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Choosing the Right Formula: Initial Report (2001)

Chapter: 1. Formula Allocation Processes: An Overview

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Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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PART I

Workshop Report

This part of the report provides an account of the presentations and discussions at the workshop (see the agenda in Appendix A). The first three chapters cover the overview, case studies, and methodological sessions, respectively. Chapter 4 summarizes the issues discussed in the roundtable and concluding sessions, with emphasis on the identification of questions that might be addressed in a panel study.

Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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1

Formula Allocation Processes: An Overview

The use of formulas to allocate federal and state funds to subordinate jurisdictions is part of a broader process of government-to-government transfer of funds. Uses of such funds by the recipients may be unrestricted, as in the General Revenue Sharing Program of the 1970s and 1980s, or they may be limited to specific purposes, for example to provide medical care and improve the education of children in poor families, assist persons to end their dependence on welfare, revitalize economically depressed cities and neighborhoods, or provide assistance to localities disproportionately affected by the HIV epidemic. At the federal level, the U.S. Congress determines how much money will be distributed and for what purposes. For some programs, the Congress appropriates a fixed total amount each year to be allocated among states or other recipients; for others, such as Medicaid, amounts may be specified as a certain proportion of all qualified expenditures by a state or other jurisdiction. In the former case, a formula dictates how much of the total goes to each recipient; in the latter case, a formula determines what proportion of each jurisdiction's amount will be matched by the federal government.

Wray Smith, of the Harris Smith Institutes, opened the workshop by presenting “An Overview of Formulas for Allocation of Funds” (Smith and Parker, 2000). He noted that nearly $200 billion of federal funds are distributed annually to states and other units of government under formula allocation programs. Amounts have more than doubled in real terms over the past 25 years; a 1975 study estimated that $35.6 billion was allocated

Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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under grants using population or per capita income as formula components.1 In fiscal year 1998, Medicaid was by far the largest formula allocation program, with $101.2 billion disbursed. Highway planning and construction grants came next, with $19.8 billion, followed by allocations under Title I of the Elementary and Secondary Education Act, with $7.8 billion. The U.S. General Services Administration's 1998 Formula Report to the Congress lists a total of 340 programs; however, some of these do not have formula provisions but have optional or required matching or cost-sharing provisions.

Formula allocation programs are characterized by the allocation of money to states or their subdivisions in accordance with a distribution formula prescribed by law or administrative regulation, for activities of a continuing nature not confined to a specific project. For some programs, the distribution formula used is a closed mathematical expression; for others, iterative processes are used to arrive at the final allocations. Block grant programs are a subset of formula allocation programs in which the recipient jurisdiction has broad discretion for the application of funds received in support of such programs as community development or the prevention and treatment of substance abuse, which are specified in the enabling legislation. Matching grant programs, such as Medicaid and certain transportation programs, require that the recipient state provide a matching percentage of funds from state sources.

ELEMENTS INCLUDED IN ALLOCATION FORMULAS

Elements included in formulas vary widely among the programs currently active. Most programs use one or more of the following:

  • A direct or indirect measure of need, such as the number of schoolage children in poverty, the number of overcrowded housing units in an area, or the number of reported cases of AIDS.

  • A measure of the capacity or capability of an area to meet the need

    1The 1975 study, “Use of Data on Population in Federal Grants-in-Aid to State and Local Government in Fiscal 1975” was prepared by Charles Ellett of the Statistical Policy Division, U.S. Office of Management and Budget, and is cited in U.S. Office of Statistical Policy and Standards (1978). The 1975 and current figures may not be precisely comparable in terms of the types of formula allocation programs included.

Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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from state, local, or private funds. Typical measures used are per capita income and total taxable resources.

  • A measure of effort, that is, the amount of available local resources actually devoted to meeting the need. In the Medicaid formula, for example, this would be a state's total eligible medical expenses under its Medicaid program. In the Title I education program it is the state's average per pupil expenditure (bounded by 80 and 120 percent of the national average).

  • An index of costs incurred in meeting program needs in an area, such as an index of wages paid to workers in the health care industry.

  • In addition to these and other formula elements, the allocation rules may include one or more of the following features:

  • A threshold, which calls for some minimum level of need before an area is eligible for any funds at all under the program. In some programs, thresholds are used to target resources to the areas with the greatest need.

