Developing and Evaluating Methods for Using American Community Survey Data to Support the School Meals Programs Interim Report (2010) / Chapter Skim
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5 Technical Approach to Estimation
5 Technical Approach to Estimation
Pages 65-86
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From page 65... ...
However, at a minimum, we expect to be able to implement and test straightforward adaptations to SAIPE methods and to assess the feasibility of a model-based approach that would support the school meals programs. In addition, through the case studies described in Chapter 4, the panel will obtain and evaluate the accuracy of digitized school attendance boundary data and develop
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From page 66... ...
REIMbuRSEMENTS uNDER PROvISION 4 Chapters 2 and 3 review basic features of the school meals programs and the ACS and sketch how ACS data might be used to determine federal reimbursements for a school, a group of schools, or an entire district that provides universal free meals under a new Provision 4. In Chapter 2, the potential role of ACS data in implementing Provision 4 was characterized by the following two reimbursement formulas: Ef Ep Er Ge 4t = R f Mt + R r Mt + R p M Et E E and G p4t = R fC fM t + R rC rM t + R pC pM t where • Ge4t is the government outlay for reimbursable meals served in month t in Provision 4 schools, based on eligibility estimates, in dollars; • Gp4t is the government outlay for reimbursable meals served in month t in Provision 4 schools, based on eligibility and participa tion estimates, in dollars; • Rf, Rr, and Rp are reimbursement rates for free meals, reduced price meals, and full-price meals, respectively; • Mt is the total number of reimbursable meals served in month t; • Ef is the estimated number of enrolled students who are eligible for free meals based on ACS and other sources; • Er is the estimated number of enrolled students who are eligible for reduced-price meals based on ACS and other sources; • E is the estimated number of enrolled students in Provision 4 schools based on ACS and other sources;
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From page 67... ...
Despite this concern and the fact that the enrollment-based formula is a special case of the participation-based formula, presenting both formulas is helpful for highlighting some of the challenges that arise in using ACS data. As noted in Chapter 3, a challenge in deriving eligibil ity estimates is that the data collected by the ACS can be used only to approximate the eligibility criteria for free and reduced-price meals.
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From page 68... ...
Before exploring the use of such methods or adjustments for potential biases, we will seek to identify the best possible measure of eligibility using ACS variables. In developing an approach to ACS direct estimation,2 the panel's first empirical task will be to examine alternative combinations of ACS variables to determine which most closely reflects the eligibility criteria of the school meals programs.
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From page 69... ...
We will evaluate differences for school districts, in aggregate and by district characteristics, such as level of need. After the panel has identified leading candidate methods for deriving direct estimates, we will work with the Census Bureau to obtain estimates for all school districts included in the bureau's geographic inventory based on 1-year, 3-year, and (eventually)
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From page 70... ...
Monthly versus Annual Income The ACS collects data on annual income and annual program benefit receipt. However, eligibility for the school meals programs is based on monthly income and current participation.
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From page 71... ...
The last three rows pertain to children under age 18. Ratios of average monthly to annual poverty rates range from 1.22 to 1.32 for all people and are about 1.22 for children under age 18, indicating that a significantly higher proportion of students may be eligible for free or reduced-price school meals on the basis of monthly rather than annual family income.
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From page 72... ...
However, the panel is not aware of data on charter and magnet schools, home schooling, open enrollment, or other public school choice programs, except possibly at the school district level. The panel will explore how best to account for the effects of programs that draw children from their neighborhood schools in collaboration with the case study districts.
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From page 73... ...
, the table gives approximate standard errors of the estimated proportion of free and reduced-price eligible students for three different-sized geographic areas. For example, for a school district with 16,000 students and a free and reduced-price eligible fraction of 0.7, the expected standard error for a 1-year ACS estimate is 0.072 -- so a 90 percent confidence interval would be 0.58 to 0.82.6 For a school, group of schools, or school district with an enrollment of 1,500 and a free and reduced-price eligibility fraction of 0.7, the standard error for a 5-year estimate is 0.101, and the 90 percent confidence interval would be 0.53 to 4 We will also consider whether direct certification information can be used more directly in the derivation of direct estimates by, for example, estimating the number of categorically eligible students from direct certification data and the number of noncategorically eligible students from ACS data.
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From page 74... ...
