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## Statistical Issues in Allocating Funds by Formula (2003) Committee on National Statistics (CNSTAT)

### Citation Manager

. "4. Components of Allocation Formula." Statistical Issues in Allocating Funds by Formula. Washington, DC: The National Academies Press, 2003.

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Statistical Issues in Allocating Funds by Formula

## 4 Components of Allocation Formulas

As their name implies, formula allocation programs allocate funds to recipients (governments or individuals) via a formula. Many formulas depend on the need of the recipient, and it is also common for formulas to include measures of fiscal capacity. And it is not unusual for aid amounts to depend on local effort. These and other inputs are common components in many formulas; however, the manner in which they are operationalized and combined does differ. Appendix B, a review of 12 of the largest federal formula allocation programs explores these issues in relation to specific programs.

### MEASURES OF NEED

In theory, the resources needed by a recipient government in order to provide a target level of services depend both on the number of individuals eligible for the services and on the cost of providing them to each eligible individual. Generally, both of these components of need must be estimated. For example, the goal of the State Children’s Health Insurance Program (SCHIP) is to encourage states to establish insurance programs that cover children in families who are not eligible for Medicaid and for whom private insurance is prohibitively costly. Thus, aid under SCHIP depends on the estimated number of children who are not eligible for Medicaid and who do not have private insurance. Importantly, the cost of providing health care to each uninsured child varies by state and, if possible,

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 Front Matter (R1-R14) Executive Summary (1-4) 1. Introduction (5-17) 2. Why Provide Aid and Use Aid Formula? (18-25) 3. Basic Features of Formula Allocation Program (26-34) 4. Components of Allocation Formula (35-39) 5. Special Features of Formula Allocations (40-49) 6. Data Sources for Estimating Formula Components (50-58) 7. A State View -- California (59-70) 8. International Perspective (71-78) 9. Conclusions and Recommendations (79-89) References (90-94) Appendix A: Background Papers (95-99) Appendix B: A Review of Twelve Large Formula Allocation Programs (100-128) Appendix C: Sources of Information (129-137) Appendix D: Handbook on Fund Allocation Formulas and Processes (138-141) Appendix E: Participation in Panel Workshop and Meetings (142-142) Appendix F: Biographical Sketches of Panel Members and Staff (143-147)

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Statistical Issues in Allocating Funds by Formula 4 Components of Allocation Formulas As their name implies, formula allocation programs allocate funds to recipients (governments or individuals) via a formula. Many formulas depend on the need of the recipient, and it is also common for formulas to include measures of fiscal capacity. And it is not unusual for aid amounts to depend on local effort. These and other inputs are common components in many formulas; however, the manner in which they are operationalized and combined does differ. Appendix B, a review of 12 of the largest federal formula allocation programs explores these issues in relation to specific programs. MEASURES OF NEED In theory, the resources needed by a recipient government in order to provide a target level of services depend both on the number of individuals eligible for the services and on the cost of providing them to each eligible individual. Generally, both of these components of need must be estimated. For example, the goal of the State Children’s Health Insurance Program (SCHIP) is to encourage states to establish insurance programs that cover children in families who are not eligible for Medicaid and for whom private insurance is prohibitively costly. Thus, aid under SCHIP depends on the estimated number of children who are not eligible for Medicaid and who do not have private insurance. Importantly, the cost of providing health care to each uninsured child varies by state and, if possible,

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Statistical Issues in Allocating Funds by Formula this cross-state variation should be reflected in aid amounts. But the true cost of insuring each eligible child will not be known and must be estimated. Many aid formulas include ad hoc adjustments for variation in need. For example, to compensate for geographic differences in prevailing salaries and thereby in the cost of education, the Title I, Part A, grants to local education agencies formula includes state per-pupil expenditure (PPE) as one factor in determining the allocation (Brown, 2002). However, to our knowledge no existing school aid formula includes cost adjustments that are closely linked to evidence on the costs of providing particular services. There is general agreement that aid formulas should account for differences in costs, but generally they do not because developing cost estimates is extremely difficult and somewhat contentious. For example, although differences in PPE reflect relative costs, they also reflect variations in local wealth and commitment to education. The SCHIP and Title I education examples highlight the important issue of whether aid should compensate primarily for costs that are beyond the control of decision makers in the recipient jurisdictions. If compensation is also influenced by controllable costs, the aid formula could generate perverse or undesirable incentives. For example, in SCHIP the method used to estimate the number of eligible children must be designed to avoid penalizing states for the success of the program (Czajka and Jabine, 2002). Also, if administrative data are used to estimate the number of eligible children or the cost per eligible child, these data must be chosen so that they are immune to manipulation. A critical task for researchers is to compare the results of the alternative methodologies with the goal of developing consensus estimates of need. Duncombe and Lukemeyer (2002) provide a superb model of the style of research that must be produced. MEASURES OF FISCAL CAPACITY Measures of fiscal capacity are the second shared component of aid formulas. While per capita personal income is the most commonly used measure of fiscal capacity, other measures are more consistent with the goals of individual aid programs (Tannenwald, 1999; Downes and Pogue, 2002). For example, Downes and Pogue (1994) and Ladd (1994) agree that, if the goal of the aid program is to close the gap between need and effort and thereby reduce fiscal disparities, capacity measures based on the representa-

