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Statistical Policy
Working Paper 1

Report on
Statistics for Allocation of Funds


Prepared by
Subcommittee on Statistics for Allocation of Funds
Federal Committee on Statistical Methodology
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U.S. DEPARTMENT OF COMMERCE
Juanita M. Kreps, Secretary
Courtenay M. Slater, Chief Economist

Office of Federal Statistical Policy and Standards
Joseph W. Duncan, Director

Issued:March 1978
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For sale by the Superintendent of Documents, U.S. Government Printing Office
              Washington, D.C. 20402






                Office of Federal Statistical
                    Policy and Standards


                Joseph W. Duncan, Director

        George E. Hall, Deputy Director, Social Statistics
     Gaylord E. Worden, Deputy Director, Economic Statistics
Maria E. Gonzalez, Chair, Federal Committee on Statistical Methodology



                   Preface

This working paper was prepared by the members of the Subcommittee on
Statistics for Allocation of Funds, Federal Committee on Statistical Methodology.
The Subcommittee was chaired by Wray Smith, Office of the Assistant Secretary
for Planning and Evaluation, Department of Health, Education, and Welfare. The
members of the Subcommittee are the authors of this report and their names are
listed below. It is hoped that this report will aid administrators and drafters of
future legislation in recognizing some characteristics of data and formulas used in
distributing Federal funds to State and local governments. The Subcommittee plans
to discuss these results with many interested parties to further disseminate the
findings of this report.









                                iii
   




                Members of the Subcommittee on
                Statistics for Allocation of Funds
                        (January 1976-June 1977)


* Wray Smith (Chair)
Office of Technical Support and Statistics, ASPE
(HEW)

Richard B. Clemmer
Division of Economic Policy, OPDR (HUD)

* Edwin J. Coleman
Bureau of Economic Analysis (Commerce)

Martin M. Frankel
National Center for Education Statistics (HEW)

* Fred J. Frishman
Mathematical Statistics Branch, IRS (Treasury)

Forrest W. Harrison
National Center for Education Statistics (HEW)

* Thomas B. Jabine
Office of Research and Statistics, SSA (HEW)

* Charles D. Jones
Bureau of the Census (Commerce)

Eli S. Marks
Bureau of the Census (Commerce)

Rajendra Singh
U.S. Postal Service

Charles D. Troob
Compensatory Education Division, National Insti-
tute of Education (HEW)

Martin Ziegler
Bureau of Labor Statistics (Labor)

Maria E. Gonzalez (ex officio, Chair, FCSM)
Office of Federal Statistical Policy and Standards
(Commerce)
Tore E. Dalenius (Consultant)
Brown University and University of Stockholm

--------------
*Member, Federal Committee on Statistical Methodology


               Acknowledgments

Chapter 1, 11, 111, and IV were written by Eli
Marks, Charles Troob, and Wray Smith on the basis
of Subcommittee outlines and discussions, as well as
on the five case studies of formula programs. Chap-
ter V (Subcommittee recommendations) is a joint
product of the Subcommittee. The appendixes were
prepared by individual members of the Subcommit-
tee and their names are given both on their papers
and in the table of contents. Research assistance was
provided to the Subcommittee in 1977 by Henrietta
Hyatt.






                                iv
 
                Members of the Federal Committee on
                        Statistical Methodology

Maria Elena Gonzalez (Chair)
Office of Federal Statistical Policy and Standards
  (Commerce)

Barbara A. Bailar
Bureau of the Census (Commerce)

Norman D. Beller
Statistical Reporting Service (Agriculture)

Barbara A. Boyes
Bureau of Labor Statistics (Labor)

Edwin J. Coleman
Bureau of Economic Analysis (Commerce)

John E. Cremeans
Bureau of Economic Analysis (Commerce)

Marie D. Eldridge
National Center for Education Statistics (HEW)

Fred J. Frishman
Internal Revenue Service (Treasury)

Thomas B. Jabine
Social Security Administration (HEW)

Charles D. Jones
Bureau of the Census (Commerce)

Alfred D. McKeon
Bureau of Labor Statistics (Labor)

Harold Nisselson
Bureau of the Census (Commerce)

Monroe G. Sirken
National Center for Health Statistics (HEW)

Wray Smith
Office of the Assistant Secretary for Planning and
  Evaluation (HEW)



                                v


                        Executive Summary

The Subcommittee on Statistics for Allocation of Funds prepared five case studies
selected from the ten largest grant-in-aid programs that use data on population
and per capita income. These five programs were then analyzed in terms of the
variables "Need", "Capability", and "'Effort". These factors were selected by the
Subcommittee as the key elements to be considered in analyzing both the formulas
and data employed by grant-in-aid programs for allocation of funds. The report
discusses the types of formulas used for allocation purposes, the required statistical
data, and the impact of errors in the data on the actual allocation of funds. Based
on the review of the case studies, the recommendations are as follows:

(1)     That program goals be specified as clearly and completely as possible in
        the statement of purpose of each grant-in-aid act and that program drafters
        guard against over-specification of the statistical data and procedures to be
        used.

(2)     That provisions be made for an active, continuous interface between legis-
        lative program drafters and the statistical community.

(3)     That statistical and program agencies provide to program drafters an analy-
        sis of the sensitivity over time of formulas and of the statistics they incor-
        porate so that possible effects on allocations can be anticipated. Also, that
        provisions be made for testing, monitoring, and assessing by program
        agencies of the performance of each specific formula or allocation rule
        prior to enactment.

(4)     That legislative drafters and program designers be advised of data problems
        and the existence of statistical practices, as exemplified in the five case
        studies, which may lead to formulas with consequences that are generally
        recognized as undesirable.

(5)     That a limited program of applied research and development be initiated
        to attack some critical problems and fill certain identifiable gaps in the
        present state-of-the-art of formula design.

(6)     That the Office of Federal Statistical Policy and Standards, with the assist-
        ance of the statistical agencies, designate a limited number of additional
        official statistical series for use in fund allocation. These would be kept as
        current and as accurate as possible for States and for local areas.

(7)     That in tiered allocation programs comparable data be used for allocation
        to States, but policy flexibility be allowed for sub-State allocations. When
        the Federal Government allows this flexibility it should be subject to the
        formulation of specific Federal statistical and administrative guidelines,
        concerning the designation of the responsible governmental unit for choosing
        among statistical series, for declaring the specific types of statistical series
        from which such a choice is permitted to be made, and for establishing
        administrative mechanisms for consideration of appeals from area govern-
        ments.

(8)     That since data errors are inevitable and since statistical resources are
        necessarily limited, priority be given to minimizing the very large errors
        which may occur in data used for the allocation of funds.

(9)     That, to minimize the effects of data errors, eligibility cutoffs be such that
        there is a gradual transition from receiving no allocation to receiving the
        full formula amount.

                                        vi

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                                                                          CHAPTER I

                        Overview and Description of
                        Allocation Techniques

                Introduction

   This report examines the formulas used in allocat-
ing Federal funds to States and local areas. To
understand the behavior of these formulas, one must
understand the various aspects of the data, such as
definitions, methods of collection, and methods of
analysis. The objective of the Subcommittee was to
study from the statistical standpoint, possible prin-
ciples or guidelines which could be used to insure
that the intent of Congress is fulfilled in the alloca-
tion of Federal funds. For the purposes of this study
it is assumed that whatever Congress specifies in the
authorizing legislation for a grant-in-aid program on
the manner of allocation of Federal funds is in prin-
ciple an equitable distribution, although anomalous
and unanticipated results may emerge in some in-
stances. In connection with the guidelines, the Sub-
committee was also to identify possible improve-
ments in statistical data and allocation processes that
might be made either by better selection of the data,
changes in data collection or tabulation methods, or
statistical adjustments to compensate for known
errors. The report is organized as follows: Chapter
I gives an overview and description of allocation
techniques; Chapter II examines the consequences
of using existing data in allocation formula tech-
niques; Chapter III presents the findings; Chapter
IV discusses ways to reduce allocation errors; and
Chapter V presents the recommendations of the Sub-
committee based on its study of the deficiencies of
existing data and allocation formulas and of possible
alternatives.
   We will now elaborate on some specific topics in
these chapters. Chapter I and Chapter II are based
on the five case studies presented as Appendixes
A-1 to A-5 of this report. These five cases were
selected from the ten largest grant-in-aid programs
that use data on population and per capita income.
In FY 1975, total formula grants for, all programs
amounted to nearly 36 billion dollars. Fiscal year
1975 grants for the five case study programs range
from 1.6 to 6.2 billion dollars and account for 47
percent of the total of formula grants.<ftnref marker="1">

   Some of the findings of Chapter III are tentative
and many of the recommendations of Chapter V
are long-term goals which may never be achieved in
the exact form presented. However, as an interim
measure, some standard practices and guidelines are
needed to aid policymakers and statisticians involved
in constructing or revising allocation schemes for
grant-in-aid programs. At the very least, such guide-
lines should warn practitioners away from some of
the more dangerous, practices with disagreeable con-
sequences that may be found in some existing formula
programs. For example, under some circumstances
such guidelines might advocate the use of a partic-
ular population or economic statistic that was
neither the most recent nor the most adequate from
the standpoint of geographic detail but which had
other statistical properties, such as stability from one
time period to the next or uniform quality across


<img src="gif3.gif">
geographic areas. The Subcommittee believes that
the development of some state-of-the-art guidelines
will lead to a general simplification and increase in
the transparency of allocation schemes to be adopted
in the future.
   The case studies show that many of the allocation
formulas also contain constraints and special rules.
For example, for administrative reasons it is neces-
sary to impose some type of limitation on how often
the allocations can be recomputed. Also, since the
States and local areas must be able to prepare their
own budgets and decide upon tax levies, capital
investments, hiring, etc., some constraints may be
imposed to prevent extreme year-to-year fluctuations
in the allocation to individual jurisdictions. Some-
times, the restraints may prevent even moderate
fluctuations in individual allocations.
   Many of the formulas contain implicitly or explic-
itly a restriction designed to insure that every State
or local area gets some amount. Sometimes this is
coupled with a restriction on the maximum amount
to be allocated to any area. The limitation is usually
not distinguishable from the limitations designed to
damp or prevent fluctuations in individual allocations
over time. To some extent, the restrictions may
represent a well-justified distrust of the behavior of
the allocation formula and of the appropriateness of
the statistics used in it.


     The Nature of Fed eral Grant-in-Aid
                  Formulas<ftnref marker="2">

   All of the allocation formulas studied deal with
activities which are recognized as functions of State
or local government but over time a feeling has
developed that Federal assistance is appropriate to
insure more equitable handling of the problem
among local jurisdictions. That is, while there is
recognition that the given function must be carried
out locally and adjusted to the realities of local con-
ditions, it is also recognized that financial resources
available for handling the problem vary considerably
among State and local governments so that it is
appropriate for Federal funds to be used to supple-
ment local funds.
   Informally it is possible to adopt a helpful statis-
tical paradigm for allocation formula research, in
which the allocation is taken to be a function of
"Need, Capability, and Effort", each of which is
assumed to be at least approximately observable at
the State or local level. There are, however, serious
definitional and interaction problems imbedded in
this model--the fact that a Need may appropriately
have different components in two geographic areas,
that taxable real estate and personal income may not
give an adequate basis for Capability, that local
tax revenue Effort may need to be analyzed in
terms of the purposes to which the revenues are ap-
plied, and so forth. Frequently, one or even all of
the factors in the model are defined neither in the
statute nor in the legislative history or, if all the
factors are defined, the measures of Need, Capability,
and Effort are inconsistent with the definitions or
with each other. Thus, the terms are used to refer
to statistical abstractions which apply only approxi-
mately (if at all) to the actual elements that make
up a given allocation formula.
   There are other elements of allocation formula
problems, for example, the sensitivity of a particular
formula to small, perhaps irrelevant, changes in the
specified data over time. Some programs may require
almost immediate reaction to the changes while, for
other programs, insensitivity to short-term changes
may be imperative. One wants the formula to re-
spond fast enough to changing conditions but not
too fast. Local government must be given some rea-
sonable assurance of the general level of Federal
funding they are to receive in future fiscal periods
in order to keep local planning from becoming
chaotic.
   Another important question is the transparency
of an allocation formula--can it be understood? Can
citizens understand it? Politicians? Statisticians?
Some formulas we have examined in existing Federal
programs deserve to be  called opaque--their behav-
ior over time cannot be simply explained and may
even exhibit some surprising and unanticipated re-
sults.
   The general statistical approach used in this re-
port conceives Federal grant-in-aid formulas as
starting with some activity which the Congress per-
ceives as properly a function of State or local gov-
ermment. In our statistical model we use the term
Need to designate the activity required. For the pur-
pose of the present report, Need is always to be
understood in terms of the services (or goods) to be
supplied--e.g., for food, shelter, etc., for AFDC
(Aid to Families with Dependent Children); or
police and fire protection, street and highway main-
tenance, etc., for General Revenue Sharing (GRS).
While Need can be defined in money terms, this


                                        2

definition involves the total amount required, 
whether or not that amount is available at the State
or local level (or even whether it is available at any
level). Thus, the Need in Title I, ESEA (Elementary
and Secondary Education Act) might be defined as
the total amount required to attain a given educa-
tional level in a local area, regardless of whether
the funds are available at the local, State or national
level, or perhaps, not at all.
   Capability is used for an area's prospective ability
to meet a stated Need--i.e., the possibility of meet-
ing the Need from local or State (or private) funds.
For example, Capability might involve the amount
that could be raised by some (standard) taxing pro-
gram whether or not actual tax revenues reach this
level. Finally, Effort is used for the actual amounts
available for the Need from local revenues. Fre-
quently, Effort is measured relative to Capability.
   Measures of State and local (relative) Need, and
Capability of meeting the Need, are components of
almost all allocation formulas. The measure of Need
is often stated (at least approximately) in terms of
the population to be served. Many allocation formu-
las also recognize that there may be considerable
variation in the proportion of the available local
resources actually devoted to meeting the Need and
include some measure of Effort.
   An important (but usually implicit) aspect of all
allocation formulas is the time reference. Some pro-
grams are dealing with immediate objectives--to
provide adequate food and shelter here and now.
Others are dealing with a more distant time refer-
ence--to equip all of the Nation's children with the
education and skills necessary to their functioning
effectively in the Nation's economy as it is in 1977
(let alone as it will be in 1990). There is also a
time reference or ability to meet a given Need. The
United States can, fortunately, meet our require-
ments for food and some sort of shelter immediately;
but building sanitary, safe, and comfortable housing
on the massive scale required in many communities
takes at least 3 years and building even a partial
rapid transit system for a major metropolitan center
takes at least 6 years (from the time the system is
designed and approved in principle).
   Structurally, the formulas vary considerably. Gen-
eral Revenue Sharing (see Appendix A-1 of this
report, "The General Revenue Sharing Program")
uses the ratio of a measure of Effort (taxes as a
proportion of aggregate personal income) to a meas-
ure of Capability (per capita money income). and
multiplies this by (total) population. Essentially,
this says that the share of a State or local area in-
creases proportionally with the increasing popula-
tion, increasing Effort, and decreasing Capability. In
the General Revenue Sharing formula, per capita
income serves as an indicator of Capability and total
population as a measure of Need. This is equivalent
to assuming that all jurisdictions have an equal Need
per capita for the services covered by General Reve-
nue Sharing. The General Revenue Sharing formula
is complicated for sub-State distributions by lower
and upper limitations on the per capita share of any
locality (not less than 20 percent and not more than
145 percent of the average per capita share for
the State). GRS allocations are also complicated at
all levels by options relating to the specific measures
to be used, but these do not affect the basic formula
structure.
   Like the General Revenue Sharing formula, the
formulas of the other programs also involve measures
of the basic factors (Need, Effort, Capability--with
Capability entering inversely). However, the other
formulas usually show some measure of Need ex-
plicitly. Often total Need in (dollars required) is
used, so that population does not appear explicitly
in the formula. Also, the formula may ignore Cap-
ability or use a single measure which reflects both
Effort and Capability (with results which the Con-
gress has found at times quite frustrating).
   Thus, in the ESEA formula (see Appendix A-3
of this report, "The Authorization and Allocation of
Funds Under Title I, ESEA") there is a measure of
Need (the number of economically disadvantaged
children<ftnref marker="3"> multiplied by (a percentage of) the
State average expenditure per pupil. Unlike General
Revenue Sharing, this measure of Effort (per capita
expenditure for the specified Need) does not relate
it to Capability. However, an adjustment for low
Capability is provided by substituting 80 percent of
the national expenditure per pupil for the State ex-
penditure per pupil, whenever the State expenditure
per pupil is less than 80 percent of the national ex-
penditure per pupil (presumably on the basis that
low State expenditure per pupil characterizes the
poorer areas, and was, therefore, a reflection of low
Capability rather than of lower Effort or of lower
unit costs for education of a given quality level).
Corresponding to this floor on the allowance for per

                                        3


pupil expenditure, the (present version of) ESEA 
also provides for a ceiling of 120 percent of the 
national expenditure per pupil. There is, however, no
allowance below the State level for variation among
school districts in either Effort or Capability.
   The AFDC formulas (regular and alternate) (see
Appendix A-4 of this report, "Aid to Families with
Dependent Children (AFDC) as a Formula Grant-In-
Aid Program") resemble the ESEA formulas in start-
ing with a measure of total Need times Effort--i.e.,
the total of money payments to families with depend-
ent children plus payment for foster care. These pay-
ments are multiplied by the complement of a meas-
ure of Capability.<ftnref marker="4"> However, in the regular AFDC
formula there are provisions for using a fixed multi-
plier for part of the Federal payment (5/6 of the
first $18 per recipient) and a maximum ($32 per
recipient) above which no Federal reimbursement
is made. As with the floor on per pupil expenditures
in the ESEA formula, the use of a fixed multiplier
for the first $18 has the effect of increasing the pay-
ments to States with very low Capabilities (measured
by the State per capita income). Payments to States
with very high Capabilities tend also to be decreased
by the maximum of $32 per recipient in the regular
formula. Since States have a choice between the two
formulas, all but a few States with very low pay-
ments per eligible child elect to use the alternate
formula based on actual payments and the computed
percentage (Federal Medical Assistance Percentage,
FMAP).
   The formulas for CETA (see Appendix A-2 of
this report "The Comprehensive Employment and
Training Act") and CDBG (see Appendix A-5,
"The Community Development Block Grant Pro-
gram") are complicated by (a) a provision for a
substantial proportion of the funds to be allocated
on a discretionary basis and (b) so called hold
harmless provisions for preventing sudden and dras-
tic changes in an area's allocation. For CDBG, the
hold harmless clauses provide for a gradual change-
over from the previous (average annual) allocation
level to the Basic Grant amount determined by the
new CDBG formula. Communities whose new allo-
cations would exceed their prior level would receive
the full new allocation in the third year and the
higher of the previous allocation and one-third or
two-thirds of the new grant level during the first two
years. Communities whose new allocation is less
than their previous allocation would receive the pre-
vious allocation for the first three years of the pro-
gram and would be cut back to the higher of the
new level and two-thirds or one-third of the prior
level during the fourth and fifth years, getting only
the new allocation for the sixth year.
   For CETA, the hold harmless provision involves
use of a moving average of the current formula
results and the previous period's allocation. This is
similar to the exponential smoothing techniques used
in economic predictions (for market planning, pro-
duction inventory control, etc.) to obtain results
which will reflect the real changes in basic economic
conditions but will be insensitive to temporary fluc-
tuations and disturbances. These averages are of
the form:

<img src="gif4.gif>

   The value of b is frequently determined (as is
apparently the case for CETA) on the basis of
expert opinion. There are methods for using past
experience to determine an improved value of b
(where a criterion for improved performance can be
established).
   CETA is further complicated by the existence of
three titles with three different allocation formulas.
All three formulas use unemployment level but one
also considers adults in low-income families and
has the hold harmless provision for smoothing short-
term fluctuations; one has a lower limit for eligibility
(6.5 percent unemployment rate for three consecu-
tive months); and the third formula is a mixture of
the other two.
   While the primary effect of the smoothing (hold
harmless) provisions of CETA is to reduce the
effects of short-term fluctuations in unemployment,
the smoothing provisions of the CDBG program are
really phase-out/phase-in provisions designed to
make a gradual transition to CDBG from the various
housing and community development programs it
replaces. After the fifth year of the CDBG program,

                                  4


the previous allocations are no longer considered in
the formula.
   The CDBG formula is different from the others
considered in that it is additive. The basic allocation
involves the weighted sum of three measures of Need,
one of which is the total population of the area. The
population measure receives a weight of 1/4 in the
formula and the two other measures of Need (pov-
erty count and number of overcrowded dwelling
units) receive weights of 1/2 and 1/4.
   The Advisory Commission on Intergovernmental
Relations<ftnref marker="5"> reviewed the allocation provisions of all
federal formula-based categorical grants to State
and local governments existing in 1975. Formula-
based programs then numbered 146 out of 442
categorical programs. A review of the 146 programs
shows that about 130 include some measure of Need;
41 programs include a measure of Effort; and 24
programs include a measure of Capability. These
data show that there are few formula-based alloca-
tion programs that include all three measures: Need,
Effort, and Capability. More than half of the pro-
grams include, only a measure of Need. However,
there are many programs which combine two kinds
of measures.

