Energy Policy 31 (2003) 1441–1458LIHEAP reconsideredMa

Energy Policy 31 (2003) 1441–1458
LIHEAP reconsidered
Mark J. Kaiser*, Allan G. Pulsipher
Center for Energy Studies, Louisiana State University, One East
Fraternity Circle, Baton Rouge, LA 70803-0301, USA
Abstract
The Low-Income Home Energy Assistance Program (LIHEAP)
is a federal block grant program established in 1981 to help
low-
income households meet a portion of their home energy costs.
The manner in which LIHEAP funds are allocated to states,
however,
has been a contentious issue since the inception of the program.
In 1984, the Health and Human Services developed a new
formula
to increase equity among the states by incorporating state
cooling requirements in an equal weighting scheme with state
heating
requirements. In addition to the new distribution formula,
various provisions were also included in the LIHEAP re-
authorization
amendment that specified when and how the 1984 formula could

be employed. These provisions have turned out to be so
constraining, however, that they have effectively disabled the
1984 formula. The purpose of this paper is to introduce realistic
policy
alternatives to the current LIHEAP allocation mechanism and to
examine the impact of each alternative. Three options are
discussed ranging from the complete elimination of the hold-
harmless (HH) provisions to a proposal that maintains the
primary HH
provision but reduces the trigger level when it is enabled. A
simple allotment block distribution based on mixing the two
competing
funding formulas is also considered. The models presented in
this paper represent the first time that policy alternatives to the
LIHEAP allocation mechanism has been examined within an
analytic framework.
r 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction
The Low-Income Home Energy Assistance Program
(LIHEAP) was authorized by Congress through Title
XXVI of the Omnibus Budget Reconciliation Act of
1981, and currently authorized through the end of FY
2004 by the Coats Human Services Re-authorization
Act of 1998, P.L.105-285, enacted on October 27, 1998,
www.acf.dhhs.gov.
The Low-Income Home Energy Assistance Act of

1981 established the Low-Income Home Energy Assis-
tance block grant program to help eligible households
meet home energy costs. States can provide assistance to
low-income households through various program com-
ponents, including home heating and cooling assistance,
energy crisis assistance, and home weatherization
(General Accounting Office, US Congress, 1986):
* Home energy assistance consists of helping low-
income households pay heating and cooling costs.
Grantees provide assistance in the form of cash,
vouchers, coupons, and two-party checks to eligible
households, and may make payments to landlords or
home energy suppliers on behalf of eligible house-
holds.
* Energy crisis assistance includes funding for weather-
related, supply shortages, and other household
energy-related emergencies. States provide cash,
shelter, emergency supplies, or supplemental heating
sources to households without heat or in imminent
danger of having their fuel supplies terminated.
* Weatherization assistance includes funding for low -
cost residential weatherization or other energy-
related home repair.
LIHEAP is limited to households that include recipients
of aid to families with dependent children, supplemen-
tary security income, food stamps, or certain veteran’s
benefits. Households with incomes less than 150% of the
poverty level, or less than 60% of the state’s median
income, whichever is greater, also qualify under the
statute.

The LIHEAP is a block grant program, meaning that
the state can—within the statutory requirements—
choose their method of administration, eligibility
criteria, benefit levels, and funding levels for program
activities. A number of legislative amendments over the
years have placed some restrictions on state program
discretion; for example, no more than 25% of LIHEAP
ARTICLE IN PRESS
*Corresponding author. Tel.: +1-225-578-4554; fax: +1-225-
578-
4541.
E-mail address: [email protected] (M.J. Kaiser).
0301-4215/03/$ - see front matter r 2002 Elsevier Science Ltd.
All rights reserved.
PII: S 0 3 0 1 - 4 2 1 5 ( 0 2 ) 0 0 2 0 0 - 8
funds can be used for weatherization and no more than
10% can be spent on state administration costs. States
can transfer a maximum of 10% of their funds to other
block grants and cannot carry more than 15% of their
allotment to the succeeding fiscal year.
The General Accounting Office by legislative mandate
is required to evaluate LIHEAP, and as requested by
various government units, have produced a number of
reports on the program, e.g., General Accounting
Office, US Congress (1986, 1987, 1990). A handful of
academic papers on federal energy assistance programs

are scattered throughout the literature (Colton, 1990;
Higgins and Lutzenhiser, 1995; Kennedy, 1987; Kings-
ley, 1992; Landsberg and Dukert, 1981), including a few
Congressional Research Service reports (Abbey, 2001;
Gish, 2000; Stoltzfus, 2002) and numerous LIHEAP
reports to Congress (Low Income Home Energy
Assistance Programs, 1983, 1985, 1994, 2000).
The federal government distributes funds to states for
LIHEAP using a legislated formula. The LIHEAP
formula was originally legislated in 1981 and then
revised in 1984 in large measure due to political pressure
from many warm-weather states that maintained that
the 1981 formula over-allocated funds to cold-weather
states. Pursuant to the re-authorization amendment for
LIHEAP in 1984, the Health and Human Services
developed a new formula to increase the overall equity
among the states. The LIHEAP formula was revised to
incorporate state cooling requirements in an equal
weighting scheme with state heating requirements, but
various additional conditions were also included in the
amendment that specified when and how the 1984
formula could be employed. To ‘‘turn-on’’ the 1984
formula for instance, LIHEAP’s regular appropriation
is required to exceed a minimum threshold level of
$1.975 billion, but because program commitment to
LIHEAP has fallen over the years, the revised allocation
mechanism has only rarely been applied—specifically,
twice over the past 17 years, and last during FY 1986.
The primary intent of the 1984 legislation to increase
the overall equity of the distribution of LIHEAP funds
has thus failed miserably, and so there is a need to
examine alternative allotment methods to bring the 1984
formula ‘‘back into’’ the allocation mechanism as
intended by the legislation. The primary purpose of this

paper is to suggest viable policy alternatives to the
current legislative framework and to develop an analytic
model to quantify the impact of each alternative. The
present work represents the first time that alternative
allocation mechanisms to LIHEAP have been modeled
and presented publicly. This model not only provides
legislators insight on competing policy proposals, but
also hopefully, provides a forum and stimulus for future
debate.
The outline of the paper is as follows. The current
LIHEAP statute is discussed in Section 2, followed by a
summary of LIHEAP funding levels in Section 3 and a
general description in Section 4 of three realistic policy
alternatives. In Sections 5–7 the policy alternatives are
examined. In Section 5, a comparison of the 1981 and
1984 formula allocation formulas are discussed by state
and region, and in Section 6, the effect of a trigger-level
reduction on state allotments and system measures are
outlined. In Section 7 a block allotment procedure is
described which combines the 1981 and 1984 formula.
In Section 8 conclusions complete the paper. To
maintain focus on the policy proposals, the theoretical
foundation of the allocation mechanisms are maintained
in separate appendices.
2. The LIHEAP statute
The LIHEAP statute currently assigns each state and
the District of Columbia an allotment percentage based
on the value of the regular appropriation $D for the
fiscal year. One of three cases can occur depending on
the value of D:
Case I : Dp$1:975B

Case II : $1:975BoDo$2:25B
Case III : DX$2:25B
Case I: Dp$1:975B: When the regular appropriation
in a fiscal year is less than or equal to $1.975B, the 1981
formula is employed to determine state allocation
percentages. In other words, the 1981 formula repre-
sents a default condition if regular appropriation does
not exceed the trigger F ¼ $1:975B: The 1981 allocation
percentages shown in Table 1 are now over 20-years old
and the arbitrary basis of their ‘‘derivation’’ forgotten
by the legislative community. Further, and more
importantly, since regular appropriations have fallen
below the trigger level every year for the past 15 years
(and counting), the high frequency of usage of the 1981
formula has helped to create a sense of ‘‘acceptance’’
and ‘‘validity’’ for its application, which is anything but
satisfactory.
Three main ‘‘problems’’ exist with the 1981 formula:
(1) The 1981 formula represented the outcome of a
political process as opposed to being based on good
science.
(2) The 1981 formula was poorly designed, extremely
complex, and arbitrarily ‘‘derived’’ in a manner that
strongly favored cold-weather climates.
(3) The 1981 formula is a ‘‘static’’ formula that fixed
the allocation percentages of states based on pre-
1980 data for state climate, fuel price, demographic,
and expenditure patterns.
The 1981 formula is unusually easy to criticize and
very difficult to defend. It is important to recognize

ARTICLE IN PRESS
M.J. Kaiser, A.G. Pulsipher / Energy Policy 31 (2003) 1441–
14581442
that the 1981 formula was designed in response
to conditions specific to the times that emphasized
the rapidly increasing fuel oil prices in the Northeast
during the late 1970s. The formula allocation caused
great consternation on the part of many warm-weather
states
1
and the continued application of the 1981
formula remains one of the better-kept ‘‘secrets’’ in
Washington.
The primary shortcomings of the 1981 formula are
easy to recognize: The 1981 formula does not nor cannot
reflect the current low-income demographic, consump-
tion, and fuel price mix in the country (since the data on
which the formula is based is over 20-years old), and
further, the formula itself cannot be ‘‘updated’’ to reflect
more recent data (since the allocation mechanism is a
static design). The most egregious aspect of the 1981
formula is that the allocation mechanism does not
distribute funds based on the need for home energy
assistance. Instead, the 1981 formula defines need in a
mysterious and complicated fashion primarily in terms
of the home heating needs of cold-climate states.
A complex and convoluted formula is not necessarily
a ‘‘bad’’ formula, but unfortunately—and more to the

point—it is not clear what the 1981 state allocation
percentages mean or if they identify the need for home
energy assistance. Four separate formulas are entangled
with the 1981 formula allotment—two House of
Representatives formula alternatives, the FY 1980 state
allotment, and the Windfall Profit Tax Act formula—
commingled with pro-rata reductions, weak hold-harm-
less (HH) provisions, and arbitrary formula compar-
isons. And as each one of the four formulas is biased
toward cold-climate states, no matter what procedural
elements are invoked, a biased
2
cold-climate formula
remains a biased cold-climate formula.
Pursuant to the re-authorization amendment for
LIHEAP in 1984, the 1981 formula was completely
revised in the ‘‘1984 formula’’, but for the 1984 formula
to be ‘‘turned-on’’ the regular appropriation must
exceed $1.975B.
Case II: $1:975BoDo$2:25B: When the regular
appropriation exceeds $1.975B in a fiscal year, then an
allocation mechanism based on the 1984 formula
coupled with two HH provisions is adopted. The first
HH condition, or primary HH provision, is enabled
when D > $1:975B: When DX$2:25B a second HH
provision kicks in.
The 1984 formula, or ‘‘new formula’’, was established
to provide a mechanism to distribute LIHEAP funds
based solely on the home energy needs of low-income
ARTICLE IN PRESS

Table 1
LIHEAP allocation percentages according to the 1981 and 1984
formula
State 1981 Formula
(%)
1984 Formula
(%)
Statutory
floor ($M)
Alabama 0.86 1.68 16.99
Alaska 0.55 0.36 10.84
Arizona 0.42 1.25 8.21
Arkansas 0.66 1.21 12.96
California 4.61 6.00 91.12
Colorado 1.61 1.15 31.77
Connecticut 2.10 1.40 41.45
Delaware 0.28 0.37 5.50
D.C. 0.33 0.27 6.44

Florida 1.36 4.16 26.88
Georgia 1.08 2.68 21.25
Hawaii 0.11 0.12 2.14
Idaho 0.63 0.28 12.39
Illinois 5.81 5.30 114.72
Indiana 2.63 2.21 51.94
Iowa 1.86 1.22 36.81
Kansas 0.86 1.07 16.91
Kentucky 1.37 1.73 27.03
Louisiana 0.88 1.79 17.37
Maine 1.36 0.55 26.85
Maryland 1.61 2.26 31.74
Massachusetts 4.20 2.91 82.91
Michigan 5.51 4.82 108.92
Minnesota 3.97 1.68 78.47
Mississippi 0.74 1.87 14.56
Missouri 2.32 2.41 45.82
Montana 0.74 0.35 14.54