The magnitude of the standard errors in the table and the width of the implied confidence intervals led the panel to consider model-based estimates to reduce the variation inherent in direct estimates for small areas. Improving Precision with Small-Domain Estimation Methods There is a substantial and growing body of statistical literature on small-domain estimation (e.g., Rao, 2003)
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From page 75... ...
Our initial work will focus on the most straightforward adaptations of the SAIPE estimation procedures to produce estimates of students eligible for free meals and students eligible for reduced-price meals at the state, county, and school district levels. 9 Likely adaptations include the adjustment of the poverty thresholds from 100 percent to 130 percent and 185 percent for the dependent variables in the regression models as well as the independent variables to which such an adjustment would be applicable and operationally feasible.
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From page 76... ...
For such a model and, perhaps, for the state and county models, we can investigate the availability and potential predictive contributions of new indepen dent variables constructed from direct certification data or the CCD, for example. One challenge in using a variable that measures the extent of direct certification is that it might reflect not only how much families need assistance from the school meals programs but also how well direct certification is implemented by a school district or a state.
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From page 77... ...
The Census Bureau's disclosure review board will need to judge whether this is also the case for estimates of free and reduced-price eligible students prepared as an adaptation to SAIPE. ESTIMATES FOR SCHOOLS AND gROuPS OF SCHOOLS Defining geographic Areas Our expectation is that estimates for individual schools or groups of schools would be produced only "on demand," that is, at the request of a school district that is considering adoption of Provision 4 but, due to substantial heterogeneity of need across schools in the district, might not adopt Provision 4 district-wide.
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From page 78... ...
Deriving Estimates Direct estimates of eligible students for schools or groups of schools will probably have to be derived by aggregating and weighting sample counts for blocks. For many schools, however, the attendance boundaries 12 I n the future, if the School Attendance Boundary Information System project (National Science Foundation, 2009)
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From page 79... ...
This information will shed light on the relative accuracy of different approaches to handling the geography of school attendance areas when developing ACS estimates of students eligible for the school meals programs. Given that geographic area definitions can be adequately addressed, the challenges in developing estimates for individual schools or groups of schools will be at least as great as, and probably greater than, the chal lenges in developing estimates for school districts.
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From page 80... ...
15 In SAIPE, direct ACS estimates are used in obtaining model-based estimates for counties, but federal income tax data are used to estimate shares for deriving school district estimates from the county estimates. Direct ACS estimates for school districts are not used by the current SAIPE estimation method.
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From page 81... ...
. understanding Differences in Eligibility and Participation To better understand the differences between the eligibility and participation distributions, the panel proposes to explore the extent to which the ACS estimates of student eligibility for the schools in the case study school districts differ from the percentages of approved students from the certification process and the participation rates (based on meals served)
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From page 82... ...
In school districts in which a large share of students eligible for free meals do not apply to the program (and are not directly certified) , using the ACS eligibility estimates as claiming percentages might increase reimbursements compared with the existing claiming percentages (all other things equal)
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From page 83... ...
The table was developed from average daily participation data for school districts that adopted Provision 2 in Texas. The percentage increases were computed by comparing meal counts in the 2 years before adoption of Provision 2 with meals counts in the 2 years after adoption of Provision 2 separately for elementary, middle, and high schools at various levels of initial participation (average daily number of lunches served divided by total enrollment)
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From page 84... ...
, we can estimate the overall increase in participation due to the adoption of Provision 2 and the increase in participation by category. Schools and school districts that are not on Provision 2 or Provision 3 are required to retain information on the number of students approved by category and average daily number of meals served by category for only 3 years,17 while those on Provision 2 need to retain their base year claiming percentage information as well as the current year number of total meals for which reimbursements were made.
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From page 85... ...
Then, the estimated coefficient for B is the estimated effect of providing free meals per student in category t. We will also explore specifications with the overall number of meals divided by enrollment as a dependent variable, controlling for each time period's claiming percentages.
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From page 86... ...
Our assessment will be primarily in terms of costs and revenues, although we recognize that a chief benefit, which is crucially important but hard to quantify, is that of expanding the school meals programs to reach more students and thereby improve their nutrition and readiness for learning. The financial impact for school districts will depend on the balance between the increased costs of providing more meals, on one hand, and the increase in reimbursements from higher participation, together with the savings from reduced administrative costs of certification, verification, and meal counting by category, on the other hand.
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