Small-Area Estimates of School-Age Children in Poverty Interim Report 3 (1999) / Chapter Skim
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2 County Estimates
2 County Estimates
Pages 11-38
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From page 11... ...
For Title I allocations, there is no single administrative or survey data source that provides sufficient information with which to develop reliable direct estimates of the number and proportion of school-age children in families in poverty by county. The March Income Supplement to the Current Population Survey (CPS)
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From page 12... ...
However, the 1995 county estimates are critical to the development of 1995 school district estimates. As a result of the lack of data at the school-district level, the Census Bureau has been constrained to use for school districts a very simple model-based method referred to as synthetic estimation, which applies the shares of poor school-age children for the school districts in a county according to the 1990 census to the updated 1995 county estimates to obtain updated school district estimates (see Chapter 3~.2 Therefore, in order to evaluate the 1995 school district estimates, it is essential to understand and evaluate the 1995 county estimates.
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From page 13... ...
Step 1: County Model The first step in the estimation process is to develop and apply the Census Bureau' s county model to produce initial estimates of the numbers of poor schoolage children. This step involves: obtaining data from the March CPS for three consecutive years to con struct a dependent variable in a county model regression equation that is the estimated log number of poor school-age children for counties with households in the CPS sample; obtaining data from administrative records and other sources that are avail able for all counties to construct predictor variables for the regression equation; specifying and estimating the regression equation to relate the predictor variables to the dependent variable; and using the estimated regression coefficients from the equation and the pre dictor variables to develop estimates of poor school-age children for all counties.
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From page 14... ...
.3 As the dependent or outcome variable, the county equation uses county estimates of the number of poor school-age children averaged over 3 years of the March CPS (data from the March 1995, 1996, and 1997 CPS, covering income in 1994, 1995, and 1996~.4 The relationships between the predictor variables and the dependent variable in equation (1) are estimated solely from the subset of counties that have households in the March CPS sample.
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From page 15... ...
, x~i = 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,6 x4i = residual for state i from a regression of the proportion of poor schoolage children from the most recent decennial census on the other three predictor variables,7 ui = model error for state i, and ei = sampling error of the dependent variable for state All states have sampled households with poor school-age children in the CPS; however, the variability associated with estimates from the CPS is large for some states. As is done for the initial county estimates, the predictions from the state model and the CPS direct estimates are combined in a shrinkage procedure to produce estimates of the proportion of poor school-age children in each state.
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From page 16... ...
This change may increase the number of IRS poor child exemptions in households with children away from home both because of the additional children and because poverty thresholds are higher for larger size families. Population Estimates To accompany county estimates of school-age children in 1996 who were in poor families in 1995, the Census Bureau produced county-level estimates of the
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From page 17... ...
The county model cannot be used for them because there are no precise equivalents for Puerto Rico of tax return and food stamp data to form predictor variables for the model. The original estimates for Puerto Rico of school-age children in 1994 who were poor in 1993 were developed with data from an experimental March 1995 income survey modeled after the CPS March Income Supplement, together with data from the decennial census and updated population estimates.
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From page 18... ...
As summarized above, the Census Bureau's county estimates of poor school-age children are produced by using a county regression model, a state regression model, and county population estimates developed with demographic analysis techniques. A comprehensive evaluation for each of these components of the estimation procedure should include "internal" and "external" evaluations.
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From page 19... ...
evaluation of the state model, including examination of regression output for 1996, 1995, 1993, 1992, 1991, 1990, and 1989 and consideration of the state raking factors by which county model estimates are adjusted to make them consistent with the state model estimates. County Model Internal Evaluations The first test of a regression model is that it perform well when evaluated internally, that is, for the set of observations for which it is estimated.
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From page 20... ...
linearity of the relationships between the dependent variable and the predictor variables, assessed by examining a variety of graphical plots; · constancy of the assumed linear relationship over different time periods, assessed through comparison of the regression coefficients on the predictor variables for the years for which the model was estimated; · whether any of the included predictor variables are not needed in the model, evaluated by looking for insignificant t-statistics for the estimated values of individual regression coefficients, and, conversely, whether other potential predictor variables are needed in the model, evaluated by looking for nonrandom patterns, indicative of possible model bias, in the distributions of standardized residuals displayed for categories of counties;9 · normality (primarily symmetry and moderate tail length) of the distribution of the standardized residuals; · whether the standardized residuals have homogeneous variances, that is, whether the variability of the standardized residuals is constant across counties and does not depend on the values of the predictor variables; and · absence of outliers.
