5
Recommendation for Title I Allocations

The Panel on Estimates of Poverty for Small Geographic Areas has examined the Census Bureau's assumptions, methodology, and evaluation tests in developing the 1993 county estimates that were produced for the Department of Education to consider in allocating Title I funds for the 1997–1998 and 1998–1999 school years. The panel focused its attention on the advisability of using those estimates for determining fiscal 1997 allocations to counties. It is the panel's assessment that considerable progress has been made in developing model-based estimates of school-age children in poverty for states and counties. The panel recognizes the efforts to produce these results and commends the Census Bureau for its work in developing these estimates.

The alternative to the use of model-based estimates for Title I allocations is the use of 1990 census estimates of school-age children who were poor in 1989. As we discuss in Section 2, the census estimates are seriously out of date. The major changes in the distribution of children in poverty that have occurred since the 1990 census make the use of those estimates for current allocations highly problematic. There was a substantial increase in the number of children in poverty between 1989 and 1993, and there is clear evidence that the geographic distribution of such children has changed markedly. Thus, the census estimates are subject to sizable error if used for current allocations. In addition, the census estimates are based on sample data and are therefore subject to sampling error. The magnitude of the sampling error is fairly large for many small counties (see Table 2-1).

The Census Bureau's model-based estimates have a clear advantage of being more up to date. However, they are also subject to error. Such error is inevitable and is not a reason for rejecting model-based estimates. Provided that the errors



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Small-Area Estimates of School-Age Children in Poverty: Interim Report I: Evaluation of 1993 County Estimates for Title I Allocations 5 Recommendation for Title I Allocations The Panel on Estimates of Poverty for Small Geographic Areas has examined the Census Bureau's assumptions, methodology, and evaluation tests in developing the 1993 county estimates that were produced for the Department of Education to consider in allocating Title I funds for the 1997–1998 and 1998–1999 school years. The panel focused its attention on the advisability of using those estimates for determining fiscal 1997 allocations to counties. It is the panel's assessment that considerable progress has been made in developing model-based estimates of school-age children in poverty for states and counties. The panel recognizes the efforts to produce these results and commends the Census Bureau for its work in developing these estimates. The alternative to the use of model-based estimates for Title I allocations is the use of 1990 census estimates of school-age children who were poor in 1989. As we discuss in Section 2, the census estimates are seriously out of date. The major changes in the distribution of children in poverty that have occurred since the 1990 census make the use of those estimates for current allocations highly problematic. There was a substantial increase in the number of children in poverty between 1989 and 1993, and there is clear evidence that the geographic distribution of such children has changed markedly. Thus, the census estimates are subject to sizable error if used for current allocations. In addition, the census estimates are based on sample data and are therefore subject to sampling error. The magnitude of the sampling error is fairly large for many small counties (see Table 2-1). The Census Bureau's model-based estimates have a clear advantage of being more up to date. However, they are also subject to error. Such error is inevitable and is not a reason for rejecting model-based estimates. Provided that the errors

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Small-Area Estimates of School-Age Children in Poverty: Interim Report I: Evaluation of 1993 County Estimates for Title I Allocations are not too large and, after thorough investigation, are not found to exhibit any specific patterns, the panel would strongly endorse the use of those model-based estimates. The development of the state-level model is an extension of work conducted and tested by the Census Bureau over many years, and the task of producing reliable estimates for states is less challenging than it is for counties. The panel considers the model-based estimates for states to be clearly preferable to the census estimates, although further work to evaluate the state-level model is desirable. The county estimates are constrained to sum to the state totals, and, as discussed in the previous section, some of the evaluations that have been conducted of the county estimates provide evidence that their use for Title I allocations may be preferable to continued use of the 1990 census estimates. However, other evaluations of the county estimates, as well as the form of the model, raise concern. In general, the panel believes that the county-level model and resulting estimates have not yet been sufficiently evaluated, especially in comparison with alternative models, for use without modification for such an important purpose as allocating funds under Title I. The necessary evaluations need to be completed before the panel would be confident in basing current Title I allocations solely on the 1993 model-based county estimates. Further research may also lead to improvements in the county-level model (see Section 6). The panel is also concerned about the effect on the allocations caused by the difference between poverty estimates obtained from the census and from the CPS. In the aggregate, the CPS produces estimates of children in poverty that are about 7 percent larger than estimates from the census, but little is known about how the differences between the estimates from the two sources may affect the relative size of the estimates for different types of counties. In time, many questions pertaining to model-based estimates can be answered. And we can expect a better understanding of the reliability of these estimates, of the effects of the differences between the census and the CPS, and of the advantages of some models over others. And alternative models, which appear to be equally viable, can be more fully explored. But the panel is faced with making a recommendation now to the Secretaries of Commerce and Education on whether to use the Census Bureau's model-based county estimates for allocating Title I funds for the 1997–1998 school year. For the current allocations, there is no time to complete the research needed to address the questions that the panel believes need to be answered. For the purpose of the Title I allocations, the problem is one of weighing the panel's concerns about the more up-to-date model-based estimates for 1993 against its concerns about using out-of-date decennial census estimates. To the panel, the Census Bureau's model-based county estimates appear, in many regards, preferable to the out-of-date decennial census estimates. The panel concludes, however, that a solution that takes advantage of the Census Bureau's work on model-based estimates but reduces the impact of possible limitations in

