Small-Area Estimates of School-Age Children in Poverty Interim Report 2, Evaluation of Revised 1993 County Estimates for Title I Allocations (1998) / Chapter Skim
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2. CENSUS BUREAU ESTIMATION PROCEDURE
2. CENSUS BUREAU ESTIMATION PROCEDURE
Pages 9-19
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to study methods for producing postcensal income and poverty estimates for states and counties by using multiple data sources and innovative statistical methods. The Census Bureau launched this program in late 1993 with financial support from a consortium of five federal agencies.
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Developing and applying the Census Bureau's revised county model to produce initial estimates of the number of poor school-age children. 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 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.
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The last section describes the differences between the revised 1993 estimates that were provided to the panel in October 1997, which are assessed in this report, and the original 1993 estimates that were provided to the panel in January 1997 and assessed in its first interim report (National Research Council, 1997~. The changes in the estimates result principally from a change in one of the predictor variables in the county model that was found to improve its performance.2 REVISED COUNTY MODEL County Equation The county equation uses as predictor variables county estimates from Internal Revenue Service (IRS)
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, ui = model error for county i, and ei = sampling error of the dependent variable for county i. Dependent Variable The Census Bureau 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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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) has two sources: model error (u)
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The total sampling variance for the CPS equation, which is obtained by subtracting the total model error variance from the estimated total squared error, is then distributed among the counties as an inverse function of their sample size. The resulting estimates of model error variance and sampling error variance are used to form weights for use in estimating the county model equation by weighted least squares.6 They are also used to determine the weight to give to the model prediction and to the CPS direct estimate in developing estimates of poor school-age children for counties with sampled households in the CPS.
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Hi = proportion of poor school-age children in state i from one year of the cps,8 A= proportion of child exemptions reported by families in poverty on tax returns in state i, x2i= proportion of people receiving food stamps in state i, x3i= proportion of people under age 65 who did not file an income tax return in state i,9 7For almost all counties that have households with poor school-age children in the CPS, most of the weight is given to the model prediction; for only 2 counties is the weight for the model prediction less than 0.5 and for only 13 counties is the weight for the model prediction less than 0.75. 8The numerator is the estimated number of poor related children aged 5-17 from the CPS, and the denominator is the estimated total population of children aged 5-17 (whether related or not)
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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.l° 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 children aged 5-17 in the state. A different denominator total CPS school-age children, rather than the slightly smaller universe of related school-age children is used for consistency with the population estimates that are available to convert the estimated poverty ratios to estimated numbers of poor school-age children.
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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.ll 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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In this instance, the county model predicts poor school-age children on the log scale; when the predictions on the log scale are exponentiated back to the original numeric scale, the result is the exponential of the expected value of the dependent variable on the log scale, which is different from the expected value of the dependent variable on the original scale. This difference is referred to as transformation bias, for which a correction is made.
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These revised estimates incorporate more complete records of births and deaths. They also include a refined raking adjustment: the estimates are derived by an iterative proportional fitting procedure that rakes the 1990 census county estimates for school-age children to independently derived county total population estimates and state estimates of school-age children for 1994.
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