   Definition and Measurement of Need in
          Grant-in-Aid Programs

   As mentioned above, the term Need is used here
to refer to the services which a given program is
designed to provide. The measure of Need would
usually be something proportional to the total cost
of providing the services in a given jurisdiction.
   The specificity of the Need to be met varies con-
siderably between Federal grant-in-aid programs. In
the examples of the Appendixes, AFDC probably
has the most specific Need, that of providing ade-
quate food, shelter, medical care, etc. for (non-
institutionalized) children whose families are finan-
cially unable to provide for these needs adequately.
At the other end of the spectrum is General Revenue
Sharing where the Federal funds are to provide fiscal
assistance for the general functions of local govern-
ment.
   The other programs fall in between AFDC and
General Revenue Sharing with respect to the speci-
ficity of the Need to be met, but are, in general,
nearer to AFDC than to General Revenue Sharing.
For example, the ESEA is directed at establishing
special education programs to help educationally de-
prived children. Most of the assistance is concen-
trated on improving basic skills such as reading,
writing, and arithmetic but ESEA also includes fund-
ing for a wide variety of programs designed to meet
other educational needs of educationally deprived
children. There was also in ESEA, as originally con-
ceived by Congress, the idea of a general antipoverty
program to help poor people and poor school dis-
tricts--e.g., the stated purpose of providing funds to
school districts "whose ability to operate adequate
educational programs is impaired by concentrations
of low-income families."
   The specificity of the aims of AFDC make it fairly
easy to develop a measure of Need--i.e., the amount
required to provide food, shelter, medical care, etc.,
to a child multiplied by the number of children in
families who are financially unable to provide this
care. The actual AFDC program accepts as the
measure of Need, the individual State's definition of
how much is needed per child and which families
are too poor to provide this amount for their
children.
   General Revenue Sharing assumes a general Need
based on the level of per capita income and the level
of taxes collected. That is, it is implicitly assumed
that the amount a State or local government requires
for general governmental functions is reflected in
how heavily it is taxing its residents. The amount re-
ceived under General Revenue Sharing is a direct
function of the level of adjusted taxes and inversely
related to per capita income squared. Population is
only brought in at the upper and lower constraint
levels.
   ESEA uses as its primary measure of Need (1)
the number of children in poverty families, (2) two-
thirds of the children in non-poverty families receiv-
ing AFDC payments and (3) the number of children
in institutions for neglected and delinquent children
and in foster homes supported by public funds. This
is directly in line with the purposes stated above.
The measure of Need originally excluded the chil-
dren described in (3) above but included 100 per-
cent of the children in nonpoverty families receiving
AFDC payments. AFDC uses, to measure Need, the
total payments made for children in poverty families
or foster homes (also see Appendix B-1, "AFDC
Counts and ESEA Title I").
   For CETA, the main measure of Need is the num-
ber unemployed. For States, the (expanded) CPS
(Current Population Survey) estimate of unemploy-
ment can be used. Below the State level, unemploy-

                                        5

ment must be estimated mostly from unemployment 
insurance data. A supplementary measure of Need 
for CETA is the number of adults in low-income
families. The estimate of such adults currently used
is derived from the 1970 Census of Population with
no updating to reflect change since that time.
   For CDBG the measures of Need are the poverty
count and the number of overcrowded dwelling
units. Both measures are derived from the 1970
Census of Population and Housing. The poverty
count is the number of persons in poverty families
as shown in the 1970 census. An overcrowded dwell-
ing unit is defined as one with 1.01 persons or more
per room.


   Measurement of Population, Capability
                and Effort

   In the General Revenue Sharing and other for-
mulas, total population as a measure of size enters
implicitly in the use of a measure of total Need
rather than per capita Need multiplied by popula-
tion. Population is also used (explicitly) in the com-
putation of per capita income which is the measure
of Capability in the General Revenue Sharing and
AFDC formulas.
   Actually, in the CDBG formula, population is
used as part of a measure of relative total Need
rather than as a simple measure of the size of the
area. That is, at each step, the allocation to an area
is the average of its relative standing (ratio of the
measure to the total for all areas in the class being
allocated) with respect to population and number of
overcrowded units (given weights of 1) and persons
in poverty families (given a weight of 2). Since these
three statistics are averaged in the formula, they
must all be taken to represent measures of total area
need for housing (relative, of course, to the total
Need for all areas in the class). The AFDC and
ESEA formulas use total population implicitly in the
form of a measure of total Need (total amount of
AFDC payments or number of 'educationally under-.
privileged' children for the area).
   Per capita income as a measure of Capability is
used by General Revenue Sharing and AFDC. The
General Revenue Sharing formula uses the recip-
rocal of per capita money income so that an area's
allocation is inversely proportional to this measure
of its Capability of raising the needed funds locally.
The AFDC formulas use per capita income
(squared) to determine the percentage of AFDC
payments to be met by State (or local) funds. This
is called the State percentage and is subtracted from
100 percent to give the percentage to be reimbursed
to States by Federal funds (subject to an upper and
lower limit on the Federal Government's share of the
AFDC costs).
   In the Title I ESEA formula, per pupil expendi-
ture is used as a measure of both Capability and
Effort. Using per pupil expenditure as a measure of
Effort, the formula provides for an area's share to
go up proportionally to this Effort measure. How-
ever, using per pupil expenditure as a measure of
Capability, there is a provision for increasing the
allocation in States with low Capability--i.e., where
the State expenditure per pupil is lower than 80
percent of the national average, 80 percent of the
national figure is used in place of the State figure.
At the other end, for States with high Capability the
per pupil expenditure is reduced to 120 percent of
the national figure.
   Capability and Effort do not appear in the CDBG
formula. As already noted, per pupil expenditure is
used as a measure of Effort and of Capability in the
ESEA formula. In the AFDC formula, payments
made to poor families with dependent children and
to foster homes are, in effect, taken as a measure of
both Need and Effort. The General Revenue Sharing
formula uses, as a measure of Effort, State and local
tax revenues divided by aggregate personal income.
This attempts to relate taxing effort to taxing
capability.

     Constraints and Time References
   
   Formula constraints tend to be aimed either at
obtaining a more equitable distribution of Federal
funds (either between States or between localities
within States) or at preventing large sudden changes
in the amount a State or local area receives. Both
types of constraint represent an attempt to balance
an allowance for real differences (in Need or Effort
or Capability) represented by the main formula,
against a concern that extreme values may represent
peculiarities due to random occurrences (or tem-
porary conditions) and defects in the formulas or
the statistical data used in them.
   General Revenue Sharing does not apply restric-
tions to the formula or data for allocations among
the States but does provide for upper and lower
limits on the allocation below the States level. The
logic of this distinction is that (a) figures for States
are probably subject to distortions for all States
whereas there may be considerable variation in the
                                               6


quality of the available data below the State level
and (b) in the State allocation one is dealing with
the entire range of non-Federal (general) govern-
ment functions while local general government units
may have a restricted range of functions.
   AFDC places restriction on the Federal Percent-
age and the Federal Medical Assistance Percentage
which apply to all jurisdictions. These operate to
curb extremely high Federal payments to States with
low per capita income as well as extremely low
Federal payments to the richer States. In the regular
formula, the restrictions are further buttressed by
providing that the State will be reimbursed 5/6 of
the first $18 per recipient paid out, regardless of the
Federal Percentage (limited to a maximum of 65
percent), and will get zero reimbursement for
amounts paid out in excess of $32 per recipient. For
AFDC also the use of constraints can be justified on
the basis of the failure of the statistics and the for-
mula to properly reflect a balance of Need, Effort,
and Capability that is equitable for all States.
   The constraints imposed to prevent large sudden
changes in the allocation to an area frequently take
the form of exponential smoothing; i.e., using an
allocation which is a weighted average of the cur-
rent computation and the allocation for the previous
period. A constraint with a similar purpose (distin-
guishing between permanent changes and temporary
aberrations) is the provision that, to be eligible for
an allocation under Title II of CETA, an area must
have an unemployment rate of 6.5 percent or more
for three consecutive months.
   Not previously mentioned are constraints on eli-
gibility for a given program designed mainly to pre-
vent the administrative nuisance and waste of han-
dling a large number of extremely small grants, thus
dissipating the available funds in areas where the
amount allocated is too small to get an effective pro-
gram going. This appears to be a relatively rare con-
straint but the provision of CETA Title II just cited
appears to be motivated as much by this considera-
tion as by the time series smoothing objective.
   The question of short-term fluctuations in Need,
and the techniques adopted to reduce their effects
upon Federal allocations is closely related to the
question of updating (keeping the statistics used in a
formula current) and to the question of what is the
appropriate time reference for a formula.
   Time reference refers to the amount of updating
which is appropriate to the particular program. Only
one of the five programs examined in the Appen-
dixes requires an immediate (i.e., month-to-month)
time reference. This is the AFDC and, even here,
since this is primarily a question of the Federal
Government providing partial reimbursement to the
States for money already spent, the only question is
the Federal vs. State Percentage. In determining the
Federal Percentage, the formulas and the data used
in them are such that a redetermination once a year
using per capita income figures for the preceding
year should be quite adequate.
   At the opposite extreme from AFDC with respect
to time reference is the CDBG program. Here, the
problem to be met is primarily an accumulated short-
age of adequate housing and community facilities.
For example, the rate at which such housing can be
planned, gotten into construction and completed, is
such that there is probably a minimum of three years
from initiation of a housing project to occupancy of
the completed project. Only one of the components
of the CDBG formula, the number of persons in
poverty families, is likely to show very substantial
changes over a three-year period and, even if one
could obtain figures on this factor for the current
year in order to recompute the CDBG entitlement
of each area, changes in work already underway
would not be possible; by the time housing based
on the new formula is underway more current data
would again be available to require a change in
plans. Overcrowding has also diminished but the
measure is not available for small areas on a current
basis. Actually, the five-year period for transition
from the old to the new housing formula is probably
not excessive (it is, in fact, desirable to permit com-
pletion of work contracted on the basis of the old
formula grants). At present, 1970 figures are being
used for housing overcrowding and poverty in the
CDBG formula along with 1973 population esti-
mates. Some updating for future computations may
be desirable but may not be as urgent for CDBG as
for some other programs.
   The appropriate time reference for General Rev-
enue Sharing, CETA and ESEA is somewhat greater
than for AFDC and considerably less than for
CDBG. For General Revenue Sharing, figures for
the preceding year probably provide a satisfactory
base (from the standpoint of time reference.) for the
current year's allocations. These can be provided for
the GRS formula at the State level (probably with
an accuracy almost as good as the 1970 figures).
Below the State level, problems of providing current
figures for all the GRS jurisdictions eligible becomes
somewhat more questionable. Actually, it has been
suggested that fluctations in GRS allocations from

                                        7


one entitlement period to the next may influence
unfavorably the fiscal policies of some local govern-
ments. Last year's figures are probably also satisfac-
tory for the ESEA formula and would also be satis-
factory for CETA, except for the hold harmless
provisions of the program. These provisions, it is
claimed, are so severe that allocations for a large
part of the CETA money are based primarily on
1970 data, even where satisfactory current figures
are available.


                Allocation to Small Areas

   All the programs mentioned here address a Need.
In each program, there is a different governmental
or quasi-governmental agency which is responsible
for administering the funds and meeting the Need:
State, county, and local governments in GRS, local
education agencies in ESEA, prime sponsors in
CETA, county welfare agencies in AFDC, and cities
and counties in CDBG. Each program must devise a
way of determining the fund level for these agencies
and each program has a different method. GRS
allocates to all eligible governments by formula. For
sub-State areas, ESEA allocates by formula to
counties. States then divide county allocations among
the school districts within each county. The State
procedure must follow Federal guidelines. CDBG
allocates to SMSA, cities, and counties by formula.
Other areas compete for funding, with total State
and SMSA allocations determined by formula.
   CETA has different procedures under each Title.
In general, CETA is distinctive in that recipients of
funding need not be preexisting  governmental units:
consortia of governments and agencies representing
areas of substantial unemployment may apply for
funding. Once applications are accepted, the money
is divided up by. formula.
   In AFDC, unlike the other programs discussed,
there is no ceiling on the Federal contribution.
County agencies expend whatever is appropriate
under State law; the reimbursement rate varies by
State. Caseload data primarily determines the level
of Federal contribution to each area.

                                        8
                                                                       CHAPTER II

                Why Existing Allocation Formula Techniques Do Not
                Fully Achieve the Stated Objectives of Federal Programs

Problems of Choice of Formula Structure
               and Constraints

   In view of the examples of formula creation and
use found in the five case studies, it is clear that the
typical allocation formula has a complex structure
entailing the identification and selection of various
options. For this reason, a decision to adopt a spe-
cific formula involves--at least implicitly--a series
of distinct prior choices. An inappropriate decision
at any of these choice points may lead to a formula
which results in allocations that do not reflect con-
gressional priorities. We realize that such choices
are, as a result of the interaction of individuals and
committees, often judgmental and sometimes not
made in a fully logical order. Nonetheless, there are
some necessary elements in any such specification
process which we feel need to be made explicit as a
basis for understanding problems and limitations of
formula selection.
   The first choice involves the definition and meas-
urement of Need. As discussed in Chapter I, any
proposal for a Federal grant-in-aid program that is
to involve a formula mechanism is motivated in some
fashion by a perception of a Need. A working def-
inition and some measure of that Need must be
adopted, whether or not there is full understanding
or agreement on all of the dimensions of Need. For
example, in the first enactment of Title I of the
Elementary and Secondary Education Act it was rec-
ognized that school districts serving large numbers of
low-income children were in some need of special
assistance. While there was general agreement that
such school districts needed more money, there ex-
isted by no means any fully consistent statement of
the nature of special burden which low-income chil-
dren represented. In fact the statute related the level
of funding to the number of low-income children but
left it up to individual school districts to assess the
requirements of their children and to plan programs
accordingly.
   A measure of Need that is perfectly congruent
with the definition of that Need is almost never
available. As a consequence the program designer
must resort to some proxy indicator, and the choice
of a suitable proxy is by no means trivial. Surround-
ing Title I, for example, there was considerable de-
bate over the proper measure of low-income status,
and the measure was in fact improved in 1974. Yet,
the 1974 debate did not resolve all questions con-
cerning the appropriate measurement of the target
population or even settle its definition. Dissatisfac-
tion with the criteria of disadvantage embodied in
the present formula led the Congress to commission
a study at HEW on the measure of poverty (which
was completed in 1976) and a related set of studies
to be carried out by the National Institute of Educa-
tion of the feasibility and probable impact of using
measures of educational rather than economic dis-
advantage for Title I ESEA fund allocations.
   As noted in Chapter I, in adopting allocation
formulas Congress frequently takes into account
some measures of what we have termed in this re-
port Capability and Effort. These are, if anything,
more difficult to define than Need, and may involve
problems of measurement as well. After the program
designer has set forth a working definition and meas-
ure of each of these elements the actual process of
formula construction properly begins. At that point
there is a wide range of possible allocation formulas
which might be constructed as well as a variety of
possible constraints and special rules.
   A central question that must be answered by the
program designer is in what way the resulting alloca-
tions should vary over the range of possible values
of the measures of Need, Capability, and Effort,
and also reflect considerations not accounted for
by these concepts. In some cases the difficulty of
ameliorating a social problem may be proportional to
the measure of Need, so that a linear allocation
formula would be appropriate. In other cases a non-
linear relation between the allocation and the Need
measure may be called for. If the designer wishes to
take into account Capability or Effort, then the max-
imum and minimum allocations for a given Need
must be decided in relation to the expected range of
measured Capability and Effort. There may also be
other desired patterns of allocation to meet policy
purposes other than those reflected in the measures
of Need, Capability, and Effort.
   Once these issues are settled, the formula can be
                                        9

constructed. This process necessarily includes both 
policy and technical considerations. The central 
technical problem is the choice of a mathematical
structure which in some sense best utilizes available
data to produce the desired allocation pattern. As
discussed further below, there are additional issues of
data limitations, of interactions between the formula
and data, of the dynamic properties of the formula,
of its understandability to the public, and of its
computational efficiencies.
   The essential elements in the choice of a mathe-
matical structure are as follows: (1) the class of the
formula (e.g., additive as in the CDBG program or
multiplicative as in General Revenue Sharing); (2)
the weights or scale factors to be applied to each of
the terms in the formula (e.g., giving unit weight to
relative population and to overcrowding, double
weight to poverty in CDBG); and (3) the specifica-
tions of constraints, if any, on either particular vari-
ables or on the resulting allocation (e.g., floors and
ceilings on the cost factor and hold-harmless levels
on the allocation in Title I ESEA). The statistical
consequences of these choices are often not fully
understood by either statisticians or program de-
signers. Although the design sequence can be de-
scribed as a set of logical choices, the sequence and
timing of such choices will vary from program to
program. In addition, both the valid demands of the
political process and the primitive state-of-the-art of
formula practice lead to choices at every stage of the
program design whose full statistical and distribu-
tional implications cannot be foreseen at the time
they are made.
   For example, floors and ceilings or other types of
constraints involve in some sense a distortion of the
ideal allocation. As noted in Chapter I, the setting
of such constraints is sometimes an attempt to limit
annual variations in allocation levels and sometimes
an attempt to modify a less-than-ideal formula by
making sure that no one gets too much or too little.
In either case, constraints may influence allocations
more strongly than they were intended to. A striking
example of this effect is seen in General Revenue
Sharing under which townships with minor govern-
mental functions are guaranteed a sizable minimum
payment--a consequence that was not generally, an-
ticipated at the, time the law was passed.
   The complexity of the task of selecting a formula
structure leads in practice to other problems. Every
allocation formula represents a simplification of the
real world. We have just pointed out that constraints
distort an ideal allocation, but the very notion that
ideal allocation could be described for reference
purposes implicitly assumes that we are willing to
determine just how much of the fine-grain complex-
ity of the real world should be captured in such an
ideal formula. While technicians might reach some
consensus on the attributes of an optimal degree of
simplification, no statement of principles based on
such a technical consensus would be immune from
criticisms that some important aspect of reality was
omitted from a formula designed according to such
principles. This point serves to reinforce our recog-
nition that formula building if it is to be successful
in implementing legislative goals should not be the
exclusive province of either the technician or the
Politician.
   An important implication of the need to accom-
modate both political and technical considerations is
that an allocation formula should be comprehensible
to all parties involved. The policymaker needs to
understand more about an allocation formula than
just bow much money it allocates to various jurisdic-
tions this year. The formula should be transparent
enough to support direct analysis of its distributional
effects --across States and within States--at a point
in time and as well as over time. The recipient--
whether local official or ultimate beneficiary--should
at the very least be able to verify the correctness of
his allocation. For example, the General Revenue
Sharing formula is extremely complicated, both in
the determination of State allocations and in the
division of funds within States. The procedure for
allocation to States, which resulted from a compro-
mise between House and Senate, combines two form-
ulas to give each State the higher of two computed
allocations. Because there is a fixed total appropria-
tion for the program, the actual computation must
be carried out iteratively, and only expert analysts
can estimate the impact of even very simple changes
in the existing formulas. Thus we see that lack of
transparency in the formula for an ongoing program
can be an important deterrent to meaningful at-
tempts at reform of existing programs.

     Problems Arising From the Nature of the
     Data Used and From Interaction of
     Data aid Formulas Over Time

   However difficult it may be to understand and
evaluate the performance of a formula at one point.
in time, the task of foreseeing and assuring good
performance through time is even more difficult.
There seem to be three issues: (1) The formula may

                                        10


require data which cannot be updated frequently,
and the degree of distortion caused by the use of
obsolescent data can neither be bounded closely in
advance nor estimated precisely at the time current
allocations are made; (2) Statistics which can be
updated for formula use may slowly or suddenly de-
part from their historical behavior and from their
assumed stable relationships with other variables;
and (3) The social or economic problem to which
the program is directed may evolve in such a way
that the measures chosen to represent Need, Capa-
bility, and Effort may cease to be the most relevant
measure available.
   All of these issues are illustrated by the history of
the measure of economic disadvantage used in Title
I, ESEA. This measure has been and continues to be
the sum of counts obtained from various sources.
Census counts for 1960 were a major component in
the Title I measure from 1965 until 1973, by which
time they were hopelessly out of date. Annual counts
of children in families receiving a high level of
AFDC payments departed from their historical be-
havior shortly after Title I was enacted, as a result
of an unprecedented increase in the AFDC caseload
and of the onset of an unforeseen price inflation.
While in 1965 the AFDC counts represented about
ten percent of the total Title I measure, by 1974
they were sixty percent of the total measure. While
some growth in the importance of the AFDC counts
might have been expected in 1965, it was not antici-
pated that they would become the dominant compo-
nent. While it could have been predicted that the
fixed dollar family low-income threshold specified in
Title I ($2,000), would become quite inappropriate
upon the introduction of 1970 income data, Congress
took no action to revise this specification until the
effects of the use of the old cutoff with 1970 data
were evident in the 1974 Title I allocations (see also
Appendix B-1, "AFDC Counts and ESEA Title I").
   Our third issue is illustrated by the rapid expan-
sion of in-kind transfer programs, such as Food
Stamps and Medicaid, whose income equivalent is
not currently counted in family income statistics
from the decennial census and the Current Popula-
tion Survey (CPS). Depending upon the distribution
of in-kind benefits, they might bias relative measures
of low-income status across geographical areas. The
degree to which they depart from such a uniform
relationship with money income is not fully known,
but the magnitude of these in-kind programs raises
the possibility of serious bias.
   Both here and at earlier points in this chapter we
have reviewed. issues which demonstrate that data
and measurement limitations may dominate all other
considerations in formula design and assessment. As
we have stressed before, no measure can be perfect
in all respects. One of the most difficult tasks in pro-
gram design is to determine in advance whether a
measure will prove to be at least minimally accept-
able. A recapitulation follows of the different ways
in which an operational measure may fail to fulfill
the objectives of the program drafter.

(1)  Lack of fit between a measure and the real
     world phenomenon it is intended to portray.

   An inappropriate measure may be chosen because
of its familiarity or its intuitive appeal. Within
CETA, for example, the local unemployment rate is
used both to measure the need for public employ-
ment, of which it is probably a satisfactory indicator,
and to measure the need for job training, for which
there may well be more appropriate though less
familiar measures. The overcrowding index used in
the CDBG program is a good example of a mea-
sure, the intuitive plausibility of which may exceed
its suitability to the program in question. What
makes the index attractive, however, is that it
conveys some information about whether the in-
adequacy of housing leads to hardship. This possible
relationship is certainly something one would want
to measure in a Federal housing program. The over-
crowding index, though, may be inferior as an indi-
cator of the quality of the kind of housing generally
available to the poor when compared to some pos-
sible physical measure of housing stock quality which
contains no overt reference to occupancy. However,
no simple measures of the physical quality of housing
is available at this time. Perhaps CDBG should con-
sider developing a more comprehensive measure of
housing needs in which the overcrowding index is
only one of the factors.
   As the case study on General Revenue Sharing
indicates, the use of per capita income as a measure
of Need has been criticized despite its obvious virtues
of familiarity and general plausibility.

(2)  Accuracy of a measure for the geographical
     area it applies to.
   This presents a problem for all programs which
require formula allocation to small areas. The un-
employment data for CETA and the poverty data for
Title I, ESEA are pertinent examples. In the case of
CETA, the flexible definition of labor market areas,
although perhaps desirable for policy reasons, is

                                        11

made less desirable because of the inadequacy of the
statistics from which area Need must be calculated.
   In the case of Title I ESEA the congressional in-
tention to allocate directly to school districts was
thwarted by the inadequacy of school district poverty
data, and instead allocations were made to counties,
with the States being responsible for subcounty allo-
cation to school districts.
(3)  Stability of a measure in relation to the fre-
     quency of updates.
   Data which are expensive to gather as well as sub-
ject to considerable variability through time may not
be cost-effective for allocation purposes. This is the
chief obstacle to the generation of small area price
deflators which could be used to adjust grant levels
to local price differences.