Nebraska 0.92 0.55 18.21
Nevada 0.20 0.51 3.86
New Hampshire 0.79 0.45 15.69
New Jersey 3.90 3.28 76.97
New Mexico 0.52 0.54 10.28
New York 12.72 8.68 251.34
North Carolina 1.90 3.14 37.45
North Dakota 0.80 0.21 15.79
Ohio 5.14 4.86 101.49
Oklahoma 0.79 1.31 15.61
Oregon 1.25 0.95 24.62
Pennsylvania 6.84 5.15 134.99
Rhode Island 0.69 0.47 13.65
South Carolina 0.68 1.44 13.49
South Dakota 0.65 0.29 12.83
Tennessee 1.39 2.08 27.38
Texas 2.26 6.60 44.71
Utah 0.75 0.54 14.76

Vermont 0.60 0.23 11.76
Virginia 1.96 3.05 38.66
Washington 2.05 1.50 40.50
West Virginia 0.91 0.96 17.89
Wisconsin 3.58 1.93 70.63
Wyoming 0.30 0.18 5.91
1
‘‘It has only been through the making of legislative history with
regard to this and previous appropriations bills for this program
that
the prejudice favoring cold-weather energy bill assistance and
opposing
hot-weather energy bill assistance has developedy it is counter
to the
American tradition of fair play. I would urge the Congress to re-
examine its conscience and design a fairer solution’’.
Additional view
of Bill Alexander, Low Income Energy Assistance, House of
Representatives Report No. 96-1244, August 21, 1980.
2
Granted, the home heating needs of cold-climate states were
particularly severe in the early 1980s but the incorporation of

these
same factors today is not defendable.
1458 1443
households—where ‘‘home energy’’ was interpreted to
mean the heating and cooling requirements of house-
holds. According to Section 2604(a)(2) of P.L. 97-35 as
amended by P.L.98-558,
‘‘y For fiscal year 1985 and thereafter, a state’s
allotment percentage is the percentage which expen-
ditures for home energy by low-income households in
that state bears to such expenditures in all statesy’’
The 1984 formula was a significant improvement over
the 1981 formula in terms of its transparency and equity
and in many regards can be considered the ‘‘ideal’’
mechanism to distribute LIHEAP funds:
(1) The 1984 formula determines state allocation
percentages according to a simple, easy-to-under-
stand, and science-based mechanism using estimates
of state expenditures for the Btu requirements of
low-income households for each fuel source con-
tributing to home heating and cooling needs.
(2) The 1984 formula is extremely well designed and
easy-to-defend and is based on the ‘‘best-available’’
statistical data.
(3) The 1984 formula is a dynamic allocation that is

updated annually to normalize for changes in
weather patterns (heating and cooling degree-days)
and fuel prices (coal, electricity, fuel oil, liquid
petroleum gases, and natural gas) at the state level.
The 1984 formula allocations are shown in Table 1
alongside the 1981 allotments, but unlike the 1981
percentage allocation values, the 1984 formula values do
not represent the final state allotment percentages. The
final allotment percentages can only be calculated after
the regular appropriation D is known for the fiscal year
and the impact of the HH and give-back (GB)
provisions are incorporated within the allocation
mechanism.
The HH condition establishes a statutory floor for
each state determined by the 1981 formula allocation
and the appropriation level F ¼ $1:975B as shown in
Table 1. If a state does not achieve its statutory floor
under the appropriation D and 1984 formula allotment,
then it is held ‘‘harmless’’ at its floor. The funds
necessary to maintain states at their floor is mandated
by a GB provision which specifies that all states above
their floor will have their allotments reduced propor-
tionally until the funds required to make-up the deficit is
achieved. Since the funds necessary to make-up the
deficit come from states that benefit under the new
allocation mechanism, these states effective allotment
percentages are reduced from their 1984 allotment.
Case III: DX$2:25B: When the regular appropriation
for a given fiscal year is equal to or exceeds $2.25B, then
another HH and GB condition is triggered, referred to
as the secondary HH-GB provision or the LTOP (less
than 1%) provision. The LTOP provision stipulates that

any state that receives less than 1% of the total
allotment funding at the appropriation level D cannot
have a smaller allotment percentage than its allotment
percentage at $2.14B. The impact of the secondary HH-
GB provision acts to maintai n a set of states at their
allotment percentage achieved at $2.14B. Since a set of
states are maintained at an allotment percentage that is
higher than dictated by the primary HH-GB provision,
the complementary set of states which are not affected
by the LTOP provision provide the funds required to
satisfy this condition.
The inclusion of the secondary HH-GB provision is
interesting because it indicates the ‘‘mind-set’’ of the
legislators at the time the LIHEAP statute was revised.
It was expected, or at least anticipated, that regular
appropriations for LIHEAP would increase in the years
ahead and might conceivably even exceed $2.25B! As it
turns out, however, due to factors such as the oil price
crash of 1986 and the Emergency Deficit Control Act,
funding levels for LIHEAP in the years following the
1984 re-authorization plummeted.
3. LIHEAP funding levels
The LIHEAP statute provides for two types of
program funds: regular block grant and emergency.
Regular funds are authorized under Section 2602(b) of
the LIHEAP statute and are currently allocated
according to the mechanism described in Section 2.
Emergency funds are authorized under 2602(e) of the
LIHEAP statute and are authorized and distributed at
ARTICLE IN PRESS
Table 2

LIHEAP funding history, 1981–2002
FY Regular appropriation ($B) Emergency ($M)
1981 1.850
1982 1.875
1983 1.975
1984 2.075
1985 2.100
1986 2.010
1987 1.825
1988 1.532
1989 1.383
1990 1.393 50
1991 1.415 195
1992 1.500
1993 1.346
1994 1.439 298
1995 1.319 100
1996 0.900 180

1997 1.000 215
1998 1.000 160
1999 1.100 180
2000 1.100 744
2001 1.400 456
2002 1.700
14581444
the discretion of the President and Secretary of the
Health and Human Services at any point in time in the
fiscal year. The funding history of LIHEAP is shown in
Table 2. The average value of LIHEAP regular
appropriation from 1981–2002 is EðDÞ ¼ $1:51B with
a standard deviation of sðDÞ ¼ $0:37B: Observe that
since the LIHEAP program was reauthorized in 1984,
funding levels have exceeded the trigger level $1.975B
only during FY 1985 and FY 1986.
4. Policy proposals
The principal condition that has prevented the
application of the 1984 formula is immediately clear.
The level of the regular funding appropriated for
LIHEAP over the years has not achieved the legislated
trigger, and so by default, the 1981 formula—despite its
obvious shortcomings—has become the effective alloca-

tion mechanism for federal funding.
To address the failure of the 1984 legislation, three
suggestions follow:
* Eliminate the trigger level,
* Reduce the trigger level or
* Devise an alternative allocation mechanism.
These suggestions are formalized as the following
options:
Option A: Eliminate the HH-GB provisions and apply
the 1984 formula allocation at a zero trigger level.
Option B: Reduce the trigger level of the HH-GB
provision and eliminate the LTOP provision.
Option C: Apply an allocation mechanism based on a
linear combination of the 1981 and 1984 formula values.
A brief description of each option is now provided
followed in Sections 5–7 by models that explore the
impact of each alternative.
Option A: This is the most dramatic approach, the
simplest, and arguably the most equitable. Unfortu-
nately, Option A is also unlikely to garner the political
support necessary to achieve passage.
The purpose of LIHEAP is to assist low-income
households meet the costs of home energy. This purpose
is clear and unambiguous and a very good allocation
mechanism already exists in the 1984 formula to satisfy
this objective—and in fact it is doubtful that a ‘‘better’’
formula can be developed unless the legislative mandate

of LIHEAP radically changes—but for the past 15 years
the 1984 formula could not be employed since the
trigger level to turn it ‘‘on’’ has never been attained.
Hence, by eliminating the HH provisions and setting the
trigger point to zero, the 1984 formula will serve as the
new default formula.
The basic premise of Option A is that any use of the
1981 formula perpetrates a distribution of funds that is
inequitable since the allocation is not based on the home
energy needs of low-income households. The manner in
which LIHEAP funds should be distributed to states
should mimic the state’s home energy expenditures
3
paid
by low-income households. Interestingly, this also
appears to be the Bush Administration position.
4
Although Option A is believed to be the fairest,
simplest and best way to revise LIHEAP, it may not be
politically viable or develop a strong enough coalition of
support, especially in the Senate since a majority of
states realize a smaller allotment percentage under the
1984 formula. The fight in Congress over Option A will
be especially difficult since Senators are not likely to
vote their state a lower allotment percentage to ‘‘right
the wrongs’’ of an archaic and cryptic formula. Be that
as it may, if legislators can be convinced to move on
LIHEAP—perhaps for the sake of good government,
good conscience, or daresay, a good formula—viability
may hinge on maintaining some form of the HH

condition as opposed to the complete elimination of
the statutory floor. One simple means to accomplish this
task is to simply re-set the trigger level of F downward
as proposed in Option B.
Option B: Any revision to LIHEAP should be realistic
and based on a politically viable strategy.
The value of the trigger point F currently represents a
level that has not, nor likely will, be surpassed in the
future, and hence its adjustment downward is necessary
to ensure that a more equitable allocation mechanism be
applied to future LIHEAP funding. The value of the
trigger point was set by legislative mandate and over
time has lost its relation to D: At one time (15-years ago)
the values of D and F were roughly comparable, while
today F appears as an upper bound that is unlikely to be
exceeded.
There is also some precedence for trigger re-adjust-
ment. When the HH-GB provision was initially devised
in 1984, F was set at the FY 1984 appropriation level of
$2.075B. In 1986, when the regular appropriation fell
below the required trigger, the value of F was reduced to
the FY 1983 level of $1.975 to bring the 1984 formula
back ‘‘in’’ the allocation mechanism.
5
Unfortunately,
FY 1986 represented the last year in which program
appropriations exceeded $1.975B, and subsequent to
this time no further action has been taken to address this
issue and/or re-adjust F:
ARTICLE IN PRESS

3
Home energy expenditures paid by low-income households is
also
relatively easy to estimate, and so there is no technical
difficulties
associated with the computation.
4
‘‘y The legislatively established formula currently used to
distribute LIHEAP block grant funds to states is based on 20-
year
old population and winter heating cost data. The Administration
is
interested in options that would make block grant allocations
more
equitable by basing the formula on current home energy
expenditures
paid by low-income households’’. Bush Administration LIHEAP
Budget for Fiscal Year 2003.
5
Apparently LIHEAP re-authorization legislation was still fresh
in
legislators minds.
1458 1445

The ideal equitable allocation mechanism would be
based on the 1984 formula with no provisions attached
(Option A), but because of the historical precedence to
couple the 1984 formula with HH and GB provisions,
and the need to satisfy a majority of votes in the Senate,
Option B is likely to be viewed as compromise
legislation.
Option C: An alternative approach to maintain the
application of the 1981 formula that does not rely
explicitly on re-adjusting the trigger level F is to
set-aside a certain percentage ðrÞ of the regular appro-
priation to be used with the 1981 formula, rD; and then
to apply the 1984 formula to the remaining funds,
ð1 � rÞD: This has an advantage over Option B since
regardless of the appropriation level the 1984 formula
would always be applied to the same portion of the
regular appropriation.
6
Option C ensures application of
the 1984 formula with no ‘‘downside risk’’ as in Option
B, but it also foregoes the ‘‘upside potential’’ when D >
F: On methodological grounds a formula mix is not
especially appealing, but as will be demonstrated in
Section 7, a linear combination of the 1981 and 1984
formula is equivalent to Option B under a suitable
correspondence.
A summary of the three options is depicted in Table 3
along with a brief description of their advantages and
disadvantages.

