15 Formula Funding and Performance Budgeting

Marc Robinson
Published Date:
October 2007
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Peter C. Smith1

Numerous instruments are needed to make operational the principles of performance budgeting. Among the most important is the mechanism whereby individual local agencies are financed. This chapter focuses on one particular type of financing mechanism: the use of mathematical formulas to determine the magnitude of funds directed towards a local public service organization. The use of such formulas has become increasingly widespread in many public services. When properly designed, it can be strongly aligned to the principle of program budgeting, as a means of systematically transmitting central policies to specific local organizations. However, formula funding also embraces a number of perils that must be addressed if it is to contribute successfully to the performance budgeting process.

This chapter summarizes the “state of the art” of formula funding as it relates to performance budgeting. It begins with a brief overview of the funding flows that are addressed by formula funding, and then explains what formula funding is. It next examines the rationale for adopting formula funding within a performance budgeting framework. The following section then describes in some detail the two main types of formula funding—case payments and capitation methods. The chapter concludes with a discussion of the incentives under formula funding, and the circumstances in which it can be aligned successfully with the performance budgeting process.

Flow of funds in public services

Most public expenditure is undertaken locally. However, the methods put in place by the national government for funding local public services have crucial implications for their nature, effectiveness, and efficiency. Figure 15.1 offers a conceptual framework for the flow of funds implicit in the financing of most public services. The prime source of central government funds is usually taxation, paid in a variety of forms by citizens and businesses. This creates a pool of revenue (A) available to the government, which must decide how it will allocate the funds to support locally delivered public service programs, either wholly or in part, consistent with its performance objectives.

Figure 15.1.Flow of funds in public services

The central government might pay local providers directly (E), as in many national systems of university education. In contrast, it might devolve purchasing powers to lower tiers of administration. In this chapter I emphasize the case where the local purchaser is an agency of the national government. The case where the agency is a local government, with some degree of local accountability, independent revenue sources, and an element of autonomy from the national government is not treated explicitly in this chapter, although many of the principles remain valid when services are devolved to local governments. My book gives an extended treatment of this topic (Smith, 2006).

Where they are used, the national government must give local purchasers the means to carry out their purchasing functions (flow B). Local service providers then receive payments either directly from the national government (flow E) or from its local administration (flow C). In some circumstances, the distinction between local purchaser and provider may be unclear (for example, schools are often directly provided for by local administrations). However, even where there is no explicit payment mechanism, local administrations must in principle purchase their services from vertically integrated providers. Finally the service user might pay a charge to the service provider (D).

This chapter is centrally concerned with two of the funding flows represented in Figure 15.1: the mechanisms for funding local administrations from national revenues (B); and the mechanisms used for paying providers (E and C). Throughout, I shall refer to the national disburser of funds as the payer, whether the payment is made to a local administration or to a provider. From a performance budgeting perspective, a central challenge for the payer is to design a payment mechanism that secures its policy objectives.

Determining satisfactory mechanisms for making financial allocations to local agencies can give rise to serious challenges for the payer. First, it is a difficult technical exercise to determine where public money is best spent in line with performance objectives. Second, any funding mechanism introduces powerful incentives for local organizations, and it is important to ensure they are in line with the payer’s intentions. Third, the political ramifications of any funding choice can be acute, particularly when parliamentary representatives are elected on a geographical basis. And finally, a national government requires reassurance that public expenditure is being spent locally in line with intentions, yet monitoring the effectiveness and efficiency of local spending is often a difficult undertaking. This is of course a fundamental concern of program budgeting.

There are numerous ways in which a national payer could determine the allocation of public funds to local agencies. At its crudest, the distribution could be based on political patronage, perhaps rewarding localities according to their political support in the past, or their importance for future elections. Although few payers would admit openly to engaging in such patronage, there is ample evidence to suggest that to some extent it informs many allocation systems that are supposedly nonpartisan (Gibson, 1998; John and Ward, 2001).

Financial allocations could instead be made according to how much localities actually spend. This approach will usually contradict principles of good public finance, as it is likely to encourage spending in excess of optimal levels and offers few incentives for efficient local management. However, it has historically formed the basis for many rudimentary funding mechanisms as it has minimal monitoring requirements, and it can be used to encourage spending when local agencies would otherwise spend below optimal levels.

Another approach in widespread use is to distribute public funds according to historical precedent. Politically, it has the great attraction that it minimizes disruption to existing public services, and avoids potentially large swings from year to year inherent in other allocation mechanisms. Its popularity is manifest in the way that more systematic approaches to distribution are frequently abated by “damping” mechanisms that seek to reduce the magnitude of year-on-year financial losses and gains to local agencies. However, sole reliance on such methods would leave a payer hostage to history, and offers few incentives for service reform or improved performance.

A fourth possibility is to allocate funds according to bids submitted by local agencies, or to make allocations contingent on some measure of local performance. In principle, this approach has much to commend it from a performance budgeting perspective. If undertaken properly, it could ensure that public funds are spent in line with national policy intentions, in a cost-effective manner. Its major weakness is that it usually entails large transaction costs, in the form of central scrutiny and policing, and the preparation of bids by local agencies. It also makes local budgets dependent on the quality of local management, and so may lead to large inequalities. Moreover, unsuccessful agencies may perceive that the allocations have been made according to patronage rather than the quality of bids, leading to further potential for perceived unfairness.

In practice, most systems of financing local public service institutions use a mix of all four types of mechanism to allocate funds. However, a fifth approach—allocation by mathematical formula—is increasingly becoming the favored approach towards determining local financial allocations. It can be defined in broad terms as the use of mechanical rules to determine the level of public funds a devolved organization should receive for delivering a specified public service. The next section examines formula funding in more detail.

What is formula funding?

Under formula funding the payer specifies in advance mathematical rules that determine the magnitude of the funding received by a local organization. Those rules might be very simple (for example, a fixed amount of funding for each user) or very complex. However, the overarching objectives of formula funding are (a) to create a budget for the local entity with which it is expected to provide local public services, and (b) to offer appropriate incentives to provide those services in line with the payer’s objectives.