  • A minimum amount to be received by each state or other jurisdiction.

  • A hold-harmless provision, which limits decreases in amounts received by areas from one time period (usually a fiscal year) to the next.

  • The inclusion of such special features sometimes requires use of relatively complicated iterative procedures to determine the allocation of a fixed total appropriation to eligible jurisdictions.

    DATA SOURCES

    Specific data sources for formula elements may or may not be identified in enabling legislation for formula grant programs. Population (total or for defined age groups) is an element in many formulas and may come from the most recent decennial census or from the U.S. Census Bureau's current population estimates. Income data may come from the decennial census, the Current Population Survey (CPS), or personal income statistics compiled by the Bureau of Economic Analysis. Possible future sources of income and poverty data are the U.S. Census Bureau's Survey of Income and Program Participation and its American Community Survey (ACS), which is currently in the developmental stage (see discussion in Chapter 4).

    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Data from administrative sources may also be used as inputs. As described in Chapter 2, the county estimates of poor school-age children used in the Title I education allocations are model-based estimates that supplement decennial census and CPS data with inputs based on individual income tax returns and records of participation in the Food Stamp Program.

    Several considerations influence choices among alternative sources of input data for elements included in a formula:

    • The conceptual fit between currently available data and the formula elements, as defined in enabling legislation or administrative regulations. If the definitions of the elements or program goals lack specificity, evaluation of the fit may require subjective judgments.

    • The level of geographic detail for which data are provided. The decennial census can provide estimates for areas as small as school districts (although with substantial sampling variability for the smaller districts), whereas estimates from the Survey of Income and Program Participation are limited to census divisions and a few large states.

    • The timeliness of the data, that is, the elapsed time between the reference period for the estimates and the period for which the allocations are being made. Here the decennial census data are at an obvious disadvantage compared with continuing or periodic sample surveys and administrative record sources.

    • The quality of the data, as measured in terms of sampling variability and bias.

    • The cost of collecting or compiling new data to provide inputs to the formula. Benefits from improvements in conceptual fit or other aspects of data quality have to be weighed against cost. Even when existing data sources are used, there may be significant costs of obtaining data in a format suitable for the allocation process.

    Clearly, there are many trade-offs among these considerations, and it is likely that no one data source will be superior to the others on all counts. One solution to this dilemma may be the use of model-based estimates that combine inputs from several different sources.

    Martin David of the University of Wisconsin, a discussant in the opening session, elaborated on these trade-offs, using the Title I education allocations as an illustration. Comparing alternative sources of income data, he noted that the most comprehensive data on income by source come from the Survey of Income and Program Participation, but that it has the

    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    smallest sample size. The CPS data are somewhat less detailed but are based on a larger sample. Individual income tax data are not subject to sampling error but cover only about 90 percent of the total population. Their utility could be improved if they were coded to the county and school district levels. Decennial census data cover a larger proportion of the population and provide more geographic detail, but they lack timeliness and are subject to greater underreporting of some types of income. Regarding conceptual fit, he argued that the current official definition of poverty could be improved by adopting proposed revisions that include in-kind income as a resource and exclude taxes paid (see National Research Council, 1995).

    HOW FORMULAS ARE DEVELOPED AND ADMINISTERED

    David McMillen, a staff member of the U.S. House Committee on Government Reform and Oversight, discussed practical considerations that affect the development of legislation to allocate federal funds to states and localities. He stated that inclusion of a funding formula in a bill makes the legislative process more difficult from beginning to end. At each stage, starting with the committee that first considers the bill and proceeding through votes in both houses and deliberations in conference committees, the sponsors and drafters of the legislation must take into account how the members most influential at each stage will fare in allocations based on the proposed formula. As with any type of legislation, there must be a majority of members voting for it as it moves to final passage. However, funding formulas place in stark contrast those who are advantaged and disadvantaged by the legislation. In simplest terms, how does one persuade a member of Congress to vote for legislation that will disadvantage his or her constituents? There must be more winners than losers, and key members of the power structure must not perceive that the outcome will be unfavorable to them.