5. A comparison of the 1981 and 1984 formula allotments
The 1981 formula is for all practical purposes a
‘‘perpetual’’ formula since the funding levels required
to ‘‘turn-on’’ the new allocation mechanism has only
rarely been achieved in the past and is unlikely to be
attained in the future. The HH and GB provisions
associated with the allocation mechanism are therefore
relaxed and the trigger level required to turn-on the 1984
formula is set equal to zero. A direct comparison is
performed between the old and new formula allotment
percentages by state and region.
5.1. Comparison by state
If the vectors f and g denote the 1981 and 1984 state
allotment percentages:
f ¼ ðf1; y; f51Þ; 0ofio1;
X
fi ¼ 1;
g ¼ ðg1; y; g51Þ; 0ogio1;
X
gi ¼ 1;
then the set of states that would benefit from a formula
change is denoted
fBg ¼ fi j fiogig;
while the set of states that would be harmed is denoted
fCg ¼ fi j fi > gig:

The sets fBg and fCg partition the 50 states and District
of Columbia (D.C.) according to states that ‘‘benefit’’
and are ‘‘harmed’’ by the formula change. If a state’s
1984 formula allotment percentage is greater than its
ARTICLE IN PRESS
Table 3
A comparison of three policy options
Policy Description Advantages Disadvantages
Option A Eliminate the primary and Simple Senate fight
secondary HH-GB provisions Fair Large percentage change in
state allotment
and nullify the trigger level Rational
mechanism
Satisfies original intent of LIHEAP
Bush Administration position
House passage likely
Option B Maintain the primary HH-GB Maintains form of
Maintains convoluted formula
provision but reduce the statute Not a rational mechanism for
distribution
trigger level when it is enabled Enables 1984 Level of fairness

not guaranteed
formula
Compromise formula
Senate support more likely
Option C Apply an allotment based Simple Formula mix
on a linear combination Easy to understand Not a rational
mechanism for distribution
of the 1981 and 1984 No downside risk Foregoes upside
potential
formula values Correspondence with
Option B
6
Under Option B, if F is re-set at a value that is ‘‘too high’’ (say
$1.5B) and D again drifts downward away from F; then the
same
inequity will return to the distribution.
14581446
1981 allotment percentage, fiogi; then state i is said to
benefit from the new policy.
In Table 4, 23 states are shown to benefit under

Option A while 28 states would be harmed. States that
benefit realize a percentage change in their allotment
ranging from 4% (New Mexico, Missouri) to 200%
(Arizona, Florida) while states that are harmed range
from �6% (Ohio) to �74% (North Dakota). A graphical
representation of allotment percentage changes is
depicted in Fig. 1. The average percentage change for
states in fBg and fCg is 81% and �35%; respectively.
Eight states in fBg realize an allocation percentage
change greater than 100% (FL, AZ, TX, NV, MS, GA,
SC, LA), while seven states in fCg realize a change in
allocation percentage greater than 50% (ND, VT, MN,
ID, SD, ME, MT).
Under the 1984 formula allotment, the set of states
that benefit from the new policy would realize a 20.4%
increase in total allotment, which would be transferred
from the states in fCg:7 The total amount of money
transferred depends on the value of D; e.g., if D ¼ $1B;
then $204M would be transferred under Option A from
fCg to fBg:
All states are impacted by the new policy. The
expected annual difference in state allocations is com-
puted in Table 4 based on the 1981–2002 average annual
regular appropriations for LIHEAP, EðDÞ ¼ $1:51B;
multiplied by the difference in allotment percentages,
gi � fi: The ‘‘big winners’’ under Option A include Texas
($65M), Florida ($42M), Georgia ($24M), California
($20M), and North Carolina ($18M), while states that
lose money include New York ð�$61MÞ; Minnesota
ð�$35MÞ; Pennsylvania ð�$25MÞ; Wisconsin ð�$25MÞ;
and Massachusetts ð�$19MÞ: See Fig. 2 for a graph of
the expected annual difference in funding under Option
A. The average annual difference in funding levels in

fBg and fCg is $13.4M and �$11:0M; respectively. The
top five states in fCg represent nearly 60% of the total
funds that would be reallocated under Option A to the
top five states in fBg: The remaining funds are
transferred among the 41 other states in fBg and fCg:
To provide a rough measure of the degree of inequity
that has been promulgated over the past decade through
the continued use of the 1981 formula, refer to the last
column in Table 4. The values depicted are based on the
ARTICLE IN PRESS
-100 -50 0 50 100 150 200 250
S
ta
te
s
Percentage Change (%)
{C} {B}
Fig. 1. State LIHEAP allotment percentage change: 1981 vs.
1984
formula.
Table 4
The impact of using the 1984 formula allocation
State Percentage

change (%)
Expected
annual
difference
($M)
10-year
cumulative
impact ($M)
Alabama 95.02 12.34 112.80
Alaska �34.34 �2.85 �26.02
Arizona 200.42 12.59 115.07
Arkansas 84.80 8.40 76.82
California 29.93 20.85 190.62
Colorado �28.38 �6.89 �63.03
Connecticut �33.41 �10.59 �96.79
Delaware 33.73 1.42 12.97
D.C. �17.24 �0.85 �7.76
Florida 205.14 42.15 385.35
Georgia 148.79 24.17 221.00
Hawaii 7.21 0.12 1.08

Idaho �55.66 �5.27 �48.22
Illinois �8.77 �7.70 �70.35
Indiana �15.88 �6.31 �57.65
Iowa �34.33 �9.66 �88.34
Kansas 24.40 3.15 28.84
Kentucky 26.51 5.48 50.08
Louisiana 103.62 13.76 125.77
Maine �54.82 �11.26 �102.89
Maryland 40.82 9.91 90.55
Massachusetts �30.64 �19.42 �177.56
Michigan �12.63 �10.52 �96.20
Minnesota �57.74 �34.64 �316.65
Mississippi 153.94 17.14 156.69
Missouri 3.98 1.40 12.76
Montana �52.58 �5.84 �53.43
Nebraska �40.55 �5.64 �51.60
Nevada 159.36 4.70 42.97
New Hampshire �42.59 �5.15 �47.11
New Jersey �15.97 �9.40 �85.89
New Mexico 3.62 0.28 2.60
New York �31.87 �61.23 �559.73
North Carolina 65.31 18.70 170.97
North Dakota �73.56 �8.88 �81.18
Ohio �5.56 �4.31 �39.42
Oklahoma 65.51 7.82 71.50
Oregon �23.96 �4.51 �41.23

Pennsylvania �24.64 �25.43 �232.51
Rhode Island �32.56 �3.40 �31.06
South Carolina 110.44 11.39 104.13
South Dakota �55.35 �5.43 �49.62
Tennessee 49.99 10.47 95.68
Texas 191.33 65.41 597.96
Utah �27.92 �3.15 �28.81
Vermont �62.14 �5.59 �51.09
Virginia 55.88 16.52 151.00
Washington �27.08 �8.38 �76.65
West Virginia 5.56 0.76 6.95
Wisconsin �45.98 �24.83 �226.98
Wyoming �39.63 �1.79 �16.37
7
Capital redistribution is a zero-sum game.
1458 1447
LIHEAP cumulative allotments from 1992–2002,
$13.80B, multiplied by the allocation differential, gi �
fi: The values shown give an indication of what states
can expect to gain and/or lose over the next decade
should Option A be implemented.
5.2. Comparison by region
Regional comparisons are especially insightful since

they indicate the inequity that the 1984 legislation was
originally intended to address. Assign each state to one
of four census regions: Northeast, North Central, South,
and West, as shown in Table 5. The percentage of the
total appropriation by region according to the 1981 and
1984 formula allocation is shown in Table 6.
States that benefit from Option A are drawn
predominately from the South and to a lesser extent
the West and North Central regions. No state in the
Northeast benefits from a formula change, and hence it
is not surprising that the Northeast forms a strong and
vocal coalition against any changes to LIHEAP’s status
quo (Pataki, 2001). Relative to the 1984 formula, the
Northeast and North Central states receive a 17.6%
over-allotment of funds, which are effectively being
withdrawn from the South. The Southern states mean-
while have expressed dissatisfaction with the mechanism
that promotes this distribution although their criticism
remains rather soft (Patton and Hodges, 2001) con-
sidering the duration and extent of the inequity—
although political considerations may also be at work
here. The Western region as a class does not realize a
noticeable difference in allotment percentages under the
two formulas, although individual states may realize
significant variation, e.g., Arizona (200%), California
(30%), Nevada (159%), Idaho ð�56%Þ; Oregon ð�24%Þ
and Washington ð�27%Þ:
5.3. The cumulative allocation
A description of the cumulative percentage allotment
provides further insight into the allocation mechanism.
Under the 1981 formula, nine states receive 53% of
LIHEAP funds (NY, PA, IL, MI, OH, CA, MA, MN,

NJ); 19 states receive 75% of total funds (WI, IN, MO,
TX, CT, WA, VA, NC, IA, CO), and 33 states receive
90% of funds. Under the 1984 formula, 10 states receive
52% of LIHEAP funds (NY, TX, CA, IL, PA, OH, MI,
FL, NJ, NC); 20 states receive 75% of the funds (VA,
MS, GA, MO, MD, IN, TN, WI, MI, LA); and 30 states
receive 90% of the funds. The placement of states under
the two formulas shift slightly, and from a global
perspective the allotments are quite similar. Under the
1981 formula allocation, 25 states receive less than 1%
of the total funding, while with the 1984 formula, 19
states receive less than a 1% allocation. A cumulative
representation of the two allocations can be compared
by first ordering the elements in descending rank and
then perform a cumulative summation. The result in
Fig. 3 shows the curves to be nearly identical. The 1984
cumulative curve falls ever so below the 1981 curve
indicating an allocation that distributes funds in
aggregate slightly more evenly across states.
ARTICLE IN PRESS
-80 -60 -40 -20 0 20 40 60 80
S
ta
te
s
Expected Annual Difference ($M)
{C} {B}
Fig. 2. Expected difference in annual LIHEAP allotments: 1981
vs.

1984 formula.
Table 6
Percentage of the total appropriation by census region
Region 1981
Allotment
(%)
1984
Allotment
(%)
Difference
(%)
Northeast 33.2 23.2 �10.0
North
Central
34.1 26.5 �7.5
South 19.0 36.6 17.6
West 13.7 13.7 —
Table 5

State assignment via census region
Northeast North Central South West
Connecticut Illinois Alabama
a
Alaska
Maine Indiana Arkansas
a
Arizona
a
Massachusetts Iowa Delaware
a
California
a
New Hampshire Kansas
a
D.C. Colorado
New Jersey Michigan Florida
a
Hawaii
a
New York Minnesota Georgia
a
Idaho

Pennsylvania Missouri
a
Kentucky
a
Montana
Rhode Island Nebraska Louisiana
a
Nevada
a
Vermont North Dakota Maryland
a
New Mexico
a
Ohio Mississippi
a
Oregon
South Dakota North Carolina
a
Utah
Wisconsin Oklahoma
a
Washington

South Carolina
a
Wyoming
Tennessee
a
Texas
a
Virginia
a
West Virginia
a
a
Indicate states that benefit from the application of the 1984
formula allotment.
14581448
6. The effect of a trigger-level reduction
Application of the 1981 formula to distribute funds is
considered fundamentally unfair since it does not satisfy
the intent of LIHEAP nor does it allocate federal dollars
in a rational manner. Application of the 1984 formula
was originally tied to a HH provision to protect states
from receiving less money under the new formula.
Unfortunately, regular appropriations for LIHEAP fell

after the 1984 legislation was passed and has come in
under the threshold 15 of the last 17 years, and so by
default, the problematic 1981 formula continues to be
used to distribute federal dollars.
The primary problem with the LIHEAP allocation
mechanism is due to the fact that the trigger level F was
set nearly two decades ago at a value commensurate to
mid-1980 appropriation levels, while actual (real)
appropriations began to slide shortly after the 1984
legislation was passed. Today, the trigger level F ¼
$1:975B is not representative of current LIHEAP
appropriation levels and future appropriation is not
expected to reach F ¼ $1:975B—let alone surpass F to
‘‘turn-on’’ the 1984 formula. To increase the chance of
allocating some funds with the 1984 formula, it is
necessary to lower the value of the trigger. Ultimately,
the value of F will need to be negotiated, and so it is
useful to understand how the selection of F impacts
global measures and individual state allotments. The
basic idea of Option B is to set F at a level below the
expected value of D:
6.1. Theoretical structure
The LIHEAP allocation mechanism described in
Section 2 is first simplified by eliminating the secondary
HH provision, and for analytical purposes, the value of
F is considered variable. The LIHEAP allocation
mechanism is constructed according to Theorem 1 and
its limiting relations are proved in Theorem 2.
Theorem 1. The LIHEAP allocation mechanism under
the primary HH-GB provision yields state allotments

according to the following recipe:
AiðF; DÞ ¼
Dfi; iAfSg; DpF;
Ffi; iAfHg; D > F;
Ffi þ Ei; iAfNg; D > F;
8><
>:
where fSg ¼ fHg,fNg; fHg ¼ fi j Ffi=Dgi > 1g;
fNg ¼ fi j Ffi=Dgip1g; Ei ¼ gðDgi � FfiÞ; g ¼ X =Q;
X ¼ D � F; and Q ¼
P
iAfNg ðDgi � FfiÞ:
Proof. See Appendix A.
the primary HH-GB yields the following limiting rela-
tions:
lim
D=F-1
aiðF; DÞ ¼ fi;
lim
D=F-N
aiðF; DÞ ¼ gi:

