Small-Area Estimates of School-Age Children in Poverty Interim Report 1, Evaluation of 1993 County Estimates for Title I Allocations (1997) / Chapter Skim
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3. MODEL-BASED ESTIMATES OF POOR SCHOOL-AGE CHILDREN
3. MODEL-BASED ESTIMATES OF POOR SCHOOL-AGE CHILDREN
Pages 17-24
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From page 17... ...
In contrast, direct estimators use only the data from one source for the area and time period in question. A model-based approach is useful when there is no single source of information that can provide direct estimates, but relationships among several variables across various data sources can be used to provide estimates with acceptable precision.
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From page 18... ...
COUNTY-LEVEL MODEL Development of the Census Bureau's county-level model for estimates of the number of poor school-age children involved several steps: determining what administrative and other data sources are available for all counties that can be used in a prediction equation; specifying and estimating an equation that relates the predictor variables to a dependent variable from 3 years of the March CPS; using the estimates from the equation, together with direct estimates for counties for which they are available, to develop estimates for all counties; and, finally, adjusting the county estimates for consistency with estimates from a separate state-level model. The state-level model and the final adjustment of the county estimates are discussed following the description of the county-level model.
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From page 19... ...
The number of child exemptions reported on tax returns for families with incomes below the poverty threshold, like the number of food stamp recipients, is 2USDA counts of food stamp recipients were not complete for all counties; the Census Bureau contacted individual state agencies to obtain missing information. 3The poverty guidelines used for determining program eligibility are derived by smoothing the official poverty thresholds for families of different sizes (see Fisher, 1992)
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From page 20... ...
Nonetheless, tax information, like counts of food stamp recipients, is a useful variable to develop predictions of poverty for school-age children. Model Specification The second step in developing a model-based estimate of the number of school-age children in poverty by county is to specify and estimate a formula, or prediction equation, that relates the administrative data and other "predictor" variables to the dependent or "outcome" variable, which is an estimate of the number of school-age children in poverty from the March CPS.
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From page 21... ...
Given that only a subset of counties is represented in the March CPS sample, the relationships between the predictor variables and the dependent variable in the model are estimated solely on this subset of counties. This subset includes proportionately more large counties and proportionately fewer small counties than the distribution of all counties.6 By calculating the relationships among the predictor variables and the CPS estimates of school-age children in poverty for the subset of counties that have households in the March CPS sample with poor school-age children, it is possible to obtain a good estimate of an equation for predicting the number of poor schoolage children in a county, even though the CPS estimate for any specific county has a measurable level of uncertainty that is large for many small counties.7 The prediction equation can then be used to predict the number of school-age children 5The population estimates for people under age 21 are the estimated resident population under age 21 derived from demographic analysis minus the estimated population in institutions and military barracks for that age group; see Appendix D
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From page 22... ...
However, it differs in a number of respects: · The state-level model uses as the dependent variable the proportion of school-age children in poverty: that is, the dependent variable is a poverty ratio rather than the number of poor school-age children, as in the county-level model.9 The numerator for the ratio is the CPS estimate of poor school-age children in a state (i.e., the estimate of the number of poor related children aged 5-17~; the denominator is the CPS estimate of the total number of noninstitutionalized children aged 5-17 in the state.~° The variation in the difference between the model prediction and the actual number of school-age children in poverty is assumed to be the same, on a proportional basis, for all counties with households in the March CPS sample. This difference is termed model error: as used in statistics, "error" is the inevitable discrepancy between the truth and an estimate due to variability in measurements and the fact that modeled relationships are not precise.
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From page 23... ...
The national estimate pertains to related children aged 5-17 so that, at this final stage, the state estimates are consistent with the county estimates in that both sets represent estimates of the numbers of related children aged 5-17 in poverty. ADJUSTMENT OF COUNTY ESTIMATES TO STATE CONTROLS The county-level model described above produces an initial set of estimates of the number of poor school-age children in each county in the United States.
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From page 24... ...
The county-level model predicts the number of school-age children in poverty. Estimates of county poverty rates for school-age children, which play an important but secondary role in the Title I allocation formula, are obtained by dividing the estimated number of school-age children in poverty from the countylevel model by an updated estimate of the county noninstitutionalized population aged 5-17, adjusted to represent related school-age children.
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