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Small-Area Estimates of School-Age Children in Poverty: Interim Report I: Evaluation of 1993 County Estimates for Title I Allocations that work is the most appropriate approach for the immediate purpose of Title I allocations. The panel's solution to this problem is to recommend that the Department of Education use an average of the two estimates for each county, as described below. This procedure is recommended only for the current Title I allocations and not for any other purpose. The rationale for our recommendation is that the averaging will take some account of the changing number and geographic distribution of children in poverty provided by the model-based estimates but will dampen any distortions that might occur with these estimates. (As an example, our recommendation will likely reduce the effects of any possible bias in the model-based estimates for different sized counties.) It will also dampen the effect of the differences between the census and the CPS poverty estimates. The procedure can be viewed as smoothing the transition to the model-based estimates for subsequent allocations, after further research has been conducted. RECOMMENDATION AND AVERAGING PROCEDURE The panel recommends to the Secretaries of Commerce and Education that funds under Title I for fiscal 1997 be allocated on the basis of estimates that are obtained by averaging two poverty rates and then applying the average rate to the 1994 population estimate. The panel recommends the following precise form of averaging: take the average of the poverty rates for school-age children (i.e., related children aged 5–17) that are obtained from the census and from the model-based estimates for a given county and multiply this average rate by the Census Bureau's 1994 population estimate of the number of children aged 5–17 in that county as adjusted to represent related children aged 5–17 (see Appendix D). The number resulting from this calculation is the estimated number of related children aged 5–17 in poverty in the county. Expressed algebraically, for each county, use: as the rate, r, of school-age children in poverty, where a is the 1990 census estimate of the number of related children aged 5–17 who were poor in 1989, b is the number of related children aged 5–17 in the 1990 census, c is the model-based estimate of the number of related children aged 5–17 in 1994 who were in poverty in 1993, and d is the 1994 population estimate of the number of related children aged 5–17. For the estimated number, n, of school-age children in poverty, use n= dr. The panel stresses that the above averaging procedure is designed to meet the need for an immediate decision on fund allocations. The solution we describe

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Small-Area Estimates of School-Age Children in Poverty: Interim Report I: Evaluation of 1993 County Estimates for Title I Allocations should be supplanted by a set of fully model-based estimates as improvements in the model and evaluations take place over time. At this time, however, we believe that averaging the model-based and 1990 census estimates of school-age children in poverty is appropriate for the purpose of fiscal 1997 fund allocations. We note that it is common practice in various areas of applied statistical analysis to average two (or more) estimates with different properties to produce improved estimates. It is, for example, standard practice in small-area estimation to average a direct survey estimate and a model-based indirect estimate to produce a composite estimate for an area (see Ghosh and Rao, 1994). This form of averaging is used by the Census Bureau in both the state-and county-level models. Other examples of its use in federal statistical programs are given in Office of Management and Budget (1993). In most applications of composite estimation, a weighted average of the estimates is used, with the weights chosen to produce the overall estimate of highest quality. For example, the estimates may be weighted inversely proportional to their mean square errors in order to produce an overall estimate with minimum mean square error.1 In order to produce such weighted estimates, it is necessary to know the relative quality of the individual estimates. When there is considerable uncertainty about the relative quality, as in the present case, then it is appropriate to use an equal (i.e., 50–50) weighting. As an example, the Census Bureau for many years developed population estimates for states and counties by averaging on an equal basis the results of three independent estimating procedures. The resulting estimates were used in making allocations under the State and Local Fiscal Assistance Act of 1972 (general revenue sharing), the Comprehensive Employment and Training Act of 1972, and the Housing and Urban Development Act of 1972 (Bureau of the Census, 1980; Zitter and Shryock, 1964). In this situation, we know that both the 1993 model-based and 1990 census estimates are subject to errors from sampling variability and other sources. The 1990 census estimates have relatively low sampling variability (for all but the smallest counties) but are in error to an unknown but presumably large amount in that they are out of date. The 1993 model-based estimates, while more up to date than the 1990 census estimates, are subject to sampling variability and other potential sources of error, which have not yet been fully analyzed. Given that there is uncertainty about the magnitude of the errors in the two estimates and that there was insufficient time and information with which to analyze the errors, we recommend a simple averaging of the two estimates. This approach is a conservative way of dealing with uncertainty. It takes advantage of the Census Bureau's work to develop more up-to-date estimates of poor school-age children but guards against possible limitations in that work. 1   Mean square error combines the errors due to sampling variability and the errors due to bias in a single statistic.

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Small-Area Estimates of School-Age Children in Poverty: Interim Report I: Evaluation of 1993 County Estimates for Title I Allocations SPECIAL CASE: PUERTO RICO Puerto Rico is also included in the Title I allocations. While the commonwealth's 1990 decennial census provides the requisite estimates for 1989, no estimates of Puerto Rican children in poverty can be made for 1993 with the Census Bureau's model because the appropriate food stamp and IRS data are not available for Puerto Rico. The Census Bureau has computed 1993 estimates for Puerto Rico on the basis of an experimental Special Family Income Survey that was conducted in the commonwealth in February and March 1995, but several adjustments had to be made to produce the estimates of school-age children in poverty in 1993. The approach adopted by the Census Bureau seems a reasonable one given the data available (see Appendix F for details). However, insufficient information was available to the panel about the quality of the underlying survey data. If, after further analysis, it is determined that the quality of the experimental income survey in Puerto Rico is adequate, then the panel would recommend that the Census Bureau's 1993 estimates of poor school-age children in Puerto Rico derived from the experimental survey be treated as equivalent to the 1993 U.S. model-based county estimates in determining the fiscal 1997 Title I allocations. In other words, the 1993 Puerto Rico estimate of the poverty rate for related children aged 5–17 from the experimental survey would be averaged with the 1989 estimate of the poverty rate for related children aged 5–17 from the 1990 census of Puerto Rico. The resulting average rate would be applied to the 1994 population estimate of the number of related children aged 5–17 to obtain the estimated number of poor school-age children in Puerto Rico for use for the fiscal 1997 Title I allocations.