Proof. See Appendix A.
The LIHEAP allocation mechanism described in
Theorem 1 and system measures derived from the
mechanism can be expressed as a function of the ratio
D=F as shown in Theorems 3 and 4.
Theorem 3. For D > F; the LIHEAP allocation mechan-
ism under the primary HH-GB provision yields state
allotment percentages
aiðF; DÞ ¼
F
D
fi; iAfHg;
F
D
fi þ
Ei
D
; iAfNg
(
that are functions of the ratio F=D:
Proof. See Appendix B.
Theorem 4. The LIHEAP system measures
sðF; DÞ; iðF; DÞ; and rðF; DÞ can be expressed in terms
of the ratio D=F as sðD=FÞ; iðD=FÞ; and rðD=FÞ:

ARTICLE IN PRESS
0
20
40
60
80
100
120
1 4 7
1
0
1
3
1
6
1
9
2
2
2
5

2
8
3
1
3
4
3
7
4
0
4
3
4
6
4
9
Number of States
C
u
m
u
la
ti

v
e
P
e
rc
e
n
ta
g
e
1981 allotment 1984 allotment
Fig. 3. The 1981 and 1984 cumulative percentage LIHEAP
allotment.
1458 1449
Proof. See Appendix B.
6.2. Universal tableaux
Application of the theoretical structure is now
presented. Theorem 1 describes how to construct
state allotments and Theorem 2 presents the limiting
cases when D ¼ F and DbF: The result of Theorems 3
and 4 demonstrate that the LIHEAP allocation percen-
tages, aiðF; DÞ; and aggregate measures sðF; DÞ; iðF; DÞ;
and rðF; DÞ—which are a function of F and D—can

be expressed in terms of one variable, the ratio D=F:
This is not only a very convenient result but
also quite useful since rather than enumerate all
the various combinations of F and D sepa-
rately, e.g., F ¼ 1; D ¼ ð1; 1:25; 1:5; 1:75; 2:0; yÞ; F ¼
1:5; D ¼ ð1:5; 1:75; 2:0; 2:25; 2:5; 2:75; 3:0; yÞ; etc. one
‘‘universal tableaux’’ suffices to present all relevant
allocation percentages and aggregate measures.
The aggregate measures employed are empirically
derived and are defined formally as follows:
H ¼
P
iAH Ffi Amount of money allocated to
H under the imposition of the
HH provision ($)
G ¼
P
iAH Dgi Amount of money allocated to
H if the HH provision was
eliminated ($)
N ¼
P
iAN Ffi þ X Amount of money allocated to
N under the imposition of the
HH provision ($)
X ¼ D � F Money available for distribu-
tion after all state statutory
floors are maintained ($)

M ¼
P
iAN Dgi Amount of money allocated to
N if the HH provision was
eliminated ($)
sðD=FÞ ¼ ðH � GÞ=D Percentage of money trans-
ferred from N to H relative to
the total appropriation
D; 0psðD=FÞp1
rðD=FÞ ¼ ðH � GÞ=M Percentage reduction in the
funding allocation to N due to
the imposition of the HH-GB
provision, 0prðD=FÞp1
iðD=FÞ ¼ ðH � GÞ=G Percentage increase in the fund-
ing allocation to H due to the
imposition of the HH-GB pro-
vision, 0piðD=FÞp1
pðD=FÞ ¼ H=D Percentage of the total funds D
allocated to H Due to the
imposition of the HH-GB pro-
vision, 0ppðD=FÞp1
qðD=FÞ ¼ G=D Percentage of the total funds D
allocated to H if the HH-GB
provision was eliminated,
0pqðD=FÞp1
H The number of states in H
N The number of states in N

Application of the tableaux follows three steps:
Step 1: Assume D:
Step 2: Select F:
Step 3: Compute D=F:
* If D=Fp1; then read the row of Table 7 (or column
of Table 8) for D=F ¼ 1:
* If 1oD=Fp3; then select the row (or column) for
D=F closest to the ratio value.
* If D=F > 3; then read the row (or column) for
D=F ¼ 3:
The tableaux is easy to use and the results are bound
through the limiting relations described in Theorem 2. A
few examples illustrate the application of the tableaux.
Example. (a) If D ¼ $1:3B and F ¼ $0:5B; then D=F ¼
2:6 and the row for D=F ¼ 2:5 should be used in
Table 7 and the column for D=F ¼ 2:5 should be used
in Table 8.
(b) If D ¼ $1:5B and F ¼ $1B; then use the row and
column in Tables 7 and 8 corresponding to D=F ¼ 1:5:
ARTICLE IN PRESS
Table 7
The impact of the primary HH-GB provision on LIHEAP
parameters
as a function of D=F for the appropriation level D ($B) and
trigger

level F ($B)
D=F sðD=FÞ rðD=FÞ iðD=FÞ pðD=FÞ qðD=FÞ #fHg #fNg
1.00 20.5 42.4 39.5 72.3 51.8 28 23
1.05 17.0 35.3 32.9 68.8 51.8 28 23
1.10 14.1 24.1 33.8 55.7 41.7 28 23
1.15 11.7 18.5 31.7 48.5 36.8 25 26
1.20 9.7 14.2 31.0 41.1 31.3 23 28
1.25 8.1 11.7 26.0 39.2 31.1 22 29
1.30 6.6 9.5 21.2 37.7 31.1 22 29
1.35 5.3 7.1 21.2 30.3 25.0 20 31
1.40 4.3 5.4 19.5 26.0 21.8 17 34
1.45 3.4 4.2 17.8 22.2 18.9 16 35
1.50 2.8 3.1 28.9 12.6 9.7 13 38
1.55 2.5 2.7 36.8 9.2 6.8 11 40
1.60 2.2 2.4 32.5 9.0 6.8 11 40
1.65 1.9 2.1 28.5 8.7 6.8 11 40
1.70 1.7 1.8 27.8 7.7 6.0 9 42
1.75 1.5 1.6 24.2 7.5 6.0 9 42

1.80 1.3 1.3 22.6 6.8 5.6 8 43
1.85 1.1 1.1 19.3 6.7 5.6 8 43
1.90 1.0 1.0 26.1 4.6 3.6 7 44
1.95 0.8 0.9 22.9 4.5 3.6 7 44
2.00 0.7 0.8 19.8 4.4 3.6 7 44
2.25 0.3 0.3 11.3 2.7 2.4 4 47
2.50 0.1 0.1 27.7 0.5 0.4 2 49
2.75 0.1 0.1 37.5 0.3 0.2 1 50
3.00 0.1 0.1 26.0 0.3 0.2 1 50
14581450
(c) If D ¼ $0:8B and F ¼ $0:75B; then D=F ¼ 1:067
and the row for D=F ¼ 1:05 should be used in Table 7
and the column entry for D=F ¼ 1:1 used in Table 8.
The impact of the primary HH-GB provision on
LIHEAP parameters sðD=FÞ; rðD=FÞ; iðD=FÞ; pðD=FÞ;
qðD=FÞ; #fHg and #fNg presented in Table 7 are
graphed in Figs. 4–6. In Table 8 the final LIHEAP
allocation percentages under the primary HH-GB
provision as a function of D=F is depicted. To determine
state allotment dollars for a given value of D and F;
compute D=F; retrieve the appropriate final allotment

ARTICLE IN PRESS
Table 8
Final LIHEAP allocation percentages under the primary HH-GB
provision as a function of D=F
State 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.5 3.0
Alabama 0.86 1.13 1.32 1.45 1.54 1.59 1.61 1.63 1.64 1.65 1.66
1.67 1.68
Alaska 0.55 0.50
a
0.46
a
0.42
a
0.39
a
0.37
a
0.36 0.36 0.36 0.36 0.36 0.36 0.36
Arizona 0.42 0.72 0.92 1.04 1.13 1.17 1.19 1.21 1.22 1.23 1.23
1.25 1.25
Arkansas 0.66 0.84 0.97 1.06 1.12 1.15 1.17 1.18 1.19 1.20 1.21
1.21 1.21

California 4.61 4.90 5.20 5.45 5.65 5.77 5.82 5.87 5.90 5.92
5.94 5.99 5.99
Colorado 1.61 1.46
a
1.34
a
1.24
a
1.15 1.15 1.14 1.14 1.14 1.15 1.15 1.15 1.15
Connecticut 2.10 1.91
a
1.75
a
1.61
a
1.50
a
1.40 1.39 1.39 1.39 1.39 1.39 1.40 1.40
Delaware 0.28 0.30 0.32 0.34 0.35 0.36 0.36 0.36 0.37 0.37 0.37
0.37 0.37
D.C. 0.33 0.30
a
0.27
a

0.27 0.26 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27
Florida 1.36 2.38 3.04 3.46 3.74 3.90 3.97 4.02 4.06 4.08 4.10
4.15 4.15
Georgia 1.08 1.64 2.02 2.27 2.43 2.52 2.57 2.60 2.62 2.64 2.65
2.68 2.68
Hawaii 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.12 0.12
0.12 0.12
Idaho 0.63 0.57
a
0.52
a
0.48
a
0.45
a
0.42
a
0.39
a
0.37
a
0.35
a

0.33
a
0.31
a
0.28 0.28
Illinois 5.81 5.29
a
5.13 5.11 5.15 5.19 5.21 5.23 5.24 5.25 5.26 5.29 5.30
Indiana 2.63 2.39
a
2.20 2.17 2.17 2.18 2.18 2.19 2.19 2.20 2.20 2.21 2.21
Iowa 1.86 1.69
a
1.55
a
1.43
a
1.33
a
1.24
a
1.22 1.22 1.22 1.22 1.22 1.22 1.22
Kansas 0.86 0.89 0.94 0.97 1.01 1.03 1.04 1.04 1.05 1.05 1.06

1.06 1.06
Kentucky 1.37 1.44 1.51 1.58 1.63 1.67 1.68 1.70 1.70 1.71
1.77 1.73 1.73
Louisiana 0.88 1.19 1.40 1.54 1.64 1.70 1.72 1.74 1.75 1.76
1.77 1.79 1.79
Maine 1.36 1.24
a
1.13
a
1.05
a
0.97
a
0.91
a
0.85
a
0.80
a
0.76
a
0.72
a
0.68

a
0.61 0.61
Maryland 1.61 1.78 1.92 2.04 2.12 2.17 2.19 2.21 2.22 2.23
2.24 2.26 2.26
Massachusetts 4.20 3.82
a
3.50
a
3.23
a
3.00
a
2.90 2.90 2.89 2.90 2.90 2.90 2.91 2.91
Michigan 5.51 5.01
a
4.74 4.69 4.70 4.73 4.74 4.76 4.77 4.78 4.79 4.81 4.82
Minnesota 3.97 3.61
a
3.31
a
3.06
a
2.84

a
2.65
a
2.48
a
2.34
a
2.21
a
2.09
a
1.99
a
1.68 1.68
Mississippi 0.74 1.14 1.41 1.58 1.70 1.76 1.79 1.82 1.83 1.84
1.85 1.87 1.87
Missouri 2.32 2.23 2.24 2.27 2.31 2.35 2.36 2.37 2.38 2.39 2.39
2.41 2.41
Montana 0.74 0.67
a
0.61
a
0.57
a

0.53
a
0.49
a
0.46
a
0.43
a
0.41
a
0.39
a
0.37
a
0.35 0.35
Nebraska 0.92 0.84
a
0.77
a
0.71
a
0.66
a

0.61
a
0.58
a
0.55 0.55 0.55 0.55 0.55 0.55
Nevada 0.20 0.31 0.38 0.43 0.46 0.48 0.49 0.49 0.50 0.50 0.50
0.51 0.51
New Hampshire 0.79 0.72
a
0.66
a
0.61
a
0.57
a
0.53
a
0.50
a
0.47
a
0.45 0.45 0.45 0.45 0.45
New Jersey 3.90 3.54
a