                                                       CHAPTER III

                                Subcommittee Findings
   In this chapter, we will present four major findings
together with some illustrations.


                Finding No. 1

   There are very real difficulties in translating con-
gressional intent into statistical terms.
   We will illustrate this finding by reference to the
Community Development Block Grant program au-
thorized by the Housing and Community Develop-
ment Act of 1974.
   a.  Section 101(c) of the Act states that "The
       primary objective of this title is the develop-
       ment of viable urban communities, by provid-
       ing decent housing and a suitable living
       environment and expanding economic oppor-
       tunities, principally for persons of low and
       moderate income."
   b.  The section goes on to say that the CDBG
       Federal assistance is for the support of com-
       munity development activities directed toward
       certain specific objectives, including "the elimi-
       nation of slums and blight and the prevention
       of blighting influences and the deterioration
       of property and ...facilities...; the elimina-
       tion of conditions which are detrimental to
       health, safety, and public welfare, through-
       code enforcement, demolition,...; the con-
       servation and expansion of the Nation's hous-
       ing stock ...; the expansion and improvement
       of the quantity and quality of community
       services...; a more rational utilization of
       land and other natural resources...; the re-
       duction of the isolation of income groups
       within communities and geographical
       areas...; the restoration and preservation of
       properties of special value for historic, archi-
       tectural, or esthetic reasons."  
   c.  As described in the CDBG case study, the al-
       location and distribution of funds is specified
       in the Act on the basis of a three-term additive
       formula counting population, poverty (weight-
       ed twice), and housing overcrowding--where
       the count for, say, a metropolitan city is en-
       tered as the numerator in each of three ratios
       with the denominators being the counts for
       all metropolitan areas. In the framework of
       our report this is a Needs formula with no
       explicit components for Capability or Effort.
   d.  Congress apparently felt that the extent of
       poverty and housing overcrowding were rea-
       sonable surrogates for its target population
       (persons of low and moderate income) and
       for the conditions it hoped to alleviate (slums,
       blight, inadequate services, etc.). They did not
       try to legislate the use of some direct measure
       of housing quality or service adequacy. But
       a paradox remains: Two communities of the
       same size, poverty count, and overcrowding
       index might have, to an impartial observer,
       two quite different levels of adequacy of hous-
       ing stock and services.
   e.  As can be seen from the above discussion, it
       would be very hard to construct a formula
       that would adequately operationalize the goals
       of the Act. It should be noted that Congress
       is expected to reconsider the CDBG formula
       during the 1977 session, partly in recognition
       of some of the problems outlined above (1.d).
   f.  The CDBG program illustrates the potential
       conflict between policy objectives and the
       rationalization of formula and data require-
       ments. In this case, the broad objectives make
       it difficult to define and measure Need in the
       program formula. Congress set up CDBG to
       consolidate a number of categorical programs.
       One objective of CDBG was to allow for con-
       siderable local discretion in the specific pur-
       poses to which the allocated funds would be
       applied.  Accordingly, a large number of pro-
       gram goals were recognized, and, purposely,
       there was no ranking of the various possible
       objectives.


                Finding No. 2

  Current administrative and statistical practices
do not always deal adequately with the problems
that have been identified in Chapter II.
   a.  A good example of "why... existing alloca-
     tion formula techniques do not fully achieve
                                13

     
the stated objectives of Federal programs"
may be found in the methods for counting
Title I ESEA eligibles.
   With regard to the problems arising from the
nature of the data used, the law specifies a
determination of the "number of children aged
five to seventeen, inclusive, from families
below the poverty level on the basis of the
most recent satisfactory data available from
the Department of Commerce for educational
agencies (or ... counties) ... utilizing the
criteria for poverty ... in the 1970 Decennial
Census." There is a parallel provision for
counting some disadvantaged children (AFDC
recipients, etc.) above the poverty level.
     (1)  The "most recent satisfactory data" may
          not in fact be recent enough to be satis-
          factory. Furthermore, in spite of the age
          of the data, no provision has been made
          for a reinterpretation of the counts in a
          way that might constitute a partial adjust-
          ment for time effects. For example, instead
          of the cohort aged 5 to 17 in 1970, the
          cohort aged 0 to 12 in 1970 (which was
          aged 5 to 17 in 1975) might be consid-
          ered as a relevant reference group for
          current allocations.
     (2)  The argument is sometimes made that 
          the Title I formula is partly protected
          from obsolescence by the inclusion of
          the AFDC factor which in some sense
          can update the eligibility counts, even if
          the poverty counts cannot be updated.
          As pointed out in Appendix B-1, the
          AFDC component is only  about 7 per-
          cent of the total and is distributed among
          States and counties very differently from
          the poverty count--in either 1970 or,
          say, 1975.
   b.  Another example is provided by the General
       Revenue Sharing program, which has been
       operational for more than six years. Much
       of the criticism of the program has been
       focused on how well the formula structure
       reflects the needs of the recipient localities.
       The GRS program distributes funds to approxi-
       mately 39,000 jurisdictions, the great majority
       of which are areas of population less than
       2,500 in the 1970 Census of Population. Be-
       cause of the complexity of dealing with differ-
       ent kinds of local governments, and the se-
       verely limited data available for this purpose,
       GRS has used a uniform procedure that treats
       similarly governmental units with very differ-
       ent sets of responsibilities.
         In addition, the use, of GRS as a counter-
       cyclical device is hampered by considerable
       data lags. Despite the procedures involved for
       updating census money income (one of the
       elements of the formula mandated by the Act),
       based on the more current IRS wage data
       (used in conjunction with BLS county and
       State wage data) and the BEA county per-
       sonal income data, there is still a lag of sev-
       eral years between the reference year of the
       data used in the formula and the year in which
       the allotment is made. Even if the currentness
       of the inputs could be improved enough to ap-
       preciably narrow the gap it could not be done
       without introducing other difficulties. Although
       improvements in the formula have been pro-
       posed, introducing other elements purported
       to be better indicators of Need, these other
       elements also can be measured only with sev-
       eral years' lag, and may not even be available
       for smaller areas or only with some sacrifice
       of precision.
         A further criticism has been that occasional
       sharp fluctuations in the size of the allotment
       for a given area from one period to the next,
       caused by unusual variations in the data inputs,
       tend to hamper long-range planning by the
       recipient governments for efficient use of the
       revenue sharing funds. However, changing a
       formula structure which has been in operation
       and has come to be generally accepted by all
       levels of government could be more disruptive
       than the occasional random fluctuations in al-
       lotments encountered with the present formula.


                Finding No. 3

   The nature of the statistical problems arising in
formula programs is such that present knowledge
does permit the identification of at least some interim
principles. There are some existing programs for
which the existing formulas or allocation rules ap-
pear to be satisfactory from a statistical standpoint.
   a.  One example may be found in the AFDC case
       study. Whether or not the resulting reimburse-
       ment levels to the individual States are com-
       pletely appropriate is a matter for Congress
       to consider from time to time. But there are


       no apparent statistical bases for concluding 
       that the resultant reimbursements are inappro- 
       priate. There is an inverse relationship between
       per capita income (PCI) and reimbursement
       rates. If this were adopted simply as a fair
       relationship it would be hard to argue that it
       is not. By that standard there would appear
       to be no serious problems with the current
       practice. If the inverse relationship were inter-
       preted as an incentive device to get the poorer
       States to set up programs comparable to those
       of the richer (higher PCI) States with higher
       benefit levels, then that Federal purpose would
       have to be seen as not fulfilled by the match-
       ing rate rules, since the poorer States have not
       so responded.
   b.  Another example concerns the Comprehen-
       sive Employment and Training Act of 1973.
       The major portions of the funds allocated by
       formula under Title I of that Act are distrib-
       uted in a manner that incorporates several
       elements that are sound from a statistical
       standpoint:
     (1)  The units to which funds ire allocated,
          the prime sponsors, are large (100,000
          or more population) and thus avoid the
          problems associated with the preparation
          of estimates for very small units.
     (2)  The prime sponsors are defined in terms
          of units of general local government.
          While these may be combined into vari-
          ous configurations, this eliminates the
          difficulties associated with the develop-
          ment of estimates for neighborhoods or
          other parts of cities or counties that do
          not have an established geographic defini-
          tion.
     (3)  The unemployment data used in the allo-
          cation is based on annual averages. It
          is, therefore, not subject to seasonal influ-
          ences and the distortions that they can
          inflict on the allocations. The use of an-
          nual averages is, in a sense, an example
          of the use of the best available data from
          a single standard source--the Current
          Population Survey (CPS). However, the
          CPS is used only for the States and 30
          SMSA's and 10 central cities; a problem
          remains for large counties and large
          cities. Moreover, the formula incorporates
          legislative determination that while all
          areas need manpower services, the need
          is greater where the number of unem-
          ployed is higher. The distribution is there-
          fore based on the number of employed.
     (4)  The problems of administering a continu-
          ing program of manpower services with a
          shifting financial base are recognized by
          providing a floor based on the preceding
          year's allocation below which the funding
          of the current year cannot fall, and a
          ceiling above which the allocation cannot
          go. Title I, CETA avoids wide year-to-
          year swings in the allocations received
          by prime sponsors. It does this both by
          distributing funds largely on the basis of
          the previous year's allocation, and also
          by providing floors and ceilings, based on
          the previous allocation, beyond which
          the current allocation cannot go. This
          facilitates the chief objective of Title I--
          to provide a continuing program of man-
          power services--by keeping funding
          levels relatively constant and predictable.
   c.  The third example concerns the sub-county
       allocation system in Title I ESEA. This is a
       creative approach to the problem of alloca-
       tion to small areas, in this case to school dis-
       tricts. The data used in the formula to allocate
       to counties--1970 poverty counts, special
       AFDC tabulations, and counts of neglected,
       delinquent, and foster children--are not cur-
       rently available at the district level to the Fed-
       eral Government. States therefore have been
       given the right to allocate county funds to the
       school districts in each county, using the most
       recent appropriate data. The Federal guide-
       lines recommend census And AFDC data, but
       States may choose among a number of data
       series. While not without problems, the sys-
       tem appears to work relatively smoothly. One
       benefit of this system is that questions about
       the correctness of the data for very small
       districts can be raised as well as resolved
       locally, by people familiar with the actual
       conditions.


                Finding No. 4

   The present state-of-the-art will not permit for-
malization of a fully definitive or wholly acceptable
set of statistical rules for formula programs. In view
of the present gaps in our knowledge there is a need

                                        15

for some short-range applied research on problems
of allocation statistics. For example, while the use of
quadratic loss functions (minimizing the mean
squared error) is well established, there appears to
be a need in formula research for the use of asym-
metric loss functions. At present there is little readily
applicable theory and some research is needed soon
on this topic as well as on related problems in ap-
proximation theory (also see Appendix B-5, "An
Agenda for Basic and Applied Research Problems").
                                        16
                                                       CHAPTER IV

     Ways to Reduce Allocation Errors and Inequities

          Introduction                                    

   It is usually easy to arrive at a consensus that the
allocation of funds under any given program is in-                  
equitable. However, it is often difficult to get any                
agreement on the nature and location of the inequities
and even more difficult to get agreement on how to
correct the inequities. There are, though, some                     
aspects of allocation formulas and the data used in             
them which lead to substantial discrepancies from
the intent of the original legislation. This chapter            
addresses this type of problem.
1.  Problems arising from the data used. In con-
    nection with data used for allocation, there are
    rather complicated trade-offs among five factors,
    three of which are relatively well understood (at
    least we think we know what they mean), namely
    bias, variance, and cost. The other two are the
    timeliness of the data (the time-frame of the
    data) and the appropriateness. The appropriate-
    ness can be defined as the extent to which the
    concept one is using (no matter how well or
    poorly it is measured), approximates the thing
    that one really wants to measure.
    a.  Updating. Before discussing the interaction
        of the five factors, a few observations are in
        order on timeliness and the question of up-
        dating statistics for use in allocation formu-
        las. As noted in Chapter I (p. 6) the appro-
        priate time reference (timeliness) varies from
        program to program. In the field of govern-
        ment action, one can distinguish between pro-
        grams to meet immediate (and very time-
        dependent) requirements and those designed
        to deal with situations which change rela-
        tively slowly over time. In the first category
        are those welfare and unemployment insur-
        ance programs designed to deal on an emer-
        gency basis with immediate problems. The
        impact of this type of problem on any given
        area at any specified time is largely unpre-
        dictable. Here one is dealing primarily with
        questions of accounting for funds after they
        have been spent, rather than of allocating
        funds to specific areas. This type of problem
        is best handled by providing for a central
        pool of Federal or State funds which is drawn
        upon as required locally. To the extent allo-
        cation of Federal funds is involved, the sta-
        tistical problem becomes one of determining
        the amount of allocations appropriate to
        maintaining the State or local pools of funds
        at (legislatively) specified levels over a time
        period of a year or more.
           Thus, even when there is the requirement
        for immediate action that varies locally from
        month-to-month (and even week-to-week),
        updating of data used for allocations is not
        necessary more frequently than once a year.
        Where the basic economic and social condi-
        tions at which a program is aimed change
        slowly, updating statistics every 2 or 5
        or even 1O years may be adequate. In the
        case of programs involving massive training
        or building programs (highway and mass
        transportation programs, slum clearance,
        teacher training or retraining of individuals
        in declining industries) frequently updated
        figures, even for rapidly changing situations,
        may be of little appropriateness for fund
        allocation, since a large portion of the work
        in progress must be completed even though
        plans for future work may need drastic re-
        vision.
    b.  Trade-offs. The total population of an area
        is a factor in many allocation formulas and
        the problem of making estimates of popula-
        tion illustrates the trade-off among bias, vari-
        ance, cost, timeliness, and appropriateness.
        The cheapest estimate that might be in any
        sense acceptable is, of course, the population
        of the area based on the most recent decen-
        nial census. However, for some allocations,
        the decennial census figures are out-of-date
        by the time they are published. Even if one
        uses the hand counts (announced locally
        immediately after completing the census field
        work) and takes the risk of major differences
        from the final revised figures, decennial cen-
        sus figures are at least 10 years old by the
        time the figures for the next decennial census
        are available.
           The recent authorization of quinquennial
                                        17

        censuses will somewhat reduce the problem
        of updating population census figures; but
        the cost of taking a 100 percent census will
        almost certainly mean that the 1985 enumer-
        ation will be on a sample basis. While the
        sampling biases and variances of a sample
        census will be small for most states and for
        major metropolitan areas, the sampling errors
        for small areas will be, at a minimum, a
        source of considerable controversy (e.g.,
        claims that "my city or county was 'robbed'
        in GRS allocations"). Even for the largest
        areas there can be considerable dispute since,
        while the relative sampling errors will be
        small, the absolute errors and the absolute
        sums of money involved may be substantial.
           For some uses, updating population figures
        every five years will be considered unsatis-
        factory; there is pressure for annual and bi-
        ennial sample surveys and for the use of
        more current statistics derived from admin-
        istrative records (birth and death registra-
        tions, income tax returns, school enrollments,
        etc.). The unit costs of a sample survey are
        high and, for a number of quite valid reasons
        (difficulties with privacy, confidentiality, pub-
        lic resistance, availability of satisfactory per-
        sonnel), are increasing, in spite of improved
        survey techniques and generally improved
        overall efficiency in the conduct of sample
        surveys. Even well funded and well con-
        ducted sample surveys (e.g., the 1976 Sur-
        vey of Income and Education) are restricted
        to small samples and also require the use
        of clustering in order to minimize travel time
        and other nonproductive expenditures. Small,
        highly clustered samples mean large sampling
        variances even for some relatively big areas,
        and also mean that many small areas will
        have no sample households at all.
           Using administrative records to update the
        population involves major problems and can
        involve serious biases. Applying statistics
        from birth and death registration records to
        the previous census should produce reason-
        ably good figures for areas which have had
        very little in-or-out-migration since the cen-
        sus. For the areas with relatively heavy (net)
        migration in the 1950's and 1960's (e.g.,
        California, Florida, Arizona, Nevada, Alaska,
        most metropolitan areas west of the Missis-
        sippi, rural areas of the South Central and
        West North Central States); estimates based
        on births and deaths tend to be improved by
        making an adjustment based on past migra-
        tion trends--e.g., using the average popula-
        tion change in any area due to migration
        (total population change less births plus
        deaths) from 1960 to 1970 as an estimate
        of the annual change due to migration since
        1970. Adjustment for past migration trends
        usually gives improved estimates for the
        areas with substantial past in- or out-migra-
        tion but it does not allow for the second
        (and higher) order derivatives of the popu-
        lation change curve for an area. Such an
        allowance can be made by using a curvilinear
        regression on past migration trends but this
        involves either using still earlier censuses
        (e.g., the 1950 and the 1960 censuses) and
        intercensal births and deaths to estimate net
        migration since 1970 or obtaining estimates
        of intercensal populations. While the use of
        past migration trends (linear or curvilinear)
        will improve most estimates of current popu-
        lation based on births and deaths, it results
        in poorer estimates for some areas because
        of the biases and variances of the estimates
        of past migration trends as well as changes
        in the shape of the population growth curve
        since the last census. While sudden and dras-
        tic changes in the shape of the population
        growth curve of an area are rare, they occur
        (e.g., the decrease in California population
        growth rates between 1960 and 1970) and
        in these cases there may be serious biases in
        the population estimates in spite of the ad-
        justment.
           Similar difficulties of bias and variance
        occur in the use of estimates based on other
        administrative records. For example, popula-
        tion estimates derived from income tax re-
        turns do not provide for persons who did not
        file a tax return for the given year. Partial
        adjustments for these omissions could be
        made by using supplementary sources (e.g.,
        W-2 files, files of welfare families) but adjust-
        merits (e.g., determining how many persons
        are represented by W-2 forms to adjust for
        the cases where the income recipient did not
        file a 1040 return) are difficult and the esti-
        mates will still be deficient for other reasons
        (e.g., individuals may not be shown as de-
        pendents or income recipients in any source).

                                        18

        The estimates can be improved by using the
        administrative records to estimate change in
        an area since the last census (rather than the
        current population level) and by applying
        this estimated change to the census figure for
        that area. Similarly, the percent change since
        the census in school enrollments can be ap-
        plied to the census population to produce a
        current estimate. One can also use a combi-
        nation of change in income tax and enroll-
        ment statistics to estimate current population
        by applying the regression of the census
        population on census-year tax returns and
        school enrollments to current-year tax re-
        turns and school enrollments.
           For some allocations updating the census
        population counts may be unnecessary. How-
        ever, even for these cases, there is a ques-
        tion of biases in the counts. The Census
        Bureau estimates that, even after very vigor-
        ous efforts (and very large expenditures) to
        obtain 100 percent coverage in the 1960 and
        1970 Censuses, there were undercounts of
        2.7 and 2.5 percent. It is likely that census
        techniques in 1980 will have to be improved,
        and efforts and expenditures per capita will
        have to be increased even to attain the 97.5
        percent coverage level of 1970.
           The trade-offs of cost, bias, variance, and
        appropriateness are particularly evident in
        the area of control and estimation of census
        coverage error. There is, for example, the
        question of trying to reduce differentials in
        coverage among areas and subgroups. For
        several reasons Black, other minority, and
        low income groups are more difficult to enu-
        merate completely than the rest of the popu-
        lation. The coverage problem is particularly
        acute for certain types of areas, e.g., sparsely
        settled rural areas and ghetto areas in large
        cities. Frequently improving coverage of the
        poorly enumerated groups and areas requires
        very much higher census expenditures per
        household, and this, in turn, raises the ques-
        tion of reducing expenditures elsewhere or
        increasing total census costs. Reducing ex-
        penditures elsewhere may mean slightly
        higher overall bias in order to decrease the
        differentials in coverage bias.
           The handling of imputations in a census
        also provides an example of the problem of
        balancing variance, bias and cost. Because
        of imperfections in the most well-designed
        census, problems of imputing for known
        errors always arise. Thus, discrepancies be-
        tween the area hand counts and the initial
        machine counts have existed for every census
        where tabulation machines or computers
        have been used. These may be due to errors
        in addition, to failure to count some census
        sheets or lines, to errors in the hand count,
        to questionnaires lost in transit to the proc-
        essing center, to questionnaires misfiled and
        lost in the sheer mass of paper, to failure to
        punch or film questionnaires or groups of
        questionnaires, to errors in punching or opti-
        cal sensing of the questionnaires, etc.
           In the 1970 Census possible errors in the
        census counts were also signaled by the
        Vacancy Recheck and PEPOC (the Post-
        Enumeration Post Office Check). These in-
        volve checking units reported as vacant to
        determine whether they were, in fact, vacant,
        and having the local post office check the
        census listing for possibly missed households
        for those areas where a post office check was
        not done before the enumeration.
           Possible census errors detected by discrep-
        ancies between hand and machine counts or
        by. a vacancy recheck or by PEPOC can be
        met by:
        (1)  ignoring the possible hand count or
             vacancy recheck or PEPOC results,
        (2)  tracing the errors and making correc-
             tions,
        (3)  reenumerating areas or units where er-
             rors are detected, and
        (4)  imputing more correct values.

