Statistical Issues in Allocating Funds by Formula (2003)

In a federal system, intergovernmental aid can help policy makers accomplish many objectives. Describing these objectives is not a purely academic task, even though, as noted in Chapter 1, the political process profoundly affects the final structure of formula allocation programs. Characterizing several of the most common objectives of aid is a first step toward understanding why some aid formulas exist and how they should be structured, particularly since different aid formulas are consistent with different objectives. This section reviews four of the more common objectives of aid: closing the gap between need and effort, treating economic equals equally, redistributing economic well-being, and encouraging spending on certain services. We then discuss implications of each of these objectives for the structure of aid formulas. In practice, aid formulas often combine elements associated with more than one of the objectives described in this chapter, because the objectives are not mutually exclusive and because the designers of most aid programs hope to accomplish more than one of them.

Many aid programs arise in response to the recognition that, if all public services provided by states or localities were financed with state-level

or local-level taxes, the effort (as measured by the revenues raised at the state or local level) required to finance a target (or an adequate) level of services would vary dramatically. (Ladd and Yinger, 1994, refer to this concept of effort as revenue-raising capacity.) The goal of aid is to make it possible for all states or localities to provide the target level of services with a reasonable effort.

At the state level, there are numerous examples of aid programs that have been designed to accomplish this goal. For instance, most state aid to local school districts is distributed via foundation aid programs. Under such programs, the state guarantees that each school district that levies a tax rate at or above some minimum will be able to spend at least a minimum or foundation amount on each student. The local contribution toward this amount is first determined by applying the minimum tax rate to the tax base. The state then provides enough aid to ensure that each student generates funding equal to the foundation level or allowance.

Downes and Pogue (2002) show that foundation aid programs are consistent with the goal of enabling all aided localities to provide a target level of services with a reasonable effort. Such explicit links between the goal of closing the gap between need and effort and the design of aid formulas are not as evident for aid programs at the federal level. Nevertheless, this goal has influenced the motivation for and the design of many federal aid programs. For some programs, like the Substance Abuse and Mental Health Services Administration’s Substance Abuse Prevention and Treatment Block Grant Program,¹ the statement of the program’s objective makes general reference to providing each state with the ability to meet local need:

In other cases, by providing more aid to states or localities with less ability to raise revenue, formulas have the explicit intent of making more

equal the capacity of recipient jurisdictions to serve their constituents. In still other cases, federal aid formulas incorporate cost adjustments as a way of accounting for variation among recipient jurisdictions in the expenditures necessary to provide the services for which aid is being provided. Closing the gap between need and effort is therefore one of the goals, if not the sole one, motivating critical elements of many of the largest federal formula allocation programs.

In the language of economics, these gaps between need and effort are referred to as fiscal disparities. In the absence of aid, fiscal disparities imply that government activities, such as the provision and financing of education, are not locationally neutral—the taxes that individuals bear to receive a given level of public services depend on where they reside and engage in economic activities. If moving is costly, fiscal disparities mean that some individuals are worse off simply because they reside in localities with higher costs or fewer taxable resources. Closing the gap between need and effort can redistribute economic well-being to those who reside in disadvantaged communities. Furthermore, if, as seems likely, individuals who move must incur real or psychic costs, then the variation in fiscal disparities can alter the location of private-sector activities, thereby creating an inefficient pattern of economic activity. In addition, without aid, fiscal disparities can result, in those localities with limited capacity, in levels of public services that are, from a societal perspective, dangerously low.

Closely linked to the objective of closing the gap between need and effort is a second objective of aid: promoting the evenhanded treatment of individuals whose economic circumstances are the same. Aid is seen as a mechanism for ensuring that individuals who are alike in their ability to pay taxes or in their need for the services that aid is being used to finance do, in fact, have the same tax burdens and receive the same benefits from government services.

In the economics literature, aid that is motivated by this objective is said to promote horizontal equity.

Many aid programs arise out of a desire to redistribute resources and, ultimately, economic well-being from those with more ability to pay the

taxes needed to finance publicly provided services to those with less ability to pay. Ultimately, the goal is to make access to the benefits of economic prosperity more equal.