With many systems of formula funding, the payer’s objective is merely to enable all local agencies to deliver some “standard” package of services. As stated, this criterion usually ducks the issue of what that standard might be. In practice, the standard is often interpreted as the national average level of services, given a locality’s social, economic, and geographical circumstances. The standard package might be defined in terms of expenditure (for example, a certain level of spending on each citizen in need of services), service levels (a stated service entitlement for citizens with specified needs), or outcome (a stated level of outcome to be secured for all users). However the standard is defined, when applied to a locality it implies a certain level of expected expenditure, which is the local agency’s “spending need.” It is this spending need that the funding formula seeks to estimate.

This traditional “needs based” funding formula makes little direct reference to performance, other than an implicit expectation that the local agency will perform at the national average level. As stated, the needs based approach offers only the opportunity to deliver the standard, and on its own offers no direct incentive to secure any performance standard whatsoever. Performance budgeting signals a desire to move away from this traditional approach of “funding needs,” toward a principle of “funding results.”

There are two broad approaches to the use of formula funding. The first reimburses the local agency on the basis of some measure of output, typically a count of the number of service users. Such case payment mechanisms are widespread in education (counts of pupils) and health care (counts of patients), and they are especially relevant when an unambiguous indicator of a service user’s need for the service can be established. Case payment methods give rise to a variable budget for the local agency, based on recorded output. They therefore incentivize increased output, but can give rise to perverse incentives to create unwarranted or inappropriate service utilization.

The other approach to formula funding is to reimburse according to the expected level of local activity. Typically, this takes a measure of the size and characteristics of a local population, and infers the expected level of local service expenditure without reference to actual local output. Because these methods are based on population counts, they have become known as capitation funding methods. They circumvent some of the perverse incentives inherent in case payment, because they do not rely on a count of service users. However, they introduce their own difficulties—most notably the failure to incenticize any sort of output, whether warranted or not. The incentives inherent in formula funding methods are discussed in more detail in the sections below.

Whatever the chosen mechanism, four institutional aspects must be in place for formula funding to be effective. First, there must exist at least some local autonomy regarding how the local public service is delivered. The recipient of funds could be very large (such as a regional government) or very small (even extending to an individual citizen in receipt of a voucher to spend on specified services). However, unless this local agency enjoys at least some autonomy as to how it can use the funds, the funding mechanism becomes one of merely reimbursing specific activities, and offers few incentives for efficiency.

Second, there must be adequate data, available on a consistent basis across all local organizations, to which can be applied a mechanical formula that determines the level of funding to be allocated to those organizations. The data should of course be verifiable and timely. Also, the formulaic rules should be specified ex ante, so that there are no immediate provisions for altering the consequent level of funding. The possibility of ex-post adjustments to the rules suggests that formula funding budgets are being moderated by considerations of actual spending or political patronage.

Third, there should be some explicit performance criteria against which the performance of the local agency is to be judged. It is meaningless to devolve funds without some statement as to their use. However, the chosen performance criteria might range from a very rudimentary check that services are delivered with some basic adherence to quality standards, to the very complex quality assurance regimes now emerging in some education and health systems (Smith and York, 2004). It is noteworthy that many existing formula funding mechanisms pay little regard to such performance issues.

Finally, there must exist some incentive to adhere to the financial allocation implied by the formula. Formula funding is a mere ritual if the recipients of public finances can with impunity ignore the resulting budgetary limits. Sanctions and rewards may take many forms. And they might apply to an organization, to a team, or to an individual manager. For example, a head teacher might face dismissal if a school’s financial allocation is persistently exceeded. Or a for-profit provider might be threatened with bankruptcy if it fails to secure enough business. There is no requirement that the sanctions should be as “hard” as these examples, but there must be some incentive for recipients of formula finance to take notice of their allocations.

Formula funding is becoming the dominant mechanism for devolving public finances. For example, Smith (2003) estimates that annually at least £150 billion of UK public expenditure is devolved in this way, and Louis et al. (2003) suggest an equivalent figure of $250 billion for federal spending in the United States. It is nevertheless important to note that many existing mechanisms have been designed primarily to address issues of fairness between local areas, and have not been explicitly aligned with the payer’s performance requirements. The extent to which they can address performance budgeting requirements is discussed in the next section.

Rationale for formula funding

There are three broad reasons why a government might introduce formula funding, relating to efficiency, equity, and political arguments. Performance budgeting “refers to public sector funding mechanisms designed to strengthen the linkage between funding and results” (Chapter 1). The interest in this chapter is the extent to which formula funding can promote performance budgeting, and efficiency concerns are therefore likely to be paramount. This section therefore examines those efficiency arguments in some detail. However, it is important to bear in mind that payers may also turn to formula funding to address equity and political objectives, so the section concludes with a brief summary of arguments in those domains.

Economic efficiency has a number of connotations. The two most fundamental are allocative efficiency (the extent to which allocations of resources are in line with society’s preferences) and managerial efficiency (the extent to which agencies perform specified functions at least resource costs). Formula funding is intended to address both aspects of efficiency. First, it seeks to align resource allocations and incentives with the payer’s intentions; second, it seeks to promote efficient management among local organizations.

No coherent system of financial transfers can be developed without first establishing clear objectives for the financial regime. Once objectives have been set, the fundamental efficiency argument for implementing formula funding is that—if properly designed—it allows the payer to implement an optimal allocation of finance in line with those objectives. Any deviation from such a formula implies a reduction in the effectiveness with which funds are used, and therefore a loss of efficiency. For example, if objectives are set in terms of service outcomes—such as maximizing school examination results—the formula should be designed to secure that objective at a national level, subject to an aggregate budget constraint. This implies designing allocations such that the expected marginal benefit (marginal improvement in exam results) for an extra unit of expenditure is equal for all local agencies. Any departure from this criterion leads to a loss in total examination success. Of course the key empirical challenge then becomes one of successfully designing a formula in line with that objective.