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From page 21... ...
The analysis looked in particular at three characteristics: the constancy of the regression coefficients on the predictor variables over time; distributions (box plots) of the standardized residuals for categories of counties to determine if there were any nonrandom patterns that persisted over time; and the phenomenon observed in the 1993 evaluations by which the variance of the standardized residuals was related to CPS sample size and the predicted value of the dependent variable (variance heterogeneity)
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From page 22... ...
number of child exemptions reported by families in poverty on tax returns; (2) number of people receiving food stamps; (3)
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From page 23... ...
The current approach essentially obtains the total sampling error variance by estimating the total squared error for the model and subtracting from that estimate the estimated model error variance from a 1989 equation in which 1990 census data form the dependent variable. The total sampling error variance is then distributed to counties by assuming that the sampling error variance in a county is inversely proportional to the county's CPS sample size.
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From page 24... ...
Second, the model shows evidence of variance heterogeneity with respect to both CPS sample size and poverty rate. The function that is used to distribute the total sampling error variance to counties should be changed to eliminate or reduce this problem, while the Census Bureau pursues longer term research on direct estimates of CPS county-level sampling variances (see Chapter 5~.
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From page 25... ...
. In addition, there 1lThe county estimates reflect the effects of the state model and the county population estimates, as well as the county regression model, but the differences in model performance vis-a-vis the census in the evaluation are due to the particular form of the county model.
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From page 26... ...
, given that the county estimates are raked to the state estimates from the Census Bureau's state model, must be attributable to the state model. Yet the evaluations showed that the state raking procedure improved the esti
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From page 27... ...
Then, local people-including staff and members of local councils of government, economic development authorities, welfare agencies, state demographic units, state data centers, and other agencies were contacted to obtain their assessment of the reasonableness of the implied trends in poverty for schoolage children given their knowledge of local socioeconomic conditions.l4 Individuals with local knowledge expressed a great deal of concern about the statistical reliability of the original 1993 county estimates, which was mostly consistent with the Census Bureau's own cautions in this regard, coupled with specific county estimates that seemed on the basis of local knowledge to be doubtful. These concerns notwithstanding, no categories of counties were identified that experienced apparent trends in the number and proportion of poor school-age children between 1989 and 1993 that were not accepted by knowledgeable local people.
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From page 28... ...
This finding is expected, given that the measurement of poverty differs between the census and the CPS because of the many differences in data collection procedures. i5This analysis is not the same as the analysis of regression output described above, in which the standardized residuals from the model for counties with sampled households in the CPS-representing the standardized differences between the model estimates and the direct estimates on the log scale-were examined for categories of counties.
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From page 29... ...
(5) Census Regiond Northeast217-2.870.81 -4.3610,708 Midwest1,055-0.490.61 -4.3111,393 South1,4254.05-0.13 4.4815,440 West444-4.16-0.95 -0.4312,141 Census Divisiond New England67-13.511.87 27.073,696 Middle Atlantic1500.050.54 -9.797,012 East North Central437-6.10-0.64 -3.046,841 West North Central61818.314.25 -7.444,552 South Atlantic5911.820.83 4.128,150 East South Central364-5.53-5.85 9.322,529 West South Central47012.001.90 2.444,761 Mountain281-3.9119.87 0.845,543 Pacific163-4.24-6.48 -0.926,598 Metropolitan Status Central county of metropolitan area493-2.75-0.91 -3.5334,343 Other metropolitan25453.75-3.64 8.442,801 Nonmetropolitan2,3941.243.50 8.3212,538 1990 Population Size Under 7,500525-17.2157.03 0.74933 7,500-14,99963019.82-23.67 -0.191,550 15,000-24,9995242.946.24 17.022,289 25,000-49,99962030.46-0.23 -4.464,204 50,000-99,999384-2.524.99 22.475,979 100,000-249,99925917.2712.12 -3.888,263 250,000 or more199-7.24-2.49 -3.1026,464 1980 to 1990 Population Growth Decrease of more than 10.0%444-2.71-22.03 -4.292,170 Decrease of 0.1-10.0%972-4.312.44 -1.3210,655 0.0-4.9%5476.043.41 3.188,015 5.0-14.9%6201.125.97 4.6111,590 15.0-24.9%260-0.07-4.11 -10.449,305 25.0% or more292-0.52-2.27 10.317,947 continued
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From page 30... ...