3.26 3.21 3.21 3.22 3.23 3.24 3.24 3.25 3.26 3.27 3.27
New Mexico 0.52 0.50 0.50 0.51 0.52 0.52 0.53 0.53 0.53 0.53
0.54 0.54 0.54
New York 12.72 11.57
a
10.60
a
9.79
a
9.09
a
8.66 8.63 8.63 8.63 8.63 8.63 8.66 8.67
North Carolina 1.90 2.28 2.56 2.76 2.90 2.99 3.03 3.06 3.08
3.09 3.10 3.13 3.13
North Dakota 0.80 0.73
a
0.67
a
0.62
a
0.57
a
0.53

a
0.50
a
0.47
a
0.44
a
0.42
a
0.40
a
0.32
a
0.27
a
Ohio 5.14 4.74
a
4.64 4.65 4.70 4.74 4.76 4.78 4.80 4.81 4.82 4.85 4.85
Oklahoma 0.79 0.95 1.07 1.15 1.21 1.25 1.26 1.28 1.28 1.29
1.30 1.31 1.31
Oregon 1.25 1.13
a
1.04
a

0.96
a
0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.95 0.95
Pennsylvania 6.84 6.21
a
5.70
a
5.26
a
5.12 5.10 5.10 5.11 5.11 5.12 5.13 5.15 5.15
Rhode Island 0.69 0.63
a
0.58
a
0.53
a
0.49
a
0.47 0.46 0.46 0.46 0.46 0.46 0.47 0.47
South Carolina 0.68 0.94 1.12 1.24 1.31 1.36 1.38 1.40 1.41
1.42 1.42 1.44 1.44
South Dakota 0.65 0.59
a

0.54
a
0.50
a
0.46
a
0.43
a
0.41
a
0.38
a
0.36
a
0.34
a
0.32
a
0.29 0.29
Tennessee 1.39 1.58 1.74 1.85 1.94 1.99 2.01 2.03 2.04 2.05
2.06 2.08 2.08
Texas 2.26 3.84 4.86 5.52 5.95 6.20 6.31 6.39 6.45 6.49 6.52
6.58 6.59

Utah 0.75 0.68
a
0.62
a
0.58
a
0.54 0.54 0.53 0.53 0.54 0.54 0.54 0.54 0.54
Vermont 0.60 0.54
a
0.50
a
0.46
a
0.43
a
0.40
a
0.37
a
0.35
a
0.33
a
0.31

a
0.30
a
0.24
a
0.23
a
Virginia 1.96 2.28 2.53 2.71 2.84 2.92 2.95 2.98 3.00 3.01 3.02
3.05 3.05
Washington 2.05 1.86
a
1.71
a
1.58
a
1.49 1.49 1.48 1.48 1.49 1.49 1.49 1.49 1.49
West Virginia 0.91 0.88 0.88 0.90 0.92 0.93 0.93 0.94 0.95 0.95
0.95 0.95 0.96
Wisconsin 3.58 3.25
a
2.98
a
2.75
a

2.55
a
2.38
a
2.24
a
2.10
a
1.99
a
1.93 1.93 1.93 1.93
Wyoming 0.30 0.27
a
0.25
a
0.23
a
0.21
a
0.20
a
0.19
a

0.18 0.18 0.18 0.18 0.18 0.18
a
Designates membership in H:
1458 1451
percentage depicted in Table 8, and then multiply by the
value of D:
AiðD=FÞ ¼ DaiðD=FÞ:
The functionals sðD=FÞ; pðD=FÞ; and qðD=FÞ are
defined in terms of the regular appropriation D; while
rðD=FÞ is defined in terms of the money allocated to the
states that fall within the set fNg: When D=F ¼ 1 þ E;
the 28 states in fHg control 72% of the total funds
allocated to the program, and as D increases, pðF; DÞ ¼
H=D declines since the number of states within fHg will
decrease and with it the amount of money that fHg
controls. This is shown in Fig. 4. At D=F ¼ 1:15;
roughly half of the states control half of the total
appropriation. The value of qðF; DÞ ¼ G=D represents
the proportion of funds that the states fHg would
control without the HH-GB provision. The difference
between pðF; DÞ and qðF; DÞ—equivalent to sðF; DÞ—
represents the distortion of the 1984 formula in
percentage terms relative to the total appropriation.
In Fig. 5 the impact of the primary HH-GB provision on
the functional rðD=FÞ represents the percentage reduc-
tion in the funding allocation to fNg due to the HH-GB
provision. The counting functions #fHg and #fNg

count the number of elements of fHg and fNg and is
depicted in Fig. 6. The counting functionals are mirror
images of one another since #fHg þ #fNg ¼ 51; and as
D=F increases, #fHg-0 and fNg-fSg:
6.3. Regional distribution
The state allocation percentages depicted in Table 8
are aggregated according to region and presented
ARTICLE IN PRESS
0
10
20
30
40
50
60
70
80
1
1.
1
1.
2
1.
3
1.
4
1.

5
1.
6
1.
7
1.
8
1.
9 2
D/F
P
e
rc
e
n
ta
g
e
o
f
D
(
%

)
s (D/F) p (D/F) q (D/F)
Fig. 4. Impact of the primary HH-GB provision on LIHEAP
functionals sðD=FÞ; pðD=FÞ; and qðD=FÞ:
0
10
20
30
40
50
1
1.
1
1.
2
1.
3
1.
4
1.
5
1.

6
1.
7
1.
8
1.
9 2
D/F
P
e
rc
e
n
ta
g
e
(
%
)
r (D/F)
Fig. 5. Impact of the primary HH-GB provision on LIHEAP
functional rðD=FÞ:
0

10
20
30
40
50
60
1
1
.1
5
1
.3
1
.4
5
1
.6
1
.7
5

1
.9
2
.0
5
2
.2
2
.3
5
2
.5
2
.6
5
2
.8
2
.9
5
D/F
N
u

m
b
e
r
o
f
S
ta
te
s
#{H} #{N}
Fig. 6. Impact of the primary HH-GB provision on the LIHEAP
counting functionals #fHg and #fNg:
14581452
graphically in Fig. 7 as a function of D=F: The limits of
the distribution for the 1981 formula allotment
ðD=Fp1Þ and the 1984 allotment ðD=FX1:5Þ represent
the endpoints of the graph and were described
previously in Table 6. As the ratio D=F increases federal
allocation percentage in the Northeast and North
Central regions are reallocated to the South, while the
Western region maintains an essentially constant allot-
ment percentage over the entire range of D=F: As D=F

exceeds 1.5 the allotment percentages stabilize as the
impact of the HH-GB provision significantly declines.
Recall from Table 7 that when D=F ¼ 1:5 less than 3%
of the regular appropriation is required to satisfy the
HH provision.
7. Allotment block procedure
An alternative approach to distribute funds that does
not depend on selecting a specific value of F is to ‘‘set-
aside’’ a given percentage of the regular appropriation
to be used with the 1981 formula and then to apply the
1984 formula to the remaining funds. This mechanism
does not hold states harmless in the sense described by
the LIHEAP statute or in the trigger-level re-adjust-
ment, but can be correlated with these allotment
procedures using an approximating algebraic correspon-
dence.
If the percentage of funds allocated through the 1981
formula is denoted by r; then a state’s allotment dollars
for a given fiscal year is given by
AiðrÞ ¼ rDfi þ ð1 � rÞDgi
and its allotment percentage is ai ¼ Ai=D or
aiðrÞ ¼ rfi þ ð1 � rÞgi; 0oro1:
The allotment percentage is a linear combination of fi
and gi and so aðrÞ ¼ ða1; y; a51Þ is an allotment
percentage sinceX
aiðrÞ ¼
X

ðrfi þ ð1 � rÞgiÞ
¼ r
X
fi þ ð1 � rÞ
X
gi ¼ 1:
The value of aðrÞ as a function of r is shown in Table 9.
ARTICLE IN PRESS
0
5
10
15
20
25
30
35
40
1
1.
05 1.

1
1.
15 1.
2
1.
25 1.
3
1.
35 1.
4
1.
45 1.
5
D/F
P
e
rc
e
n
ta
g
e
(
%

)
Northeast
North Central
South
West
Fig. 7. Regional distributional of funds.
Table 9
Weighted linear combination of the 1981 and 1984 formula,
aiðrÞ ¼
rfi þ ð1 � rÞgi
State r
0.2 0.4 0.5 0.6 0.8
Alabama 1.51 1.35 1.27 1.19 1.02
Alaska 0.40 0.44 0.45 0.47 0.51
Arizona 1.08 0.92 0.83 0.75 0.58
Arkansas 1.11 0.99 0.93 0.88 0.77
California 5.72 5.44 5.30 5.17 4.89
Colorado 1.24 1.33 1.38 1.43 1.52
Connecticut 1.54 1.68 1.75 1.82 1.96

Delaware 0.35 0.33 0.33 0.32 0.30
D.C. 0.28 0.29 0.30 0.30 0.31
Florida 3.59 3.04 2.76 2.48 1.92
Georgia 2.36 2.04 1.88 1.72 1.40
Hawaii 0.11 0.11 0.11 0.11 0.11
Idaho 0.35 0.42 0.45 0.49 0.56
Illinois 5.40 5.50 5.55 5.60 5.71
Indiana 2.30 2.38 2.42 2.46 2.55
Iowa 1.35 1.48 1.54 1.61 1.74
Kansas 1.02 0.98 0.96 0.94 0.90
Kentucky 1.66 1.59 1.55 1.51 1.44
Louisiana 1.61 1.43 1.33 1.24 1.06
Maine 0.76 0.91 0.99 1.06 1.21
Maryland 2.13 2.00 1.93 1.87 1.74
Massachusetts 3.17 3.43 3.55 3.68 3.94
Michigan 4.96 5.10 5.17 5.24 5.38
Minnesota 2.14 2.60 2.83 3.06 3.51
Mississippi 1.65 1.42 1.30 1.19 0.96

Missouri 2.39 2.38 2.37 2.36 2.34
Montana 0.43 0.50 0.54 0.58 0.66
Nebraska 0.62 0.70 0.73 0.77 0.85
Nevada 0.44 0.38 0.35 0.32 0.26
New Hampshire 0.52 0.59 0.62 0.66 0.73
New Jersey 3.40 3.52 3.59 3.65 3.77
New Mexico 0.54 0.53 0.53 0.53 0.52
New York 9.48 10.29 10.70 11.10 11.91
North Carolina 2.89 2.64 2.52 2.39 2.14
North Dakota 0.33 0.45 0.51 0.56 0.68
Ohio 4.91 4.97 5.00 5.02 5.08
Oklahoma 1.20 1.10 1.05 1.00 0.89
Oregon 1.01 1.07 1.10 1.13 1.19
Pennsylvania 5.49 5.82 5.99 6.16 6.50
Rhode Island 0.51 0.56 0.58 0.60 0.65
South Carolina 1.29 1.14 1.06 0.98 0.83
South Dakota 0.36 0.43 0.47 0.51 0.58
Tennessee 1.94 1.80 1.73 1.66 1.53

