Small-Area Income and Poverty Estimates Priorities for 2000 and Beyond (2000) / Chapter Skim
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3 Current SAIPE Models
3 Current SAIPE Models
Pages 44-81
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From page 44... ...
Indirect estimates of poor school-age children for school districts are derived by using decennial census data to allocate the updated county estimates among districts. The March Current Population Survey (CPS)
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From page 45... ...
The weighted average approach for combining the model predictions and the direct estimates is advantageous in that it strikes an effective tradeoff of the model error of the model predictions and the sampling error of the direct estimates. The state-level model predictions are obtained from regression models in which a state's direct CPS estimate for the reference year is the dependent variable and the predictor variables are obtained from such sources as Internal Revenue Service (IRS)
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From page 46... ...
According to Census Bureau calculations, the SAIPE estimates, on average, have more variability due to sampling error and prediction error than the census estimates. However, the out-of-date census estimates have considerably more bias.
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From page 47... ...
(The potential uses of these sources in the SAIPE program are discussed in Chapter 4.) As noted above, the lack of administrative data at the school district level led the Census Bureau to use a simple shares approach based on 1990 census data for allocating the updated SAIPE county estimates of poor school-age children among school districts.
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From page 48... ...
of the poor school-age children in a county who are in a particular school district in the reference year is the same as it was in the 1990 census. Input Data Both the state and county models of poor school-age children use input data from five sources: the March CPS; the previous census; the Census Bureau's population estimates program; food stamp administrative records; and IRS individual income tax returns.
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From page 49... ...
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 reference year, Xjj= 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, X4j= residual for state j from a regression of the proportion of poor school-age children estimated from the prior decennial census on the three predictor variables, (Xjj, X2j, X3j) , for the census reporUng period, Uj = model error for state j, and e = sampling error of the dependent variable for state j.
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From page 50... ...
An initial estimate of the number of poor school-age children for a state is obtained by multiplying the estimated proportion poor (yj) by the estimated total number of noninstitutionalized school-age children in the state, which is obtained from the Census Bureau's program of population estimates.
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From page 51... ...
, Vji = model error for county i of state j, and aji = sampling error of the dependent variable for county i of state j. It is assumed that Vji ~ NI(O, 62)
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From page 52... ...
The estimate 6v is treated as fixed in the final estimation. Counties that are in the CPS sample and that have one or more poor school-age sampled children are included in the estimation data set for the county model, and those with no poor school-age sampled children are omitted.
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From page 53... ...
School District Procedure Because of the lack of administrative data at the school district level for constructing predictor variables, the school district estimates of poor school-age children are produced by a shares approach rather than by regression modeling. This shares approach allocates the updated county estimates among school districts in the same proportions that poor schoolage children were distributed across the districts in the 1990 census.
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From page 54... ...
Evaluations As recommended by the National Research Council panel, the Census Bureau conducted an extensive set of evaluations of the SAIPE estimates of poor school-age children for states and counties. Due to data constraints, more limited evaluations were conducted of the estimates of poor school-age children for school districts.
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From page 55... ...
State Model Results of the internal evaluations of the state model (estimated for each of the years 1989 to 1993, 1995, and 1996) largely supported the model's assumptions.8 There was no evidence of nonlinearity in the relation between the dependent variable and each predictor variable; the regression coefficients were generally similar across years; only one regression coefficient was not statistically significant (at the 5% level)
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From page 56... ...
With this procedure, if the estimates of sampling error variances are too large, the estimate of model error variance will be too small. County Model Internal evaluations were conducted for alternative county models, which were estimated for 1989 and 1993,9 and for the current county model, which was estimated for 1989, 1993, and 1995.
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From page 57... ...
Two sources of comparison values have been used for external evaluations of the SAIPE state and county models for poor school-age children-the previous census and weighted aggregates of CPS direct estimates-but neither source is ideal for this purpose. The census estimates can provide an evaluation for only one year, 1989.
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From page 58... ...
County Model Estimates of poor school-age children in 1989 from the SAIPE county model and several alternative models and four simpler procedures were compared to 1990 census estimates for all counties and for categories of counties (see National Research Council, 2000c:Ch.6~. Overall, the SAIPE model and alternative models performed better than the simpler procedures.ll For example, the average absolute difference between the 1989 estimates from the SAIPE county model and the 1990 census estimates was 11 percent of the average number of poor schoolage children.
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From page 59... ...
Evaluations of the School District Model Evaluations of the school district estimates of poor school-age children in 1995 were constrained by lack of comparison data. An internal evaluation assessed the sampling variability of the 1990 census estimates, 14The current SAIPE model uses the population under age 18 as predictor variable W3; the previous candidate model used the population under age 21.
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From page 60... ...
An external evaluation compared estimates of poor school-age children in 1989 from several shares models with 1990 census estimates.~5 All of the methods evaluated exhibited large differences from the census estimates-much larger than the differences of the SAIPE county model estimates from the 1990 census estimates (see National Research Council, 2000c:Ch.7~. However, the shares method that was analogous to the Census Bureau's procedure for the 1995 school district estimates (which applied 1980 census school district shares of poor school-age children within counties to 1989 county model estimates)
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From page 61... ...
In both cases the variance of the model prediction component of the weighted average is estimated from the regression model using maximum likelihood estimation. The variances of the state direct estimates are estimated from a generalized variance function that reflects the CPS sample design.
