Choosing the Right Formula Initial Report (2001) / Chapter Skim
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3. Effects on Formula Outputs of Errors in Formula Inputs
3. Effects on Formula Outputs of Errors in Formula Inputs
Pages 37-44
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From page 37... ...
Thus, one session of the workshop was devoted to formal, statistical issues via presentation and discussion of two papers that explored how estimation errors in formula inputs can affect formula outputs in a single year and over time. This session focused on the interactions among data sources, estimation methods, and formula features and their combined effects on formula outputs, which are like the formula inputs statistical quantities.
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From page 38... ...
Formulas often contain features that cause allocations to be disproportionate to need even though proportional allocation may be the primary objective. Such features include holclharmless provisions that limit downward fluctuations in funding ancl thresholds that require a minimum level of need for distribution of funcls, thus concentrating funding where it is most neeclecl.1 In the remainder of his presentation, Zaslavsky focused on the interactions between the statistical properties of data sources, estimation methocls, ancl the resulting estimates of formula inputs ancl the features of funding formulas.
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From page 39... ...
If the estimation procedure and the funding formula are linear, allocations will be unbiased, that is, correct on average over time. After describing these relatively straightforward, general results, Zaslavsky presented simulation results that illustrate the more complex interactions between the statistical properties of estimates and the features of allocation formulas.
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From page 40... ...
to be distorted more than the allocations for larger areas. This implies that the sampling plan for the data source used to produce estimates can affect the allocation of funds, an effect that is almost certainly not anticipated when statisticians specify the sampling plan or when policy makers specify a threshold for a formula.
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From page 41... ...
Policy makers could then take account of the properties of potential data sources and estimation methods when designing formulas, and statisticians could take account of policy objectives and formula properties when evaluating new data sources or estimation methods. David Betson of the University of Notre Dame gave the second presentation.
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From page 42... ...
Thus, as noted earlier in the presentation by Alan Zaslavsky, attractive policy objectives are often in conflict in practice, even when policy makers agree on the objectives. Paul Siegel of the U.S.
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From page 43... ...
Thus, it may not be hard to convince policy makers that a smoother function would be desirable. One drawback to a smoother function that would have to be addressed is that some of the amounts allocated will be smaller than the amount implied by the threshold of the original step function.
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From page 44... ...
For example, obtaining better estimates of poor children for Title I allocations may not improve the overall effectiveness of Title I funds in improving educational outcomes for the target population. Alan Zaslavsky responded to this point, noting that even if the input to a formula were exactly the sole measure of program success and there were no conceptual problems in measuring the input from available data, the problem of sampling error in estimating the input would still exist.
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