The community development block grants offer one example of an aid program that has as its goal the redistribution of economic well-being. The grants provided under this program are intended “to develop viable urban communities, by providing decent housing and a suitable living environment, and by expanding economic opportunities, principally for persons of low and moderate income” (Appendix B). Clearly, the hope is that aid will provide low- and moderate-income individuals with improved access to the fruits of economic prosperity.

Aid programs that are designed to shift resources toward those who are less well-off economically are attempting to produce a distribution of economic well-being that is more vertically equitable. The degree to which the correlation between economic well-being and ability to pay is reduced determines the extent to which an aid program results in a distribution of economic well-being that is more vertically equitable.

Frequently, architects of aid programs design them with the hope of inducing changes in the spending behavior of recipient governments by altering the incentives they face. For example, the matching element of the State Children’s Health Insurance Program (SCHIP) exists 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 (see Appendix B).

Aid can also be used to encourage recipient jurisdictions to make different uses of the resources available to them. Making aid contingent on measurable improvement in the quality of services provided, as is implicitly done in the No Child Left Behind Act of 2001, is intended to force recipient governments to eliminate inefficiencies and direct resources toward those services that are most needed by the target populations.

Aid programs can alter behavior in less subtle ways. Maintenance of effort requirements, such as those that exist under the Temporary Assistance for Needy Families (TANF) program, mandate the extent to which revenues raised by the recipient government can decline after aid has been received. Such mandates are intended to reduce the extent to which aid substitutes for local resources. Similarly, conditioning aid receipt on the

implementation of specific policies, as was done when receipt of highway aid was linked to passage of state speed limit and drinking-age laws, is an example of the use of aid as a lever to get recipient governments to implement policies that federal policy makers determine to be in the national interest.

Such levers are necessary only if the national interest and the interest of the recipient government diverge. Frequently, a mismatch in local and national interests exists because the benefits of the public service in question accrue not just to the residents of the recipient jurisdiction but also to some individuals who have no voting interest in the locality’s receiving aid. For example, local governments might choose to spend too little on education because the direct beneficiaries of that spending are not current voters and the community’s elected leaders perceive that the lower tax rates associated with the lower spending levels will help attract commercial and industrial investment. In such situations the benefits of the public service spill over the boundaries of the providing jurisdiction either geographically or in time. If spillovers of this type exist, provision of the public service will be inefficient in the absence of some intervention by the state or the national government. Properly designed aid formulas can create incentives for local governments to increase or decrease spending on the aided function and thus implicitly account for the external benefits associated with that spending. In other words, linking the receipt of aid to the pursuit of certain policies can ameliorate (or even eliminate) inefficient provision of a public service attributable to a mismatch between the jurisdiction that provides the service and members of society who benefit from it.

Objectives like closing the gap between need and effort and encouraging spending on certain services can be addressed relatively effectively using intergovernmental aid, since those objectives are stated in terms of communities, not individuals. However, the objectives of promoting equal treatment of equals and of redistributing economic well-being are stated in terms of people, not communities. Not all people in wealthy communities are wealthy; not all people in poor communities are poor. As a result, redistributing resources across communities may not result in very effective redistribution across individuals.

So, if policy makers hope to accomplish these objectives, why use intergovernmental aid, as opposed to direct aid to individuals? Inter-

governmental aid programs tend to be simpler to administer than programs that provide direct aid to individuals. Furthermore, aid programs in general and formula aid programs in particular are the product of compromises between different interests. Some legislators who support a particular aid program are motivated by specific goals. For example, proponents of certain key elements of the No Child Left Behind Act, which reauthorized the Elementary and Secondary Education Act and with it the Title I education program, pushed these modifications to the Title I program because of their concern about the achievement gap between poor and disadvantaged students and their more affluent peers. Others are more concerned with the impact of these programs on the resources flowing into their states and districts. Crafting a compromise between these competing interests may be easier if aid is directed to communities rather than to individuals, since calculating the resources directed to legislators’ key constituencies can be done more easily under intergovernmental aid programs and since the economic status of individuals tends to be correlated with the economic status of the communities in which they live. Those who hope to use aid to redistribute economic well-being know that poor people tend to live in poor communities. Thus, even if aid is motivated by an objective that is stated in terms of individuals, administrative simplicity or political feasibility may result in intergovernmental aid. Intergovernmental aid may, in the language of economics, be a second-best policy.

