Small-Area Estimates of School-Age Children in Poverty Evaluation of Current Methodology (2000) / Chapter Skim
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Estimation Procedure for Counties
Estimation Procedure for Counties
Pages 31-43
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From page 31... ...
The March Income Supplement to the Current Population Survey (CPS) can provide reasonably reliable annual direct estimates of such population characteristics as the number and proportion of poor children at the national level and possibly for the largest states.
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From page 32... ...
. The estimation procedure involves the use of separate county and state regression models.2 The chapter also summarizes differences between the state and county models used to develop the 1995 county estimates and the models used to develop the original and revised 1993 county estimates.
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From page 33... ...
The county estimation process involves: obtaining data from administrative records and other sources that are available for all counties to use as predictor variables; specifying and estimating a regression equation that relates the predictor variables to a dependent variable, which is the estimated log number of poor school-age children from 3 years of the March CPS for counties with households with poor school-age children in the CPS sample; and using the estimated regression coefficients from the equation and the predictor variables to develop estimates of poor school-age children for all counties. For counties with households in the CPS sample, the predictions from the model are then combined by a "shrinkage" procedure with the CPS estimates for those counties.
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From page 34... ...
, log~number of poor school-age children in county i in the previous vi = model error for county i, and al = sampling error of the dependent variable for county i. Dependent Variable The Census Bureau originally decided to model the number of poor school-age children, instead of the proportion, because of concern that the county population estimates of school-age children that would form the basis for converting the estimated proportions to estimated numbers were of uncertain quality.
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From page 35... ...
The number of child exemptions reported by families in poverty on tax returns and the number of food stamp recipients were included as variables that are indicative of poverty and available on a consistent basis (or reasonably consistent basis, in the case of 5The reason why the 1993 model estimation included a higher proportion of counties than the 1995 model estimation is because a redesign of the cPs sample was phased in between April 1994 and July 1995. some counties were included in the old design but not the new and vice versa; the estimation included all counties that had at least 1 year of CPS data in the 3 years centered on the estimation year.
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From page 36... ...
A reason to use logarithms is the wide variation in the CPS estimates of the dependent variable and the values of the predictor variables among counties when they are measured on the numeric scale: transforming the variables to logarithms made their distributions more symmetric and the relationships between some of them and the dependent variable more linear. Estimation of Model and Sampling Error Variance The total squared error of the county estimates (the difference between the model estimates and the direct estimates from the CPS)
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From page 37... ...
The resulting estimates of model error variance and sampling error variance are used to determine the weights to give to the model prediction from the maximum likelihood procedure and to the CPS direct estimate in developing estimates of poor school-age children for counties with sampled households with poor school-age children in the CPS. Combining the County Equation and CPS Estimates 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 with poor school-age children in the March CPS sample, it is possible to obtain a good estimate of a regression equation for predicting the number of poor school-age children in a county, even though the CPS estimates for many small counties have large levels of uncertainty.
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From page 38... ...
Step 2: 1995 State Model State Equation The state model equation takes the following form: yj = 0CO + OClxlj + OC2x2; + OC3X3j + ~4X4j + Uj + ej ~ (2) where: yj = estimated proportion of school-age children in state j who are in poverty based on the March CPS that collects income data pertaining to the estimation year,9 xlj = proportion of child exemptions reported by families in poverty on tax returns in state j, x2j = proportion of people receiving food stamps in state j, X3j = proportion of people under age 65 not included on an income tax return in state j,10 9The numerator is the estimated number of poor related children aged 5-17 from the CPS; the denominator is the estimated total population of children aged 5-17, whether or not they are related to a family, from the CPS.
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From page 39... ...
Differences from the County Equation The Census Bureau' s state model for estimates of poverty among school-age children is similar to the county model. However, it differs in a number of respects: Dependent Variable The state model uses the proportion of school-age children in poverty in each state as the dependent variable: that is, the dependent variable is a poverty ratio rather than the number of poor school-age children, as in the county model.
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From page 40... ...
Form of the Variables The variables in the state model are proportions rather than numbers and are not transformed to a logarithmic scale as is done in the county model.l2 A log-based model was examined, but the Census Bureau decided not to transform the variables because, unlike the situation with the county model, the state-level distributions of the estimated proportions for the predictor variables are reasonably symmetric, and the relationships of the statelevel estimated proportions with the dependent variable are approximately linear. Combining the State Equation and CPS Estimates All states have sampled households in the CPS; however, the variability associated with estimates from the CPS is large for some states.
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From page 41... ...
The corrected data were also used to reestimate the 1989 state and county models for evaluation purposes (see Chapter 6~. · Several changes were made to the food stamp data for input to the state model: instead of using data for July of the estimation year, the number of food stamp recipients was changed to a 12-month average centered on January 1 of the following year; counts by state of the numbers of people who received food stamps due to specific natural disasters were obtained from the Department of Agriculture and subtracted from the counts of the total number of recipients; time-series analysis of monthly state food stamp data from October 1979 through September 1997 was used to smooth outliers; and food stamp recipient data for Alaska and Hawaii were adjusted downward to reflect the higher eligibility thresholds for those states.
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From page 42... ...
The variability of the standardized residuals increased with the number of CPS sample cases rather than remaining constant, and this pattern was common to a variety of alternative models that were examined. The revised 1993 county model includes a slight revision to the procedure for estimating the sampling error variance, which moderated but did not eliminate the anomalous pattern.
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From page 43... ...
Hence, in comparison with the original 1993 estimates, the revised 1993 model predictions are given somewhat more weight and the CPS direct estimates are given somewhat less weight when weighted estimates are formed for counties that have sampled households with poor school-age children in the CPS. However, this difference had relatively little effect on the county estimates.
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