Mathematical formulas are used to allocate more than $250 billion of federal funds annually to state and local governments via more than 180 grant-in-aid programs. These programs promote a wide spectrum of economic and social objectives, such as improving educational outcomes and increasing accessibility to medical care, and many are designed to compensate for differences in fiscal capacity that affect governments’ abilities to address identified needs. Large amounts of state revenues are also distributed through formula allocation programs to counties, cities, and other jurisdictions.

The essential feature of a formula allocation program is that fund distribution is determined by the application of a formula that uses statistical information to calculate or estimate the values of its inputs. The allocation process consists of a basic calculation using a mathematical formula or algorithm; it often includes adjustments that place constraints on levels or shares (percentages of the total allocation) or on changes in levels or shares. Many programs use official statistics as inputs in the estimation of the central formula components—need, capacity, and effort. The kinds of data used vary widely: total population, population by age group, per capita income, and proportion of persons with family income below the poverty line are a few examples. In several instances, data collection programs were initiated or expanded specifically to provide data needed for funds allocation.

Allocation formulas are designed with one or more objectives and are developed in the context of a complex political process. In addition to

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Statistical Issues in Allocating Funds by Formula
Executive Summary
Mathematical formulas are used to allocate more than $250 billion of federal funds annually to state and local governments via more than 180 grant-in-aid programs. These programs promote a wide spectrum of economic and social objectives, such as improving educational outcomes and increasing accessibility to medical care, and many are designed to compensate for differences in fiscal capacity that affect governments’ abilities to address identified needs. Large amounts of state revenues are also distributed through formula allocation programs to counties, cities, and other jurisdictions.
The essential feature of a formula allocation program is that fund distribution is determined by the application of a formula that uses statistical information to calculate or estimate the values of its inputs. The allocation process consists of a basic calculation using a mathematical formula or algorithm; it often includes adjustments that place constraints on levels or shares (percentages of the total allocation) or on changes in levels or shares. Many programs use official statistics as inputs in the estimation of the central formula components—need, capacity, and effort. The kinds of data used vary widely: total population, population by age group, per capita income, and proportion of persons with family income below the poverty line are a few examples. In several instances, data collection programs were initiated or expanded specifically to provide data needed for funds allocation.
Allocation formulas are designed with one or more objectives and are developed in the context of a complex political process. In addition to

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Statistical Issues in Allocating Funds by Formula
providing a mechanism for addressing changes in need and other formula components without Congress having to revisit the issue annually, formula-based allocations can help build consensus for and the credibility of a program. Use of a formula (rather than a possibly arbitrary specification of amounts to be given to recipient jurisdictions) facilitates informed debate and a degree of transparency about the allocation process by providing documentation of assumptions and computations. Furthermore, a formula offers legislators an effective way of explaining the allocation process to their constituents. However, when funds are allocated according to a formula, there is no guarantee that objectives will be fully met. In particular, properties of data sources and statistical procedures used to produce formula inputs can interact in complex ways with formula features to produce consequences that may not have been anticipated or intended.
This report identifies key issues concerning the design and use of formulas for fund allocation and advances recommendations for improving the process. Most of the panel’s conclusions and recommendations fall into one of two overlapping sets: the first pertains to issues created by the interaction between the political process and formula design, the second to internal design and data issues more narrowly. In addition, the panel makes two specific programmatic recommendations.
In the first area, the panel emphasizes the importance of finding the proper balance between legislative control and program agency autonomy. At one extreme, the basic formula, the variables used to estimate its components, the data sources, and the special features would be fully specified in legislation. At the other extreme, the legislation would define the general objectives of the program, and the program agency would develop the specific formula and allocation procedures. The panel calls on formula allocation program designers in both the legislative and executive branches to be aware of and to evaluate the potential for behavioral responses by the funded jurisdictions aimed at influencing input data or other factors that affect calculated funding levels.
In addressing the design and data issues, the panel begins with guidance about how to evaluate trade-offs in timeliness, quality, costs, and other factors that are inherent in the selection of the variables used as formula components and in the data sources and methods used to estimate them. The panel strongly recommends that careful evaluation of the potential effects on allocations associated with special formula features—such as hold-harmless provisions, thresholds, and minimums—be part of any formula review protocol. Evaluations should focus on how use of these features

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Statistical Issues in Allocating Funds by Formula
may cause unintended departure of allocations from estimated need levels. In this context, use of simulations during program development and reauthorization review should be expanded, and they should be used to examine both cross-sectional and longitudinal allocation patterns. Simulations are also recommended as a means for exploring cross-cutting issues, such as those that arise when assessing alternative measures of fiscal capacity, and the relative merits of using hold-harmless provisions or moving averages to dampen the effects of large changes in the formula inputs.
The panel makes targeted recommendations to the General Services Administration (GSA) and the Office of Management and Budget (OMB). The GSA’s Catalog of Federal Domestic Assistance is an excellent tool, but several specific changes could improve its value for users seeking information about federal allocation programs. The panel also recommends that OMB establish a standing Interagency Committee on Formula Allocations charged with developing improved simulation and quality-control techniques for use in formula design and fund allocation procedures. Appendix E of this report contains a template that could be used by the interagency committee to develop a handbook that would serve as an introduction to underlying concepts and practical considerations in the use of formula-based fund allocation. It would be valuable to those in the legislative and executive branches who are involved in the design and operation of formula allocation programs and could be used in training programs for various audiences.
Chapter 9 presents the panel’s recommendations. They are supported by the discussion of statistical and political issues throughout the report and also by a set of papers, commissioned by the panel, which appear in the Journal of Official Statistics (September 2002).

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Statistical Issues in Allocating Funds by Formula
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