Allocation Formula in Budgeting
Patricia Moore
Kean University, Union, New Jersey, U.S.A.
Keywords: Budget allocation; Demand-driven formula; Resource-constrained formula;
Congressional intent
ABSTRACT
Allocation formula is one of the decision rules used to allocate resources in the public
sector. Usually, an allocation formula is specified in legislation, but sometimes it is
provided by regulation. A good allocation formula is understandable, equitable,
adequate, and predictable. Formula allocation makes justification for budget requests
easier. Citizens tend to be accepting of allocations that are based on formulas, because
they have an aura of objectivity and fairness. Nevertheless, their effectiveness can be
severely hampered by data that are stale, inaccurate, and irrelevant.
1. INTRODUCTION
Allocation by formula is one of the decision rules used in the United States by budgeters
to allocate scarce resources in the public sector. Other rules include budget allocation in
terms of existing base plus a fair share of the increment or decrement, top-down
containment rules and targets and relative merit.(1) Mikesell described an allocation
formula as a quantitative mathematical equation used to distribute grant funds to eligible
recipients.(2) Wildavsky suggested that allocation formulas for public-sector program
expenditures evolved out of recurrent budget processes.(3) Usually, an allocation formula
is specified in legislation, but sometimes it is provided by regulation.
In the Western world, the underlying theory surrounding formula allocation seems to be a
calculative logic that formulas are sensitive to the concerns of democratic government.
These concerns include equity, efficiency, and effectiveness of service provision on
behalf of the (voting) population. In the United States, prior to World War II, budget
allocations were often based on historical precedent or negotiation; however, since that
time, federal and state governments have progressively shifted in favor of distributing aid
to states and localities by formulas.(4) This shift to formula allocation may have
dampened the political problems naturally arising from the annual competitive budget
appropriation process in Congress at the federal and state levels of government.(5)
A good allocation formula should be free from perverse manipulations, open to review,
and should distribute resources equitably across governmental units. Moreover, it should
be understandable, equitable, adequate, and predictable. It should also be reasonable in
reporting requirements, fiscally accountable, and politically acceptable.(6) Grizzle(1)
suggested that the design of an allocation formula should give primary consideration to
program objectives, operational measures of objectives, data availability, and simple
methods.
Although formulas can be used to direct funds to individual service providers,
historically, they have been directed at aggregations of service providers: state
governments, hospitals, counties, municipalities, and school districts. In the United
States, formulas are frequently used to determine allocation levels for various
intergovernmental fund transfers, such as general revenue sharing, block grants, and
categorical grants.(7) While formulas are used to allocate resources for many different
governmental functions, they are most widely used in education, health, housing, and
commerce.(8)
2. WHY ARE ALLOCATION FORMULAS USED
WIDELY IN BUDGETING?
Formula allocation is appealing in public budgeting, because it has several advantages.
Formula allocation makes justification for budget requests easier. It also has an
appearance of neutrality and rationality, because a formula allocation is expressed as a
mathematical equation. Using a precise mathematical formula can make the allocation
plan less controversial and, therefore, more politically acceptable. A multitude of
(redundant) statistical variables may be politically necessary to rationalize a program, to
at least give the appearance of responding to special circumstance. (9)
Furthermore, allocation formulas allow for greater precision and accuracy and thus save
legislative time and energy in arguing about the intended appropriation. Allocation
formulas provide local government a reasonable assurance of the general level of funding
they are to expect; thus, they keep planning from being chaotic. Another advantage of
formula allocation is that it suggests consistency and fairness. When the objective is
equalization, allocation formulas seem to be an effective instrument for redistributing
public resources. Their transparency and stability tend to reduce the possibility of
manipulation, therefore, facilitating equity.
A well-designed allocation formula simplifies program administration, reduces
paperwork, as well as provides state and local governments a reasonable degree of fiscal
certainty. In addition, formula allocations reduce the discretion of federal administrators
in the review process, allowing public administrators to insulate themselves from political
pressures.
3. TECHNICAL NATURE OF ALLOCATION
FORMULAS
The typical allocation formula has a complex structure entailing the identification of
several variables. For example, the United States Department of Agriculture allocates
funds to school districts for their Breakfast Program using the following formula:
M = The amount of federal funds given the school district.
NAP1 = A National Average Payment.
NAP2 = A National Average Payment prescribed for free breakfasts.
NAP3 = A National Average Payment for reduced priced breakfasts.
NRB = Number of reduced priced breakfasts.
NFB = Number of free breakfasts.
Allocations to school districts are calculated by multiplying the number of paid breakfasts
served to eligible children during the fiscal year by a National Average Payment (NAP);
multiplying the number of breakfasts served free to eligible children by a NAP prescribed
by the Secretary of Agriculture for free breakfasts; and multiplying the number of
reduced price breakfasts served to eligible children by a NAP prescribed by the Secretary
for reduced priced breakfasts. School districts also receive an additional six cents for
every breakfast served. Schools with a high percentage of needy children and high
breakfast costs may receive additional payments.(10)
In adopting allocation formulas, the United States Congress commonly uses measures
that closely represent at least one of the following characteristics of the recipient
government: need, capability, and effort. (11) Kreps and Slater suggested that few
allocation formulas include all three measures, however, more than half include a
measure of need. Need often refers to the population to be served, while capability
refers to the ability of a jurisdiction to meet the defined need from local or state funds.