It could be argued that an efficient allocation could be secured through means other than formula funding. For example, one could envisage an iterative mechanism under which the national government makes incremental changes to local budgets each year in the light of where it feels the funds are best spent (increasing budgets where the marginal benefit appears high, and reducing them where it seems low). Apart from requiring an indefinite time horizon over which to converge to an optimal allocation, such methods are vulnerable to gaming on the part of the local agencies. For example, they may have an incentive to underperform in order to imply that they would benefit from increased funding. In contrast, well-designed formulas can secure an instantaneous solution, and can be designed so that they are not susceptible to such gaming.

A central concern of many payers is the extent to which the mechanism for financing local organizations relies on data provided those same agencies. This can give rise to two difficulties: data manipulation and fraud, and the creation of perverse behavioral incentives. An example from the nineteenth century illustrates both issues. The government rejected a proposal to reimburse English local authorities according to the number of “indoor paupers”—or workhouse residents—(a) because the count of “indoor” paupers was vulnerable to fraud and (b) it may have encouraged unnecessary use of the workhouse (in order to raise numbers of indoor paupers, the proposed basis for payment). Even in systems in which such responses are rare, a suspicion that they exist may undermine the credibility of the funding mechanism.

Many of the most creative systems of formula funding therefore seek deliberately to minimize the use of data emanating from local agencies, or to rely only on independently verified and audited data, so reducing the danger of moral hazard in the actions and reporting of local agencies. Such approaches allow the center to develop funding mechanisms that rely more on objective indicators of service needs and outcomes, and that are therefore independent of special pleading or gaming on the part of the local organization. Formula funding therefore offers a practical means of accommodating the information asymmetry between the payer and the local agency.

Implicit in these arguments is the belief that the use of formulas economizes on the analysis, audit, and oversight required at the center. With careful design, the payer can reduce the need for detailed scrutiny of the case for funding local agencies. In turn, the local agency does not need to make a case to the center, and must instead concentrate on delivering local services. Furthermore, and perhaps most importantly, it has less incentive or opportunity to distort behavior in order to suggest a need for more funding. Compared with most other funding mechanisms, formula funding can therefore economize on agency costs, both at the center and locality. Of course, in practice, even under a formula funding system, local agencies are likely to make representations to the center about the accuracy or fairness of the formula. However, special pleading is likely to be less profitable and more easily rebutted if a well-designed formula is in place.

Formula funding can have important implications for managerial efficiency, as it leads to the creation of clearly defined incentives and rules for the creation of budgets in the local agency. A clearly defined and predictable system of reimbursement enables the local agency to put in place proper financial management and business planning arrangements. When implemented alongside decentralization of power, the setting of a clear budgetary regime offers local organizations freedom to respond to local circumstances, to innovate, and to seek out economies, in line with the prescriptions of the new public management (Osborne and Gaebler, 1992). Properly designed, the use of mathematical formulas is an important means of enabling the center to set a credible and robust budgetary regime that can be used to promote its performance objectives.

Rather than these efficiency concerns, which are central to the principles of performance budgeting, many systems of formula funding have traditionally been concerned more with promoting some concept of equity, in seeking to reimburse “needs” rather than “results.” So far as a payer is concerned, the pursuit of equity might be valued for its own sake, or it might be valued because it secures acceptance for the redistribution implicit in the assignment of government revenues to pay for local public services. Central governments raise much of their revenue through national taxes, levied at some standard rate across the country. In order to secure support for such taxation, they may wish to redistribute revenues in a fashion that appears fair and in line with concepts of natural justice (Rice and Smith, 2001b).

Indeed, there is a rich “political economy” of formula funding (Glennerster et al., 2000; McLean, 2005). It may appear that, by delegating the rules for setting budgets to the technical domain, formula funding circumvents the political problem. Such a view assumes the existence of an enlightened payer able to articulate an explicit set of objectives in respect of public services. However, enlightenment may not be the only principle informing the payer’s motivations, and a more self-interested payer may wish to use a funding formula to further its own interests.

Moreover, there are numerous actors associated with the funding of public services beyond the immediate payer who may seek to influence the deployment of funding formulas, including politicians, central and local bureaucrats, local governments, providers, interest groups, and the general public. Depending on the institutional arrangements in place, such actors may play an important role in influencing, constraining, or enabling the design and implementation of funding formulas. Indeed, the payer may use the formula funding mechanism to reconcile these various interests. In short, it is important to note the complex political economy underlying the design of public service funding mechanisms.

In reading the literature on funding formulas, therefore, it should be kept in mind that many existing systems have been used not to promote performance objectives, but rather to resolve the competing claims of various agencies. Hence the frequent emphasis on needs-based funding. This is an important and legitimate role of formula funding. However, it is not considered further here. Instead, the following sections focus on the role of formulas in systems of results-based funding.

Elements of formula funding

This section describes the two broad approaches to designing funding formulas in common use. In the case payment approach, local services are reimbursed according to some measure of the actual level of output. In the capitation approach, an estimate is made of the expected costs the local agency will experience if it were to deliver some standard level of service to its local population. The section concludes with a discussion of the information needs of formula funding.

Case payments: reimbursing according to outputs

It is often perfectly feasible to quantify the outputs of a local agency, for example, in the form of the number of users who receive a specified service. Such counts form the basis of most systems of case payment. An example is schooling, where the number of pupils completing some specified program can usually be readily counted. Other services where outputs can be readily counted and audited, and therefore case payments are likely to be feasible, include much of health care, long-term social care, prisons, and housing.

The fundamental objectives of case payment methods are (a) to encourage local agencies to increase the number of service users and (b) to implement efficiency improvements so as to reduce unit costs. Case payment methods are therefore often strongly aligned with performance budgeting when the payer’s objectives are to stimulate the volume of outputs and to increase technical efficiency.

The usual approach to case payment is to reimburse according to some measure of the expected expenditure on a service user. For example, the case payment might be based on an estimate of the national average cost per case, perhaps with some reduction for assumed efficiency gains. Or it might be based on (say) the lower 25 percentile of costs, assuming these represent a challenging but feasible cost target for the majority of service providers. Any surplus of the case payment over the local cost is usually retained by the agency.