           All of these methods were used in the
        1970 Census. Small discrepancies between
        hand and (initial) machine counts were
        ignored; some misfiled questionnaires were
        detected and the appropriate counts cor-
        rected; a sample of vacant units and a sample
        of the enumeration districts where PEPOC
        showed possibly missed households was re-
        enumerated; the results from the Vacancy
        Recheck and PEPOC samples were used to
        impute corrections for the nonsample vacant
        units and the nonsample enumeration dis-
        tricts of PEPOC; and imputations were also
        made where the initial machine count was
        well below the hand count and investigation
                                        19
     
        confirmed that the hand count was more
        accurate.
           With respect to updating and coverage
        error and imputations, possible solutions in-
        volve some compromise among the five fac-
        tors. Thus, in a quinquennial sample census
        there may be a satisfactory compromise be-
        tween the low cost, low variance, and poor
        timeliness of using decennial population fig-
        ures, and the increased cost, high variance
        and bias, and good timeliness of using annual
        sample survey estimates. Essentially making
        imputations based on a sample check (as
        was done for the Vacancy Recheck and
        PEPOC) is a compromise between the bias
        and low cost of not correcting for the known
        census error, and the lower bias and higher
        cost of trying to follow-up and (re)enumerate
        all of the questionable cases.
           A form of compromise which seems par-
        ticularly desirable for the problems of up-
        dating and adjusting for undercoverage is the
        use of low bias and high variance data from
        a small sample study to adjust higher bias
        but low variance estimates from a larger,
        scale study. Thus, for updating population
        data we could use the high variance and low
        bias of changes measured from, a small
        annual or biennial sample survey to correct
        the bias of (zero variance) statistics derived
        from administrative records. By substituting
        regression of the changes on other character-
        istics, we decrease the variance of the result-
        ant estimates with some (hopefully small)
        increase in bias. In estimating undercoverage,
        we can correct biased estimates from a large
        sample survey by the low bias results of
        small samples of administrative records (from
        IRS, Medicare, driver's license files, etc.)
        matched to the census. By using regression
        techniques, we can obtain considerable reduc-
        tion in the biases of the estimates from the
        large sample source and avoid the high vari-
        ances of the estimates for individual areas in
        the small sample study. The impact of errors
        on allocation is discussed in Appendix B-2,
        "Technical Notes on Sensitivity Analysis".
        Raking as a statistical adjustment procedure
        may be used to reduce error in data (see
        Appendix B-4).
   c.   Data Comparability. Where different areas
        (States, counties within a State, school dis-
        tricts within a county) are in competition for
        a share from the same pot, equity dictates
        that the allocation data for the competing
        jurisdiction be as nearly comparable as
        possible. Comparability is usually attained
        by taking the estimates for all competing
        jurisdictions from the same source. Thus, the
        population estimates for all States might
        come from the census, and adjustments for
        updating would all be computed in the same
        way--e.g., from the regression of data from
        a national sample survey on the numbers of
        taxpayers and dependents (determined from
        Federal income tax records) and current
        school enrollments.
           The fact that comparability between com-
        petitive jurisdictions is frequently best served
        by taking the data for these governmental
        units from the same source, has been ex-
        tended into a rule that data for all jurisdic-
        tions, competitive or noncompetitive, must
        come from the same source. Such a rule can
        actually lead to less rather than more com-
        parability. It may, in fact, force the use of
        grossly inadequate data because the only
        source available for all jurisdictions is a very
        inferior source. In tiered allocation systems <ftnref marker="6">
        it may be better to use a common data
        source at any one level but not to insist on
        using it at all levels. Thus, sample survey
        estimates of current State populations might
        be the best estimates for the allocation of
        funds to States, but, for allocating the total
        for a State among cities and counties, we
        might use estimates based on adjusting 1970
        Census populations for changes in school
        enrollments and in the number of income tax
        payers and dependents.
           It may even be desirable to use different,
        data series for allocations within different
        States. Thus, one State may be able to get
        a quite good estimate of the population of
        each city and county (and also of each town-
        ship and city ward) in the State from the
        regression of census population on the num-
        ber of registered voters plus school enroll-
        ments, while the voter registration and school
        enrollment statistics would be much inferior
                                        20

        for another State in projecting past inter-
        censal population increases.
           The use of different data series for differ-
        ent levels and for different allocations within
        a level is a case where the use of non-
        identical data actually helps to maintain
        comparability. A much more difficult prob-
        lem is the availability of better data for a
        few jurisdictions in a set of competing juris-
        dictions. For example, one city in a State has
        a special census taken which shows a popu-
        lation increase for the area of 30 percent
        since the previous census, as against the esti-
        mates of population growth of five to nine
        percent obtained for this city and other cities
        and counties of the State by projecting popu-
        lation trends shown by the last three decen-
        nial censuses. Is it proper to use the popula-
        tion figure from the special census for this
        particular city when no comparable figures
        are available for the other cities and counties
        of the State? One could argue that using the
        special census estimate gives an unfair ad-
        vantage to this city since other cities or coun-
        ties may have had similar or greater popula-
        tion growths. On the other hand, it could be
        argued that there are, at most, two other
        areas in the State that had more than nine
        percent population growth and that it is
        unfair to penalize this city because the other
        areas of the State had no reason to take a
        special census. Solutions to the problem
        might be:
        (1)  to try to find some method using already
             existing data which would properly re-
             flect post-censal population growth for
             all areas of the State, or
        (2)  to execute a small sample survey to
             determine whether any other city or
             county has had unusual population
             growth and follow up by larger sample
             surveys of those jurisdictions which do
             show large population changes.
   Problems arising from the formula. There are
   many alternatives in the construction of alloca-
   tion formulas. For some of these alternatives (e.g.,
   the use of an additive versus a multiplicative
   formula) the pros and cons are pretty evenly
   balanced and the choice becomes a matter of
   purposes to be served, the data available, and
   individual tastes. There are a few alternatives
   which are clearly inferior from both a statistical
   and policy standpoint. The handling of cutoffs
   is one of these.
   a.  Additive versus multiplicative formulas. In
       a multiplicative formula the allocation is
       automatically, equally sensitive to variation in
       any of the factors. That is, a 10 percent
       change (or a 10 percent difference between
       two areas) in any factor will mean a 10 per-
       cent difference in the allocation (unless the
       formula includes a cutoff provision). In an
       additive formula weighting is needed to de-
       termine the relative sensitivities of the allo-
       cation to the different factors in the formula.<ftnref marker ="7">
       Weights are frequently arbitrary and poor
       choice of weights can lead to serious dissatis-
       faction with the operation of an additive for-
       mula. On the other hand, if a multiplicative
       formula is used, a small error in one factor
       can throw the whole allocation seriously off.
       Thus, one is damned if one does, and damned
       if one doesn't. The choice of the formula
       type must, then, depend upon judgments of
       the accuracy of the various data to be used
       versus the availability of suitable weights for
       an additive formula. It is important to pro-
       vide for constant monitoring of the allocation
       system so that major errors in the data can
       be promptly detected and corrected for mul-
       tiplicative formulas, or so that a poor choice
       of weighting factors (or a major shift in the
       underlying causal system) can be promptly
       detected and corrected for additive formulas.
   b.  Cutoffs. Undesirable discontinuities may be
       introduced into an allocation system by cut-
       offs, especially by eligibility cutoffs. For
       example, if an area must have an unemploy-
       ment rate of five percent before it can receive
       any funds, a very trivial error in the estima-
       tion of the unemployment rate can easily-
       throw an area from under five percent or
       from over five percent into the other group.
       Here a very small error can make a tremen-
       dous difference and lead to continual com-
       plaints about the accuracy of the data on the
       part of governmental units which feel the
       cutoff operates to their disadvantage.
          A common solution to controversies over
       cutoffs is to provide alternative formulas and
       to permit each jurisdiction to select the for-
       mula which is most advantageous. While this
                                        21
     
       works moderately well, it has the disadvant-
       age of making it difficult to predict in ad-
       vance (and budget for) the amount required
       for the program if no fixed overall sum to be
       allocated is specified. If an overall sum is
       specified but each jurisdiction may choose
       which formula it will use in determining its
       share (with the computed amounts totaled
       over all competing jurisdictions, so that the
       percent of the total allocated to each juris-
       diction can be determined), one gets a float-
       ing cutoff, where the amount one jurisdic-
       tion gets depends upon the decisions made
       by other jurisdictions.
          For eligibility cutoffs it is almost always
       possible to devise a formula such that there
       is a gradual approach to zero (or to some
       cutoff point lower than the existing absolute
       cutoff). Here small errors in the data lead
       only to small changes in the allocation and
       the tendency to prolonged (and insoluble)
       arguments over minor errors is removed. Of
       course, major errors will and should con-
       tinue to be the subject of controversy but one
       will be spared the waste of time and effort
       involved in the use of a formula which re-
       quires data of unattainable accuracy.
   c.  Sensitivity to change. In most cases it is
       desirable for allocation rules to be relatively
       insensitive to short-term fluctuations in the
       data but responsive to long-term changes.
       However, short-term and long-term are in
       the eye of the beholder. How short is short-
       term and how long is long-term? The answer
       varies from one program to the other. The
       CDBG obviously needs at least a four or five
       year period even to permit contemplation of
       a building project or the planning of any
       substantial building program. What one needs
       is something that will not be thrown totally
       off the target by short-term fluctuations. On
       the other hand, gradual change in response
       to changing needs is desirable and some type
       of damped dynamic system (for example, an
       exponential smoothing type of function) is
       required.
          CDBG appears to be the only one of the
       case studies which tried to use such a damped
       dynamic system (for bridging the transition
       to a drastically changed allocation system).
       The CDBG formula used for this purpose
       involves a so-called hold harmless provision.
       However, it should be noted that the hold
       harmless provisions of most allocation for-
       mulas are the reverse of damped dynamic
       systems. At one end, hold harmless clauses
       create a totally static situation, permitting an
       area to claim its allocation of last year (and
       possibly of several years previously) although
       conditions may have changed permanently so
       that a considerably reduced allocation would
       be quite adequate. At the other end, an area
       can claim a sharply increased allocation due
       to a temporary change in the local situation.
          When responsiveness to short-term prob-
       lems is desired, fixed annual allocations for
       every funding level usually are not appropri-
       ate. Switching of funds as needed, both from
       one time period to another and from one
       jurisdiction to another, may be required. In
       AFDC, funds are allocated for a year so that
       jurisdictions can determine approximately
       what to expect. The specific allocations are
       determined as the money is spent and can
       vary from month to month.
3.  Setting feasible accuracy goals. A major ques-
    tion is to what extent should one adjust the data
    to fit the accuracy requirements, and to what
    extent should accuracy requirements be adjusted
    to fit the data. Some people tend to think in
    terms of statistics that are literally correct and in
    terms of an absolute truth which must be met in
    fund allocations. Many law suits deal with errors
    in the data and with other errors which cannot
    possibly be avoided at a reasonable cost. We
    need to learn to accept the fact that the function
    of the statistician is not to provide error free
    data but to pick out those errors which are
    largest, and try to control them. As for the
    smaller errors, we must learn to live with them.
       Recognizing that errors in the data and result-
    ant inequities in the allocations are inevitable,
    major attention must be given to deciding which
    errors need to be reduced. As mentioned above,
    a subject of considerable controversy is whether
    one should try to minimize the sum of the abso-
    lute errors or of the relative errors (or of some-
    thing in between) in the data for individual
    areas.<ftnref marker="8"> When sample data are used, minimizing
    the sum of the relative sampling errors of the
    individual area figures leads to allocating the

    same number of sample cases to each area (e.g.
    to each State); minimizing the sum of the abso-
    lute errors leads to allocating a number of sam-
    ple cases proportional to the total population of
    the area.
       A commonly used compromise between the
    two allocation rules mentioned above (minimiz-
    ing the sum of the absolute errors vs. minimizing
    the sum of the relative errors) is
    a.  to minimize the sum of the absolute errors
        by assigning cases proportional to the area
        population;
    b.  if this would give any area a relative error
        larger than the predetermined error limit,
        increase the sample for the area(s) to the
        level necessary to give the desired relative
        error; and
    c.  reallocate the residual sample for the areas
        not changed by (b) above, proportionally to
        area populations.
       For fund allocation, this sampling design fits
    the logic that a big relative error for a small area
    leads to a serious error in the amount allocated
    to that area, but cannot have an appreciable
    effect on fund allocation to the other areas
    (since the amount of funds going to the area is
    small in any event), while, for the larger areas,
    even a small relative error can involve a sub-
    stantial sum of money and thus lead to inequi-
    ties in the allocations to all areas when the total
    amount to be allocated to all subdivisions is a
    fixed sum.
       The technique of proportional allocation with
    the overall sample set to give a predetermined
    maximum relative error for an individual area
    has some limitations. For example, the amount
    budgeted for the survey may not permit a sample
    large enough to achieve the predetermined maxi-
    mum relative error. An alternative is to use pro-
    rtional sampling for larger areas but to take a
    sample sufficient to achieve the maximum rela-
    tive error limit for the smaller areas. Further dis-
    cussion of these issues may be found in Appen-
    dix B-3, "Some Considerations in Designing
    Samples to Obtain, Data for Use in Allocation
    Formulas."
       Finally, there is no such thing as an ideal
    formula or ideal data. Therefore, one may have
    to sacrifice something in the formula and some-
    thing in the data in order to reach a reasonable
    compromise between an ideal formula with poor
    data or a poor formula with ideal data.
                                        23
                                        CHAPTER V

                Subcommittee Recommendations

   In Chapter II of this report, a number of causes
were identified that contributed to a phenomenon
encountered in the five case studies--that "existing
allocation formula techniques do not fully achieve
the stated objectives of Federal programs." Our re-
view identified problems of formula structure and
constraints, problems of implicit and explicit assump-
tions, problems arising from the data used, and some
effects of the interaction of formulas and data. In
Chapter III the Subcommittee has presented some
general findings on the basis of the five case studies
and in Chapter IV has identified some specific ways
to reduce allocation errors and inequities. On the
basis of these general and specific findings, the Sub-
committee has formulated the following set of recom-
mendations to improve the Federal process for spe-
cifying and administering the formula aspects of
grant-in-aid, programs, for dealing with statistical
considerations in formula construction, and for relat-
ing programmatic measures to ongoing statistical
series.
   The Subcommittee recognized in its review of the
five case studies that there were pervasive problems
in the obsolescence of key data, particularly where
decennial census data were required to be used, and
in the choice of statistics to represent small geogra-
phic areas. The Subcommittee feels that it is quite
important to recognize these elements as important
problems early in the program design process so that
sufficient attention can be devoted to the generation
of at least partially satisfactory solutions. The, spe-
cific recommendations on these points are as follows:

RECOMMENDATION  1. Program Goals and
Statistics:
   That program goals be specified as clearly and
completely as possible in the statement of purpose of
each grant-in-aid act and that program drafters guard
against over-specification of the statistical data and
procedures to be used.

Comment:

   Vague specification of program goals and over
specification of statistical procedures are common
problems. Providing flexibility to program admini-
strators in the choice of statistics for allocation is
sometimes desirable for a variety of reasons, but in
the absence of reasonably clear and complete goal
statements, administrative decisions which involve
use of that flexibility will necessarily be arbitrary to
some degree, and may run counter to the intent of
Congress. The AFDC counts in Title I, ESEA are an
example of highly specified statistical procedures
written into authorizing legislation. The Education
Amendments of 1974 describe with some precision
how to determine the number  of AFDC children
counted for Title I, ESEA funding, which year's
poverty standard to use, which of the many poverty
cutoffs (nonfarm family of four), and which month's
caseload data. What is lacking is a clear statement of
what the resulting total is supposed to represent.
   The Subcommittee has recognized in its review of
the five case studies that some Federal programs
have an extensive list of specific purposes and
amount to a form of special revenue sharing, or are
directed toward some broad categorical objective in,
say, education or community development. The Sub-
committee does not expect legislative drafters to alter
markedly the kind of purposes set forth in future
allocation legislation, but rather to recognize the
problem of translating such statements of purpose
into programmatic measures. If goal statements can
be made clear then there will be less necessity to
build into legislation in rigid form the specification
of the statistics and techniques to be used. For ex-
ample, Congress might decide to specify a certain
mechanism for allocation to, say, the State level,
might leave to Federal-State negotiations and admin-
istrative determination the mechanisms for making
allocations to lower levels. It should be recognized
that sound, flexible administration depends on clear
and distinct statutory goals. When goal statements
are not clear, then an administering agency which
exercises discretion may be subject both to political
pressure and to litigation.

RECOMMENDATION 2. Legislative-statistical
Interface:
   That provision be made for an active, continuous
interface between legislative program drafters and
the statistical community.

Comment:

   This recommendation by the Subcommittee is mo-
tivated in part by a recognition that Recommenda-
tion 1 will be most difficult to achieve without

                                        25


sustained professional interchange between program
and statist ical staff, both executive and legislative.

RECOMMENDATION 3. Formula Performance
Testing and Monitoring:
   That statistical and program agencies provide to
program drafters an analysis of the sensitivity over
time of proposed formulas and of the statistics they
incorporate so that possible effects on allocations can
be anticipated. Also, that provisions be made for
testing, monitoring, and assessing by program agen-
cies of the performance of each specific formula or
allocation rule prior to enactment.

Comment:

An example of the type of analysis that might be
provided, is that given in the Bureau of the Census
report "Coverage of Population in the 1970 Census
and Some Implications for Public Programs,"<ftnref marker="9"> which
describes some possible effects on the distribution of
General Revenue Sharing funds of adjusting the
1970 Census of Population for the estimated under-
count and for error in income reporting.
   Before an allocation procedure is adopted, it
should if possible be subjected to a test. In some
cases this could be done by using data from prior
years to determine whether or not the proposed
procedure would have allocated funds for each prior
year in accordance with Congressional intent. In
cases where data from prior years are not available
the testing would have to rely on simulation tech-
niques. It is important that allocations be neither un-
duly sensitive to short-term fluctuations nor lacking
in sensitivity to long-term changes in programmatic
measures. Once a program is in place, a built-in
monitoring mechanism is needed to provide early
warning to the executive branch and the Congress
that a particular formula or allocation rule may not
be behaving as expected.

RECOMMENDATION 4. Undesirable Formula
Practices:
   That legislative drafters and program designers be
advised of data problems and the existence of statis-
tical practices, as exemplified in the five case studies.
which may lead to formulas with consequences that
are generally recognized as undesirable.

Comment:
CETA allows ASU's (Areas of Sustantial Un-
employment) considerable freedom in drawing their
own boundaries. They need not follow jurisdictional
lines. While it may (or may not) be going too far
to say political jurisdiction boundaries should be fol-
lowed, the current procedure may be too free offer-
ing substantial opportunity for drawing boundaries
in an artificial way. In addition, ASU's in order to
qualify for CETA Title II funds must experience an
unemployment rate of 6.5 percent or more for three
consecutive months. This specific eligibility cutoff
introduces the problem that small errors close to the
cutoff of 6.5 percent may have serious effects on the
distribution of funds. These two factors substantially
complicate the data collection and may lead to pos-
sible inequities as well. An alternative might be to
base the amount allocated on the difference between
the unemployment rate and some lower cutoff, for
example 5 percent, arranging the formula so areas
above some upper limit point (say eight percent) get
the allocation provided by the present formula.
The GRS program distributes funds to approxi-
mately 39,000 jurisdictions, the great majority of
which are areas of population less than 2,500 in the
1970 Census of Population. For these areas the prob-
lems of obtaining intercensal estimates of population
and per capita income are very serious.

RECOMMENDATION S. Needed Formula Re-
search:
   That a limited program of applied research and
development be initiated to attack some critical prob-
lems and fill certain identifiable gaps in the present
state-of-the-art of formula design.

Comment:

   As discussed further in Appendix B-5, "An
Agenda for basic and Applied Research on Allocation
Formula Problems," the identification and character-
ization of key technical problem areas involves the
following elements: equity considerations, structural
aspects and the nature of the data required for the
computational formula, performance criteria, pres-
ence or absence of constraints and other specification
or modeling problems. Furthermore, relevant meth-
odological tools and relevant areas of substantive
theory need to be brought together if we are to
achieve a coherent approach to allocation problems.
Some of the statistical research issues of allocation
procedures can be illuminated by theoretical prin-
ciples from other fields. We need to bring together
into a concerted research effort knowledge and tools,
not only from theoretical statistics, but also from
applied areas such as decision theory, welfare eco-
nomics, data adjustment techniques, and income
measurement procedures.
                                        26
RECOMMENDATION 6. Designation of Official
Statistics:
   That the Office of Federal Statistical Policy and
Standards, with the assistance of the statistical agen-
cies, designate a limited number of additional official
statistical series for use in funds allocation. These
would be kept as current and as accurate as possible
for States and for local areas.

Comment:

   Official statistics presently designated in the Di-
rectives for the conduct of Federal statistics are:
(1)  Directive No. 13, Standard Data Source  of
Total Population Used in Distributing Federal Bene-
fits, designates as current data on total population
those published by the Bureau of the Census in
Current Population Reports, P-25, P-26, except
where data from a decennial census are more current.
(2)  Directive No. 11, Standard Data Source for
Statistical Estimates of Labor Force and Unemploy-
ment, specifies that the Federal executive branch de-
partments, agencies, and establishments shall use the
most current national, State, or local area labor
force or unemployment data published by the Bureau
of Labor Statistics. These data shall be used for all
program purposes including the determination of
eligibility for and/or the allocation of Federal re-
sources.
(3)  Directive No. 14, Definition of Poverty for
Statistical Purposes, designates the poverty statistics
published in Census Series P-60 as official. This
series is frequently designated as the series to be used
in allocation formulas as a proxy for economic de-
privation.
(4)  Other general-purpose statistics are now only
available in fine geographic detail at each decennial
census (and prospectively at the planned mid-decade
census).

RECOMMENDATION 7. Data Comparability:

   That in tiered allocation programs comparable
data should be used for allocation to States, but
policy flexibility may be allowed for sub-State allo-
cations. When the Federal Government allows this
flexibility it should be subject to the formulation of
specific Federal statistical and administrative guide-
lines, concerning the designation of the responsible
governmental unit for choosing among statistical
series, for declaring the specific types of statistical
series from which such a choice is permitted to be
made, and for establishing administrative mechan-
isms for consideration of appeals from area govern-
ments.

Comment:
   Unique statistical series may be available in some
States that would objectively improve the precision
and equity of sub-State allocations and those States
should not be penalized simply because other States
might not have access to such unique series for their
own sub-State areas. At any one level of distribution
of funds (for example, to counties within a State)
one and only one formula should be used. However,
two different States might properly distribute funds
to counties using different formulas, and similarly
two different counties within the same State might
use different formulas for subcounty allocations if
the Federal legislation authorizes this flexibility. For
example, in Title I ESEA, individual States select
the data sources to be used for subcounty allocation
to school districts under guidelines established by
and with the oversight of the Office of Education.

RECOMMENDATION  8. Data Accuracy Goal:
   That since data errors are inevitable and since sta-
tistical resources are necessarily limited, priority be
given to minimizing the very large errors which may
occur in data used for the allocation of funds.