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From page 62... ...
However, in practice the weights for the state direct estimates are zero for all but one of the estimation years because the model error variance was estimated to be zero, and they are mostly zero for the county direct estimates because most counties had no CPS sample. The Census Bureau
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From page 63... ...
method used to account for the effect of these statelevel controls on the variances of the county estimates currently incorporates the state variances but ignores the correlation between a county estimate and the corresponding state estimate. Estimation of the variances of the state and county estimates of poor school-age children depends heavily on the estimates of the model and sampling error variance components in the regression models.
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From page 64... ...
In this case, the regression model uses the state's March CPS median household income for the reference year as the dependent variable and has two predictor variables: median household income from the most recent decennial census and an estimate of median house) 6The models for poor related children aged 5-17 and all poor children aged 5-17 differ only in the dependent variable.
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From page 65... ...
The regression model uses the 3-year average of median household income from the March CPS (not transformed to logarithms) as the dependent variable and six predictor variables: median adjusted gross income from tax returns; the ratio of the number of dependent tax returns to the total number of returns; the logarithm of the proportion of the Bureau of Economic Analysis (BEA)
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From page 66... ...
. The final county estimate of median household income is produced as a weighted average of the regression prediction and the direct estimated POPULATION ESTIMATES The SAIPE Program uses total population estimates and estimates for particular age groups as predictor variables in the state and county models.
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From page 67... ...
The Census Bureau has an extensive and long-standing program to produce small-area population estimates by using the previous census updated with administrative records. The extent of geographic and demographic detail provided by the estimates program has expanded since it first began producing U.S.
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From page 69... ...
For school districts, total population estimates are currently developed by a shares method. In this approach, 1990 census within-county 19The methodology for national-level population estimates includes an "inflation-deflation" procedure in which census estimates for age groups are adjusted for net undercount as estimated from demographic analysis.
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From page 70... ...
School district estimates for children aged 5-17 are developed from a shares approach, similar to that described for total population estimates 20See the Census Bureau's web site: http://www.census.gov/population/estimates/ state.html.
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From page 71... ...
For all children aged 5-17, the average absolute difference between the 1990 population estimates and the 1990 census counts was 4.9 percent of the average number of school-age children for counties and 12.0 percent of the average number of school-age children for school districts. These differences are much smaller than the average absolute difference for poor children aged 5-17, which was 10.7 percent of the average number of poor school-age children for counties and 22.2 percent of the average number of poor school-age children for school districts (National Research Council, 2000c:Ch.7; see In.
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From page 72... ...
Each variant predicted the log poverty rate for school-age children; one variant converted estimated poverty rates to estimated numbers of poor schoolage children by using 1980 census-based population estimates for schoolage children for 1990; the other variant converted rates to numbers by using 1990 census population counts. The average absolute difference between the model-based estimates of poor school-age children and the 1990 census estimates was only slightly higher for the first variant than for the second variant (see National Research Council, 2000c:App.C)
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From page 73... ...
Several sources could contribute to this variability, including the different measurement scales used in the state and county models (proportions for the former, logarithms of numbers for the latter) , the use of 3-year averages of CPS estimates as the dependent variable in the county model versus single-year estimates in the state model, sampling variability, and, possibly, individual state effects that are not captured in the county model.
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From page 74... ...
In an effort to determine whether the state raking factors could reflect state effects that are missing from the county model, the Census Bureau examined a county regression model that included fixed state effects. The use of this model did not reduce the spread of the raking factors; rather, it increased it.
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From page 75... ...
can be used to combine the model and direct estimates. While the application of generalized linear modeling is fairly routine in many applications, the complex sample design of the CPS must be taken into account in the estimation of the regression coefficients and in estimating the variances of the model predictions.
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From page 76... ...
. Improved Estimation of Variance Components Both the state and county models have two variance components, model error and sampling error.
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From page 77... ...
In the county model, the model error variance is equated to the model error variance in a corresponding regression model for 1990 census data; that model error variance is estimated in the manner described for the state model error variance, with the census sampling error being estimated with a GVF for the census long-form sample. The total sampling error variance in the county model is then obtained by maximum-likelihood estimation and partitioned among counties in inverse proportion to CPS sample size.
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From page 78... ...
Since these estimated numbers are based on small long-form sample sizes for many school districts, they are subject to substantial sampling error (see National Research Council, 2000c:Ch.7~. To improve the precision of census long-form estimates, the Census Bureau builds in adjustments as part of regular census data processing to make long-form totals conform to short-form totals for key short-form items for weighting areas (subcounty areas or sometimes entire counties that have a specified minimum number of sample persons)
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From page 79... ...
Although only a modest improvement in the school district census estimates may be achieved with these further adjustments, any improvement would be helpful. Another approach for improving the census school district estimates is to use a smoothing procedure to reduce the sampling errors in the longform estimates of the proportions poor of school-age children.
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From page 80... ...
This assumption only has to be approximately correct for this procedure to provide a benefit. Another possible approach-that could be combined with raking the state estimates to the latest year-would be to construct the dependent variable in the county model as a weighted average of the 3year CPS estimates that gives more weight to the most recent year.
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From page 81... ...
Also important is work on the role that new data sources could play in improving the state and county income and poverty estimates and the estimates of poor school-age children for school districts. We discuss data sources in the next two chapters.
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