When users are reasonably homogeneous, such as university students, it may be feasible to use a single case payment for all users. However, for most services, a fundamental challenge with case payment methods is that service users are often not homogeneous. For example, in health care, it is clearly the case that the expected expenditure on a patient requiring an appendectomy is much in excess of that on a patient requiring treatment for minor abrasions. If such variations in spending needs exist and a case payment system does not reimburse providers fairly for the costs of more intensive users, providers may seek to “cream-skim” only low-cost users. More intensive users may then find it difficult to secure access to services because their expected costs exceed reimbursement levels. For example, if reimbursed at a flat rate per pupil, schools might seek to recruit only pupils who have a high probability of completing their studies without undue difficulty, and to deter pupils with higher perceived probabilities of failure or other complications.

The potential for cream-skimming has led to the development of the methods of “risk adjustment,” which seek to vary payments according to the dependency of users. The most celebrated of such schemes is the system of “diagnosis related groups” (DRGs) used in many health systems, under which the case payment varies according to the diagnosis of the patient (Fetter et al., 1980; Fetter, 1991) (see Box 15.1). DRG payment systems are now used in most mature health systems (Langenbrunner et al., 2005). They are demanding to design, and introduce potentially costly data recording and audit requirements to ensure that providers record the diagnosis accurately. However, they are needed in order to reimburse providers fairly and avoid widespread cream-skimming. Analogous systems are needed in schooling when the abilities of pupils (and therefore their expenditure needs) show marked variations.

Box 15.1.Diagnosis related groups in health care

The longest-standing and most celebrated of case payment mechanisms in health care is the system of diagnosis related groups (DRGs) introduced in 1983 as the basis for reimbursing providers under the US Medicare system. It led to manifest cost savings and efficiency improvements compared to the previous “fee-for-service” reimbursement system (Fetter, 1991). Medicare’s DRG system was the starting point for other DRG systems inside the US. It also secured great international interest, and health systems throughout the developed world have adopted their own versions of the DRG payment mechanism (Busse et al., 2006).

The first purpose of DRGs is to offer an accurate assessment of the costs of treating a given patient, in the light of observable and measurable patient characteristics, especially the diagnosis—but, to a varying degree, also the interventions chosen. Indeed, the antecedents of today’s DRG systems were developed as a method of adjusting the performance of providers for the different mixes of patients they treat rather than a mechanism for reimbursing providers (Fetter et al., 1980).

In this role, the main challenge is a technical one of ensuring that the risk adjustment process is unbiased and accurate. This requires careful decisions on the design of the DRG system, such as the hierarchy and algorithms used to classify patients into a limited number of groups. In principle, patients within one group should have homogeneous costs. Moreover, cases allocated to one group should form a clinically distinguishable entity based on main diagnosis, severity, co-morbidity, and/or treatment performed. But what exactly is homogeneous? When are costs and/or clinical diagnoses so different that a group should be split? In practice, most DRG-type systems use several hundred different categories of patient, based on criteria such as clinical diagnosis, procedures undertaken, length of hospital stay, and age.

However, the role of DRGs as a payment mechanism is not only to reimburse providers fairly for the work they undertake, but also to encourage efficient delivery and discourage the provision of unnecessary services. This requires carefully balanced incentives as well as a methodologically sound system. The sorts of incentives a DRG-type system introduces include:

  • encouraging treatment of patients whose expected costs are lower than the associated reimbursement. This might be beneficial (if those patients will benefit from treatment) or adverse (if the benefits are questionable)

  • discouraging treatment of patients whose expected costs are higher than the associated reimbursement (so-called “dumping” of high-dependency patients)

  • encouraging more coding of complications (“upcoding”) if this leads to an upgrading in the severity of DRG, and therefore increased reimbursement

  • encouraging more intensive treatment of patients if such treatment leads to an upgrading in the severity of DRG, and therefore increased reimbursement (but only if the increase in reimbursement exceeds the increased costs of treatment)

  • within a treatment group, the payment mechanism gives a strong incentive to minimize costs, or to shift the costs of treatment onto other parties (such as the user or a social care agency)

  • on their own, pure case payments offer no incentive to maintain quality of care (indeed there may be strong incentives for “quality skimping”).

Therefore, in addition to quantifying the associated efficiency improvements, any evaluation of a DRG-type system should examine the extent to which low-risk patients are favored at the expense of high-risk patients (“cream-skimming”), unnecessary treatment is provided (for example, supplier-induced demand), data manipulation or fraud occurs, or the quality of care is compromised. Many of the continuing design challenges reflect attempts to address these concerns (Schreyögg et al., 2006).

There may be considerable variation in patient costs even within a DRG, so there may still be an incentive to cream-skim within the group. Generally, the local provider always has a clearer picture of the likely costs of a specific user than the central payer. This information asymmetry between payer and provider leads to pressures to define a finer gradation of user types, for example, by increasing the number of DRGs. However (even if this is technically feasible), as the gradation becomes finer, so the payment becomes closer to reimbursing providers according to actual costs. The incentive to reduce costs becomes diluted. There is therefore a fine balance to be struck between the coarseness of the case payment categories, the incentives for cost-reduction, and the incentives for cream-skimming.

Under case payments, local organizations usually have an incentive to reduce unit costs, subject to satisfying the payer’s quality requirements. Yet they also have an incentive to ensure that they secure the maximum possible case payment for each service user. Where risk adjustment is used, it is often the case that the level of case payment depends to some extent on the type of service delivered. This may encourage providers to “gold-plate” services in order to secure a higher case payment (where the extra case payment outweighs the additional costs of service delivery).

For example, under many DRG systems, a patient’s case payment category may increase if there are “complications” associated with the treatment, in some cases offering physicians an incentive to over-treat patients in order to secure a higher DRG payment. The phenomenon of “DRG creep” has been a source of widespread concern in health care. Even if provider treatment patterns do not change, the DRG system offers incentives to ensure that all possible indicators of case severity are properly recorded, and software packages have been developed to help medical coders maximize DRG revenue, giving rise to the phenomenon known as “upcoding.”