    In the Senate, where an individual senator can block legislation from coming to the floor, it is important that members representing small states not feel that the allocation formula treats them unfairly. All members of Congress must face the reality that they will be held accountable for every vote they cast and that their constituents will be more inclined to judge them on how their state or district fared in the allocation than on the overall goals of the program. Thus, formulas that finally emerge from the political process may represent compromises between substantive program goals and the need to generate the required number of votes at each stage.

    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    In some extreme cases, it has proven to be too difficult to devise a formula that would give the desired percentages to each state, so the actual percentages have been specified in the legislation.

    In response to a question, McMillen said that members of Congress and their staffs frequently request that the Congressional Research Service and the U.S. General Accounting Office provide information used to evaluate proposed formulas. However, Congress has relatively little contact with the statistical community in this context. One exception was the initiative by Congressman Tom Sawyer of Ohio which led to the replacement of outdated census data by more current small-area estimates of income and poverty in the Title I education allocations (see Chapter 2 for more details).

    Program agencies in the Executive Branch also play a significant role in the funding allocation process and in the formulation of rules and regulations that govern how the funds are used by the jurisdictions that receive them. In a few instances the agencies, following general guidelines in legislation, develop the specifics of the allocation formula or process. Funds are sometimes provided for agencies to conduct or sponsor research to determine to what extent the allocations have led to the achievement of program goals and to develop recommendations for improved formulas and better data sources.

    At the state and local levels, authorities are generally required to follow prescribed administrative procedures in order to receive the funds that have been allocated to them and to account for their use. Typically, legislation or regulations allow for some proportion of the total funds to be used for such administrative purposes.

    PREVIOUS STUDIES OF THE STATISTICAL ASPECTS OF ALLOCATION FORMULAS

    The paper by Smith and Parker that was presented at the workshop summarized selected previous studies that they considered relevant to its themes. The first four studies related to the General Revenue Sharing (GRS) Program. Between 1972 and 1986, the GRS program allocated federal funds to approximately 39,000 local jurisdictions using a formula based on population and per capita income:

    • The General Revenue Sharing Data Study by the Stanford Research Institute (1974). This pioneering study focused on questions of the degree to which equitable allocations to states, and thence to localities, were de-

    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    pendent on the quality of the data used in the GRS allocation formulas. Several methods of improving the timeliness and accuracy of the estimates were recommended. The study addressed difficulties in making the estimates for small jurisdictions that were mandated by the GRS legislation.

  • A 1975 study of alternative formulas for the GRS program undertaken by the Center for Urban and Regional Study at Virginia Polytechnic Institute and State University under a grant from the National Science Foundation. The study recommended inclusion of a poverty factor in the intrastate allocation formula and allocations on a per capita basis for units of government for which reliable estimates of income and poverty were unavailable.

  • The 1980 report of the CNSTAT panel on Small-Area Estimates of Population and Income (National Research Council, 1980). This panel was asked to evaluate the U.S. Census Bureau's procedures for making postcensal estimates of population and income, a task largely motivated by the use of these estimates in the GRS program. The panel made several recommendations for improving the estimates. It also recommended that some limits be imposed on congressional and other requirements for the U.S. Census Bureau to make such estimates for very small areas.

  • A staff report of the Federal Reserve Bank of Minneapolis (Stutzer, 1981). The GRS allocation formula included an element designed to reward localities with higher tax efforts (a ratio of state and local tax collections to total personal income). This study used simulation methods to evaluate the effects of such provisions on the recipient government's tax effort, spending levels, and welfare.

  • Two major studies of the statistical aspects of allocation formulas appeared toward the end of the 1970s. The first was Statistical Policy Working Paper 1, Report on Statistics for Allocation of Funds, prepared by a subcommittee of the Federal Committee on Statistical Methodology (chaired by Wray Smith). The subcommittee's goal was “to study, from the statistical standpoint, possible principles or guidelines which could be used to insure that the intent of Congress is fulfilled in the allocation of federal funds” (U.S. Office of Statistical Policy and Standards, 1978:1). The report included 5 case studies selected from the 10 largest programs using population and per capita income data as formula components. It considered the problem of measuring population, capability, and effort and took into account the effect of constraints and hold-harmless provisions on formula

    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    performance. It also discussed the special problems that arise in administering allocations to small areas. The subcommittee recommended that the goals of each allocation program be specified as clearly as possible and made several recommendations designed to assist program designers and drafters of legislation in meeting these goals more effectively.