Comment:
   Data used to distribute funds to competing areas
need to be evaluated differently for large areas versus
small ones. To the extent that error measurements
are available for small geographic areas one should
check that relative errors are no greater than a pre-
specified maximum, but one should not be overcon-
cerned with small errors since their effect on the
total distribution is relatively minor. For a large area
a relatively small error may represent a substantial
absolute error and have a large impact on the total
amount of funds distributed, and therefore it is nec-
essary to keep the absolute errors to a minimum. In
the case of administrative record data, edits and
cross checks should be applied to surface major
changes in the relative distributions, but efforts to
develop better methods of measuring the errors not
detected by these means should continue (e.g.,
matching studies such as the completeness of birth
registration studies.).

RECOMMENDATION 9. Eligibility Cutoffs:
   That, to minimize the effects of data errors, eligi-
bility cutoffs be such that there is a gradual transition
from receiving no allocation to receiving the full
formula amount.
                                        27
Comment:
   CETA Title II provides that an area must experi-
ence an unemployment rate of 6.5 percent or more
for three consecutive months to qualify for benefits
under this title. When an area has an unemployment
rate near 6.5 percent, data errors will frequently
lead to its being wrongly classified as eligible or in-
eligible (with substantial sums turning on the classi-
fication). Recognizing this problem, when CETA
Title VI was added, it provided that part of the
amounts allocated under the title be based on the
difference between the unemployment rate and a
lower cutoff of 4.5 percent. Areas with an unemploy-
ment rate above 4.5 percent would receive some
funds, the amount received being proportional to the
amount of unemployment in excess of 4.5 percent.
Note that the policy underlying both titles is the
same, namely to make minimal allocations to areas
with relatively low unemployment rates and use the
money saved on these areas for the areas with high
unemployment rates. However, Title II allocations
magnify the effects of small data errors in the neigh-
borhood of the desired cutoff, while the errors in
Title VI allocations are proportional to the errors in
the data.

   Much has been learned about generating and im-
plementing formula-based grant-in-aid programs at
the Federal level. No allocation procedure, we now
know, can come very close to an ideal. The diversity
of local conditions, and the limited amount of data
reflecting these conditions, prevent a tight match
between a theoretical model of what a program
is intended to accomplish, and a practical rule
for giving out the funds. But though the programs we
studied are far from ideal, they are also far from
unacceptable. Much imaginative work has already
gone into program design. If the unresolved prob-
lems are addressed seriously, we can expect consid-
erable improvement in the future.
                                        28

                                           APPENDIX A-1 

     THE GENERAL REVENUE SHARING (GRS) PROGRAM

                       
                       prepared by

Edwin Coleman, Bureau of Economic Analysis, U.S. Department of Commerce

                        Introduction

  The General Revenue Sharing (GRS) Program 
allocates funds in sequence to States, county areas,
Indian Tribal Councils and Alaska Native Villages,
county governments, townships and other local gov-
ernments.  Basically, however, the revenue sharing
allotments are derived at two levels, the State level
and the sub-State level.  Each level has a separate
formula.
  At the State level there are five possible factors
which are used in the allocation of funds:
  1.  Population
  2.  Per capita total money income
  3.  Personal income
  4.  Urbanized population
  5.  State income tax collections.
These factors interact in what is referred to as 3-
factor and 5-factor formula to determine the State
allocation. The effective formula varies from State
to State determined by which of the two yields the
higher allotment.
  In the sub-State allocation, only a 3-factor formula
is used.  The data elements are:
  1.  Total population
  2.  Per capita total money income
  3.  Adjusted taxes (tax revenues excluding those
      earmarked for education).
  The sub-State allocation procedure also includes
three constraints:
  1.  No unit below the county level may receive
      less than 20 percent of the State average per
      capita payment.
  2.  No sub-county unit may receive more than
      145 percent of the State average per capita
      payment.
  3.  No unit may receive more money in revenue
      sharing funds than 50 percent of its adjusted
      taxes plus intergovernmental transfers.
Moreover, the Secretary of the Treasury has, at his
discretion, the ability to use other source data pro-
vided he determines that such data will provide for
equitable allocation.
  The interaction of the two sets of factors at the
State level and the constraints at the sub-State level
make the formula specified for revenue sharing in-
determinant in the sense that no exact equation may
be written for its operation.  Rather, its operation
must be simulated and its answer derived through
computation until a desired element is reached and
the allocation is said to be final.
  The objectives of the revenue sharing program
are (1) that the size of the allotment should be
responsive to relative need in terms of the degree of
dependency of the area's constituency on govern-
mental services (determined by how income is distrib-
uted among the residents of the jurisdiction); the
local fiscal capacity to service the needs of the con-
stituency; and the division of responsibility for pro-
vision of services among the various levels of govern-
ment within each State and (2) that the allocation
procedure be equitable.
  Per capita (money) income, the variable in the
allocation formula which serves as indicator of con-
stituency need or capacity to pay, is subject to error
because of underreporting of income and misreport-
ing of income.  Since it is a per capita measure, it is
also affected by the nationwide undercount of Blacks
in the census population estimates.  There has been
a growing concern that the impact is disproportional,
resulting in a Net loss of revenue sharing funds to
central cities.  It is not possible, however, to assess
the validity of such a concern since the Bureau of
the Census has not yet developed a procedure for
allocating the undercount below the national level.
  The underreporting of income is well documented.
However, there is little known about the geographic
distribution of the underreporting and, therefore, its
impact cannot be assessed.  If the underreporting is
proportional throughout the country, then obviously
the impact of the allocation of funds would be small.
On the other hand, if it is not proportional, then
biases in the allocation of funds are likely to result.

                          29

  The misreporting of income is the reporting of in-
come of one type incorrectly as that of another.  Al-
though distorting the type of income, it has no effect
on the revenue sharing formula.
  Per capita income has also been subjected to
criticism related to concept and currency of data.
Conceptually, questions have been raised as to the
adequacy of per capita income as a measure of need.
Areas having the same per capita income, but whose
cost of living differ, may vary as to degree of need.
Moreover, per capita income does not indicate the
type of services needed nor does it indicate the in-
come mix.  Finally, income as a measure of well-
offness has its limitations.
  The problem of currency relates to the fact that
data on money income are collected by the Bureau
of the Census only in the decennial census of popu-
lation. In order to update the benchmark, a variety
of sources and statistical procedures are used.  Wages
are updated on the basis of data from the Federal
individual income tax returns.  Other types of income
are updated, at the State and county levels, on the
basis of special money income estimates made by the
Bureau of Economic Analysis (by adjusting its esti-
mates of personal income, by type of payment, to
conform to the money income concept).  Below the
county level, the updating procedures are more ten-
uous since there are practially no relevant income
data for small areas.
  Fiscal capacity in the allocation formula is meas-
ured, in the 3-factor allocation formula, by adjusted
taxes.  By ignoring assessments and user charges,
local variations in sources of revenue are not re-
flected.  The smaller and newer municipalities tend to
rely upon current charges as a source of revenue,
relative to taxes, to a greater extent than do the
larger and older cities.
  The formula structure itself fails to reflect varia-
tions among States in relation to taxing authority and
to responsibility for services by level of government
and discourages States from taking over some local
government responsibilities even though a more cen-
tralized provision of some services would be more
economical.
  The tiered sturcture of the allocation procedures,
so designed that there are different allocation form-
ulas for the several sub-county area levels of govern-
ment (county governments, townships, and all other
units of local government), tends to lessen the like-
lihood of equitable allotment of funds among sub-
county area governments because of the lack of re-
liable data for small areas.
  The constraints built into the allocation procedure
also affect the equitableness of the allocation.  The
20 percent rule tends to keep alive some essentially
dormant governments.  Moreover, it tends to increase
the allotments of many of the relatively high income
suburbs.  The 145 percent rule, on the other hand,
puts a limit on money that areas receive even though
they are in need of the money.  The 50 percent
budget limit tends to reduce the size of the allotment
to rural areas.
  Finally, fluctuations in the amount of the allot-
ment from one entitlement period to the next, en-
gendered by the sometimes large, unusual variations
in the data inputs into the allocation formulas, tend
to influence the fiscal policies of local governments.
The uncetainty caused by these fluctuations under-
mines the recipient government's ability to plan for
the efficient use of the Federal funds and to accom-
plish the implied goals of the revenue sharing pro-
gram.  They tend to deter the inauguration of new
programs and, instead, encourage the use of the al-
lotments for capital expenditures.
  Modifications to the General Revenue Sharing
formulas that have been suggested include:
  1.  Eliminating or modifying the 20 percent and
      145 percent per capita limits and the budget
      constraint.
  2.  The inclusion of current charges as eligible
      revenue in measuring fiscal capacity.
  3.  Modifying the tier structure so that allotments
      for small areas are not based on inadequte
      or unavailable data.
  4.  Addition of percent of families below poverty
      level to the 3-factor formula.
  5.  Setting limits on the amount of fluctuations
      in the size of allotment from one entitlement
      period to the next to encourage fiscal plan-
      ning in keeping with the goals of the program.
  Other suggested alternatives such as including a
cost-of-living index in the allocaiton formula, sub-
stituting taxable property values for aggregate in-
come as a measure of fiscal capacity, or including a
measure of wealth as an indicator of well-offness
are hampered by the problems of availability and
validity of data.
  Since the revenue sharing program has been in

                           30

operation for a number of years, changes in formula             
or allocation procedures that produce moderate im-              
provements in equity and responsiveness to need                 
would be more acceptable than those that would                 
radically alter the distribution. The latter could be       
more disruptive than the current problems caused by             
fluctations of allotments between entitlement periods.          
The Office of Revenue Sharing in the U.S. De-                 
partment of the Treasury, through its experiences in            
implementing the General Revenue Sharing Pro-                   
gram, has offered several suggestions that should be            
considered in the development of future programs                
that involve the distribution of Federal funds with             
regard to data that are specified in the program for        
use as the basis for allocation:                            
1. Data upon which funds are to be allocated                
   should be comparable and readily available               
   for all participants (eligible recipients) in
   the program prior to its inauguration. The use 
   of data from different statistical sources that
   purport to measure the same factor often re-
   sults in irreconcilable biases for or against
   some of the participants.
2. When drafting a program, comments on the
   availability and quality of data required
   should be solicited from the statistical agency
   that will have the responsibility of providing
   the data, prior to the enactment of the legisla-
   tion.  Data specified in a statute may not be
   the most comprehensive available to accomp-
   lish the goals of the program, and statistical
   methodogy cannot overcome such deficiences.
3. The data and statistical methodologies used
   in a program should be generally understood
   and accepted by both administrators and par-
   ticipants.  This would engender wide accept-
   ance of the program itself as well as confidence
   in the individual allocation of funds.








                     31

                APPENDIX A-2

The Comprehensive Employment and Training Act (CETA)

                 Prepared by
Martin Ziegler, Bureau of Labor Statistics, U.S. Department of Labor

                Introduction

  The Comprehensive Employment and Training
Act of 1973 was enacted "to provide job training
and employment opportunities for economically dis-
advantaged, unemployed, and underemployed per-
sons, and to assure that training and other services
lead to maximum employment opportunities and en-
hance self-sufficiency by establishing a flexible and
decentralized system of Federal, State and local
programs."
  The approach embodied in CETA represents a
vast shift in administrative procedures for Federal
attempts to solve and anticipate manpower problems.
In the preceding 12 years the Federal Government
gained considerable experience in dealing with the
specific problems of employment and underemploy-
ment, with the economically disadvantaged persons
and with different target groups such as youth and
minorities. Each of these was treated under different
legislative authorities involving several Federal agen-
cies. These programs were funded, administered, and
planned directly by the Federal Government. State
and local governments had little or no decisionmak-
ing power. As a result, this patchwork of programs
began to overlap, were seldom coordinated, and
began to be viewed as an inefficient use of public
funds.
  Several years of debate in Congress resulted in a
significant change in the orientation of Federal man-
power programs. The primary goal--Federal com-
mittment to improving the earnings and employabil-
ity via manpower services--did not change with
CETA. The major change was to provide, for the
first time, for the meaningful involvement of State
and local elected officials in the analysis and design
of programs to meet the needs of their populations
and job markets. The law is predicated on the belief
that State and local governments can be more re-
sponsive to the particular problems facing individual
areas of the country. It was also felt that local gov-
ernments can be held more accountable to the people
of the area than can the Federal Government. While
striving to meet national goals, Federal attempts
often failed to deal effectively with the unique local
manifestations of manpower problems. Under
CETA, therefore, the basic responsibility for plan-,
ning, administering and evaluating programs is
placed on the State and local governments, under
broad Federal direction.
  This is accomplished through decategorized fund-
ing, that is, Federal funds are transferred to prime
sponsors with only general guidelines as to how to
spend them. Prime sponsors are generally defined as
State and local governments, or combination of gov-
ernments called consortia, having 100,000 popula-
tion or more.
  The second major thrust of CETA was to con-
solidate most of the growing number of Labor De-
partment programs under one roof. Thus, rather
than a large number of sometime overlapping con-
tracts from separate Federal agencies confusing con-
trol and administration, a small number of block
grants to State and local governments leave officials
relatively free to institute a coordinated set of pro-
grams for greater effectiveness in solving local prob-
lems.

                 Provisions

  CETA is made up of seven titles, of which only I,
II and VI are relevant for discussion here.
  Title I is entitled "Comprehensive Manpower
Services." The primary focus is to institute and ad-
minister employment and training programs. Prime
sponsors must submit plans to the Secretary of Labor
for review and acceptance. These plans must explain
in detail the programs and services to be provided
and indicate how these will work to solve the prob-
lems of the area.
  Upon acceptance of the plans, funds are allocated
by a formula whose effect is to avoid great fluctua-
tions in the level of funding each prime sponsor re-
ceives from year to year. Eighty percent of Title I

                     33

funds are allocated according to the following form-
ula: 50 percent of the funds are allocated according
to the relative share of the prime sponsor's previous
year's funds; 37.5 percent are allocated according to
the relative share of U.S. unemployment; and 12.5
percent according to the relative number of adults
in low income families.
  Thus, half of the formula provides a measure of
stability. This can be important if sponsors use part
of their funds to institute long-term programs. Addi-
tional provisions state that no prime sponsor receive
less than 90 percent nor more than 150 percent of
the previous year's level of funds.
  Of the remaining 20 percent, 6 percent is for the
Secretary of Labor to use at his discretion, but first
for ensuring that no sponsor has received less than
90 percent of his prior year grant; 5 percent is for
consortium incentives (the bulk of this is not needed
for consortia; the excess reverts to the Secretary as
discretionary funds)'; 5 percent is for supplemental
vocational education grants to governors; and 4 per-
cent is for governors to use at their discretion.
  Title 11, entitled "Public Employment Programs,"
is "to provide unemployed and, underemployed per-
sons with transitional employment in jobs providing
needed public services in areas of substantial un-
employment and, where feasible, related training and
manpower services to enable such persons to move
into employment or training not supported under
this title."
  All funds under Title 11 are allocated to areas of
substantial unemployment (ASU), which are defined
by law as areas experiencing an unemployment rate
of 6.5 percent or more for three consecutive months.
The Employment and Training Administration
(ETA) has interpreted the definition of an ASU to
include any area (including Census tracts) which has
a population of 10,000 or more. Eighty percent of
the funds are allocated according to the number of
unemployed in each area compared to the number of
unemployed in all such areas, and 20 percent are
allocated at the discretion of the Secretary.of Labor
taking into account the severity of unemployment.
  Title II is aimed at aiding areas with high unem-
ployment by providing funds to hire unemployed and
underemployed persons in temporary public service
jobs.
  The formula has raised some controversy. First of
all, there is some question as to whether there is suf-
ficient weight given to degrees of unemployment
greater than 6.5 percent. Thus, depending on popula-
tion size, an area of 8 or 10 percent unemployment
may not receive substantially greater funding than an
area of 6.5 percent unemployment.
  The three-month period for defining ASU's is an-
other problem in that it allocates funds by relying
on a factor subject to seasonal fluctuations.
  Title VI, added to CETA by the Emergency Jobs
and Unemployment Assistance Act, is designed to
react quickly to cyclical unemployment through
creating temporary public service jobs. For this pur-
pose, the allocation. formula, covering 90 percent of
Title VI funds, is based entirely on unemployment:
50 percent are alloted based on total unemployment
in the prime sponsor area; 25 percent based on un-
employment in ASU's; and 25 percent generally on
the basis of unemployment in the sponsor area above
4.5 percent. The remaining 10 percent of funds
under Title VI are reserved for discretionary use of
the Secretary of Labor.

     Statistics Used in the Allocation Formula

Unemployment (Titles 1, II and VI)

  The monthly State and local area unemployment
estimates are the product of a Federal-State coopera-
tive program in which State employment security
agencies prepare labor force and unemployment esti-
mates using concepts, definitions and technical pro-
cedures established by the Bureau of Labor Statis-
tics. The estimates are developed from a complex
formula which makes use of unemployment insur-
ance (UI) data and certain assumed statistical rela-
tionships between the unemployed covered by UI
and those not eligible to receive benefits. In the 10
largest States, New York City and the Los Angeles-
Long Beach, California SMSA unemployment esti-
mates are obtained from the monthly Current Popu-
lation Survey. In the remaining 40 States and the
District of Columbia the preliminary estimates de-
rived from UT data are benchmarked to annual data
derived from the Current Population Survey. The
benchmark procedure also provides bias adjustment
factors for use in extrapolating the estimates to the
current month.
  The estimates which are derived from this pro-
gram are of varying quality. The variation reflects
the fact that the underlying UI data which are as-
sembled as a byproduct of the operations are not yet
standardized for statistical use.
  In addition, the unemployment estimates for por-
tions of labor market areas are often based on fixed
decennial census relationships which may change over

                          34

time. The Bureau of Labor Statistics has made an
assessment of the quality of the estimates and has
grouped the areas into three broad categories. The
best data are for States and SMSA's for which there
are independent estimates for both employment and
unemployment components, and for which on the
employment side there are BLS approved estimates
of nonagricultural employment. Within this group,
the greatest confidence can be placed in those States
which are independently benchmarked to the Cur-
rent Population Survey or for which monthly CPS
data are used directly.
  The second group, in which less confidence can
be placed, consists of individual cities and counties
that are frequently parts of labor market areas for
which estimates are derived synthetically by using
UI claims and current population estimates or
fixed census ratios. CETA prime sponsors (Title
I) and program agents (Title II) are included in
this group. Also included in this group are cities and
counties that are not SMSA's for which independent
estimates may be, prepared, but for which there is no
BLS approved nonagricultural wage and salary em-
ployment estimate.
  The third group, in which the least confidence can
be placed, consists of smaller cities and counties and
the estimate for areas that are parts of other geo-
political units. Areas of substantial unemployment
(Title II of CETA) are often part of this category.
  The Bureau of Labor Statistics has taken steps to
improve the methods to be used in the preparation
of the unemployment estimates and to assist the
States to upgrade the quality of the UI data available
for use in developing the estimates. In addition, as
of February 1977 the BLS (under contract with the
Bureau of the Census) has expanded the CPS sample
to cover all States.

Low Income Data

  The method for determining the relative number
of adults in low income families for Title I alloca-
tions was changed by the Employment and Training
Administration in 1975 and used in FY 1976 allo-
cations. The low income definition was raised from 
the $7000 used in 1970 to $8000 in 1973 to reflect
the change in the Consumer Price Index over the
same period, as mandated in the CETA legislation.
The use of 1973 data in FY 1976 allocations was
due to the delay in obtaining the data.
  CPS data for March 1970 and March 1974 (re-
porting 1973 income data) provided an estimate of
the change in the number of low income adults in
each State for the 19 States where the CPS sample
was considered adequate by the Bureau of Labor
Statistics for 1973. For other States, the overall re-
gional change, for census regions, was used. Prime
sponsor and consortium component estimates were
developed from State totals using a census-share
method.
  The actual calculation process is as follows for
each State: The CPS derived proportion of all adults
(18 and over) with low family income for 1973 is
divided by the 1970 proportion. The resultant factor
is multiplied by the 1970 census proportion of low
income adults to obtain an updated proportion.
Then, this figure, is multiplied by the 1974 census
population estimate of all adults in each State re-
sulting in a numerical estimate of low income adults
incorporating the most current estimate of popu-
lation.
  Within-State relationships are maintained for
prime sponsor estimates by the census-share method
using 1970 and 1973 CPS data. The resulting State
estimates are modified by controlling regional esti-
mates to the national total and controlling State esti-
mates to the regional totals.
  Since these data are based on the most recent
March CPS, they provide adequate reliability for
national and regional estimates. The CPS is also rea-
sonably reliable for the 19 larger States separately,
but even there the data are subject to considerable
sampling variability. The overall regional change is
assumed to be applicable for each of the smaller
States within a region and is used as a basis for de-
riving their current estimates. The procedure for the
smaller States involves an assumption of homogen-
eity and may be less reliable than the estimates for
the larger States. It should also be noted that by
comparison with estimates developed from the Na-
tional Income Accounts, the CPS survey based esti-
mate of aggregate income (as do all survey based
estimates of aggregate income) tend to be under-
reported overall; nonwage and nonsalary income
tends to be an income more underreported than
wages and salaries.