Case payment systems are especially prevalent where users have the freedom to choose their provider. They effectively enable the payer to offer the user a voucher for the service in question, which the user is free to spend on approved providers (Steuerle et al., 2000). The voucher will usually be for a fixed payment for a specified service. Therefore, use of vouchers requires a clear assessment of the needs of the user and the services to which the user is entitled. This might be quite straightforward in (say) education, where there pupils are reasonably homogeneous. However, it becomes much more problematic in (say) health care, where the professional assessing patient needs may be the same professional delivering the service. A particularly interesting example of user needs assessment is found in English social care, where some local governments are experimenting with offering individualized vouchers to adults requiring long-term care on the basis of a periodic independent “needs assessment” (Commission for Social Care Inspection, 2004).

Case payment methods rely fundamentally on the local quantification of the volume of outputs, in the form of the number of service users and (where appropriate) their risk characteristics. Payers should always be alert to the dangers of reliance on counts of service users as the basis for reimbursement for a number of reasons, such as:

  • the counts often rely on the local organization’s own information sources and so may be vulnerable to fraud and difficult to verify

  • using the actual number of service users as a basis for reimbursement may encourage the local organization to stimulate demand for services rather than invest in preventative measures or otherwise manage local demand

  • the payer does not know in advance the total number of service users, and so may not be able to control aggregate expenditure satisfactorily.

The use of case payments therefore generates fundamental requirements to check on the validity of the local data, and the appropriateness of the services being delivered. Such audit requirements will in some circumstances be costly and administratively demanding.

Furthermore, although encouraging increases in outputs, case payment methods rarely consider the ultimate outcomes to service users, and local agencies therefore often have an incentive to stint on quality if the payer places no quality constraints on them. For example, further education colleges in England were for a while reimbursed according to numbers of students enrolled in courses. Without countervailing quality controls, this created an incentive to enroll students in courses without regard to their suitability or probability of success, and led to high student dropout rates and a clearly inefficient outcome. Subsequent reforms therefore based case payments on the numbers of students completing their courses of study (Learning and Skills Council, 2004).

Thus, although in many respects consistent with the principles of performance budgeting, case payment methods can give rise to important unintended consequences. The issue of incentives under formula funding, and how they might be aligned with performance budgeting, are discussed further below.

Capitation funding: reimbursement according to expected activity

Case payment methods reimburse local agencies according to actual output. In contrast, capitation methods seek to estimate an agency’s expected level of output, and to reimburse accordingly. In contrast to case payments, which are attached only to service users, a capitation payment is attached to every member of the population “at risk.” So, for example, an annual case payment of $400 might be attached to each user of a day center for older people. The service provider’s revenue is then the number of users multiplied by $400. However, if the probability of a member of the “at risk” older population requiring the service is only 0.15, then the equivalent capitation payment would be $400 x 0.15 = $60. The service provider’s revenue would then be the size of the entire “at risk” older population multiplied by $60. The revenue would of course be the same under both payment mechanisms if 15 percent of the local older population did in fact use the service. This highlights the key difference between case payment and capitation methods: under the latter, the local agency almost always has an incentive to reduce demand for its services, as it receives the same revenue regardless of output, while under the former the incentive will often be to stimulate demand.

The reduction in output associated with capitation may in some circumstances be desired. For example, if the output of the fire service is measured in numbers of fires attended, it would clearly be perverse to use case payment methods, and thereby stimulate demand for fire-fighting. Properly designed fixed budgets, in the form of capitation payments, are more likely to stimulate preventative measures, and a desired reduction in demand for fire-fighting. Similar arguments are likely to be relevant to other public protection services, such as public health and policing.

However, the objective of capitation systems is usually to reimburse local agencies for variations in needs, and not to encourage efficiency among local agencies. For the reasons set out above, addressing equity issues has often been a higher priority among national payers than funding results. Capitation methods are well aligned with such needs equalization. However, although, properly designed, they may give a local agency the means to deliver the payer’s desired levels of output, on their own they offer no incentive to reach that level. They are therefore often in conflict with the objectives of performance budgeting when results are measured in terms of volume of services, and so should be deployed with caution.

Under capitation, the most rudimentary formula for paying the locality is to reimburse an equal amount per head of population, without regard to variations in the personal characteristics of that population. This approach can be justified when differences in expected service use between citizens in different social circumstances are not substantial, or when the local agencies in receipt of funds have only small differences in socio-demographic profile. It may also be justified if there is no further information with which to refine payments. However, simple capitation methods are manifestly crude, and will not satisfy the payer’s efficiency objectives when there are substantial differences between the expected service use of different types of citizen.

A modest refinement to the crude capitation payment may be to confine the population “at risk” to any obvious demographic stratum from which service users will be drawn. For example, school financing is clearly better distributed according to the estimated number of children than the total population. An example of such simple stratified capitation funding is the formula for social services for older people in England (Office of the Deputy Prime Minister, 2003). In 2003, this formula implied an expected expenditure requirement of £337.77 for each person over 65.

However, capitation payments are often further adjusted to account for more subtle variations in expected spending needs, using the principles of risk adjustment discussed under case payments. For example, the expected expenditure requirement of a person for personal social services is known to increase with age, so the estimates of expected expenditure needs should therefore be disaggregated by age. The above social services example was refined using an age adjustment that implies a capitation payment of £158.62 for people aged 65-74, £482.97 for people aged 75-84, and £1,252.54 for people aged over 84. This sort of risk adjustment amends the capitation payment attached to an individual according to certain measured characteristics of the population.

In principle, numerous approaches to risk adjustment can be envisaged, ranging from such rudimentary age adjustments, to the extraordinarily ambitious schemes found in some health care systems (Rice and Smith, 2001a). As new risk adjusters are added, so the capitation payments can be presented in the form of a contingency table. A particularly comprehensive example is a matrix of capitation payments developed for Stockholm health care. This took advantage of a comprehensive register of Swedish citizens that records both personal characteristics and health care utilization in some detail.

In such circumstances, the number of potential capitation payments to be estimated could in principle be very large—for example, with age (two groups), sex (two), social class (five), employment status (three), housing tenure (two), and marital status (two), the number of distinct capitation payments to be estimated might in principle be 8 x 2 x 5 x 3 x 2 x 2 = 2,160. Under these circumstances, an important challenge is to reduce the potentially massive matrix of capitation payments to manageable proportions, by minimizing the number of risk adjusters used and amalgamating cells of the matrix wherever possible (Andersson et al., 2000). The abridged matrix of capitation payments recommended for Stockholm acute care, giving estimates of the expected monthly expenditure on health care, is summarized in Table 15.1.

