Small-Area Income and Poverty Estimates Priorities for 2000 and Beyond (2000) / Chapter Skim
Currently Skimming:
Appendix: Interactions Between Survey Estimates and Federal Funding Formulas
Appendix: Interactions Between Survey Estimates and Federal Funding Formulas
Pages 167-190
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 167... ...
Schirm Federal programs that allocate funds to states and localities for the low-income population have typically used estimates from the decennial census in the allocation formula. As one example, the Title I education program historically used census estimates of poor school-age children for allocations; recently, however, the program has used more up-to-date estimates.
|
From page 168... ...
DATA SOURCES AND ESTIMATION APPROACHES Funding formulas typically require estimates of numbers of people who are eligible to receive a benefit distributed through some intervening agency. For example, the number of children in certain age ranges that are in low-income families is required for calculation of grants to states for the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC)
|
From page 169... ...
. Since then, however, state and county estimates of children in poverty have been estimated using a complex empirical Bayes model fitted to CPS data, in which decennial census estimates appear as a covariate along with income tax poverty and nonfiling rates and numbers of food stamp recipients.
|
From page 170... ...
Simple indirect estimators may average over spatial domains (e.g., combining several school districts in a county to estimate a single poverty rate that will be used for all of them) or over time (cumulation over years)
|
From page 171... ...
Consequently, funding formulas have an aspect of indirectness, in the sense that an increase in allocation to one domain implies a decrease somewhere else, although the effect of each domain's allocation on each other domain is generally small. Proportional allocation of funds may be modified by hold-harmless provisions and thresholds.
|
From page 172... ...
Estimates from the 1980 census were used from the early 1980s until fiscal year 1994, when 1990 census estimates were used. Title I of the Elementary and Secondary Education Act provides federal funds to school districts for education programs for disadvantaged children.
|
From page 173... ...
INTERACTIONS AMONG DATA SOURCES, ESTIMATION PROCEDURES, AND ALLOCATION FORMULAS General Findings Data sources, estimation procedures, and allocation formulas each play a role in the successive steps of calculation of fund allocations. In practice, the distinction between the roles played by the estimation procedure that generates the inputs to the funding formula and the formula itself can be formal and legalistic because the same calculations often may be positioned either in the estimator or in the formula.
|
From page 174... ...
For another example, a formula may specify that a school district's eligibility for a category of funds depends on the poverty rate in the district, but if estimates are calculated only for counties and then applied directly to the districts, the effect is the same as if eligibility were calculated at the county level. In that case, developing a capability to estimate poverty rates by district effectively changes the formula.
|
From page 175... ...
Fourth, if each year's samples are independent, or almost so as in the ACS, then variances can be reduced by cumulation, that is, by calculation of a moving average. Assuming uncorrelated sampling error with equal variances in each year, using a 3-year equally weighted moving average multiplies variances by a factor of one-third (.333~.
|
From page 176... ...
· The formula has four possibilities: allocation is equal to the standardized poverty rate (PROP) ; allocation is equal to the rate with an 80 percent hold-harmless provision (HH)
|
From page 177... ...
. TABLE A-1 Results for Scenario (1~: Effects of Sampling Variability with a Threshold, Single-Year Estimator True Standardized Poverty Rate 1.3 1.1 0.9 0.7 Sampling Standard Deviation (SD)
|
From page 178... ...
relationship between population rate and expected payoff. It is arguable that sharp thresholds in funding formulas are not entirely sensible and that a smoother transition would give more stability and less importance to very small shifts near the threshold.
|
From page 179... ...
Expected allocations in the first year are all equal to 1 because we assume no effect of hold harmless in the first year. In successive years the expectation climbs because the allocation is "ratcheted up" that is, when it is increased by sampling variability in one year, it cannot decrease very much in the following year.
|
From page 180... ...
X 1.0 1.5 2.0 2.5 Year Estimator: 3-Year Exponential Average 3.0 3.5 4.0 FIGURE A-1 Effects of sampling variability with a constant poverty rate and hold-harmless provision: Correct allocations and three estimation methods. NOTE: Results for scenario (2~; see text for details.
|
From page 181... ...
Scenario 3: Effects of Various Linear Estimation Methods with a Trend Figure A-2 shows a hypothetical downward trend (solid line) in standardized population poverty rates, assumed to start in year 2 after a period of constant rates, and the expected allocations with three estimation methods: single-year data (SINGLE = triangles)
|
From page 182... ...
Scenario 5: Comparison of Hold Harmless and Moving Average as Methods for Moderating Downward Jumps In this set of three scenarios, estimates fluctuate around a mean of 1 with SD = 0.5. These fluctuations represent the sum of sampling error and uncorrelated year-to-year variability in the population rate.
|
From page 183... ...
APPENDIX o g 1.' o 0.~q o ~ 1.1o 0.8 o ~ 1.1o _ 0.8 183 · >< — , ~ Estimator: Single Year 1 Estimator: 3-Year Exponential Average FIGURE A-3 Effects of a downward trend with a hold-harmless provision: Correct allocations and three methods. NOTE: Results for scenario (4~; see text for details.
|
From page 184... ...
... a-,- - - ~ 2 3 Year Estimator: 3-Year Moving Average 1 1 1 1 1 1 1 4 an- , -_~^ 3 Year Estimator: 3-Year Exponential Averane 4 FIGURE A-4 Effects of an upward trend with a hold-harmless provision: Correct allocations and three methods.
|
From page 185... ...
(If variability is entirely due to sampling error, this reduction in the standard deviation could be obtained by multiplying sample size by 3.) The third scenario assumes that a formula without a hold-harmless provision is applied to a 3-year moving average (MA3, no HH)
|
From page 186... ...
We must note, however, that the assumption of a fixed global budget may also be an oversimplification, since Congress may respond to an increased demand for funds due to increasing poverty rates by increasing the total amount available for distribution. Congress may also increase the total amount when reallocation of a fixed global budget would reduce funds to some areas by more than it can collectively tolerate, even if poverty rates have not increased on average.
|
From page 187... ...
The statistical sampling distribution of £i depends on xi and some sampling characteristic or characteristics si, which one might think of as the sampling standard error of the estimate and perhaps some more complex properties of the error distribution. Finally, suppose that the expected allocation for an area, taking the expectation over the distribution of £i given si, isfs~xi,si,09.
|
From page 188... ...
, fairly similar results would nonetheless apply: that is, areas for which the sampling properties of their estimates augment their expected allocations the most with fixed values of ~ are also advantaged when they must share a global budget with other areas. CONCLUSIONS From a legalistic and formal standpoint, modification of the estimation procedure and modification of the formula are two entirely different enterprises.
|
From page 189... ...
Results of some nonlinear methods, however, may be greatly affected, even on the average and in the long run, by sampling variances. This effect is problematical, because it almost inevitably leads to situations in which larger or smaller units tend systematically to get more than their proportional shares, other factors (poverty rates)
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.