    The second broad study of these issues was conducted by the Center for Governmental Research (1980) under a grant from the National Science Foundation. This project was primarily concerned with “developing and applying analytical tools to evaluate the distributional and equalization effects of federal grant-in-aid formulas and to improve formula performance.” The project final report called for several modifications of existing formulas, including “elimination of dual formula systems, updating of data elements, elimination of constraints, adjustments for cost-of-government differentials, and use of income per need unit ratios.”

    An article by Spencer (1982a) examined interactions between statistical issues and the technical and political aspects of formula design. Spencer recommended further statistical and policy research to explore a series of trade-offs: the use of simple versus more sophisticated formula components, the use of general-purpose data versus data produced primarily for use in allocation programs, the use of abrupt versus gradual eligibility thresholds, and updating versus not updating the statistical variables used in formulas. He recommended that statisticians and policy analysts collaborate in research on these issues.

    The Smith and Parker paper also reviewed three studies conducted in the 1990s. A study by the Urban Institute reviewed a broad range of options for Reforming the Medicaid Matching Formula. It discussed several elements that could be included in the formula, “particularly emphasizing a broader-based measure of fiscal capacity, adding cost of living and cost of health care adjustments, and adding a new component that would incorporate health care needs” (Blumberg et al., 1993:vi).

    In 1996 the U.S. General Accounting Office, at the request of the Committee on the Budget, U.S. House of Representatives, conducted a study that focused on “the extent to which the grant system succeeds in two objectives frequently cited by public finance experts: (1) encouraging states to use federal dollars to supplement rather than replace their own spending on nationally important activities and (2) targeting grant funding to states with relatively greater programmatic needs and fewer fiscal resources” (U.S. General Accounting Office, 1996:1). The report, which was called Federal Grants Design Improvements Could Help Federal Resources Go Further, con-

    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    cluded, “for the most part, the federal grant system does not encourage states to use federal dollars as a supplement rather than a replacement for their own spending on nationally important activities” (p.2) but added that not every grant is intended to do so. The report also concluded, “federal aid is not targeted to offset these fiscal imbalances. Consequently, lower income states face greater fiscal strain in financing federally aided services than higher income states with lower measurable needs” (p.2).

    Finally, Smith and Parker described a report from the RAND Drug Policy Research Center, Review and Evaluation of the Substance Abuse and Mental Health Services Block Grant Allocation Formula (Burnham et al., 1997). These grants were the subject of the third case study presented and discussed at the workshop (see Chapter 2).

    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    Suggested Citation:"1. Formula Allocation Processes: An Overview." National Research Council. 2001. Choosing the Right Formula: Initial Report. Washington, DC: The National Academies Press. doi: 10.17226/10178.
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    The workshop was a direct outgrowth of a previous study by the CNSTAT Panel on Estimates of Poverty for Small Geographic Areas. That panel, established under a 1994 act of Congress, began its work with a very specific mission: to evaluate the suitability of the U.S. Census Bureau's small-area estimates of poor school-age children for use in the allocation of funds to counties and school districts under Title I of the Elementary and Secondary Education Act.

    In carrying out their assignment, panel members came to realize that the properties of data sources and statistical procedures used to produce formula estimates, interacting with formula features such as thresholds and hold-harmless provisions, can produce consequences that may not have been anticipated or intended. It also became evident that there is a trade-off between the goals of providing a reasonable amount of stability in funding from one year to the next and redirecting funds to different jurisdictions as true needs change. In one instance, for example, the annual appropriation included a 100 percent hold-harmless provision, ensuring that no recipient would receive less than the year before. However, there was no increase in the total appropriation, with the result that new estimates showing changes in the distribution of program needs across areas had no effect on the allocations.

    Choosing the Right Formula provides an account of the presentations and discussions at the workshop. The first three chapters cover the overview, case studies, and methodological sessions, respectively. Chapter 4 summarizes the issues discussed in the roundtable and concluding sessions, with emphasis on the identification of questions that might be addressed in a panel study.

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