Table 15.1.The abridged Stockholm capitation matrix for medical and surgical health care, 1994 (Swedish krona per month)
AgeOwner occupierRented
Higher non-manual3,1003,600
Other non-manual3,7004,300
Not employed5,3006,400
Higher non-manual3,6003,900
Other non-manual3,6004,200
Not employed5,1005,400
Living alone15,40018,200
Living alone24,20029,400

Same level of payment irrespective of owner/rented status.

Source: Diderichsen et al. (1997).

Same level of payment irrespective of owner/rented status.

Source: Diderichsen et al. (1997).

Capitation methods promote aggregate cost control and address equity concerns. However, they offer no incentive to increase outputs, and share many of the weaknesses of case payment methods, such as a lack of attention to the quality of outcomes. The principal reason they might prove attractive to payers from a performance budgeting perspective are (a) they may encourage appropriate preventative measures for services where this is an important objective of the payer, (b) they remove the incentive for supplier induced demand, where this is a problem under case payment, and (c) they reduce reliance on output data provided by local providers, and therefore avoid the incentives for manipulation and fraud discussed above. The issue of data under both types of funding mechanism is now briefly discussed further.

Data considerations

Fundamental to any type of formula funding is the information to be used as the basis for reimbursing local organizations. It is very rare to have available independent “engineering” evidence of what levels of reimbursement each devolved entity should receive. Instead, in order to infer optimal reimbursement levels, payers are highly dependent on historical expenditure patterns among the intended recipients of funds. The reliance on past spending as a basis for current funding can give rise to profound philosophical and practical difficulties for the payer.

These difficulties can be illustrated in their most extreme form when the payer bases reimbursement to each organization solely on the historical spending of that organization—for example, by basing the organization’s current budget on expenditure last year. Such budget-setting rules are endemic within many bureaucracies, and were also a central feature of the Soviet planning system, which tended to set production levels and budgets “from the achieved level” (Nove, 1980). They lead to many adverse consequences, and contain few incentives for efficiency or effectiveness.

As a result, payers have sought out funding mechanisms that reduce the reliance on an organization’s own past expenditure in setting its future budgets, and instead rely on some form of statistical analysis of general patterns of expenditure among all (or at least a substantial proportion) of the public service organizations that will be in receipt of the payer’s funds. This section summarizes the main considerations that arise when relying on such empirical data as the basis for formula funding.

In the first instance, case payment methods require a reliable count of the number of service users. This can be straightforward, as in school education, or highly contested, as, for example, in a count of people in “need” of sheltered housing accommodation. A prerequisite for satisfactory case payment methods is a clear statement by the payer of the national criteria that entitle a user to secure access to the service, in order to yield the required measure of output. In contrast, capitation methods can allow an element of local discretion on entitlement. The difficulty and reliability of specifying entitlement and counting the numbers of service users will often be an important determinant of whether case payment or capitation methods are preferred.

Capitation methods require a verifiable count of population, disaggregated where necessary into demographic groups. Although the population count used in a capitation system is often uncontentious, it can give rise to difficulties when it relies on local reporting, as there are obvious incentives for local organizations to maximize the population on which their revenues are based. For example, for many years UK general medical practitioners received a large part of their income on the basis of unreliable estimates of the size of the population registered with the practice. There was widespread acknowledgment that the registered population sizes were inflated to very different extents in different practices, arising from factors such as delay in removing patients from the register when they died or changed provider, transient populations, and fraud (Ashworth et al., 2005).

Although counts of the number of service users or the “at risk” population can be problematic, it is usually the risk adjustment process that leads to most technical debate, and where the analysis of past expenditure patterns comes into play. Key issues are the choice of characteristics to include as “risk adjusters,” and the relative weight to attach to each factor. Different technical choices can lead to major changes in payment rates, and there is often little methodological guidance for those seeking to design risk adjustment schemes.

It is important to note that in many circumstances the range of satisfactory data available for risk adjustment purposes may be highly circumscribed. The first criterion in the design of risk adjustment will therefore always be feasibility. For example, some obvious risk adjusters in health care would be measures of chronic health status. However, these can rarely be reliably collected at reasonable cost, although some imaginative schemes have been tested, such as the use of routine prescribing data as a proxy for some chronic health condition (Fishman and Shay, 1999).

Even where potentially useful data do exist, there is frequently tension in the design of formulas between a desire to model expected expenditure accurately, and a desire to avoid perverse incentives. For example, in health care the best predictor of an individual’s current health care expenditure is his/her previous history of expenditure and utilization, and such variables are often used in systems of competitive health insurance in order to model individual expenditure accurately (and so reduce the incentive for insurers to cream-skim only healthy patients) (Van de Ven and Ellis, 2000). However, policy-makers in other countries have sought to avoid the use of such data in the design of health service formulae, on the grounds that they may offer a perverse incentive for providers to increase provision in order to secure an increased capitation payment for the individual in the future.

Any proposed risk adjuster must be reliably and consistently recorded across all recipients of funds. There will often be a need for a strong audit function to reassure all localities that payments are fair. A suggestion that some localities are manipulating information may be seriously corrosive. For this reason, a payer may often feel unable to use some otherwise suitable metrics as risk adjusters because they cannot be satisfactorily verified. This is an important reason for the use in many funding mechanisms of area-wide data, such as those collected from periodic censuses of population, which obviates reliance on data provided by local agencies. Fraud is an ever-present danger when funding systems are based on data provided by the recipients of funds and has been a persistent concern in the US Medicare scheme (Becker et al., 2005). A fundamental constraint hampering many analytic endeavors is the extent to which the scope for misrepresentation may rule out the use of certain types of risk adjustment.