Effort refers to the actual amounts of local or state revenues available for the need. One
common measure of capability is per capita income. School districts often use per pupil
property values as a measure of need, while per pupil expenditures is frequently used to
measure effort.
4. TYPES OF ALLOCATION FORMULAS
Formulas may be demand driven or resource constrained.(1) The main characteristic of a
demand-driven formula is that allocations are driven by the need of the different units,
e.g., school districts, states, or municipalities. It is mainly used to stimulate action by the
recipient government as much as possible. Demand-driven formulas are more appropriate
when policy makers value controlling agency behavior more than agency spending.(12)
One of the disadvantages of a demand-driven formula is its unpredictability in terms of
the level of total spending that will result. Medicaid in the states and the federal
government shares an example of a demand-driven formula. Total spending depends on
the number of people entitled to have their medical care paid for by the government,
those who apply for help, and the basket of services for which the states reimburse health
care providers.
On the other hand, resource-constrained formulas place a limit on the resources available
for a specific purpose. Each unit s allocation is determined by its percentage of the total
appropriation. An example of a resource-constrained formula is the equation used to
allocate resources to the airline industry in the aftermath of the September 11, 2001,
attack on the World Trade Center in New York City. According to the Air Transportation
Safety and System Stabilization Act, the federal funding formula was based on each
carrier s share of the industry s flying capacity, measured in available seat miles.(13)
Specifically, the allocation for each airline was the total aid provided by the federal
government multiplied by the percent of the industry s total flying capacity, i.e., number
of seats multiplied by total miles. This formula determined what fraction of the total
appropriation each airline received. When controlling spending is more important, the
resource-constrained funding formula is more likely to be effective in containing
spending than demand-driven formulas.(12) The main difference between the two is that
demand-driven formulas may not have funding ceilings but resource-constrained
formulas do.
5. WEAKNESSES OF ALLOCATION FORMULAS
Allocation formulas are often incredibly complex.(14) Frequently, they require a
bewildering combination of mathematical calculations, i.e., addition, multiplication,
subtraction, squaring, and even quadratic equations that all too frequently produce
unsatisfactory results. Quite often, they are not clearly understood by policy makers,
program designers, or even the statisticians. Mathematical models, from which policy
makers derive allocation formulas, fail, even with the best available data, to produce the
desired allocation pattern, because models generally represent an oversimplification of
the real world.
Although proponents of allocation formulas suggest that predictability is one of their
strengths (especially when compared with policy makers caprice), in many instances,
public administrators find they cannot predict the results the formula will produce. Also,
often, the formula or model does not reflect the complexity of natural and social
phenomena. Unpredictability, as a result, cripples long-term planning and budgeting at all
levels of government. This inability to plan, ironically, makes for poor policy execution
because of the simplicity of the models and formulas.(4)
It is not an easy task to design a formula that closely approximates congressional intent;
however, the job gets more difficult when the legislature does not make the goals and
objectives of a particular program clear. As one might expect, a decision to adopt a
specific formula involves a series of distinct prior choices. An inappropriate decision at
any of these steps in the process may lead to a formula, which results in skewed
allocations. Generally, in the United States, Congress does not legislate the use of direct
measures in the mathematical formula, so statisticians have the arduous task of finding
measures that adequately operationalize legislative intent. Quite often, this is not
achieved.
A central dilemma for formula allocation is that while it simplifies justifications for
budget requests, it frequently presents difficulties in reconciling various policy
objectives. For instance, the U.S. Department of Transportation Highway Funding
Formula attempts to meet a relatively large number of objectives, some of which are in
conflict with one another. For example, one objective is to return funds to the states. At
the same time, the program must address national goals and deal with externalities,
which often require redistributing resources from one state to another.(15)
6. PROBLEMS RELATING TO DATA SOURCE
Allocation formulas rely on data that need to be reliable and valid. But frequently, bias
and corruption in the gathering and use of data create serious problems, which might not
be easily corrected. For instance, the U.S. Department of Transportation developed a
formula for allocating aid to the airline industry in the aftermath of the September 11,
2001, attack on the World Trade Center in New York City. Larry s Flying Service, one of
the 112 airlines that recently received federal aid claimed that it was too honest to get its
fair share. (16) In other words, it suspected that other airlines might not have submitted
valid data.
Another concern with formula allocation is that irrelevant or outdated factors often
undermine the funding calculations for certain services. For example, the formula for
apportioning federal highway funds among states is derived from a complicated set of
calculations. The U.S. General Accounting Office (GAO) described the formula as
cumbersome, relying on factors and data, which, in some cases, are outdated and
irrelevant.(17)
In many cases, allocation measures are selected solely on the basis of of familiarity,
plausibility, and ease of administration. One measure that is frequently used is per capita.