Texas 5.73 4.86 4.43 4.00 3.13
Utah 0.58 0.62 0.64 0.66 0.71
Vermont 0.30 0.37 0.41 0.45 0.52
Virginia 2.83 2.61 2.50 2.39 2.18
Washington 1.61 1.72 1.77 1.83 1.94
West Virginia 0.95 0.94 0.93 0.93 0.92
Wisconsin 2.26 2.59 2.75 2.92 3.25
Wyoming 0.20 0.23 0.24 0.25 0.28
1458 1453
7.1. The correspondence between aðD=FÞ and aðrÞ
A useful exercise is to correlate the values of aðrÞ and
aðD=FÞ; that is, for a given value of D=F determine the
value of r such that aðrÞ achieves an allocation
percentage ‘‘equivalent’’ to aðD=FÞ: The limits of the
relation are obvious:
lim
D=F-N
aiðD=FÞ ¼ gi ¼ lim
r-0
aiðrÞ;

lim
D=F-1
aiðD=FÞ ¼ fi ¼ lim
r-1
aiðrÞ
and so we are interested in the correspondence between
aðD=FÞ and aðrÞ for 0oro1: A correspondence using a
least-squares criteria is derived in Theorem 4.
Theorem 5. For a given value of D=F; the final allocation
percentages specified by aðD=FÞ correspond to aðrÞ ¼
rf þ ð1 � rÞg for the least-squares estimator
r ¼ rðD=FÞ ¼
P
aiðD=FÞðfi � giÞ �
P
giðfi � giÞP
ðfi � giÞ
2
Proof. See Appendix C.
The correspondence between aðD=FÞ and aðrÞ is
determined through the value of rðD=FÞ shown in
Fig. 8 and provides a useful means to interpret the
HH condition in terms of a simple (linear) allocation
mechanism. For example, when D=F ¼ 1:3; the value of
r that ‘‘equates’’ aðD=FÞ in the least-squares sense with

aðrÞ is given by r ¼ 0:25; or in other words, when D=F ¼
1:3; the allocation mechanism determined through
Option B is roughly equivalent to taking 25% of the
1981 formula values plus 75% of the 1984 formula
values g: The main use of Fig. 8 is as a tool to establish
the relation between competing alternative policies:
* For a given value of D=F; the user can determine how
the average state HH allotment aðD=FÞ distributes
funds in terms of the allocation mechanism aðrÞ ¼
rf þ ð1 � rÞg:
* Since the value of aðrÞ and aðD=FÞ are equivalent
under the derived correspondence, the fairness
criteria employed for aðD=FÞ translates to aðrÞ under
rðD=FÞ:
* A decision maker that can determine a range of
acceptable percentage values for the contribution of f
to the final allotment mechanism can use the
functional rðD=FÞ to determine acceptable D=F
ratios.
7.2. Induced hold-harmless allotment percentages
To illustrate one application of the correspondence
the allotment percentage induced through a reduced
trigger level is computed.
The correspondence functional rðD=FÞ describes the
percentage of the HH provision funding that is allocated
according to the 1981 formula. Hence, using the
correspondence we can determine the effective weight
of the 1981 formula as a function of the trigger level.
Given rðD=FÞ and the historic LIHEAP funding levels
from 1981–2002, the ratio D=F is computed each year

based on the regular appropriation D and trigger level
F; rðD=FÞ is computed, and then the average value of
rðD=FÞ reported:
/rðD=FÞS ¼
P2002
t¼1981 rðD=F; tÞ
21
:
The value /rðD=FÞS describes the expected contribu-
tion of the 1981 formula allotment to the final allotment
percentages for a given value of F:
In Fig. 9 the contribution of the 1981 formula to the
final allotment percentages as a function of the
trigger level F is shown. Since the current trigger
level is F ¼ $1:975B; Fig. 9 illustrates that 98% of
the LIHEAP funds has effectively been allocated based
on the 1981 formula, with 2% of the funds allocated
using the 1984 formula. If F ¼ $1B; then based on
historic levels of LIHEAP funding, 28% of federal
dollars would have been allocated using the 1981
formula with the remaining 72% allocated with the
1984 formula.
ARTICLE IN PRESS
0
0.2
0.4

0.6
0.8
1
1.2
1
1.
1
1.
2
1.
3
1.
4
1.
5
1.
6
1.
7
1.
8
1.
9 2

D/F
r
(%
)
Fig. 8. The correspondence between aðD=FÞ and aðrÞ:
0
0.2
0.4
0.6
0.8
1
1.2
1.975 1.75 1.5 1.25 1 0.75 0.5 0.25
F ($B)
r
(%
)
Fig. 9. Induced allotment percentage of the HH-GB provision
based
on LIHEAP funding levels, 1981–2002.
14581454

7.3. Re-interpreting the primary hold-harmless provision
The LIHEAP allocation percentages under the
primary HH provision (Option B) can be interpreted
in a manner analogous to the allotment block proce-
dure. Recall that for states iAfNg;
AiðF; DÞ ¼ Ffi þ Ei ¼ Ffi þ gðDgi � FfiÞ
¼ ð1 � gÞFfi þ gDgi
or
aiðF; DÞ ¼ ð1 � gÞkfi þ ggi;
where k ¼ F=D and g ¼ X =Q: For a given value of D >
F; ko1; and so the term kfi represents a reduction in
the 1981 formula percentage. As D increases, k
approaches zero while the term g approaches one (recall
Theorem 1), indicating that the contribution to aiðF; DÞ
from fi will approach zero. The LIHEAP allocation
percentages in Option B is thus similar in structure to
the allotment block procedure, but while the parameter r
is a decision parameter, the value of k and g is dependent
on D=F and is not controllable unless the ratio D=F is
legislated.
8. Simplified legislative road map
The main issues surrounding the LIHEAP debate are
summarized as follows:
* The 1981 distribution formula is not an appropriate

baseline.
* Corporate scandals are sexy and good publicity
issues, while government ‘‘scandals’’ resist debate.
* Impetus to change LIHEAP will always be an uphill
struggle since the votes for change simply do not add
up for any of the alternatives described.
* Full ‘‘disclosure’’ and transparency may help lead to
change.
* Shame is a good motivator for change.
* Arguments should be based on essential facts and a
clear storyline.
A legislative ‘‘road map’’ of sorts is suggested to help
push LIHEAP along in the right direction. Since a
simple count of votes is not expected to add up in favor
of changing the LIHEAP allocation mechanism, the
story presented must be moral tale and based on
established facts. Shame is used as the primary
motivator for change.
Fact 1: The high trigger level established within the
1984 re-authorization legislation has disabled the
application of the 1984 formula.
Shame/result: The 1981 formula is still being used to
distribute LIHEAP funding to this day (inequitable
program).
Fact 2: The 1981 formula allotments hold little
meaning 20 years after their creation and should not
be used to distribute federal dollars.

Shame/result: LIHEAP allotments to states are not
distributed in a rational manner (poorly executed
program).
Fact 3: The primary intent of LIHEAP is to assist
low-income households meet their home energy needs.
Shame/result: LIHEAP funds are not being distrib-
uted in accord with the program intent (irrational
program).
9. Conclusions
The purpose of this paper was to propose policy
alternatives for distributing LIHEAP funds to states and
to quantify the impact of each alternative. Three policy
alternatives were examined.
In the first alternative, the LIHEAP trigger level is
nullified and the HH-GB provisions attached to the
allocation are eliminated. The 1984 formula is applied in
‘‘pure’’ form unencumbered by the weight of additional
provisions or conditions. This policy alternative paral -
lels the Bush Administration position expressed in the
FY 2003 federal budget and is the simplest and probably
the best of the three options considered, although it is
not expected to develop the political support necessary
to achieve passage.
In the second alternative, the primary HH-GB
provision of the LIHEAP statute is maintained but the
trigger level when it is enabled is reduced. Regular
appropriations for LIHEAP generally do not exceed the
current trigger F ¼ $1:975B; and in fact, have only
exceeded this level twice in the past 17 years—the last

time in FY 1986. At one time (15-years ago) the values
of D and F were roughly comparable, while today F
appears as a large (mostly unattainable) upper bound.
Reducing the current trigger level increases the like-
lihood that the 1984 formula will be applied, and since
this alternative does not involve the complete disman-
tling of the legislative statute, it is also likely to garner
more political support. It should be mentioned, how -
ever, that even under this alternative a majority of states
are still worse off under the new allocation percentages,
and hence, even the passage of compromise legislation
might fail to generate sufficient support. Legislation that
sponsors a trigger-level reduction must be crafted to
ensure the reduction is significant or further drift
between D and F may result in the future. Re-adjusting
F downward may yield the desired outcome, but from a
programmatic perspective, also perpetrates the applica-
tion/justification of the 1981 formula, which is con-
sidered a major drawback.
In the third alternative, a simple allocation mechan-
ism was examined that set-aside a given percentage of
ARTICLE IN PRESS
1458 1455
the regular appropriation to be used exclusively with the
1981 formula with the remaining funds allocated under
the 1984 formula. The advantage of this mechanism is
that the 1984 formula will always be incorporated within
the allotment procedure regardless of the level of regular
appropriation, and hence the downside risk (i.e., when
DpF ) is always covered. On the other hand, it may be

difficult to negotiate the value of r; and once selected, r
fixes the allotment percentages and does not allow the
upside potential of the 1984 formula (i.e., when D > F )
to be realized. Since the upside potential of the 1984
formula has only a low probability of occurrence,
however, this does not seem to be an extenuating factor.
‘‘Mixing’’ the formula allocations is also not a preferred
procedure from a legislative or methodological perspec-
tive, although as shown in Theorem 4, a correspondence
does exists between the mixed formula and the triggered
hold-harmless provision. Hence, the user can always
view the allotment block procedure in terms of a trigger-
level enabled mechanism.
Acknowledgements
The authors would like to acknowledge the role
Carolyn Drake had in introducing the LIHEAP
problem to the authors and suggesting its initial
formulation. Her encouragement, guidance, and pa-
tience is kindly recognized. The authors would also like
to thank Kathy Baskin, Elizabeth Jones, Beth Osborne,
Ed Rissing, and Fred Zeytoonjian for their support,
insight, and useful criticisms of this work. Funding for
this research was provided in part by the Southern
States Energy Board, but all opinions, findings, and
results remain the responsibility of the authors.
Appendix A. Derivation of the LIHEAP structure
equations
the primary HH-GB provision yields state allotments

according to the following recipe:
AiðF; DÞ ¼
Dfi; iAfSg; DpF;
Ffi; iAfHg; D > F;
Ffi þ Ei; iAfNg; D > F;
8><
>:
where fSg ¼ fHg,fNg; fHg ¼ fi j Ffi=Dgi > 1g;
fNg ¼ fi j Ffi=Dgip1g; Ei ¼ gðDgi � FfiÞ; g ¼ X =Q;
X ¼ D � F; and Q ¼
P
iAfNg ðDgi � FfiÞ:
Proof. If DpF; then following the current LIHEAP
statute, AiðF; DÞ ¼ Dfi for all iAfSg: If D > F; then
partition fSg into two sets according to whether state i
satisfies Ffi > Dgi or FfipDgi: The class of states labeled
fHg ¼ fi j Ffi=Dgi > 1g are the HH states which are held
at their statutory floor. The class of states labeled fNg ¼
fi j Ffi=Dgip1g will have an allotment falling above
their floor. All states in fHg are assigned their statutory
floor, while states in fNg are assigned their statutory
floor plus an amount Ei that needs to be determined
AiðF; DÞ ¼
Ffi; iAfHg;
Ffi þ Ei; iAfNg:

(
Since statutory floors are maintained across all states,
the HH-GB provision in essence captures F of the
regular appropriated dollars D:
D ¼
X
iAfSg
AiðF; DÞ ¼
X
iAfHg
Ffi þ
X
iAfNg
ðFfi þ EiÞ
¼
X
iAfHg
Ffi þ
X
iAfNg
Ffi þ
X

iAfNg
Ei
¼ F
X
iAfSg
fi þ
X
iAfNg
Ei ¼ F þ
X
iAfNg
Ei:
The value
X ¼
X
iAfNg
Ei ¼ D � F
represents the dollars available to the states in fNg after
the statutory floor money is assigned to all the states in
fSg:
To determine the extra allotment that each state in
fNg receives, state i’s allotment ‘‘above the floor’’

Dgi � Ffi; iAfNg
is computed, and since
Q ¼
X
iAfNg
ðDgi � FfiÞ > X ;
the value of Q will need to be reduced so that it matches
the available funds X : The value of X is thus a binding
constraint. The reduction factor g ¼ X =Q is applied
across each state’s money above the floor, and the value
of Ei is calculated as
Ei ¼ gðDgi � FfiÞ:
Observe that the sum of the ‘‘extra’’ state allotments is by
construction equal to the available funds X as required:X
iAfNg
Ei ¼ g
X
iAfNg
ðDgi � FfiÞ
¼
X
Q

X
iAfNg
ðDgi � FfiÞ ¼ X : &
the primary HH-GB yields the following limiting relations:
lim
D=F-1
aiðF; DÞ ¼ fi;
lim
D=F-N
aiðF; DÞ ¼ gi:
ARTICLE IN PRESS
14581456
Proof. By the definition of the allocation mechanism,
when D=F-1; it is clear that
lim
D=F-1
aiðF; DÞ ¼ fi; iAfSg:
On the other hand, as the ratio D=F increases it is clear
that #fHg-0 and fNg-fSg: Then since Q ¼P

iAfNg ðDgi � FfiÞ;
lim
D=F-N
X
iAfNg
ðDgi � FfiÞ ¼
X
iAfSg
ðDgi � FfiÞ
¼ D
X
iAfSg
gi � F
X
iAfSg
fi ¼ D � F;
i.e.,
lim
D=F-N
g ¼ lim
D=F-N
X

