Under 2,500 11.9 43.4 13.8 2,500-4,999 14.3 30.4 4.2 5,000-7,499 17.5 31.6 -0.1 7,500-9,999 10.8 32.5 -4.4 10,000-14,999 12.5 34.8 13.2 15,000-19,999 9.5 21.6 4.0 20,000-29,999 10.8 37.8 21.4 30,000-39,999 5.3 31.5 -2.0 40,000-49,999 2.9 33.6 9.4 50,000-99,999 3.9 18.3 -0.4 100,000 or more 0.8 10.4 -10.4 1980- 1990 Population Growth Decrease of 10.0% or more 3.9 31.2 26.2 Decrease of 5.0-9.9% 12.0 13.7 -4.2 Decrease of 0.1-4.9% 24.4 20.8 -3.7 Increase of 0.0-4.9% 21.8 31.1 9.9 Increase of 5.0-9.9% 15.9 30.1 2.2 Increase of 10.0% or more 22.0 32.4 2.9 Percentage of Poor School-Age Children, 1990 0.0% 2.3 0.0 0.0 0.1-5.9% 34.2 53.4 40.3 6.0-8.9% 16.1 34.0 9.6 9.0- 12.4% 17.0 22.2 4.5 12.5- 16.4% 15.1 22.7 -2.1 16.5-23.9% 11.9 19.0 -14.8 24.0% or more 3.5 11.3 -10.1

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APPENDIX 105 Free Lunch Mean Absolute % Error Free and Reduced-Price Lunch Mean Algebraic % Error Mean Mean Absolute Algebraic % Error % Error 22.3 38.5 31.6 34.2 32.6 32.0 24.9 36.3 27.9 34.0 21.0 3.4 9.8 10.2 17.2 32.5 29.9 39.0 0.0 47.1 34.3 36.3 19.6 18.2 5.4 1.6 -7.4 -11.2 1.3 -4.6 6.8 0.9 13.8 3.1 -6.8 -1.5 3.4 2.2 -3.8 1.9 8.6 0.3 2.0 0.0 -5.3 2.8 19.5 -1.6 1.4 -0.6 24.2 39.2 31.8 34.9 30.0 35.6 28.7 39.7 28.1 35.6 24.0 5.3 24.2 17.0 17.1 33.1 30.6 38.0 0.0 52.1 36.7 38.5 20.0 16.2 9.1 1.3 -4.5 -7.3 3.9 -4.5 10.9 5.3 21.1 3.4 -6.3 -3.2 -3.0 7.7 9.8 1.1 11.5 3.3 4.6 0.0 8.7 8.6 23.5 -2.3 -3.3 -7.8

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106 TABLE A-3 Continued SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY Census Constant 1980 Share Percent of Mean Mean Districts Absolute Algebraic Category (N = 623) % Error % Error Change in Poverty Rates for Children, 1980- 1990 Decrease of 10.0% or more 4.5 79.3 75.3 Decrease of 5.0-9.9% 11.9 47.0 38.1 Decrease of 0.1-4.9% 46.1 32.1 23.1 Increase of 0.0-4.9% 29.2 19.0 -15.0 Increase of 5.0-9.9% 7.1 16.9 -15.7 Increase of 10.0% or more 1.3 10.6 -10.6 Percent of Population Black, 1990 0.0-0.9% 15.1 21.4 -0.5 1.0-4.9% 36.9 24.4 0.5 5.0-9.9% 34.7 30.1 2.4 10.0-24.9% 13.3 16.9 -0.6 Percent of Population Hispanic, 1990 0.0-0.9% 22.6 22.7 0.7 1.0-4.9% 49.3 20.1 -0.5 5.0-9.9% 28.1 34.8 4.1 NOTE: See notes to Table A-2. using school lunch data results in significant gains in estimating school-age chil- dren from poor families. ESTIMATES OF THE CONCENTRATION GRANT THRESHOLD Eligibility for Title I concentration grants is based on having a school-age poverty rate of at least 15 percent or at least 6,500 poor children.3 Current Title 3Children eligible for Title I are not limited to school-age children from poor families (see Chap- ter 1). However, for the purpose of this analysis, which is to examine the census constant-share estimates of school-age children from poor families, eligibility is so characterized.