                         35

                                    APPENDIX A-3

The Authorization and Allocation of Funds Under Title 1,
    Elementary and Secondary Education Act (ESEA)

                 Prepared by

Martin Frankel, Herman Miller, and Forrest Harrison, National Center for Education Statistics,
U.S. Department of Health, Education and Welfare

         Objectives of Title I, ESEA

  Title I of the Elementary and Secondary Educa-
tion Act of 1965 established the major program of
Federal aid for elementary and secondary schools. It
provides funds to local school authorities for the
establishment of special programs to help educa-
tionally deprived children. The law requires that
local school authorities assess the special needs of
their educationally deprived children and that they
design programs to meet those needs with Title I
funds. The local authorities submit applications for
funds which are reviewed by State educational agen-
cies; programs which are approved are then moni-
tored and evaluated by the State agencies. Because
of the emphasis on local response to individual needs,
a great variety of programs are funded with Title I
aid. Most of the assistance is concentrated on im-
proving basic skills such as reading, writing and
arithmetic. School districts however, also fund sci-
ence and social science programs, cultural activities
and other programs designed to meet the health,
psychological and nutritional needs of educationally
deprived children.
  Annual appropriations under Title I increased
from about $1.0 billion in 1966 to about $2.3 billion
in 1978. About 6 million children were served by
Title I programs in 1974 and annual appropriations
in that year were about $1.8 billion. Therefore, in
1974, Federal assistance under Title I amounted to
about $300 per child. This amount is small relative
to the average expenditures per pupil; but, it is sig-
nificant in the poor school districts where expendi-
tures per pupil tend to be quite low
  The Elementary and Secondary Education Act
was originally conceived by Congress as an antipov-
erty program designed to help educationally dis-
advantaged children in low income areas. The major
instrument for achieving this objective was Title I
of this Act.<ftnref marker="10">


     Development of Title I Formula to
              Meet Objectives

  The clear intent of Title I was to distribute sub-
stantial Federal aid to school districts which were too
poor to provide adequate educational programs on
their own.<ftnref marker="11"> To achieve this objective, Congress de-
veloped a formula for authorizing funds to counties.
Authorizations were made to counties because ade-
quate data were not available at the school district
level.  This formula defined the eligible population
and the payment rate. In 1965, two groups were in-
cluded in the eligible population: (1) all children
in families with incomes under $2,000 in the 1960
census; and (2) all children in families with AFDC
payments of $2,000 or more. The payment rate was
set at 50 percent of the State expenditure per pupil
or 50 percent of the national average expenditure per
pupil, whichever was higher. The following formula
describes these Title I authorizations:


<img src="gif5.gif">

<img src="gif6.gif">


When the Title I formula was prepared in 1965 (and
even at present) the decennial census was regarded
as the best sources for estimating the count of poor
children in each county. This is the only source
which provides income distributions for the entire
population for small geographic areas throughout
the country. The major shortcoming of these data is
that they are available only at the beginning of each
decade. If they are to be used for this purpose, there-
fore, a procedure must be developed for updating
them periodically. "That update," according to a
congressional report prepared in 1974, "was writ-
ten into the original law as the portion of the formula
which counts AFDC children."<ftnref marker="12">
  If the cost of providing educational services were
the same throughout the country, the count of poor
children alone would have provided an adequate
basis for allowing Title I funds to counties. These
costs, however, do vary considerably. In the interest
of equity, Congress decided to adjust the payments
to reflect differences in the cost of providing educa-
tional services. The current expenditures per pupil
(CEPP) in each State were used for this purpose.
There is no explicit statement that Congress had this
in mind when it adopted the use of CEPP in the
allocation formula. This conclusion however, can be
inferred from the congressional report for 1974. In
discussing a change in the payment rate, this report
states that payments based on CEPP "reflect much
more accurately the differences in providing com-
pensatory education throughout the country."<ftnref marker="13"> Pre-
sumably, therefore, both the original and the revised
payment rates were intended to adjust Title l pay-
ments for differences in the cost of providing educa-
tional services.
  After several years, Congress found that both key
elements on the allocation formula--the count of
poor children and the payment rate--were not work-
ing according to expectations. The count of children
in AFDC families with grants above $2,000 proved
to be a very poor substitute for the actual count of
all poor children in each school district. As a result
of sharp increases in AFDC payments and mush-
rooming caseloads the number of AFDC children
counted under the formula increased very rapidly,
whereas the count of poor children based on the
1960 census remained fixed. As a result, the AFDC
component of the eligible population increased from
10 percent of the total in 1966 to over 60 percent in
1974.<ftnref marker="14"> These changes did not occur uniformly
throughout the country. AFDC payments tend to be
highest in the large, high-income, urban States and
these States also contain most of the children in
families with AFDC payments above $2,000. As a
result, these States made the greatest gains in the
number of eligible children to be counted under the
formula. In 1965, for example New York had 5.4
percent of all the children in the Nation eligible to
be counted under the Title I formula. By 1972, this
proportion more than doubled to 13.4 percent. Sim-
ilar changes took place in California and New Jersey.
The greatest relative losses in eligible population were
in States with low AFDC payments. Most of these
States are in the South where reductions of 50 per-
cent in the eligible population were typical. After
reviewing similar data, Congress concluded "clearly,
the present Title I formula, because of its great re-
liance on AFDC statistics, has become skewed heav-
ily in favor of the wealthier States in the Country.
That result is completely contrary to one of the prin-
cipal purposes of Title I: To provide assistance to
school districts and States whose ability to operate
adequate educational programs is impaired by con-
centrations of low-income families."<ftnref marker="15">
  As noted above, in the interest of equity, Congress
decided to adjust the payments to each State to re-
flect differences in the cost of providing education.
Under the formula adopted in 1965, counties were
eligible to receive either one-half of the State or
national average expenditure per pupil, whichever
was higher for each State. Although the national
average was used as the minimum payment rate, no
upper limit was set on the amount each county
could receive. After several years of operation, Con-
gress decided that this aspect of the formula "also
contributed to a distortion in the distribution of Title
I funds among States."<ftnref marker="16"> Particularly onerous was

                        38

the large amount received by New York under this
formula. The congressional report for 1974 point
out that New York was eligible to receive $772 per
child as compared to $465 per child for California
and it concludes that "there are few who would con-
tend that it costs that much less to live in California
than it does in a similar area in New York."<ftnref marker="17"> As a
result, Congress decided to change the payment rate
in such a way as to bring the payment rate among
States closer to the national average.
  In 1974, the present authorization formula was
adopted after considerable debate. An attempt was
made to correct some of the more important defects
in the earlier formula; but, the basic allocation pro-
cedure remained much the same. The eligible popu-
lation was redefined to include the following three
groups: (1) children 5-17 in Poor families as de-
fined in the 1970 census,<ftnref marker="18"> (2) two-thirds of the
children in families receiving AFDC payments which
exceeded the poverty line; and (3) children residing
in institutions for neglected and delinquent children
and children in foster homes supported with public
funds.
  The payment rate was also revised. The new pay-
ment rate is based on 40 percent of the State current
expenditure per pupil. The minimum was set at 40
percent of 80 percent (i.e., about one-third) of the
national average expenditure per pupil and the max-
imum rate was set at 40 percent of 120 percent (i.e.,
about one-half) of the national average. In addition,
each county was guaranteed an allotment of at least
85 percent of the allotment received the preceding
year, a provision referred to as the "floor" and as the
"hold harmless provision."

     The Rule for Authorizing and Allocating,
           Funds to States and Counties
                   Under Title I

  The following formulas describe the current
authorization and allocation procedures.
  Define as follows:

i = Subscript denoting State within United States
j = Subscript denoting county within State

<img src="gif7.gif">

                         39

The following ratable reduction procedure is then
followed:

<img src="gif8.gif">


       Examination of the Impact of Alternative
       Authorization Proc edures and Alternative
                 Poverty Populations

  In 1974, when Congress became concerned that
Title I funds were not being fairly distributed, they
mandated under Public Law 93-380 that an examina-
tion be made of the impact on the allocation of Tide
I funds of (1) a change in the poverty definition; and
(2) an updating of the 1970 census estimates of
the number of children in poverty.
  An analysis of the impact of changing the pov-
erty definition<ftnref marker="19"> was carried out by calculating the
allocation of $1.5 billion in Title I funds in 1975
under the 13 definitions of poverty defined in Chap-
ter V of the report, The Measure of Poverty.<ftnref marker="20"> (Data
were from the one percent sample of the 1970
census.)  A concomitant change was made in the
AFDC population above the poverty line to reflect
the change in the level of the poverty definition. All
13 poverty concepts were tested, and 5 of them are
discussed here:  the current measure, 125 and 150
percent of the current measure, a single poverty
threshold based on half of the national median
family income, and a single poverty threshold based
on the poverty threshold for a nonfarm family of
four. The results for most of the other poverty defi-
nitions fall somewhere within the range of the 5
presented here.
  There is good reason to be concerned about dis-
tributing Title I funds in 1975 on the basis of the
1970 census estimates of the number of poor chil-
dren in each State. During the past few years, the
Nation has suffered a recession which has undoubt-
edly affected some parts of the country more than
others The current allocation formula assumes that
the distribution of poor children by State is the same
today as it was in 1970, which is unlikely. To test
this assumption, allocation based on the 1970 census
estimates were compared with the allocations based
on estimates of the number of poor children by State
for 1973, the most recent year for which such esti-
mates could be made. Two estimates for 1973 were
used: one by the Bureau of the Census and the
other by the Bureau of Economic Analysis, both in
the Department of Commerce.
  With the exception of 1973 BEA estimates, alter-
native poverty populations are not available at the
county level. Therefore, authorization and allocation
procedures were performed at the state level. Al-
though the results obtained from State allocations
differ from the results obtained from county alloca-
tions, the state analysis gives good insight into the
effect of using alternative poverty populations.
In addition, the hold harmless provision was not
taken into account in allocating funds because this
provision tends to minimize differences in alloca-
tions based on alternative poverty population and
alternative Title I authorization formulas.
  In analyzing the impact of revised poverty defini-
tions and of updating the count, the basic tabula-
tions were performed assuming that the current allo-
cation formula was unchanged. In order to identify
separately the effects of various components of the
formula, additional tabulations were made to explore
the impact of: the hold harmless provision (the 85
percent floor); omitting the AFDC children; and
omitting the AFDC children and the CEPP factor.
  Chapter VIII of the report, Measure of Poverty,


                     40

shows in detail the impact of alternative authoriza-
tion procedures and alternative poverty populations.
The discussion of the general conclusions of that
study follows.

Impact of changing the poverty definition

  For each of the 50 States and the District of
Columbia, a comparison was made of the Title I
funds received under the current poverty concept
with the funds that would be received if the poverty
line were increased by 25 percent or 50 percent,
and commensurate changes were made in the num-
ber of AFDC children above this new poverty line.
A 25 percent increase in the poverty line would pro-
duce a reduction in the funds going to several of the
largest States and, with a few exceptions, would
redistribute these funds to the rest of the country.
With few exceptions, the pattern described above
would prevail if the poverty line were raised by 50
percent. In most cases the changes resulting from a
50 percent increase are in the same direction, but
larger than those resulting from a 25 percent
increase.
  The largest States would lose funds primarily be-
cause as the poverty line is increased, the influence
of the AFDC add-on becomes negligible.
  The two other alternative poverty populations
studied are two different single thresholds: one-half
the U.S. median family income in 1969 ($4,795)
and the poverty threshold for a nonfarm family of
four persons in 1969 ($3,748). If the higher thresh-
old were used, the results would be very similar
to those obtained using the current concept. The
allocations to only 7 States would differ by more
than 10 percent of the present allocation, and most
of these differences would be in the smaller States,
representing relatively small amount of money. If
the lower. threshold were used, most of the largest
States would have gains in funds, largely at the
expense of southern States. The reason for this
change, as previously explained, is that the lower
poverty line would include more of the AFDC
children among the eligible population under the
Title I allocation formula. Most of these children
live in the larger northern States.

Impact of updating the poverty count

  Comparisons were made of the amount of Title I
funds each State would receive in 1975 with no
change in the authorization formula, with a replace-
ment of the 1970 census estimate of the number of
school-age children in poverty with the census esti-
mate for 1973, and with a replacement of the 1970
census. estimate with the estimate for 1973 prepared
by the Regional Economic Analyses Division
(READ).
  These comparisons show that the substitution of
current estimates of children in poverty for the 1970
census estimates, with few exceptions, transfers
funds from the smaller rural States to the larger
industrial States. The impact of updating the poverty
count is greater than the impact of changing the
poverty definition.
  Although there are some differences between the
Census Bureau and the READ estimates, both sets
of data support this conclusion. This change un-
doubtedly reflects the fact that the slow economic
growth experienced in the United States between
1969 and 1973, had a much greater negative impact
on the larger industrial States than it had on the
smaller ones. As a result, relatively more of the
Nation's poor children in 1973 were located in the
large States than was the case in 1969.

Impact of changing the authorization formula

  Comparisons were made of the amount of Title I
funds each State would receive in 1975 under the
current authorization formula with the funds that
would be received if the authorization formula itself
were changed.
  If the current authorization formula were replaced
with a formula that authorized Title I funds solely
on the basis of the number of children in poverty as
reported in the 1970 census, most large industrial
States would receive a sharp reduction in Title I
funds, and most smaller rural States would receive
a sharp increase in such funds. This change is due
largely to the elimination of current expenditures per
pupil from the allocation formula.
  Using CEPP to determine funding tends to trans-
fer funds from those States with large proportions
of poor children to those that make relatively large
expenditures per capita on education.
  Of all the factors considered, it appears that the
allocation formula itself, and particularly current
expenditures per pupil, exerts the greatest impact
on the allocation of Title I funds. The greatest
change in the allocation of funds among States would
take place if the funds were allotted on the basis
of the number of children in poverty rather than
according to the present formula. If the present
formula is retained, an increase in the poverty line
would have a relatively minor impact on the alloca-
tion of Title I funds; however, an updating of the

                        41

number of children in poverty would appreciably
increase the funds going to the larger States and
would decrease those funds to the smaller States.

Joint impact of changing the poverty definition
and updating the poverty count

  In the preceding sections attention was focused on
the impact of a change in the definition of poverty
or an update in the count of poor children. We shall
now examine the impact of a joint change in these
variables. Title I allotments to each State in 1975,
assuming a 25 percent increase in the poverty line
and using the 1973 estimated number of poor chil-
dren were compared with the amounts each State
would receive if the current formula were used with
the 1969 estimate of poor children.
  The change in both variables would, with some
important exceptions, have the same impact as that
previously described for updating of the poverty
count alone.   That is, there would be a transfer of
funds from the small States to the large ones. New
York, an important exception, would have gained
considerably from an update of the poverty count
alone, but would lose slightly if both variables were
changed at the same time, due to the AFDC factor.
The gains for the other large States were largely
offset by declines in most of the 12 moderately large
States and in nearly all of the moderately small
Stites. On the other hand, most of the 13 States with
less than 1 million inhabitants would gain as a result
of this change; however, these changes are subject
to large errors of estimation.







                     42

                                 APPENDIX A-4                                                 APPENDIX A-4

    Aid to Families with Dependent Children (AFDC)
          as a Formula Grant-In-Aid Program

                 Prepared by
Charles Troob, National Institute of Education, U.S. Department of Health, Education and We are
                
                Introduction

  The Aid to Families with Dependent Children
program involves a Federal contribution to welfare
programs legislated and run by States. It is a varia-
ble matching grant program: the Federal Govern-
ment matches State expenditures at a rate which is
higher for States with low per capita income. The
Federal contribution to each State depends on the
State's caseload, on the State's payment rates, and
on the Federal matching rules appropriate to that
State.
  Because AFDC is aimed at a recipient population,
it is only partially appropriate to think of it as an
intergovernmental transfer. In other words, in judg-
ing the equity of the AFDC formula, it is appro-
priate to consider interpersonal equity as well as
interstate equity. At present, the AFDC recipient in
a wealthy State is likely to get far more from both
the State and the Federal Government than the
AFDC recipient in a poor State. (Since this outcome
is largely a matter of State law, it is unclear whether
interstate "equity" is violated.)<ftnref marker="21">
  As for our Need, Effort, Capability paradigm, the
major issues are:
  1. Is it appropriate for the Federal support of
     a State's payment to an individual to be related
     to the Effort of the State in which he resides?
  2. Does the funding formula take proper account
     of interstate differences in fiscal capacity? 

              The Two Formulas

  There are two reimbursement formulas in the
AFDC program. In general, States may use the one
which is more favorable to them in each quarter,
although there are certain restrictions concerning,
how frequently they can shift from one to the other.
  The regular formula is used by a small number of
States with low levels of AFDC payments, while the
alternate formula is more generous to high-spending
States. The alternate formula reimburses all pay-
ments at the Federal Medical Assistance Percentage
(FMAP). The regular formula reimburses regular
maintenance expenditures differently from foster
care and places a ceiling on reimbursement. For
maintenance expenditures, the regular formula reim-
burses 5/6 of the first $18 (per recipient per month),
and the Federal Percentage (FP) of, the next $14,
with no reimbursement on payments over $32. The
regular formula was used, in 1976, in Alabama,
Arizona, Georgia, Mississippi, South Carolina,
Tennessee, and Texas.
  More precisely, the monthly reimbursement under
the regular formula is a function of five parameters:

<img src="gif9.gif">

                         43

<img src="gif10.gif">

  The Federal Percentage is related inversely to
State per capita income, with a floor of 50% and a
ceiling of 65%. The Virgin Islands and Puerto Rico
have FP's of 50%.
  It is computed as follows: Department of Com-
  merce estimates of personal income are divided
  by census estimates of population to get per capita
  income estimates. These are averaged over three
  years. The figures for 1971-73 were used in
  August 1974 to calculate the rates for the period
  July 1, 1975 to June 30, 1977 (extended to
  September 30, 1977). In August 1976, data for
  1973-75 were used to calculate rates for October
  1,1977 to September 30, 1979. After the per
  capita income estimates are averaged, the ratio
  between the State average PCI and the Federal
  average PCI is squared. This is multiplied by
  50 percent to get the State percentage. The result
  is subtracted from 100 percent to get the Federal
  percentage.  FP's below 50% are raised to 50
  percent. FP's above 65% are lowered to 65 per-
  cent.

  Example:

  <img src="gif11.gif">

  A State with FP of 50 percent receives a maxi-
mum of $22.00 by the regular formula. 
  A State with FP of 65 percent receives a maxi-
mum of $24.10.
  The alternate formula for AFDC reimbursement
has no maximum. It is also decidedly simpler--reim-
bursement is total money and foster care payments
times the Federal Medical Assistance Percentage.
  The Federal Medical Assistance Percentage is
similar to the Federal Percentage except:

<img src="gif12.gif">



     Analysis of the Two Formulas

  The amount of money received by a State (to
give to its residents) depends on (a) reimburseable
AFDC payments, and (b) the Federal matching rate.
  The State, through law and administrative prac-
tice, can strongly influence the total level of AFDC
payments (and therefore its own share) by (a)
setting eligibility standards--including choosing
whether or not to participate in the AFDC-unem-
ployed parent program; (b) adjusting payment
standards; and (c) making it easy or difficult for
eligibles to get on the AFDC rolls.
  The Federal contribution to a State's AFDC pro-
gram therefore reflects: Need, in the incidence of
poverty in the population of potential eligibles;
Effort, in the willingness of the State to put people
on welfare and to support them generously; popula-
tion, in that larger States are likely to have more
poor individuals; Capability, in that matching rates
vary with PCI. The formula does not take into con-
sideration cost-of-living differences or other factors
affecting individual need, except insofar as the State
considers these factors in its AFDC standards.
  The alternate formula uses a wide range of match-
ing rates. In this sense it is progressive. But the ab-
sence of a ceiling on reimbursement in this formula
turns out to be very important. Despite the difference
in matching rates, States with high per capita in-
comes tend to have higher payment levels than
poorer States, and this means that Federal AFDC
payments are given to wealthier States out of pro-
portion to their caseload.  Note that any formula
which rewards State Effort adds a second dis-
advantage to potential recipients living in low Effort
States.  This is a problem in all programs that use
Effort rewards as incentives.  In principle, one might
wish to reward Effort unrelated to State fiscal capa-
city, but not reward Effort which reflects a greater
ability to pay. In practice, it is hard to sort these
things out.
  At any rate, there is not clear justification for set-
ting the floors at 50% in the current formulas. The
reimbursement rates under the regular formula are
identical for all States at or above mean PCI. Under
the alternate formula, the FMAP floor sets rates the
same for all States for which

>img src="gif13.gif">

i.e., all States with PCI greater than 5% above the
national average.

                     44

     Other Questions and Policy Issues

The role of PCI in the reimbursement formulas

  1. Use of lagged values of PCI. The reason
     for the legally mandated lag seems to be the
     desire to set and announce reimbursement
     rates substantially in advance of the period
     to which they will apply. How necessary is
     this to State budget planning?
  2. Use of squared values of PCI. This tends to
     exaggerate the impact of statistical errors.
     If the purpose of squaring is to create a
     strongly negative relation between PCI and
     FP, is it preferable to devise a linear for-
     mula which would achieve the same effect?
  3. Is PCI the best attainable measure of State
     Capability? Should it be modified by the
     addition of a variable representing those
     revenue sources available to the State which
     are not represented in income statistics?
     Should it be modified by a price deflator?
     Should it be modified by the elimination of
     transfer income from the income definition?

Caseload error

  1. What is the appropriate way to measure
     caseload error? The current procedure is to
     review a sample of cases at the shared
     expense of the State and Federal Govern-
     ments. The size of the sample varies with
     the size of the caseload: from 150 to 1200.
     Approximately 90 percent of the funds go
     to 27 States with samples of 1200. The
     number 1200 seems to have been chosen to
     create a 95 percent confidence interval of
     .01 around an error rate of .03. True error
     rates are much higher, so that the actual
     confidence intervals are much wider and
     wider still for States with smaller samples.
     Error rates are computed for eligibility
     errors (ineligibles mistakenly on the rolls),
     overpayment errors, underpayment errors,
     and, effective July 1, 1977, the number
     wrongly rejected. There is no continuing
     attempt to estimate the number of eligibles
     who did not seek assistance.
  2. What is the appropriate penalty for case-
     load error? Implicit in the quality, control
     system put into effect by HEW has been
     that the Federal Government would refuse
     to reimburse the States for all errors in
     excess of tolerance limits, and for some per-
     centage of erroneous payments. In effect,
     reimbursement would be based on a revised
     estimate of the true AFDC reimbursable
     level, after subtracting out estimates of
     erroneous payments. The current procedure
     intends to penalize States by refusing to
     reimburse them for the difference between
     the error (considered to be the lower bound
     of the 95 percent confidence interval around
     the estimated error rate) and the tolerance
     rate. This penalizes more heavily States with
     small confidence, intervals (large sample).
     There has been some discussion about re-
     placing the lower bound with the point
     estimate.
  3. What is the appropriate tolerance level for
     caseload error? Assuming that the States
     will be denied reimbursement for errors in
     excess of tolerance, the Federal Govern-
     ment might set these levels by:
     1. examining analogous Federal-programs
     2. examining model State AFDC programs
     3. examining analogous private programs.
     Whatever method we choose, different
     levels might be set for different demo-
     graphic groups.
     The current system, which was recently re-
     jected by the Courts, set limits of 3 percent
     on ineligibility errors and 5 percent on
     overpayment errors.     
     The courts have enjoined HEW from assess-
     ing disallowances in 13 States on the
     grounds that the tolerance levels are capri-
     cious, arbitrary and unreasonable.
  4. How should errors other than caseload
     errors be dealt with? HEW has an account-
     ing and auditing procedure, which examines
     State accounts to determine whether inap-
     propriate or excess administrative activities,
     support services, vendor payments, etc. are
     charged to AFDC.  If so, payment is rou-
     tinely refused. The States must bear the full
     cost of any error or malfeasance--at least
     in principle. After payments are refused,
     the State has the option of entering a recon-
     ciliation process.