(5) Percentage of Poor School-Age Children, 1980 Less than 9.4%5162.74 7.22 -1.0714,980 9.4-11.6%5241.39 5.28 4.3512,291 11.7-14.1%530-10.01 -6.49 -6.729,837 14.2-17.2%5231.28 -5.82 0.445,217 17.3-22.3%5199.32 17.41 0.234,623 22.4-53.0%5231.05 -14.81 4.112,734 Percentage Hispanic, 1990 0.0-0.9%1,7701.26 -0.75 3.1312,848 1.0-4.9%8479.33 1.45 4.3216,966 5.0-9.9%193-2.81 17.24 6.386,999 10.0-24.9%181-4.02 -5.14 -8.297,236 25.0-98.0%150-7.90 -3.29 -5.265,633 Percentage Black, 1990 0.0-0.9%1,4468.32 8.02 5.0910,929 1.0-4.9%6157.41 1.04 -1.8310,630 5.0-9.9%2945.41 -2.07 0.958,646 10.0-24.9%381-4.89 -0.75 3.5113,437 25.0-87.0%405-6.85 -2.82 -6.306,040 Persistent Rural Poverty, 1960- l 99oe Rural, not poor1,740-2.62 1.53 5.479,734 Rural, poor53522.45 -0.15 14.811,698 Not classified866-1.28 -0.28 -2.6838,250 Economic Type, Rural Countiese Farming556-24.56 -29.31 -12.411,634 Mining14646.97 27.59 40.67901 Manufacturing506-7.10 -3.58 -1.512,369 Government243120.13 27.59 59.391,661 Services323-12.18 -12.42 -11.862,760 Nonspecialized4846.99 18.35 23.892,018 Not classified883-1.18 -0.20 -2.5938,339 Percentage of Group Quarters Residents, 1990 Less than 1.0%5453.32 22.03 16.603,494 1.0-4.9%2,187-1.58 -1.27 -1.8441,648 5.0-9.9%29911.90 -1.22 4.513,980 10.0-41.0%11049.44 -6.28 17.02560
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From page 31... ...
, Ymode1 is the estimated number of poor school-age children from the county model, and YCps is the estimated number of poor schoolage children from a 3-year weighted average of the CPS, is Hi (Ymode!
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From page 32... ...
· The model estimates are consistently very different from the weighted CPS estimates for some categories of rural counties classified by economic type. In particular, the model estimates for rural counties characterized as government are much higher than the corresponding weighted CPS estimates.
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From page 33... ...
State Model Evaluation The state model plays an important role in the production of county estimates of poor school-age children. Evaluations conducted of the state model for the assessment of the revised 1993 county estimates included an internal evaluation of the regression output for 1989 and 1993 and an external evaluation that compared 1989 estimates from the model with 1990 census estimates of proportions of poor school-age children.
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From page 34... ...
. Linearity Plots of standardized residuals against the four predictor variables in the state model-the proportion of child exemptions reported by families in poverty on tax returns, the proportion of people receiving food stamps, the proportion of people under age 65 who did not file a tax return, and a residual from the analogous regression equation using the previous census estimate as the dependent variable-support the assumption of linearity.
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From page 35... ...
Finally, there is no evidence of outliers from examination of the residual plots or displays of the distributions of the standardized residuals from the state regression model. Model Error Variance One problem in the state model concerns the variance of the model error (ui in equation (2~.
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From page 36... ...
These results suggest that the state model is performing reasonably well: differences between model and direct estimates are neither unusually large nor strongly persistent. However, more work should be conducted to evaluate the current procedures for estimating the sampling error variance of the state model and the effects on the model estimates (see Chapter 5)
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From page 37... ...
Regression Estimate Minus Direct Regression Estimate Estimate (4)
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From page 38... ...
The panel urges the Census Bureau to estimate the variance of the state raking factors to determine if the variability that they exhibit for 1993 and 1995 is consistent with random error. If it is not, the panel urges the Census Bureau to further investigate the state raking factors, including consideration of whether there is any feature of the state model that might explain the variation.
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