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Statistical Issues in Allocating Funds by Formula tive tax system (RTS), variants of which are used in state-level school aid programs and in the Canadian equalization program, should be used. The use of RTS-style measures of capacity ensures that all localities receiving aid will be able to finance a basic package of public services by levying average tax rates. Thus, no recipient governments will be at a competitive disadvantage (Ladd, 1994). If the goal is redistribution of economic well-being or equal treatment of economic equals, the appropriate choice is a capacity measure that is based on an adjusted measure of income, for example, the total taxable resources (TTR) measure of capacity that is used in the community mental health services block grant and substance abuse block grant programs. TTR is based on the rationale that if the objective of aid is to redistribute from rich to poor or is to promote the evenhanded treatment of individuals whose economic circumstances are the same, the measure of capacity should reflect the cumulative ability of the residents of a locality receiving aid to pay taxes (Tannenwald, 1999). Using such a measure of capacity ensures that localities with equal abilities to pay taxes for public services will be treated equally and that localities with less ability to pay will get more aid. TTR is preferred to per capita income because it provides a more comprehensive measure of ability to pay. For example, accrued capital gains are included in TTR. Any measure of capacity must be estimated, usually at a refined level of geographic and temporal resolution. The difficulties of generating income estimates for small areas are well known (National Research Council, 2001). The estimation problems become more daunting when adjustments need to be made for the extent to which taxes can be exported (shifted to non-residents) (Bradbury and Ladd, 1985; Downes and Pogue, 1994). Even capacity measures derived using the RTS methodology can be subject to large errors. Taylor et al. (2002) document some of the measurement problems that arise in the Canadian context; Tannenwald (1999, 2001) provides graphic evidence of the difficulty of generating state-level measures of fiscal capacity using the RTS methodology. MEASURING EFFORT A measure of effort is the final component common to many aid formulas. Recall that effort is measured by the revenues raised at the state or local level and spent on providing the service for which aid is provided. Effort measures are central elements in matching aid formulas, since for

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Statistical Issues in Allocating Funds by Formula most recipient jurisdictions the amount of aid is a (possibly variable) percentage of effort. Effort is also an important part of any aid formula that imposes a minimum effort requirement. It would seem that effort is the component of an aid formula that is easiest to measure using direct information. Local tax rates are readily observable, as is spending on the service for which aid is being provided. However, measuring effort is not quite so straightforward. If aid amounts depend on spending on the targeted services, the recipient government has a strong incentive to overstate effort by classifying spending on other services as spending on the targeted services.1 Similar incentives to overstate effort operate if aid is contingent on minimum effort. Nevertheless, of the three shared components of aid formulas, effort can be measured with the smallest error. COMBINING COMPONENTS Most formulas combine two or more measures of need, fiscal capacity, and effort. Appendix B provides examples of the varied ways in which these measures are combined. Ideally, for programs with explicit goals, components should be combined to target these goals (Downes and Pogue, 2002); however, frequently there is not such a tight link. No matter how a formula is constructed, the choice of a particular combination of the components will influence how they interact. A simple example helps clarify how errors in the measurement or estimation of the different components of an aid formula can interact. Chapter 2 presents a formula showing how components might be combined to close the gap between need and effort. Errors in the number of eligibles (n), the level of spending per eligible individual needed to achieve the target service level (F), the cost index that adjusts for interlocality differences in the cost per eligible individual of providing given public services (C), or the fiscal capacity of the recipient jurisdiction (V) will produce discrepancies between the actual and desired aid distributions. Reducing the error in measuring one component may not produce an improvement. Suppose, for example, that fiscal capacity is measured with- 1   In the rare instances in which aid amounts are reduced by increased local effort, the recipient governments might attempt to understate effort by hiding expenditures or using funding mechanisms that are not counted as part of local effort.

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Statistical Issues in Allocating Funds by Formula out error but that the errors in estimating the number of eligibles and the cost per eligible are negatively correlated. The aid distributed might then be relatively close to the desired distribution. Reducing the error in estimating the number of eligibles while making no improvement in estimating the cost per eligible could result in an aid distribution that lines up less well with the desired distribution. Changes in the aid distribution resulting from proposed improvements in the measurement of one or more components should be evaluated. Evaluations should include a study of how the relations between formula outputs (allocations) and inputs (measures of need, fiscal capacity, and effort) are affected by the change, taking into account the effects of hold-harmless provisions and other special features of the allocation process.

Representative terms from entire chapter:

aid formulas