                     45

                                       APPENDIX A-5

The Community Development Block Grant (CDBG)
                   Program

                 Prepared by
Richard Clemmer, Department of Housing and Urban Development, and Rajendra Singh, U.S. Postal Service

                Introduction

  The CDBG program is basically a program that
allocates funds to local areas on the, basis of a for-
mula, which is based on population, poverty
(counted twice), I and overcrowded housing.<ftnref marker="22"> It was
designed to replace several categorical programs,
such as model cities and urban renewal, and to allow
for greater local control over community develop-
ment funds.
  In the words of Section 101 of the Housing and
Community Development Act of 1974, "The pri-
mary objective of this title is the development of
viable urban communities, by providing decent hous-
ing and a suitable living environment and expanding
economic opportunities, principally for persons of
low and moderate income." This is to be achieved
through "(1) the elimination of slums and blight and
the prevention of blighting influences and the deter-
ioration of property a nd neighborhood and commu-
nity facilities of importance to the welfare of the
community, principally persons of low and moderate
income; (2) the elimination of conditions which are
detrimental to health, safety, and public welfare,
through code enforcement, demolition, interim reha-
bilitation assistance, and related activities; (3) the
conservation and expansion of the Nation's housing
stock in order to provide a decent home and a suit-
able living environment for all persons, but princi-
pally those of low and moderate income;  (4) the
expansion and improvement of the quantity and
quality of community services, principally for per-
sons of low and moderate income, which are essen-
tial for sound community development and for the
development of viable urban communities; a
more rational utilization of land and other natural
resources and the better arrangement of residential,
commercial, industrial, recreational, and other
needed activity centers; (6) the reduction of the
isolation of income groups within communities and
geographical areas and the promotion of an increase
in the diversity and vitality, of neighborhoods through
the spatial deconcentration of housing opportunities
for persons of lower income and the revitalization
of deteriorating or deteriorated neighborhoods to
attract persons of higher income; and (7) the restora-
tion and preservation of properties of special value
for historic, architectural, or esthetic reasons."
"It is also the purpose of this title to further the
development of a national urban growth policy by
consolidating a number of complex and overlapping
programs of financial assistance to communities of
varying sizes and needs into a consistent system of
Federal aid which (1) provides assistance on an
annual basis, with maximum certainty and minimum
delay, upon which communities can rely in their
planning; (2) encourages community development
activities which are consistent with comprehensive
local and areawide development planning; (3) fur-
thers achievement of the national housing goal of a
decent home and a suitable living environment for
every American family; and (4) fosters the under-
taking of housing and community development activi-
ties in a coordinated and mutually supportive
manner."  According to the Conference Report ac-
companying the Act, the Senate version stressed the
development of viable urban communities as being
the prime objective, while the House version stressed
national growth. Both provisions were contained in
the final version.
  Eighty percent of the overall appropriation for the
program (after deductions for certain discretionary
funds) is allocated to SMSA's and the remainder
goes to nonmetro areas. The sequence of fund-allo-
cation process of the overall appropriation is pre-
sented in Figure 1. Since the purpose of this report
is to consider the effects of Federal statistics on the

                            47

FIGURE 1. SEQUENCE OF FUND ALLOCATION PROCESS



<img src="gif14.gif">




                            48

allocation formulas, matters dealing with discretion-
ary allocations will not be considered in any detail,
except perhaps for the hold  harmless provision of 
the Housing and Community Development Act of
1974.
  A major adjustment to the formula amounts is 
the hold harmless (grandfather) allocations and
phase-out and phase-in provisions of the program.
After the fifth year of the program, however, these
provisions will no longer apply, so the formula will
bear more of the burden of fund allocation than at
present.  Generally, an area that made extensive use
of the categorical programs replaced by CDBG will
have a large hold harmless amount, which is deter-
mined by the average amount of grants or loans 
approved over the period FY 1968 to FY 1972.  In
brief, if the hold harmless amount is greater than
the formula amount, then for three years the area
receives the hold harmless amount, and then this is
phased down to the formula entitlement over the next
three years, in three equal steps.  Thus, in the sixth
year of the program, hold harmless amounts would
have been phased out.  If the formula amount is
greater than the hold harmless amount, then the area
receives the greater of 1/3 of the formula amount
or the hold harmless amount in the first year, 2/3
of the formula amount (or the hold harmless amount)
in the second year, and the formula amount in the
third year, and in future years.

                      The Formula

  The formula used at several steps of the allocation
process is straightforward:

  <img src="gif15.gif">

                Allocation of SMSA Funds

  Ignoring hold harmless provisions, the metro-city
share of the SMSA fund is determined by using the
sum of metro-city statistics in the numerators, and
the sum of all SMSA statistics in the denominators.
Then, each metro city receives its share on the basis
of the formula calculated using its statistics in the
numerator and the sum of all metro-city statistics in
the denominator.
  Next, the urban county (plus central city) amount
is determined by using the urban county plus metro-
city statistics in the numerator, and the SMSA totals
in the denominators.  Then, the allocation to each
urban county is determined by using its statistics in
the numerators, and the metro city plus urban county
statistics in the denominators.  In effect, urban coun-
ties are treated as if they were metro cities, and the
roundabout procedure above is followed because of
statuatory requirements.
  After SMSA funds are allocated to metro cities
and urban counties, the remainder, after allowance
for hold harmless allocations, is available for distri-
bution to other parts of the SMSA's on a competitive
basis, not unlike the old categorical allocation pro-
cess, except the proposals are not directed to the
narrow categories as before.  As it turned out, in
Fiscal 1975, far more urban counties qualified for
formula grants than had been anticipated, so discre-
tionary funds were limited in the first year.  Because
of this, Congress appropriated an additional $54
million for discretionary grants to SMSA's.

             Allocation of Non-SMSA Funds

  Non-metro CDBG funds are allocated to States on
the basis of the allocation formula, applied to non-
SMSA population, poverty, and overcrowding.  Local-
ities within each State compete for these funds on the
basis of their applications, so that after the State
allocation is determined, the formula has no further
bearing on allocation.  Of course, as in the cases
above, hold harmless provisions apply, but there are
no grant entitlements at this level, so this precludes
problems of phasing in or out with respect to a
block grant entitlement.  The phase-out provisions of
hold harmless amounts would apply in this case,
however.


      Statistics Used in the Allocation Formula

  The Housing and Community Development Act of
1974 directed HUD to use the most current data
available in allocating funds under the CDBG pro-
gram, and this translates to mean the poverty counts
and overcrowding counts are available on an ade-
quate geographic breakdown only in the decennial
census of population and housing.  On the other
hand, population estimates are more current, and
1973 estimates are used in the current allocation.
While this is determined by statute, there is still
considerable controversy involved in whether statis-
tics from different years ought to be used for the

                             49


allocation. On the one hand, central cities are losing
population, so with the other statistics unchanged,
they automatically lose entitlement funds. The prob-
lem is that such cities may be gaining in poverty
population compared to the Test of the SMSA's, so
a poverty count in a more recent year might leave
their allocations unchanged. Existing data limitations
would thus seem to suggest reverting to a single
year, the census year until other adequate sources
become available. This does not solve the  problem
however. For one thing, we cannot be sure that the
three variables in the formula will continue to move
in opposite directions. If they move in the same
direction, then an adjustment based on only one of
the variables will at least be some improvement.
Further, with population growth in certain areas,
new metro cities and urban counties may qualify,
between census years. It would be quite difficult to
ask a city to wait ten years for its entitlement, be-
cause the other variables in its allocation are not
current. However, the following alternative may be
suggested to improve the fund allocation.
  The data on the three variables might be collected
every two or three years and the estimates of the
populations representing each variable should be
obtained for intervening years. Regression techniques
or other appropriate statistical techniques could be
used to derive these estimates. Some smoothing of
these estimates might be appropriate to avoid large
annual changes in entitlements. The main drawback
of this alternative is of course a fairly large addi-
tional cost of data collection, and a less ambitious
approach might be to rely on mid-decade census
estimates.  On the other hand, local governments
may desire to collect data in order to base their
entitlements on more recent estimates. This might
be allowed, and monitored by a Federal agency
(such as HUD, Census, or BLS).  Alternatively,
local governments could request a special census,
paid for by them. In this way, the objectivity of the
data can be assured without excessive monitoring  
and local governments could receive an update,
based on a new count.


     Meaningfulness of the Formula

  One of the goals of the CDBG program was to
replace several categorical programs with a single
program, simplifying problems of application and
red tape on the part of the local jurisdictions, and
transferring much of the control over the allocation
to local governments. While these goals seem to
have been adequately met, this is not germane to
the particular formula selected, however, since other
formulas might serve as well. When the formula was
being debated in Congress, computer runs were
available that indicated the probable allocations of
funds under alternative weightings of the formula
variables. In particular, a single weighting of poverty
was considered. The legislative decision at that time
was to go with the double weighting of poverty, but
HUD was directed to study the formula in detail,
and report to the Congress by March 31, 1977.
HUD has completed an internal study of the form-
ula, as well as contracting for an evaluation by the
Brookings Institution on the topic.
  Some issues that were raised are related to the
items included in the formula. For example, it is
well known that overcrowding does not correlate
especially well with overall housing quality. For
example, some families with very high income live
in "crowded" dwellings according to the definition.
Older dwellings may tend to be in need of repair
to a greater extent than new, and a variable based
on the age of the housing stock may be a better
indicator of housing needs than relying totally on
the overcrowding measure. It appears that an altera-
tion of the formula might result in a better fit be-
tween allocations and goals of the program.
  The stated goals of the CDBG program, other
than to consolidate and replace existing programs,
were to prevent slums and blight, and to conserve
and expand the housing stock. Apart from these
primary goals, there are many subgoals, including
improvement of local services and encouragement
of more rational land development patterns. The
very generality of these goals leads one to consider
whether an examination of the formula itself might
provide a better indication of the legislative intent
of the program than a study of the stated goals. To
pursue this, we could conclude that in the overall
context of community development, cities and urban
counties with greater population, poverty, and over-
crowding somehow need more funds. The popula-
tion variable would seem to be a measure of need
in that it is a close proxy, for the housing stock,
at least in terms of numbers. The poverty variable,
which is of course weighted twice, is a proxy for
inadequate housing, and need for community serv-
ices. The overcrowding variable, already discussed,
is another proxy for poor housing, but poor in the
sense that there are not enough physical units,
whereas the poverty proxy might measure another

                          50

                                             
aspect, inadequate housing due to the inability to 
afford well-maintained housing.                              
                              
                              
                   Conclusion

  In one sense, the CDBG program is relatively
simple in that it allocates funds on the basis of needs
without consideration of local effort.  The formula
itself is very simple, with complexity arising only
because of repeated applications of the formula,
and the impact of hold harmless and phase-in and
phase-out rules.  Since the goals of the program are
difficult to define in operational terms, it is difficult
to evaluate the effectiveness of the formula in meet-
in the goals of the program.  A development of a
better proxy or set of proxies for housing condition
than overcrowding (and perhaps poverty) might
lead to an improved allocation of funds.  Studies now
under way should shed more light on this.  We still
have the question of whether to use the most current
data, even though not all variables in the formula
can be updated.  Were Congress to fund adequate
data collection to support the standards they place
on programs, such problems would be resolved.  In
a context of continued inadequate data, the question
of whether to update on the basis of only those
variables where data is adequate remains an open
issue.



                     51

                                             APPENDIX B-1

        AFDC Counts and ESEA Title I

                 Prepared by
Charles Troob, National Institute of Education, U.S. Department of Health, Education, and Welfare
                
                Introduction

The Title I formula includes three measures of
eligible children:
     1. children in families with incomes less than
        the poverty line (the poverty line varies
        with family size, other family characteristics,
        and farm-nonfarm residence);
     2. children in families receiving high levels of
        assistance through Aid to Families with De-
        pendent Children (AFDC); and
     3. children in institutions for the neglected and
        delinquent, or maintained in foster homes at
        public expense.
  In FY 77, these categories accounted for approxi-
mately 90 percent, 7 percent, and 3 percent of the
total.
  We are concerned with the second group of eligi-
bles, the "high AFDC" children. They are measured
as follows: the poverty line for a nonfarm family
of four is divided by twelve, to convert it to a
monthly figure. The States provide to HEW the
number of children of ages five through seventeen
whose families during a given month received AFDC
payments greater in dollar amounts than this monthly
standard. Note that this standard does not vary with
family characteristics, but is uniform for all families.
For this reason, AFDC children from large families
(which receive the largest cash benefits) are most
likely to be counted.
  The number of high AFDC children is reduced
by one-third when calculating a county's eligible
total. The other two groups (the children in poor
families and the children in institutions or foster
homes) are fully weighted.
  Four arguments are frequently heard as justifica-
tions for the counting of high AFDC children.
  1. AFDC children should be eligible for Title I
     assistance whether or not they are poor, be-
     cause the need for AFDC assistance reflects a
     social disadvantage likely to create special ed-
     ucational needs. The AFDC children who are
     in poor families are counted in the first group
     of Title I eligibles. The high AFDC measure
     includes the remaining AFDC children.
  2. Families receiving high levels of assistance,
     which bring them over the poverty line, would
     have been poor had they not been aided by the
     State AFDC program. If children in these
     families are not counted for Title I purposes,
     the Federal Government is in effect reducing
     aid to the States which assist children gener-
     ously through AFDC.
  3. The poverty counts used to enumerate the first
     category of eligibles are available only at the
     decennial census. The 1960 census counts
     were used until 1973. AFDC counts are col-
     lected monthly, and their use adjusts the for-
     mula to reflect more recent population trends.
  4. The AFDC counts direct additional funds to
     large cities. This is appropriate because:
      a. the poverty level is unreasonably low for
         central cities;
      b. educational problems in cities are particu-
         larly great, more than proportional to
         poverty counts; and
      c. urban budgets are particularly strained by
         the need to deal with a wide variety of
         social problems, and these problems are
         related to high rates of in-migration of
         low-income families from other areas.
  These arguments are complex and controversial.
It is for Congress to judge their validity and import-
ance. In this paper I will simply describe the rela-
tionship between the actual AFDC measure, and
the arguments advanced for its use. Whether or not
these arguments are themselves valid, the AFDC
measure currently in use bears only a loose relation-
ship to them.

           Categorical Eligibility

There are Federal programs for which eligibility
is reserved to those who are either poor, or receiv-

                            53

ing AFDC or public assistance. Either condition is
considered to be an adequate indicator of need. In
view of commonly held attitudes about the impact
of family structure on learning (attitudes that may
have been confirmed by, for example, the Coleman
Report), it might be appropriate to set a similar
requirement for Title I eligibility.
  Defining the Title I eligibles as those who are
either poor or on welfare raises a double-counting
problem: how can we determine the total number
of those who are either poor or AFDC recipients,
if the only data we have are poverty counts and
AFDC counts?
  One way of interpreting the high AFDC criter-
ion--the enumeration of AFDC recipients only if
they receive more than a certain amount--is a way
out of this problem. Some people believe that the
high AFDC recipients are unlikely to be poor, so
that adding only them to poverty counts will mini-
mize the risk of double counting.

     Pre-Transfer or Post-Transfer Poverty

  An eligibility criterion which excludes those who
have been brought out of poverty by AFDC pena-
lizes generous States and localities. It also introduces
incentives to be less generous, though these are
probably negligible. Of course, the generous States
and localities are being generous with Federal money
(at least 50 percent), which cuts somewhat the force
of this argument. But only somewhat: had only the
Federal share of AFDC been given to these families,
nearly all of them would have remained poor.
  The argument against reducing assistance to States
with high assistance standards is entirely different
from the argument for categorical eligibility for all
AFDC children, but the two arguments lead to simi-
lar conclusions: to count the AFDC nonpoor. But
the high AFDC children that are counted are not
necessarily a good proxy for the AFDC nonpoor,
for two reasons.
  First, other sources of income are not counted in
determining high AFDC status, though, of course,
they are counted when totals of children in poverty
are calculated. Thus, the high AFDC statistic omits
the AFDC nonpoor who receive only a portion of
income from AFDC. This problem is compounded
by the fact that the AFDC rolls are examined only
for one month. Certainly the largest group of AFDC
nonpoor are those who are able to earn substantial
income for part of the year, and must rely on AFDC
assistance at other times. The size of the AFDC
payment during the months they receive assistance
may bear little relation to whether or not they are
poor on an annual basis. In fact, large numbers of
AFDC families have sufficient other income so that
they are not poor even when their AFDC payments
are disregarded.
  Second, as mentioned in the introduction, the uni-
form cutoff produces a standard which can, in
general, only be reached by large families, since
AFDC payments are related to family size. Large
families receiving high levels of assistance may still
be poor, because the poverty fine is higher for large
families. Thus, large families may be counted twice,
as poor families and as high AFDC families. Con-
versely, two- or three-person families who are non-
poor AFDC recipients may fail to be counted either
as poor families or as high AFDC families.
  Both these problems could be avoided if the
AFDC nonpoor were counted directly. One way to
do this is to use 1970 census data. Income data in
the census, is collected in disaggregated form. If
transfer payments were excluded from the income
definition when poverty status was determined, then
many AFDC nonpoor would simply be counted as
poor. Because it is known that transfer payments
are more under-reported than wage and salary in-
come, the pre-transfer poverty counts might well be
more accurate than current poverty counts.
  Of course, if 1970 census income data is used,
the updating argument for AFDC counts is ignored.
To this we now turn.

                  Updating

The need for an update arises because the pov-
erty measure--the census low-income population
can be computed only once every ten years.<ftnref marker="23"> While
AFDC data can perhaps be used to update poverty
counts, it is not appropriate to use high AFDC data
for this purpose. There is no reason to think that
year-to-year changes in the high AFDC total help
bring the poverty counts up to date.
  In other words, the formula might use two meas-
ures derived from AFDC data: one estimating the
AFDC nonpoor (which need not be up to date),
the other estimating current shifts in poverty. The
current AFDC measure does neither task very well.
Yet, although year-to-year changes in poverty are

                           54

not well measured by year-to-year changes in the
high AFDC measure, the high AFDC counts can
be thought of as an updater in one important sense.
Since 1970, a larger percentage of the poor live
in the North and in metropolitan areas. As the
AFDC eligibles are also concentrated in the North
and in metropolitan areas, adding the AFDC counts
to the poverty counts has to some extent offset the
obsolescence of the 1970 counts. For this purpose,
the currency of the AFDC data is irrelevant--1970
high AFDC counts would serve equally well as
would a number of other similar adjustments to the
poverty counts.

              Urban Assistance

  That poverty has become increasingly urban since
1970 is another argument for an urban adjuster, to
be added to those given in the introduction: that the
poverty levels are somehow inappropriate to the
cities; that educational problems are more than pro-
portional to poverty counts; that cities need partic-
ular assistance because of overburden and fiscal
crises.
  We cannot here evaluate these arguments. Let it
be simply said that whatever the general merits of
AFDC statistics as indicators of urban distress, high
AFDC statistics are inappropriate because payment
levels in AFDC vary extensively from State to State.
There are currently no AFDC eligibles at all in
Texas, Tennessee, Georgia, and nine other States,
and there are small numbers in Ohio, Florida, North
Carolina, Colorado, and Indiana. At present, if Con-
gress wishes to aid large cities, it could be done
effectively in a number of ways, most obviously by
using a different formula for cities over a given size.

                           55

                                            APPENDIX B-2

   Technical Notes On Sensitivity Analysis

                 prepared by

     Rajendra Singh, U.S. Postal Service

          The Allocation Procedure

  For each program separately, the allocation of
funds to the individual States is computed by means
of a formula which mirrors the Need, Capability
and Effort of each State with respect to the pro-
gram. In a typical case, Need may be expressed in
terms of the population of the State, Capability in
terms of the State revenue, and Effort in terms of
local tax revenue.
  In what follows we will focus on one program
to be denoted by P, and one State to be denote
by S. It is helpful to make a distinction between the
ideal allocation and the actual allocation to that
State under that program.


<img src="gif16.gif">
<img src="gif17.gif">

  In the interest of keeping the example simple, we
will restrict the assessment to the impact of using
alternative estimates m(N) of the ideal measure
M(N) = the number of children in poverty. More
specifically, we will consider three estimates, viz.:
     1.Using 1970 Bureau of the Census estimates;.
       this is in fact the approximation actually used.
     2.Using 1973 READ estimates, i.e., estimates
       prepared by the Regional Economic Analysis
       Division, Department of Commerce.
     3.And using 1973 Bureau of the Census esti-
       mates.
  The allocations which result from using these
three estimates are summarized in Table 1, col. 1-3;
in col. 4 and 5, the allocations using 1973 READ
estimates and 1973 Bureau of the Census estimates,
respectively, are expressed in percent of the actual
allocation.
     As shown in Table 1, the actual allocation to
California was (in millions) equal to 1 8. Had

                           57


<img src="gif18.gif">                    

                           58

the 1973 READ estimates been used, California
would have received $139.3, that is an additional
9 percent. Had the 1973 Bureau of the Census esti-
mates been used, this State would have received
$146.2, that is an additional 14 percent. For other
States, for example Texas, the outcome would make
the allocation less than the actual one. The table
shows that the allocation is sensitive to the choice
of an approximate measure, which is exactly the pur-
pose of sensitivity analysis. It does not address,
however, the question whether the procedure is too
sensitive to that choice.
  In summary, Table 1 shows that using 1973
READ estimates or 1973 Bureau of the Census
estimates tends to transfer funds from the smaller,
rural States to the larger, industrial States.

     Some Additional Considerations

  The discussion in the above section has been lim-
ited to the impact of using alternative measure m(.).
As indicated in the section on The Notion of Sensi-
tivity Analysis, the scope of sensitivity analysis may
be broadened by encompassing, in addition, the im-
pact of using alternative allocation formulas.
  We will not enter upon this aspect here. We will,
however, state that this specific aspect is a virgin
area for applied formula research (for further refer-
ence see Chapter IV, Recommendation 5).

                Selected References

  The need for sensitivity analysis has generated a
sizeable literature. With respect to analysis of the
impact of errors in population statistics on alloca-
tion of public funds, reference may be given to
Siegel (1975) and references given in that docu-
ment. For discussion of additional techniques, refer-
ence is given to Cruz (1973), Garvin (1960), Gass
(1975), and Taha (1971).