Nevertheless, the disconnect between individual-centered objectives of aid and the community-centered structure of aid can create confusion in the discussion of aid programs. For example, if the objective of an aid program is equal treatment of equals, those constructing and evaluating this program tend to ask if communities are treated fairly under it. But fair treatment of communities is not necessarily consistent with equal treatment of equals. Similarly, if the objective is to redistribute economic well-being, the tendency is to design an aid program to redistribute from rich to poor communities—but that may not redistribute from rich to poor individuals.

As was noted in Chapter 1, formulas do not represent the only mechanism for allocating aid to states or localities. Do they offer any advantage

over legislating shares, for example, as is done in the Evironmental Protection Agency’s State Capitalization Grants Program?

One clear advantage of formulas is that they permit linking the structure of the aid program to its objectives. The commissioned paper by Downes and Pogue (2002) provides a more extensive discussion of the link between objectives and the structure of aid programs.

Suppose, for example, that the objective of aid is to make it possible for all recipient jurisdictions to provide the target level of services with a reasonable effort. In this case, the objective maps directly into the aid formula. Specifically, as Ladd and Yinger (1994) and Downes and Pogue (2002) observe, the formula that gives the appropriate amount of aid for any recipient jurisdiction is:

where F is the level of spending per eligible individual needed to achieve the target service level, n is the number of eligible individuals in the recipient jurisdiction, C is a cost index that adjusts for interlocality differences in the cost per eligible individual of providing given public services, t^* is the formula tax rate, which is multiplied by each recipient government’s fiscal capacity to determine its contribution to financing the target level of spending, and V is the fiscal capacity of the recipient jurisdiction. The formula tax rate t^* is chosen so that, if a locality chooses to levy that rate, it will be able to provide the target service level with a reasonable effort. The formula tax rate t^* and the level of spending needed to achieve the target service level F are policy parameters; these quantities would be the same for all recipient jurisdictions. Typically, policy makers would set the value of t^* at what they feel is the minimum fair tax rate. Recipient jurisdictions typically choose local tax rates that differ from t^*; providing aid according to this formula closes the gap between need and effort but does not prevent residents of any single recipient jurisdiction from choosing to provide more or less of the public service in question.

The other objectives of aid discussed above also map directly into elements of aid formulas. For example, changing the incentives facing recipient jurisdictions can encourage spending on a particular service. This can be done using matching, which reduces the amount by which local tax revenues must be increased in order to increase spending on the aided func-

tion by one dollar. In other words, matching aid programs like SCHIP encourage more spending on the aided function by reducing the “price” of that function from the perspective of the recipient government.

Because the objectives of promoting equal treatment of equals and redistributing economic well-being focus on individuals, not communities, mapping these objectives into specific elements of aid formulas is more challenging. Still, aid can come closest to accomplishing these objectives if it is distributed according to a formula. Suppose, for example, that the goal is redistribution. Then, given that poor individuals tend to reside in poor communities, aid should go disproportionately to poor communities (Ladd, 1994). This will happen if aid is distributed using an aid formula that accounts for a community-level measure of ability to pay such as total taxable resources (TTR), with aid amounts varying inversely with ability to pay.

As was noted in Chapter 1, aid exists in a domain somewhere between the idealized world in which aid programs are designed to fulfill explicit objectives and the purely political world in which aid programs simply divvy up pots of money. Many of those who advocate for aid programs are motivated by specific objectives, but they must make compromises to get the authorizing legislation approved. Formulas can offer political cover to those involved in the process of compromising (Melnick, 2002). Also, formulas can simplify the process of compromising by reducing the dimensionality of the problem. In other words, if a formula is used to distribute aid, agreement needs to be reached on the structure of the formula and the statistical inputs to that formula. Without the aid formula, the programmatic description that allocates decision-making responsibility to a federal agency must be crafted to generate sufficient support (Melnick, 2002). Finally, formulas make it easier to quantify the impact of alternative compromises.