Q
¼
D � F
D � F
¼ 1:
Then since AiðF; DÞ ¼ Ffi þ Ei ¼ Ffi þ gðDgi � FfiÞ ¼
ð1 � gÞFfi þ gDgi;
lim
D=F-N
AiðF; DÞ ¼ lim
g-1
½ð1 � gÞFfi þ gDgi
¼ Dgi
or
lim
D=F-N
aiðF; DÞ ¼
AiðF; DÞ
D
¼ gi: &
Appendix B. One-dimensional LIHEAP system measures
Theorem 3. For D > F; the LIHEAP allocation mechan-
ism under the primary HH-GB provision yield state

allotment percentages
aiðF; DÞ ¼
F
D
fi; iAfHg;
F
D
fi þ
Ei
D
; iAfNg
(
that are functions of the ratio F/D.
Proof. Let k ¼ F=Da0: It is sufficient to show that
aiðF; DÞ is a constant:
(i) If iAfHg; then aiðF; DÞ ¼ ðF=DÞfi ¼ kfi; which is a
constant since fi is constant.
(ii) If iAfNg; then aiðF; DÞ ¼ ðF=DÞfi þ ðEi=DÞ ¼ kfi þ
ðEi=DÞ:
It is sufficient to show Ei=D is constant.
Ei
D
¼

X
DQ
ðDgi � FfiÞ ¼
X
Q
gi �
F
D
fi
�
¼
X
Q
ðgi � kfiÞ ¼ k
0 X
Q
;
where k0 ¼ gi � kfi is constant since gi is constant. Now
X =Q ¼ X =D=Q=D and
X
D
¼

D � F
D
¼ 1 �
F
D
¼ 1 � k
a constant, and
Q
D
¼
D
P
iAfNg gi � F
P
iAfNg fi
D
¼
X
iAfNg
gi �
F
D

X
iAfNg
fi ¼
X
iAfNg
gi � k
X
iAfNg
fi:
The summation terms
P
iAfNg fi;
P
iAfHg fi;
P
iAfNg gi;
and
P
iAfHg gi are all constant since the elements of
fHg ¼ i j
Ffi
Dgi
> 1

�
¼ i j k
fi
gi
> 1
�
;
fNg ¼ i j
Ffi
Dgi
p1
�
¼ i j k
fi
gi
p1
�
are constant, and so Q=D is constant, and thus, X =Q is
constant. Hence, aiðF; DÞ is a constant and can be
expressed as aiðF=DÞ; or equivalently, since k ¼
F=Da0; as aiðD=FÞ: &

Theorem 4. The LIHEAP system measures
sðF; DÞ; iðF; DÞ; and rðF; DÞ can be expressed in terms
of the ratio D=F as sðD=FÞ; iðD=FÞ; and rðD=FÞ:
Proof. Let k ¼ F=Da0: It suffices to show that
sðF; DÞ; iðF; DÞ; and rðF; DÞ are constants. By definition
of the functionals sðF; DÞ; iðF; DÞ; and rðF; DÞ;
sðF; DÞ ¼
H � G
D
¼
H
D
�
G
D
¼
F
P
iAfHg fi
D
�
D
P

iAfHg gi
D
¼ k
X
iAfHg
fi �
X
iAfHg
gi;
is a constant, and so sðF; DÞ can be expressed in terms of
the ratio sðD=FÞ: Similarly,
iðF; DÞ ¼
H � G
G
¼
H
G
� 1
¼
F
P
iAfHg fi

D
P
iAfHg gi
� 1 ¼ k
P
iAfHg fiP
iAfHg gi
� 1
a constant, and
rðF; DÞ ¼
H � G
M
¼
H
M
�
G
M
¼
F
P
iAfHg fi
D

P
iAfNg gi
�
D
P
iAfHg gi
D
P
iAfNg gi
¼ k
P
iAfHg fiP
iAfNg gi
�
P
iAfHg giP
iAfNg gi
a constant, and so iðF; DÞ and rðF; DÞ can be expressed
as iðD=FÞ and rðD=FÞ: &
Appendix C. Derivation of the least-squares estimator
Theorem 5. For a given value of D/F, the final allocation
percentages specified by aðD=FÞ correspond to aðrÞ ¼
ARTICLE IN PRESS

1458 1457
rf þ ð1 � rÞg for the least-squares estimator
r ¼ rðD=FÞ ¼
P
P
giðfi � giÞP
ðfi � giÞ
2
:
Proof. For a given value of the ratio D=F; the value of r
that minimizes the sum of the squared differences
between aðD=FÞ and aðrÞ is determined as follows. Let
f ðrÞ ¼
X
ðaiðD=FÞ � aiðrÞÞ
2:
Then the solution to minr f ðrÞ is determined by solving
dðf ðrÞÞ=dr ¼ 0 orX
ðaiðD=FÞ � aiðrÞÞ
daiðrÞ
dr

¼ 0:
Since aiðrÞ ¼ rfi þ ð1 � rÞgi; dðaiðrÞÞ=dr ¼ fi � gi; and
solving for r yields
r ¼
P
P
giðfi � giÞP
ðfi � giÞ
2
:
The second-derivative test yields
d
2
f ðrÞ
dr
¼ �
daiðrÞ
dr
� 2
o0
ensuring that r is a minimum value of f ðrÞ: &
References

Abbey, C.W., 2001. The low-income home energy assistance
program:
how are state allotments determined? CRS Report RS 20893,
Washington, D.C., April.
Colton, R., 1990. Client consumption patterns within an
income-based
energy assistance program. Journal of Economic Issues 24 (4),
1079–1093.
General Accounting Office, US Congress, 1986. Low Income
Energy
Assistance: state responses to 1984 amendments. Report to
Congressional Committees, GAO/HRD-86-92, Washington,
D.C., May.
General Accounting Office, US Congress, 1987. Energy
conservation:
funding state energy assistance programs. Fact Sheet for the
Ranking Minority Member, Committee on the Budget, United
State Senate, GAO/RCED-87-114FS, Washington, D.C., March.
General Accounting Office, US Congress, 1990. Low Income
Home
Energy Assistance: a program overview. Briefing Report to the

Chairman, Subcommittee on Human Resources, Committee on
Education and Labor, House of Representatives, GAO/HRD-91-
1-BR, Washington, D.C., October.
Gish, M., 2000. The low-income home energy assistance
program.
CRS Report 94-211, Washington, D.C., June.
Higgins, L., Lutzenhiser, L., 1995. Ceremonial equity: low -
income
energy assistance and the failure of socio-environmental policy.
Social Problems 42 (4), 468–492.
Kennedy, J.M., 1987. Public support for residential energy
assistance.
Sociology and Social Research 71, 308–311.
Kingsley, G.A., 1992. US energy conservation policy: themes
and
trends. Policy Studies Journal 20, 114–123.
Landsberg, H.H., Dukert, J.M., 1981. High Energy Costs:
Uneven?
Unfair? Unavoidable? Johns Hopkins University Press,
Baltimore,
MD.

Low Income Home Energy Assistance Programs, 1983. Report
to
Congress For Fiscal Year 1982, US Department of Human
Services, Administration for Children and Families, Office of
Community Services, Division of Energy Assistance, November.
to
Community Services, Division of Energy Assistance, May.
to
Community Services, Division of Energy Assistance, October.
to
Community Services, Division of Energy Assistance,

September.
Pataki, G.E. (Governor), 2001. Statement of the Coalition of
Northeastern Governors to the House Appropriations Subcom-
mittee on Interior and Related Agencies regarding FY 2002
appropriations for the US Department of Energy’s
Weatherization
Assistance Program and State Energy Program, April 16.
Patton, P., Hodges, J. (Governors), 2001. Resolution regarding
the
national energy policy. Southern Governors’ Association 67th
Annual Meeting, Lexington, KY, September 9.
Stoltzfus, E., 2002. The low-income home energy assistance
program
(LIHEAP). CRS Report 94-211, Washington, D.C., January.
ARTICLE IN PRESS
14581458
CRS Report for Congress
Prepared for Members and Committees of Congress

The LIHEAP Formula: Legislative History and
Current Law
Libby Perl
Specialist in Housing Policy
September 8, 2010
Congressional Research Service
7-5700
www.crs.gov
RL33275
The LIHEAP Formula: Legislative History and Current Law
Summary
The Low Income Home Energy Assistance Program (LIHEAP)
provides funds to states, the
District of Columbia, U.S. territories and commonwealths, and
Indian tribal organizations
(collectively referred to as grantees) primarily to help low -
income households pay home energy
expenses. The LIHEAP statute provides for two types of
funding: regular funds (sometimes
referred to as block grant funds) and emergency contingency
funds. Regular funds are allocated to
grantees based on a formula, while contingency funds may be
released to one or more grantees at

the discretion of the Secretary of the Department of Health and
Human Services based on
emergency need.
Regular LIHEAP funds are allocated to the states according to a
formula that has a long and
complicated history. (Tribes receive funds based on either their
number of federally eligible
LIHEAP households compared to the total number in the state
or on agreements with their states,
whereas territories receive a set percentage of total LIHEAP
regular funds.) In 1980, Congress
created the predecessor program to LIHEAP, the Low Income
Energy Assistance Program
(LIEAP) as part of the Crude Oil Windfall Profits Tax Act (P.L.
96-223). Because Congress was
particularly concerned with the high costs of heating, funds
under LIEAP were distributed
according to a multi-step formula that benefitted cold-weather
states. In 1981, Congress enacted
LIHEAP as part of the Omnibus Budget Reconciliation Act
(P.L. 97-35), replacing LIEAP.
However, the LIHEAP statute specified that states would
continue to receive the same percentage
of regular funds that they did under the LIEAP formula.
When Congress reauthorized LIHEAP in 1984 as part of the
Human Services Reauthorization Act
(P.L. 98-558), it changed the program’s formula by requiring
the use of more recent population
and energy data and requiring that HHS consider both heating
and cooling costs of low-income
households (a change from the focus on the heating needs of all
households). The effect of these
changes meant that, in general, funds would be shifted from
cold-weather states to warm-weather

states. To prevent a dramatic shift of funds, Congress added two
“hold-harmless” provisions to
the formula. The result of these provisions is a current law,
three-tiered formula (sometimes
referred to as the “new” formula), the application of which
depends on the amount of regular
funds that Congress appropriates.
The Tier I formula is used to allocate funds when the total
LIHEAP regular fund appropriation is
less than or equal to the equivalent of a hypothetical FY1984
appropriation of $1.975 billion.
Above this level, funds are allocated according to Tier II of the
formula, which includes a hold-
harmless level to prevent certain states from losing LIHEAP
funds. Finally, Tier III applies to
appropriations at or above $2.25 billion, and includes a second
hold-harmless provision, the hold-
harmless rate. Since FY1986, LIHEAP regular fund
appropriations have exceeded the equivalent
of an FY1984 appropriation of $1.975 billion in FY2006, when
the regular fund appropriation
was $2.48 billion; in FY2008, when appropriations slightly
exceeded the trigger; and in FY2009
and FY2010, when Congress directed that $840 million be
distributed according to the “new”
LIHEAP formula.
This report will be updated when new formula data are released
and when proposed funding
levels change (see Appendix C).

Contents
Introduction
...............................................................................................
................................. 1
Predecessor Programs to LIHEAP
...............................................................................................
2
Community Services Administration Energy Assistance
Programs......................................... 2
Low Income Energy Assistance Program (LIEAP)
................................................................ 5
The LIEAP
Formula..................................................................................
...................... 6
Enactment of LIHEAP
...............................................................................................
................. 8
Continued Use of the LIEAP Formula
................................................................................... 9
The 1984 LIHEAP Reauthorization: A New Formula
............................................................ 9
Formula Discussions
...............................................................................................
........ 9
Introduction of a Hold-Harmless
Level.......................................................................... 10
Introduction of a Hold-Harmless Rate

........................................................................... 10
LIHEAP Formula Statutory Language
........................................................................... 11
Determining LIHEAP Regular Fund Allotments Using the
“New” Formula ............................... 12
Calculating the New Formula Rates
.................................................................................... 12
Using the New Formula Rates to Allocate Funds to the States
............................................. 14
Tier I: Below $1.975
Billion....................................................................................
...... 15
Tier II: From $1.975 Billion up to $2.25 Billion
............................................................ 15
Tier III: At or Above $2.25 Billion
................................................................................ 16
Implementation of the “New” LIHEAP Formula
................................................................. 17
Figures
Figure B-1. Estimated Low Income Home Energy Assistance
(LIHEAP) Allocations at
Various Hypothetical Appropriations Levels for Three Types of
States ................................... 27
Tables
Table 1. Select Energy Assistance Formulas, FY1975-FY1980
.................................................... 4
Table 2. Distribution of Funds Under

LIEAP............................................................................... 8
Table 3. Low-Income Home Energy Program (LIHEAP): “Old”
and “New” Allotment
Rates by State,
2010.......................................................................................
........................ 17
Table 4. Recent State Allotment Rates Under the “New”
LIHEAP Formula ............................... 20
Table A-1. LIHEAP Estimated State Allotments for Regular
Funds at Various
Hypothetical Appropriation Levels
......................................................................................... 23
Table C-1. LIHEAP Actual State Regular Fund Allotments for
FY2006 through FY2010
and Estimated FY2011 Allotments
......................................................................................... 30
Appendixes
Appendix A. Estimated Allotments to the States Under Various
Hypothetical
Appropriations Levels
...............................................................................................