Risk adjusters should be plausible, in the sense of being manifest drivers of expenditure. But the payer will wish to use only factors that are legitimate drivers of expenditure, and will seek to avoid use of illegitimate factors (Rice and Smith, 2001a). Loosely speaking, legitimate drivers of expenditure are influences on the costs of delivering the required service that lie entirely outside the control of local organizations, and so can be used as risk adjusters. Examples might be local input prices and some (but not necessarily all) user characteristics. Illegitimate drivers of expenditure are influences on costs function that arise from the organizations’ own policy choices, and so should not be used as risk adjusters.

A persistent theme in the literature is the tension between parsimony in the use of data and the need to model spending needs sensitively. Generally speaking, many payers prefer simple funding mechanisms as they can be more readily understood and therefore promote accountability. However, there will often be an element of rough justice in a simple funding formula, so those local organizations that feel they are adversely affected by the choice of a simple mechanism will press for “refinement,” in the form of an increased number of risk adjusters and added complexity. Balancing simplicity and sensitivity of the funding mechanism is a key role for the payer.

One final issue of great importance relates to the variation in expenditure that is not captured by the chosen funding model. Even on those rare occasions when the statistical methodology explains a high proportion of individual variation in expenditure, a considerable element of unexplained variation often remains. The unexplained variation can be ascribed to two broad sources: omitted explanatory variables and random fluctuation. Clearly, given the paucity of data available, there is an ever-present danger of variable omission, especially as some important but illegitimate determinants of expenditure (such as variations in teacher effectiveness in education) may have to be omitted from the funding model.

However, it is also important to recognize that there is a large element of unpredictable variation in the use of many public services (most notably health care) that will always defy systematic modeling. This is particularly true under capitation, when both the probability of using a service and the expected costs of that use are subject to large random variation. For example, although an average health care capitation payment of (say) £550 per annum may be assigned to a male aged 40-44, it would be absurd to expect every such individual to require that level of expenditure per annum. Rather, the capitation payment offers an expected level of expenditure, around which there might exist substantial variation.

In summary, numerous criteria for selecting risk adjustment characteristics have been indicated. For example, they should:

  • be feasible, with low administrative cost

  • be consistently, reliably, verifiably, and universally recorded

  • not be vulnerable to manipulation or fraud

  • be legitimate predictors of expected public service expenditure

  • encourage efficient delivery of public services, and be free from perverse incentives

  • respect confidentiality requirements

  • be parsimonious and plausible, thereby promoting transparency and accountability.

In practice, this often severely limits the choice of variables, as in many contexts only very restricted information on the characteristics of individuals or areas exists that conforms to such criteria.

Incentives under formula funding

It is important to note that funding formulas are more than reimbursement mechanisms. The previous sections imply the existence of some very strong incentives for the recipient of funds that are inherent in pure formula funding systems. Under case payments these include:

  • increasing activity

  • cream-skimming

  • cost containment and increasing technical efficiency

  • skimping on service quality

  • upcoding

  • manipulating data.

Under capitation they include:

  • reducing outputs

  • preventative measures and reducing demand for services

  • encouraging low effort and technical inefficiency

  • skimping on service quality.

Some of these are intended and virtuous, and serve to promote the payer’s performance objectives. Others are unintended and adverse, and may thwart such objectives. The payer will therefore wish to reinforce the intended incentives and abate the adverse responses.

To some extent this can be achieved by adjusting the payment mechanism. Possibilities include refining the risk adjustment mechanism (to reduce the gains from cream-skimming) and using mixed payment systems (to moderate the stark activity incentives inherent in the pure systems). For example, if a capitation system of fixed budgets is inducing local agencies to underprovide certain services, this might be addressed by augmenting the fixed budgets with a certain element of case payment. If a pure case payment system is inhibiting access for some high-needs service users, then it might be augmented by a degree of cost sharing between payer and locality if the expenditure on a particular user exceeds some threshold. Such blended mechanisms are far more likely to be effective if specified explicitly ex ante, by means of a formula, than if addressed arbitrarily on a case-by-case basis.

However, the payer will usually also have to augment any payment mechanism with other regulatory instruments in order to ensure that desired outcomes are secured. In short, although a well-designed payment mechanism is a necessary condition for securing the payer’s objectives, it is not on its own sufficient. In the context of this chapter, formula funding must be viewed not in isolation, but within the context of the entire system of performance budgeting. This section summarizes some of the more important tools for ensuring the payment mechanism works as intended.

Under either funding method, but especially capitation, there is no direct incentive for local organizations to deliver services to any standard. There is therefore a fundamental need for the payer to put in place mechanisms to ensure that services are delivered at the required level and quality. These mechanisms might take a number of forms. For example, a frequently used but costly regulatory instrument is to undertake periodic inspection of local services. This is especially important for provider organizations, and is routinely found in schooling and health care, where it is often the case that only accredited organizations are permitted to provide public services.

Performance measurement is another widely used instrument for ensuring service standards. By collecting and disseminating data on issues such as unit costs, access to services, activities, and outcomes, payers can compare organizations, identify those where performance is anomalous, and put in place corrective action. Such data can often form the basis for managerial incentives and concerted organizational improvement efforts.

Many payers are experimenting specifically with public reporting of local performance data. Here the intention is to help citizens (as taxpayers) to hold their local services to account, often via the media. Performance reporting is therefore likely to be especially effective where strong local democratic procedures are in place. However, its effectiveness depends heavily on the precise mode of dissemination. For example, researchers in health care have found low impact of public dissemination of performance data where little attention is paid to how the data are presented to the public or their representatives (Mannion and Goddard, 2001). In contrast, aggregating a local organization’s performance data into a “star rating,” with extensive media coverage, has been highly influential in attracting public attention to NHS performance in England (Smith, 2002). The appropriate means of disseminating performance data to managers, the media, the public, and local governing boards is a promising area for future research.

Another mechanism for stimulating performance improvement is to offer public service users a choice of services within a local market of providers. The success of this approach depends heavily on ensuring real competition between providers, and giving users the means to make an informed choice. Performance data should therefore also play a central role in the implementation of formula funding. Citizens as service users are likely to require more detailed information than citizens as taxpayers, the nature and effectiveness of which is also an important research issue (Hibbard et al., 2003). It is noteworthy that such market systems must usually rely, at least in part, on some sort of case payment mechanism for reimbursing providers.