States in the northeast tend to have an advantage when formulas are based on per capita,
because they are more densely populated. Those in the south tend to fare better when the
formula requires units of $1000 of personal income. On the other hand, states in the west
topped distribution figures when the formula relied on a percentage of local general
revenue.(18)
Furthermore, allocation formulas frequently require census data; however, census data
have problems. Census data tend to undercount persons living in rural areas, ghetto areas,
and large cities. Critics of the use of census data maintain that large numbers of
Hispanics, African Americans, American Indians, and Asians are frequently missed by
the census, with the undercount resulting in a loss of federal funds to minorities. But,
others argue that the debate over the significance of the undercount has been highly
distorted, even misleading.(18)
In terms of the fiscal stakes, the GAO 1998 study found that only 0.5% of the $185
billion distributed by the federal government was affected by the overall undercount.(18)
The reason suggested is that population is only one of several factors in most federal
grant formulas, and many programs designed to help distressed communities actually
reduce funding when population increases. Even when grant increases are pegged to
population gains, the critical factor for a given jurisdiction is not merely its absolute
population, but its population relative to other jurisdictions a result that can obviously
hurt as well as help minorities.
However difficult it may be to understand and evaluate the performance of a formula, the
task of foreseeing and assuring good performance is even more difficult.(11) There seems
to be three issues. First, the formula may require data that cannot be updated frequently.
Policy makers often argue that the formula makes allowances for the data. But often, the
degree of distortion caused by the use of obsolescent data cannot be estimated precisely
at the time allocations are made. Second, data, which can be updated, may depart from
their historical behavior and from their assumed stable relationships with other variables.
Third, the social or economic problem to which the program is directed may evolve in
such a way that the measure chosen may no longer be the most relevant measure
available.
7. CONCLUSION
Allocation formulas reflect political and economic relationships among federal, state, and
local governments. They are effective and convenient tools used to translate
congressional intent. When used correctly, they give a predictable framework for
government organizations to use to meet needs through goal setting, careful planning,
control, oversight, and review. Formula allocation generally guarantees funds to state and
local governments based on economic or demographic factors outlined in the formula.
Citizens tend to be accepting of allocations that are based on formulas, because they have
an aura of objectivity and fairness. Nevertheless, their effectiveness can be severely
hampered by data that are stale, inaccurate, and irrelevant.
8. REFERENCES
1:G. Grizzle, J. Rabin Ed, H. Bartley Ed & G. Miller Ed Five Issues in Budgeting and
Financial Management Handbook of Public Administration (1989) pp. 197-206 (Marcel
Dekker Publishers New York)
2:J. Mikesell Fiscal Administration: Analysis and Applications for the Public Sector
(2006) (Harcourt Brace Publishers Orlando, FL)
3:A. Wildavsky The Politics of the Budgetary Process (1984) (Little Brown Boston, MA)
4:W. Fessler The Politics of the Administrative Process (1996) (Chatham House
Publishers New Jersey)
5:P. Dugdale The better practice program funding formula Aust. J. Public Adm. 56:3
(1997) pp. 65-67
6:T. Parish Removing Incentives for Restrictive Placements. Fiscal Issues in Special
Education (1995) (US Department of Education Washington, DC series: CSEF Policy
Paper 4) ED.377608
7:A. Bowman & R. Kearney State and Local Government (2005) (Houghton Mifflin
Company Boston, MA)
8:U.S. General Accounting Office Federal Funding 2001 http://financenet.gov ( )
9:B. Spencer Technical issues in allocation formula design Public Adm. Rev. 42 (1982)
pp. 524-529
10:General Service M Administration 11.553 School Breakfast Program www.cfda.gov
11:J. Kreps & C. Slater Report on Statistics for Allocation Formulae (1978) (Federal
Committee on Statistical Methods Washington, DC series: Statistical Policy Working
Paper) (NTIS PB86-211521/AS)
12:D. Cothran Some sources of budgeting accountability Public Budg. Finance 6 (1986)
pp. 45-62
13: United States Public Law 107-42, Washington, DC, September 22, 2001
14:D. Parry The Highway Trust Fund Uses a Complicated Allocation Formula
EconomicResearch Service (1999) p. 3 (USDA Washington, DC series: Agriculture
Information Bulletin) http://www.ers.usda.gov/publications/aib753b
15:D. Parry The Highway Funding Has Been Criticized (1999) pp. 4-5 (Economic
Research Service, USDA Washington, DC series: Agriculture Information Bulletin)
http://www.ers.usda.gov/publications/aib753-1
16:J. O Donnell Airline bailout grants USA Today, Money Sec. B (2006)
17:U.S. General Accounting Office Highway Funding Alternatives for Distributing
Federal Funds Report to Congressional Committees (1995) GA1.13:RCED-96-6 ([0546D(MF)]
18:P. Skerry Race, Group Identity and the Evasion of Politics (2000) (Brookings
Institution Press Washington, DC)