............. 22
Appendix B. Further Depiction of How State Allotments Depend
Upon Appropriation
Levels
...............................................................................................
..................................... 26
Appendix C. Actual LIHEAP Regular Fund Allocations to the
States, FY2006-FY2010
and Estimated Allocations,
FY2011...................................................................................
..... 28
Contacts
Author Contact Information
...............................................................................................
....... 34
Congressional Research Service 1
Introduction
The Low Income Home Energy Assistance Program (LIHEAP)
is a block grant program
administered by the Department of Health and Human Services
(HHS) under which the federal
government gives annual grants to states, the District of
Columbia, U.S. territories and

commonwealths, and Indian tribal organizations to operate
multi-component home energy
assistance programs for needy households.1 Established in 1981
by Title XXVI of P.L. 97-35, the
Omnibus Budget Reconciliation Act, LIHEAP has been
reauthorized and amended a number of
times, most recently in 2005, when P.L. 109-58, the Energy
Policy Act, authorized annual regular
LIHEAP funds at $5.1 billion per year from FY2005 through
FY2007.2
The federal LIHEAP statute has very broad guidelines, with
almost all decisions regarding the
program’s operation made by the states. Recipients may be
helped with their heating and cooling
costs, receive crisis assistance, have weatherizing expenses
paid, or receive other aid designed to
reduce their home energy needs. Households with incomes up to
150% of the federal poverty
income guidelines or, if greater, 60% of the state median
income, are federally eligible for
LIHEAP benefits. States may adopt lower income limits, but no
household with income below
110% of the poverty guidelines may be considered ineligible.
Note, however, that in the FY2009
and FY2010 appropriations acts (P.L. 110-329 and P.L. 111-
117), Congress gave states the
authority to raise eligibility limits to 75% of state median
income. The most current HHS data
show that an estimated 5.5 million households received winter
heating or winter crisis assistance
in FY2006 (the largest share of LIHEAP funds pay for heating
assistance).3
The LIHEAP statute provides for two types of program funding:
regular funds—sometimes

referred to as block grant funds—and emergency contingency
funds. Regular funds are allotted to
states on the basis of the LIHEAP statutory formula, which was
enacted as part of the Human
Services Reauthorization Act of 1984 (P.L. 98-558).4 The way
in which regular funds are
allocated to states depends on the amount of funds appropriated
by Congress. The second type of
LIHEAP funds, emergency contingency funds, may be released
and allotted to one or more states
at the discretion of the President and the Secretary of HHS.5
The funds may be released at any
point in the fiscal year to meet additional home energy
assistance needs created by a natural
disaster or other emergency.6
The remainder of this report discusses only the history and
methods of distributing regular
LIHEAP funds.
1 For additional information on LIHEAP, see CRS Report
RL31865, The Low Income Home Energy Assistance
Program (LIHEAP): Program and Funding, by Libby Perl.
2 LIHEAP is codified at 42 U.S.C. §§8621-8630.
3 U.S. Department of Health and Human Services,
Administration for Children and Families, FY2006 LIHEAP
Report
to Congress, April 22, 2009, p. 21.
4 The formula section is codified at 42 U.S.C. §8623.
5 Depending on how Congress appropriates them, contingency
funds may remain available for distribution in more than
one fiscal year or they may expire with the fiscal year for which
they were appropriated.
6 The statutory definition of emergency includes a significant
home energy supply shortage or disruption, a significant

increase in the cost of home energy, a significant increase in
home energy disconnections, a significant increase in
participation in a public benefit program, a significant increase
in unemployment, or an event meeting such criteria as
the Secretary determines to be appropriate. 42 U.S.C. §8622.
Predecessor Programs to LIHEAP
The mid- to late-1970s, a time marked by rapidly rising fuel
prices, also marked the beginning of
federal energy assistance funding for low-income households.
The first national program to help
low-income households was created in early 1975 to assist
families with energy conservation
primarily through home weatherization. This assistance was
provided through a new Emergency
Energy Conservation Program (EECP), enacted as part of the
Headstart, Economic Opportunity,
and Community Partnership Act of 1974 (P.L. 93-644). The
funds were administered by the
Community Services Administration (CSA), the successor
agency to the Office of Economic
Opportunity, which was responsible for many of the programs
created as part of the 1964 war on
poverty. Beginning in 1977, funds were also made available
through the CSA to help families
directly pay for fuel (as opposed to weatherization expenses)
via a variety of programs. Each of
these programs had in common a focus on the need for heating
assistance (versus cooling

assistance).
Congress continued to appropriate funds for energy assistance
programs through FY1980, at
which point a new program, the Low Income Energy Assistance
Program (LIEAP) was enacted
as part of the Crude Oil Windfall Profits Tax Act of 1980 (P.L.
96-223). LIEAP, which was
administered by the Department of Health and Human Services
(HHS), was funded for one year,
FY1981, before the creation of LIHEAP. Like the CSA
programs, LIEAP emphasized heating
over cooling needs. This preference was reflected in both the
CSA program formulas and the
LIEAP set of formulas, which used variables that benefitted
cold-weather states to determine how
funds would be distributed. The LIEAP set of formulas
continues to have relevance for the way in
which LIHEAP funds are distributed. This section of the report
describes these predecessor
programs to LIHEAP and their distribution formulas.
Community Services Administration Energy Assistance
Programs
On January 4, 1975, President Ford signed into law the
Headstart, Economic Opportunity, and
Community Partnership Act of 1974 (P.L. 93-644), which
contained funds for a new program,
called the Emergency Energy Conservation Program (EECP).
The program was to be
administered by the Community Services Administration (CSA),
and its purpose was
to enable low-income individuals and families, including the
elderly and the near poor, to
participate in energy conservation programs designed to lessen

the impact of the high cost of
energy ... and to reduce ... energy consumption.
The law governing EECP listed a number of eligible activities
in which states could participate,
including energy conservation and education programs;
weatherization assistance; loans and
grants for the purchase of energy conservation technologies;
alternative fuel supplies; and fuel
voucher and stamp programs. Despite the variety of activities
that could be funded through the
program, the first CSA funding notice regarding the program
limited eligible activities to
“winterizing” homes and to giving emergency assistance “to
prevent hardship or danger to health
due to utility shutoff or lack of fuel.”7 During the four years the
EECP was funded, the majority
of funds were used for weatherization expenses.8
EECP funds were distributed to states via a formula that
benefitted those states with high heating
costs. One formula variable in particular, a measure of
“coldness” called heating degree days,
benefitted cold-weather states. Heating degree days measure the
extent to which a day’s average
temperature falls below 65° Fahrenheit. For example, a day with
an average temperature of 50°
results in a measure of 15 heating degree days. Because heating

degree days are higher in cold
weather states, including the heating degree day variable in a
formula favors states with greater
heating needs. Squaring the heating degree days magnifies this
effect.9 The EECP formula took
the number of population-weighted heating degree days in each
state, squared them, and
multiplied the result by the number of households in poverty
that owned their homes to determine
how funds would be allocated.10 The CSA acknowledged the
emphasis on heating needs in its
formula, stating that the FY1975 allocation “was heavily
weighted to the coldest areas.”11 In the
three fiscal years that followed the first appropriation for the
EECP, from FY1976 through
FY1978, the CSA changed somewhat the way in which it
allocated funds to the states; however,
the factors continued to favor cold-weather states through use of
either heating degree days or
heating degree days squared.12
The first year that Congress specifically appropriated funds for
direct assistance to help low-
income households (those at or below 125% of poverty) pay
their energy costs (instead of funds
that went primarily for weatherization and conservation
activities) was FY1977. The FY1977
Supplemental Appropriations Act (P.L. 95-26) provided $200
million for a Special Crisis
Intervention Program to be administered by CSA. States could
use funds to make direct payments
to fuel providers on behalf of low-income families lacking the
financial resources to pay their
energy bills. The CSA directed states to target households
where utilities had been shut off (or
were threatened with shut off) and who could prove dire need

due to large energy bills.13
Although the law did not reserve funds exclusively for heating
costs, the way in which funds
were allocated to the states emphasized heating need. Funds
were distributed to the states based
on a formula that used (1) heating degree days squared, (2) the
number of households in poverty,
(3) the number of persons above age 65 with incomes below
125% of poverty, and (4) the relative
cost of fuel in the region.14 Congress again appropriated $200
million for crisis intervention in
7 Community Services Administration, “Character and Scope of
Specific Community Action Programs: Emergency
Energy Conservation Program,” Federal Register, vol. 40, no.
145, July 28, 1975, p. 31603.
8 See, for example, House Appropriations Committee, report to
accompany H.R. 4877, the FY1977 Supplemental
Appropriations Act, 95th Cong., 1st sess., H.Rept. 95-68, March
11, 1977: “The funds in this program are used primarily
to purchase materials to insulate the homes of low -income
families.”
9 For example, if a southern state experiences 700 heating
degree days in a year and a northern state experiences 7,000,
the northern state has 10 times as many heating degree days as
the southern state. However, if both numbers are
squared, the northern state has 100 times as many heating
degree days as the southern state.
10 Community Services Administration, “Emergency Energy
Conservation Program: Submission of Funding Plans,”
Federal Register, vol. 41, no. 208, October 27, 1976, p. 47096.
11 Federal Register, vol. 41, no. 208, October 27, 1976, p.
47096.
12 See Ibid., pp. 47096-47097.
13 Community Services Administration, “Special Crisis

Intervention Program: General Information, Application
Procedures, and Post Grant Requirements,” Federal Register,
vol. 42, no. 125, June 29, 1977, p. 33240.
14 The formula was described in the Senate Appropriations
Committee report to accompany H.R. 4877, the FY1977
Supplemental Appropriations Act, 95th Cong., 1st sess., S.Rept.
95-64, March 24, 1977. The CSA implemented this
formula, which it described in guidance to the states. See the
Federal Register, Ibid.
both FY1978 and FY1979.15 In FY1978, funds were available
to households with the need for
assistance as the result of an energy-related emergency such as
lack of fuel, a natural disaster, fuel
shortages, and widespread unemployment.16 In FY1979, funds
were made available to assist
families facing “substantially increased energy costs and/ or life-
or health-threatening situations
caused by winter-related energy emergencies.”17
In FY1980, Congress appropriated a total of $1.6 billion for
energy assistance. Of this amount,
$400 million was appropriated for the Energy Crisis Assistance
Program (ECAP, a CSA program
similar to the Special Crisis Intervention Program) through two
separate appropriations.18 The
remainder, $1.2 billion, was appropriated as part of the FY1980
Department of the Interior
Appropriations Act (P.L. 96-126) to the Department of Health,

Education, and Welfare (HEW, the
predecessor to HHS) for cash assistance and crisis intervention
due to high energy costs. This
appropriation to HEW is sometimes referred to as Low Income
Supplemental Energy Allowances.
Of this $1.2 billion, $400 million was to be distributed
specifically to recipients of Supplemental
Security Income (SSI). The rest of the funds appropriated to
HEW, approximately $800 million,
as well as the ECAP funds, were distributed to states on the
basis of three factors: heating degree
days squared, the number of households below 125% of poverty,
and the difference in home
heating energy expenditures between 1978 and 1979. The
formula used to distribute the $400
million for SSI recipients used these same factors but also
included the number of SSI recipients
in each state relative to the national total.
Table 1. Select Energy Assistance Formulas, FY1975-FY1980
Emergency Energy
Conservation Program:a
FY1975
(P.L. 93-644)
Special Crisis
Intervention Program:b
FY1977
(P.L. 95-26)
Low Income Supplemental Energy
Allowances:c

Energy Policy 31 (2003) 1441–1458LIHEAP reconsideredMa

Energy Policy 31 (2003) 1441–1458LIHEAP reconsideredMa

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