The ultimate logic of the principle of provider choice is to offer users a voucher for the service to which they are entitled that can be used with any accredited provider. Systems such as DRG payments in health care and pupil case payments in schooling effectively become voucher systems when the user has a degree of choice over the provider. Important policy choices for the payer are then the range of providers from which a user may choose, and the extent to which users are able to “top up” the case payment with their own private payment if the provider charges a fee in excess of the case payment. Formula funding has a fundamental role to play in voucher systems in setting the level of reimbursement for the provider.

User choice can also be applied to local purchasers as well as providers. For example, a number of health care systems, such as Belgium, Germany, Israel, the Netherlands, and Switzerland, offer citizens a choice of social health insurers (Saltman et al., 2004). In the UK, the system of general practitioner fundholding offered patients some choice of GP purchasers (Glennerster et al., 1994). In these systems, the use of a capitation payment (as a pseudo insurance premium) becomes the main funding mechanism, and securing an adequate funding formula to set the level of this “premium” becomes a key determinant of the success of the policy.

Implementing managerial incentives alongside formula funding is one of the most effective approaches to correcting some of the adverse organizational incentives inherent in payment mechanisms. Managerial incentives can take many forms other than direct financial rewards, such as increased autonomy and personal advancement. For example, the systems of organizational ratings used in much of the English public sector (such as the NHS performance ratings and local government comprehensive performance assessments) are directed mainly at the prestige and career prospects of senior management (Smith, 2002). They have undoubtedly been successful in focusing the attention of managers on the national government’s performance priorities, although of course poorly designed managerial incentives can in turn produce their own unintended consequences (Smith, 1995).

Moreover, it is possible to incorporate quality standards directly into the payment mechanism (Smith and York, 2004). Carefully designed, this is likely to be fruitful when paying providers, especially when a local provider market is operating. However, to make financial allocations to local purchasers conditional on performance risks exposing citizens to a double jeopardy—in one period they could experience poor-quality services, and as a consequence their local administration would secure lower budgets in a future period. This is likely to be inefficient, and to offend most concepts of natural justice. Rather, it is likely that the most promising innovations would be to direct rewards (and sanctions) for organizational performance at the managers of such organizations.

Finally, a central theme of this chapter has been the key role that information plays in all funding mechanisms, both to serve as a basis for calculating funding levels and as a means of checking on performance standards. More generally it is a crucial input into activities as diverse as inspection, user decisions and setting managerial rewards. Much of the information on which the public services rely emanates from the services themselves, and there is a clear danger that data will become corrupted as the stakes attached to them increase. Any threat to the perceived probity of the public services risks undermining confidence in those services, and popular support for them. Therefore, a key role for the payer is to decide on the nature and scope of independent data audit needed to counter any incentives for manipulation.

This section has sketched in only the briefest outline some of the additional mechanisms a payer may need to implement alongside formula funding in order to reinforce desired behavior and address perverse incentives. A full treatment is beyond the scope of this chapter. Rather, the intention has been to alert the policymaker of the need to consider how formula funding fits into the whole system of performance budgeting. Most of the initiatives, such as inspection, performance reporting, user choice, provider markets, and managerial incentives, are means of correcting the natural tendency of funding mechanisms to reduce service standards or (in the case of capitation) to ignore technical efficiency considerations. The payer has a formidable challenge in ensuring they fit together into a coherent design for the whole public service system.


The central objective of performance budgeting is to align the funding of public agencies with the results they achieve. Formula funding is a key instrument within many public sectors, and this chapter has examined the extent to which it can promote or hinder the implementation of performance budgeting.

Any funding mechanism must give local agencies both the means and the incentives to deliver the payer’s objectives if it is to promote the objectives of performance budgeting. Hitherto, most formula funding systems have emphasized the first role, often seeking to give local agencies the resources needed to deliver some standard level of service. In contrast, relatively few payers have paid much attention to whether the incentives for local agencies implicit in formula funding are aligned with their performance objectives.

The chapter has identified two broad types of formula funding mechanism: case payments and capitation payments. Case payment systems generally give local agencies the incentive to increase output and efficiency, which in many circumstances will be a central objective of the payer. Therefore, they will in important respects often be strongly aligned with the principles of performance budgeting. However, I have also drawn attention to some of the potential weaknesses of case payment methods, most notably the risks of cream-skimming, and the challenges in addressing those weaknesses.

Capitation methods generally emphasize the “fair funding” principle of giving the local agency the means to deliver some standard of service, with few if any direct incentives to secure the desired results. They are in general therefore less well aligned with performance budgeting. However, they may be appropriate when the services in question are mainly preventative in nature (crime, public health, fire). They are also often less demanding of administrative data and audit requirements than case payment methods. Because of the stark incentives inherent in pure case payment and capitation systems, it may be the case that some blend of the two mechanisms may be appropriate for many systems of performance budgeting.

Moreover, neither approach addresses the issue of service quality at all securely, mirroring the preoccupation in many performance budgeting systems with outputs rather than outcomes. The ultimate objective of performance budgeting should be to move towards an outcomes-based concept of performance, so the logic should be that formula funding systems should focus on outcomes, in the form of the quality of outputs. In this respect, there are some interesting developments in health care, where the “payment for results” movement has assumed increasing importance, particularly in the United States (Casalino et al., 2003). The notion of making case payments wholly or partially contingent on outcomes has also made some headway in education services (Ross and Levacic, 1999).

The chapter indicates that formula funding has an important role to play in making operational the principles of performance budgeting. It has nevertheless concluded that funding mechanisms cannot on their own secure all the objectives of performance budgeting. There will always be a need to align other performance budgeting instruments with formula funding mechanisms if they are to be effective. Examples include policies on regulation, provider markets, performance reporting, and good-practice guidelines. However, if these instruments are deployed carefully, and are made to articulate with each other, they offer the potential for enormous gains in the performance of public services.


The author would like to thank the participants at the IMF seminar, and especially Marc Robinson, for perceptive and constructive comments on earlier drafts. This chapter draws on my forthcoming book Formula Funding of Public Services to be published by Routledge. Preparation of the book was funded by UK Economic and Social Research Council fellowship R000271253.


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