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APPENDIX 107 Free Lunch Free and Reduced-Price Lunch Mean Mean Mean Mean Absolute Algebraic Absolute Algebraic % Error % Error % Error % Error 64.9 41.4 36.0 20.9 8.5 5.5 22.4 23.6 32.0 9.8 23.5 15.0 40.8 19.5 31.7 7.1 -4.8 -5.2 -1.2 -2.6 0.5 4.6 0.0 0.0 0.5 5.4 68.2 43.1 37.9 21.1 12.0 7.8 23.8 24.6 32.1 14.5 25.5 18.1 39.3 23.5 32.4 12.0 -3.6 -10.5 -7.7 -0.9 0.0 4.1 -0.3 0.7 0.0 5.2 I allocations employ a two-stage eligibility criterion. A district must be in a county that meets the 15 percent (or 6,500) rule, and the district itself must meet that criterion. Under the proposed direct allocation system, grants will be made directly to districts and, as such, eligibility will be determined solely with regard to district poverty rates, without regard to county poverty rates. The proposed direct allocation method also permits states to aggregate the allocations to dis- tricts that have total population of less than 20,000 and reallocate this total based on alternative data, such as those from the National School Lunch Program. It is of interest to examine eligibility for concentration grants in those districts with less than 20,000 population under three different scenarios: the current two-stage process, the direct allocation process to districts without controls, and direct

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08 SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY allocations when school district poverty estimates must sum to the census county totals. We examine how concentration grants eligibility differs under these cir- cumstances when school lunch data are used rather than census constant-share estimates, using 1990 census ratio-adjusted counts as the measure of truth. Of the 623 districts in New York State that are in the census evaluation universe, 476 are in districts that had less than 20,000 total population in 1990. As shown in Table A-4, these 476 districts represent 76 percent of all districts in the evaluation universe for New York, but they contain only 35 percent of the poor children age 5-17 in the census evaluation universe. Tables A-5 to A-8 examine estimates of the number of districts and percent- age of school-age children who are in poor families under alternative estimation methods in 1990. The census counts are the ratio-adjusted estimates of school- age children who are in poor families from the 1990 census. Census-based estimates (synthetic method (2) estimates) use the 1990 census counts of county school-age children who are in poor families and allocate these totals to school districts by the school district's share of county totals from the 1980 census. The model-based estimates (synthetic method (1) estimates) use a similar approach, but with the county estimates of school-age children who are in poor families in 1989 produced from the Census Bureau's county model. The school lunch esti- mates are produced, as outlined above, by using 1990 county ratio-adjusted esti- mates of school-age children who are in poor families from the 1990 census and allocating them to constituent school districts by the share of that school district's free (or free and reduced-price) school lunch eligibles relative to the county total. Tables A-5 and A-6 provide estimates for the two-tier concentration grant eligibility for districts with total population (from the 1990 census) of less than 20,000. That is, districts must be in counties where at least 15 percent (or 6,500) of the school-age children are poor and in a district that also meets this criterion.4 If we take the census counts as our measure of "truth," then employing school lunch data will likely overstate eligibility. As shown in Table A-5, roughly 50 percent more districts and school-age children are estimated to be eligible with free school lunch data than with the census counts. This problem is further magnified when the free and reduced-price lunch counts are employed. Table A- 6 illustrates where each method errs relative to the eligibility categorization of the census counts: as might be expected, the school lunch estimates produce a substantial number of false positives. Tables A-7 and A-8 provide a similar analysis for direct allocations. Now districts must only meet the single criterion that the district has at least 15 percent 4In Tables A-5 and A-6, county eligibility is determined by the county counts from the 1sso census. Within each of these eligible counties, the alternative methods listed are used to determine school district eligibility.

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APPENDIX TABLE A-4 New York State Districts in Evaluation Universe Above and Below the 20,000 Population Threshold for Pooling Allocations (N = 623) 109 Districts Poor Children Age 5-17 Category Number Percent Number Percent School District Total Population Less than 20,000 At least 20,000 476 76.4 147 23.6 61,236 35.0 113,556 65.0 TABLE A-5 Concentration Grant Eligibility at County and School District Level, Various Methods for New York State Districts in Evaluation Universe with Less than 20,000 Population, 1990 (N = 476) Districts Method Poor Children Age 5-17 Number Percent Number Percent Census Counts 76 16.0 16,689 27.3 Census-based Estimates 78 16.4 14,162 23.1 Model-based Estimates 76 16.0 14,134 23.1 Free Luncha 112 23.5 21,662 35.4 Free and Reduced- 136 28.6 24,515 40.0 price Luncha NOTES: Cell entries are for school districts and poor school-age children that would be eligible for concentration grants according to various methods (see text) under the current two-stage allocation process (i.e., both county and school district have more than 6,500 or more than 15% poor school-age children). The total number of poor school-age children in districts with less than 20,000 population is 61,236. aSome school districts (54 or 11.3%) did not report school lunch data.

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APPENDIX 111 TABLE A-7 Concentration Grant Eligibility at School District Level, Various Methods for New York State Districts in Evaluation Universe with Less than 20,000 Population, 1990 (N = 476) Districts Method Poor Children Age 5-17 Number Percent Number Percent Census Counts 115 24.2 25,343 41.4 Census-based Estimates 114 24.0 19,596 32.0 Model-based Estimates 109 22.9 18,285 29.9 Free Luncha 214 45.0 39,222 64.1 Free and Reduced-price 294 61.8 48,835 79.8 Luncha Free Lunch with 124 26.1 25,024 40.9 Controlsa, b Free and Reduced-price 127 26.7 24,045 39.3 Lunch with Controls NOTES: Cell entries are for school districts and poor school-age children that would be eligible for concentration grants according to various methods (see text) under a direct allocation process (i.e., the school district has more than 6,500 or more than 15% poor school-age children). The total number of poor school-age children in districts with less than 20,000 population is 61,236. aSome school districts (54 or 11.3%) did not report school lunch data. bControls are imposed at the county level so that number of poor children and number of children in the school district must sum to county census counts for 1990. of its school-age children who are poor (or at least a total of 6,500~. These estimates also show the effect of imposing county controls on the use of school lunch estimates. (The county controls are equivalent to the estimates produced by equation 1, above.) The school lunch estimates without controls greatly overstate concentration grant eligibility. Imposing county controls substantially improves the accuracy of these estimates. Table A-9 shows mean algebraic and absolute percentage errors for the various estimation methods. Here the school lunch estimates have either been controlled to the statewide total of school-age children living in poor families for the 476 districts with populations of less than 20,000 or to a similar county total. With these controls in place, each of the methods has roughly the same algebraic and absolute percentage errors. This result is interesting as the school lunch estimates with county controls had the potential to be either better or worse than the estimates with state controls. We would in general expect them to be better as there is a tighter level of control imposed. It is possible that they are worse as a result of lack of precision that occurs when school districts cross county bound- aries and school lunch data are coded to the county where the district office is located.

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4 SMALL-AREA ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY PROBLEMS WITH THIS APPROACH Using school lunch data to estimate the number of poor children for each school district has several potential problems, based on the experience in New York State. As has been widely acknowledged: Participants in the National School Lunch Program are not the target population of Title I: There are differences in eligibility between Title I and school lunch. There are differences in reporting geography: Title I counts resi- dents, school lunch counts by location of the school the child attends. Not all eligible students apply for the school lunch program, and applica- tion rates appear to be uneven across schools. Some schools choose not to participate in the school lunch program. Other difficulties include: New York State has a number of regional (groups of counties) educa- tional authorities with students, and they participate in the school lunch program; how to allocate these students is an issue. In New York State, the school lunch program is administered separately from most other programs, which can make use of the administrative data diffi- cult (e.g., schools sometimes have separate identification numbers, which makes matching to other data very time consuming).