                 References:

Cruz, Jr., J. B. (ed.). System Sensitivity Analysis
  (Benchmark papers in electrical engineering and
  computer science). Dowden, Hutchinson & Ross,
  Inc., 1973.

Garvin, W. W. Introduction to Linear Program-
  ming. McGraw-Hill, 1960.

Gass, S. I. Linear Programming Methods and Appli-
  cations. McGraw-Hill, 1975.

Siegel, J. S. "Coverage of Population in the 1970
  Census and Some Implications for Public. Pro-
  grams," Current Population Reports, Series P-23,
  No.- 56, 1975.

Taha, H. A. Operations Research. An Introduction.
  The MacMillan Co., 1971.








                     59

                                             APPENDIX B-3

    Some Considerations In Designing Samples
      To Obtain Data for Use in Allocation
                    Formulas

                 prepared by
Thomas B. Jabine, Social Security Administration,U.S. Department of Health, Education, and Welfare

  In this appendix we consider the problems of
designing sample surveys when the data will be used
in allocation formulas. Special attention will be paid
to sampling errors; the discussion applies in principle
to other types of error, such as errors due to non-
response and incomplete coverage. The allocation of
funds may be unsatisfactory either because the for-
mula for distribution of funds is not well designed or
because the data used contain errors large enough to
affect the intended distribution of funds. The discus-
sion in this appendix relates only to errors in the
data.
  Information is usually not free, so there will be
some cost incurred to obtain the data elements re-
quired by the allocation formula. If we are willing
to tolerate some error in the allocations resulting
from sampling error, the cost will be less than if we
require values based on complete counts.
  The first question, then, is whether or not to
sample. Second, if we do use sample estimates, how
large should the samples be and how should they
be distributed over States, SMSA'S, etc.? Or more
generally, how should the effort to reduce. errors be
distributed over various political subdivisions in
order to approximate the, allocation which. would
be obtained with error-free data?,
  For the potential beneficiary of the funds alloca-
tion, this is essentially a question of insurance. If
we assume that the cost of estimating the formula
elements must be deducted from the total amount
available for allocation, then the question of sample
size can be restated as follows:
     How much reduction in expected benefits
     is desirable in order to control the risk of
     an unsatisfactory result in the allocation
     actually made from the particular sample
     data used?
  It will probably seem desirable to spend 'some
amount to insure a reasonably accurate alloca-
tion. If the allocation is poor, then its objectives
will not be met everywhere, and certain social costs
will be incurred. On the other hand, we might find
that the cost of a complete count would be equal to
or more than the funds to be allocated, in which
case we would almost certainly reject this alterna-
tive.
  Best solutions probably lie somewhere between
these extremes. We have not yet developed any neat
way of finding a best solution in particular cases,
and we suggest this as an area for research. Cer-
tainly as a first step we should compare the cost
of complete count information with the size of the
funds to be allocated.
  Once we have decided how much insurance to
buy, i.e., how much to spend to obtain sample esti-
mates of the formula elements, there is a further
question, namely, how should the data collection
and other statistical resources be allocated to the
political subdivisions participating in the funds allo-
cation. Obviously, the allocation of statistical re-
sources to political subdivisions should be such as
to minimize the data errors and the resultant de-
partures of fund allocations from those which would
result if error-free data could be obtained. How-
ever, with fixed overall statistical resources, in-
creased efforts to reduce the expected error in one
political subdivision must inevitably mean decreased
efforts and increased expected errors in other polit-
ical subdivisions.
  The answer to this allocation question (alloca-
tion of the sample, not of the funds) is by no means
obvious. It will depend both on the formula being
used for the allocation of funds and on the desired
relation between expected errors in amounts allo-
cated to different political subdivisions. We use the
expression "error criteria" to describe such relation-
ships. Thus, one error criterion might be to have
the same expected squared error in relative terms

                          61

for the amount allocated to each subdivision. An-
other might be to have the same expected squared
error in absolute terms for the amount for each
subdivision. There are many other possibilities.
  The choice of the error criterion to be used in
any particular allocation is essentially a political
one. However, it seems desirable that such decisions
be made with knowledge of the consequences. of
alternative choices. In this appendix we describe
the consequences and the sample allocations for se-
lected error criteria.
  Table 1 presents the sample allocations implied
for two different fund allocation formulas and for
several different error criteria.
  Formula A is one which allocates funds to sub-
divisions in proportion to estimated numbers of
eligibles. Algebraically:


<img src="gif19.gif">

  For each of these formulas, the sample allocation
formulas were derived for several different error
criteria, some based on relative errors and some on
absolute errors.<ftnref marker="24">  For those error criteria applicable
to both funds allocation formulas, the indicated
sample allocations are the same for both formulas.
The result for equal absolute errors, i.e., to allocate
the sample to areas in proportion to the square of
their populations, is clearly not one which would be
seriously proposed; it has been included merely for
the purpose of showing sample allocation results for
a wide array of possible error criteria.
  The criterion "minimize error of sum" was used
only for Formula B, since in Formula A, the total
funds to be allocated are fixed. For both relative
and absolute errors, this criterion leads to propor-
tional allocation of the sample. Minimizing the
error of the sum, i.e., in the total funds paid out,
might be the criterion of choice for the Federal
Government. However, it would not necessarily be
equally attractive to the areas receiving the funds.
Several assumptions were used in deriving the
formulas for allocation of the sample. These were:

<img src="gif20.gif">

                           62

4. The cost per individual of collecting the in-
 formation is the same for all subdivisions.


<img src="gif21.gif">


  Even for the two funds allocation formulas treated
in Table I there are many other error criteria that
could be used. For example, under Formula A, one
could establish a maximum acceptable relative error
per subdivision<ftnref marker="25"> and then minimize the sum of the
absolute errors over all subdivisions subject to this
constraint.
  Exhibit I presents part of a recent paper<ftnref marker="26"> that
examined the implications of a different set of error
criteria on the allocation of a fixed sample to obtain
data for allocating funds under Formula A. In that
paper, it was assumed that within each subdivision,
each eligible individual would benefit (directly or
indirectly) equally from the use of the funds allo-
cated to that subdivision under the formula.
  Under this assumption, the effects of sampling
errors on the benefits to individuals were examined.
Two error criteria for errors in individual benefits
were used:
  1. Equal errors for individuals in all subdivisions.
  2. Minimize the sum of individual errors over
     all subdivisions.
  Using assumptions similar to those described above,
criterion 1 led to equal sample sizes for all subdi-
visions and criterion 2 led to allocation of the sample
in proportion to the square root of total population
in each subdivision.

                           63

                                               EXHIBIT 1

Allocations of Funds to Political Subdivisions Based on Sample Data<ftnref marker="27">


                Introduction

  Federal funds are often allocated to political sub-
divisions on the basis of formulas using population
counts and other statistics, such as numbers of school
age children, per capita incomes, or unemployment
rates. Complete count data are not available for
some of these items and for others are available only
once every 10 years from the decennial census.
Hence, for allocations to reflect the current situation,
estimates based on sample data must often be used
in the allocation formulas.
  Because the allocations are affected by sampling
error, some individuals will receive less than they
would have in the absence of sampling error and
others will receive more. This consideration leads
to a question of equity or fairness to individuals,
namely, how should resources for the collection of
sample data be allocated among the political sub-
divisions to which the funds are to be distributed?
In this section, a simple funds allocation model
is used to examine the effects of alternative criteria
for sample allocation. The alternatives considered
are:
     1. A sample allocation which insures equal
        treatment for eligible individuals in all polit-
        ical subdivisions.
     2. A sample allocation which minimizes for all
        eligible individuals, the sum of squared dif-
        ferences between actual and "correct" per
        capita allocations, but does not necessarily
        insure equal treatment for individuals in dif-
        ferent political subdivisions.
  These alternative criteria lead to different allo-
cations of the resources available for collecting
sample data. The first alternative leads to approxi-
mately equal sample sizes for all States. The second
alternative leads to allocation in proportion to the
square root of total population.

                Model and Assumptions

  It is postulated that the Federal Government is to
allocate a fixed amount of money among the States,
in proportion to the number of residents of each
State who have some specified characteristic, such
as being of school age. Since current counts of per-
sons with the specified characteristic are not avail-
able, a sample survey will be taken to obtain esti-
mates. A fixed amount of money is available for the
survey.
  The problem is how to allocate the resources avail-
able for the sample among the States. The follow-
ing assumptions are made:<ftnref marker="28">

     1. Sampling error is the only source of error in
        the allocations.
     2. Counts, or good estimates of total popula-
        tion, are available for all States.
     3. A simple random sample of persons will
        be used in each State.
     4. The only cost attached to the gathering of
        the sample information in each State is a
        fixed cost per individual in the sample.
     5. Within each State, the amount allocated will
        be shared equally by each person with the
        specified characteristic.

Notation--

<img src="gif22.gif">


                     64



<img src="gif23.gif">



                     65


<img src="gif24.gif">

                     66

<img src="gif25.gif">

                    67

                                           APPENDIX B-4

Raking as a Statistical Adjustment Procedure

                 Prepared by

       Tore Dalenius, Brown University

  In many situations, the statistics produced may
not be the best. For example, in estimating an un-
known parameter P (or more generally, a set of
parameters P), the statistician may have neglected
using available prior information about the param-
eter(s) in the estimation procedure. In a special
case, this prior information may be in the nature of
one or more constraints which may be imposed on
the estimate of P. One technique for estimating the
parameter(s) is called "raking". This technique may
also find applications for the purpose of adjusting
for effects from nonresponse and other deviations
from a survey design.
  In this appendix, we will consider the special case
where prior information constraints have been im-
posed on the estimate of P. Thus, there is a popula-
tion of N objects of some kind. With each object we
associate a value of a characteristic Y. This value
may be a measured quantity such as income or tax,
or it may simply be a count.
  The population is divided into RxC (mutually
exclusive) categories or cells on the basis of two
classification characteristics A and B:

<img src="gif26.gif">
<img src="gif27.gif">





                     69

these estimates to statistical adjustment. A com-
monly used term for such a procedure is "raking".
Raking has an old standing in statistical practice.
The following procedure, known as "iterative pro-
portional fitting", was discussed in considerable
detail in Deming and Stephan (1940). The raking is
carried out in one or more cycles, each of which com-
prises two steps, as illustrated below:


<img src="gif28.gif">


  Raking is eminently well suited to the use of large-
scale computers. The advances with the respect to
computing capability in the last few years have
served to stimulate important research and develop-
ment with the respect to both the theory and the
methods for raking, as evidenced by the recent refer-
ences given below.


                 References

Deming, W. Edwards, and Frederick F. Stephan.,
  "On a Least Squares Adjustment of a Sampled
  Frequency Table When the Expected Marginal
  Totals are Known," Annals of Mathematical Sta-
  tistics, 11, no. 4 (1940), pp. 427-444.

Some additional references:

Causey, Beverly D. "Sensitivity of Raked Contin-
  gency Table Totals to Changes in Problem Condi-
  tions," Annals of Mathematical Statistics, 43, no.
  2 (1972), pp. 656-658.
El-Badry, M. A. and Frederick F. Stephan. "On
  Adjusting Sample Tabulations to Census Counts
  J.A.S.A. (Sept. 1955), pp.. 738-762.
Ireland, C. Terrance, and Solomon Kullback. "Con-
  tingency Tables with Given Marginals." Biome-
  trika, 55, no. I (I 968), pp. 179-188.
Smith, John H., "Estimation of Linear Functions of.
  Cell Properties," Annals of Mathematical Statis-
  tics, 18, no. 2 (1947), pp. 231-255.
Stephan, Frederick F. "An Iterative Method of Ad-
  justing Sample Frequency Tables when Expected
  Marginal Totals are Known," Annals of Mathe-
  matical Statistics, 13, no. 2 (1942), pp. 166-178.
Thionet, Pierre. "L'ajustement des resultats des
  sondages sur ceux des denombrements", Revue
  Institut International de Statistique, 27: 1/3
  (1959), pp. 8-25.
 
                                            APPENDIX B-5

     An Agenda for Basic and Applied Research on
         Allocation Formula Problems<ftnref marker="29">

                 Prepared by

Tote Dalenius, Brown University, and Wray Smith, U.S.- Department of Health, Education, and Welfare

  In the course of its work the Subcommittee
adopted a useful paradigm for analyzing the formula
allocation problem. This paradigm was expressed in
terms of three entities--Need, Capability, and Effort
--assumed to be measurable at the State and local
level. The Subcommittee recognized that there were
many definitional and other problems embedded in
this apparently simple formulation. Such problems
need to be addressed within a framework of a
program of research on allocation formula prob-
lems. Although a variety of formula problems de-
serve to be analyzed in detail, it seems advisable to
concentrate the modest resources which are likely
to be available on a few selected problems. We are
therefore selecting just three problem areas for im-
mediate research. These problem areas are:
  1. The nature of the interaction effects arising
     from the choice of allocation formula and the
     choice of estimates of Need, Capability, and
     Effort.
     It has been observed in the past that the use
     of different estimates may yield strikingly dif-
     ferent allocations under a given formula. At the
     beginning of work in this research area a com-
     prehensive review needs to be made of these
     previous experiences. The availability of more
     than one set of estimates of Need, Capability,
     and Effort presents the program designer with
     the practical problem of choosing the best al-
     location formula to be used with a given set of
     estimates, where one formula may be preferable
     with one set of estimates, and another formula
     may be preferable with another set of estimates.
     Research in this problem area should focus on
     the nature of the interaction mechanisms be-
     tween estimates from specific statistical series
     and allocation formulas with specific structural
     differences.
  2. The deterioration over time of various estimates
     of Need, Capability, and Effort.
     To some degree, any estimate based on sta-
     tistical data collected at a point in time will,
     between periodic recollections of such data,
     deteriorate with the passage of time. One esti-
     mate, say, of Need, may quickly become very
     inaccurate, while another estimate, say, of Capa-
     bility, may remain reasonably accurate for a
     longer period of time.
     Research in this area should aim at analyzing
     how information about the behavior of such
     estimates over time can be taken into account
     in the design and administration of allocation
     programs so that the actual allocation will re-
     main close to the ideal allocation as time pro-
     gresses between updates.
  3. The issue of possible adjustment of future al-
     locations to compensate for past inaccurate
     allocations.
     As a consequence of the inherent delays in the
     production of statistics, it is always necessary
     to use old statistics in an allocation formula.
     When the new statistics become available it is
     possible to compare the actual allocations in
     past years with recomputed allocations based
     on the new statistics. The policy issue is
     whether or not this kind of information should
     be taken into account in future allocations:
     Should States which received too little or too
     much in the past have their future allocations
     adjusted upward or downward to compensate
     in full or in part for underpayments or over-
     payments?
     The research in this issue area should focus on
     measuring the distributional impact of using
     old statistics and on developing criteria for the
     use of accounting correction versus equity com-
     pensation. In our context, accounting correction
     is meant to include the actual adjustments re-
     quired to make a stream' of benefits conform

                              71


    as closely as possible to a known entitlement.
     On the other hand, equity compensation entails
     additional considerations in terms of the legis-
     lative intent of the program.

  Taken together, the three research areas discussed
above constitute a manageable agenda for studies
of allocation formula problems. As part of an im-
plementation of this agenda, each research area
would be reviewed in terms of:
  a. the level of precision achieved or achievable
     in translating legislative goals into fund allo-
     cations under existing programs;
  b. the implicit and explicit performance criteria
     for the particular Federal program;
  c. the related modeling questions such as: "How
     well does a particular formula reflect the real-
     world dynamics it is designed to address?"
  d. the structural aspects of typical allocation for-
     mulas, including additive, multiplicative, itera-
     tive, and mixed structures;
  e. the effects of the presence or absence of con-
     straints such as floors or ceilings (e.g., hold
     harmless provisions); and
  f. the data required to compute the allocations
     by means of the chosen formula.
  Furthermore, attention would be paid to the spe-
cial problems involved in various allocation pro-
grams. For example, Need may, appropriately, have
different components in two differing geographic
areas; that taxable real estate and indicators of per-
sonal income may not provide an adequate basis
for Capability; and that local tax revenue Effort
would be most appropriately analyzed in terms of
the purpose to which the revenues are applied.
  The proposed research would be primarily applied
in nature. It would, to a large extent, make use of
existing substantive theories and methods. While it
would be highly speculative to try to make an ex-
haustive list of potentially useful tools, we will
briefly mention those disciplines which should prove
to be of instrumental value in this research. These
disciplines are:
1.   Statistics and Stochastic Modeling
     The relevance of these areas is exemplified in
     a paper by Savage stating a "working hypothesis
     . . . that the collection of the major statistical
     series and some of their important uses can be
     formulated as a statistical decision problem"
     (Savage, I. R. (1975), "Cost-benefit analysis
     of demographic data", Supplement to Advances
     in Applied Probability, 7, 62-71) and in a
     paper by Singer and Spilerman in which they
     discuss "how to select the specific structure ...
     which should be associated with the empirical
     process" and also the problems of modeling
     with fragmentary data and observations con-
     taining noise and other sources of error (Singer
     B, and Spilerman, S. (1976), "The representa-
     tion of social processes by Markov models",
     American Journal of Sociology, 82, 1-54). Both
     of these papers emphasize the need to improve
     basic data.
2.   Applied Mathematics and Control Theory
     We want to emphasize the potential usefulness
     of techniques from linear and nonlinear pro-
     gramming, as well as other optimization tech-
     niques (e.g., generalized Lagrange multipliers),
     since some allocation formulas may be viewed
     as generating constrained optimization prob-
     lems. Extensions of existing raking and other
     adjustment techniques may require the applica-
     tion of advanced topological concepts and the
     development of new computer software. Incor-
     poration of equity considerations may require
     tools from both control theory and system
     simulation.
3.   Economics and Utility Theory
     The meanings of such terms as "best alloca-
     tion" and "equitable allocation" are by no
     means self-evident. The crucial question here
     is how the intent of the Congress is to be trans-
     lated adequately into objectives within the
     framework of formula allocation techniques.
     The appropriate choice of a utility or loss func-
     tion for overshooting or undershooting a de-
     sired allocation requires consideration of the
     issues discussed recently in R. N. Waud
     (1976), "Asymmetric policymaker utility func-
     tions and optimal policy under uncertainty,"
     Econometrica, 44, 53-66.
  We must be mindful in our proposed research
that there is a lack of extant theory which is fully
suitable to our allocation problems and while we
seek new theory we must continue to explore and
improve our approximation techniques.

                     72

<ftnote>1 The amount of grant-in-aid funds has increased in the past two
years, and a number of new programs have also been added.

<ftnote>2 Portions of this section were adapted from an invited paper
sented by W. Smith at the August 1976 meeting of the American
Statistical Association held in Boston.

<ftnote>3 The method of estimating this number has varied, originally taking
into account children in poverty families plus children in families
receiving AFDC payments greater than the poverty cutoff, and sub-
sequently altering the mix of these two factors and adding children
in institutions for neglected and delinquent children and in publicly
supported foster homes.

<ftnote>4 In the AFDC formulas the measure of Capability is the State
Percentage or the State Medical Assistance Percentage both based on
the State's relative per capita income (State per capita income/
national per capita income). This measure is subtracted from 100
percent to get the complements (Federal Percentage or FMAP) used
in the formulas. The Federal Percentage has a floor of 50 percent
and a ceiling of 65 percent. The FMAP has a floor of 50 percent
and a ceiling of 83 percent.

<ftnote>5 Categorical Grants: Their Role and Design. Washington, D.C.:
U.S. Government Printing Office, forthcoming, 1978, Chapter VII.

<ftnote>6 These are systems where an allocation is made to each State and
each State total is, in turn, allocated among the jurisdictions within
the State.

<ftnote>7 Of course, one can provide for differential sensitivities in a multi-
plicative formula by attaching exponents to the different factors.

<ftnote>8 Since more effort devoted to reducing error in one area means
less effort and bigger error in another area, we have to talk in
terms of reducing the sum of the errors rather than of each indivi-
dual error.

<ftnote>9 Current Population Reports, P-23, No. 56, August 1975, Wash- 
ington. D.C.

<ftnote>10 "Title I can be considered as another very potent instrument to
be used   in the eradication of poverty and its effects. Under Title I
of this legislation the schools will become a vital factor in breaking
the poverty cycle by providing full educational opportunity to every
child regardless of economic background. The major thrust of this
legislation is contained in Title I where it is proposed that approxi-
mately $1.06 billion be provided to local school districts for the
purpose of broadening and strengthening public school programs in
the schools where there are concentrations of educationally disad-
vantaged children." Quoted from U.S. Congress, House of Represen-
tatives, Elementary and Secondary Education Act of 1965, Report
Number 146, 89th Congress, 1st Session, April 6, 1965, p. 5.

<ftnote>11 U.S. Congress. House of Representatives, Elementary and Secondary
Amendments of 1974, Report Number 93-805, 93rd Congress, 2nd
session, P. 5.

<fnote>12 Ibid., p. 9.

<fnote>13 Ibid., p. 13.

<ftnote>14 Ibid., P. 9.

<ftnote>15 Ibid., p. I 1.

<ftnote>16 Ibid.. p. 13.

<fnote>17 Ibid., P. 13.

<ftnote>18 The measure o f poverty used in the authorization formula was
originally developed by Mollie Orshansky of the Social Security
Administration in 1964. The measure is built around the Department
of Agriculture's economy food plan of 1961 and the national average
ratio of family food expenditures to total family after-tax income as
measured in the 1955 Household Food Consumption Survey. The
measure consists of 124 separate poverty cutoffs differentiating
families by size, number of children, age and sex of head, and farm
or nonfarm residence.

<fnote>19 Preliminary analyses from U.S. Department of Health. Educa-
tion. and Welfare. The Measure of Poverty, Technical Paper XVI,
Implications of Alternative Measures of Poverty on Title I of the
Elementary and Secondary Education Act.

<fnote>20 U.S. Department of Health. Education, and Welfare, the Measure
of Poverty, A Report to Congress as Mandated by The Education
Amendments of 1974 (Washington, D.C.: U.S. Government Printing
Office, 1976).

<fnote>21 This nontechnical use of the term- "equity" is meant to reflect
notions of fairness which inform congressional debate. It does not
imply that existing arrangements, once approved by Congress, can be
judged "inequitable."

<fnote>22 At the time of this writing, Congress was considering a revision
in the allocation formula. While the form of the revision has not
been determined, it could include other formula elements, such as
loss of population or age of the housing stock. Also, the new for-
mula may allow the local government to choose between two sepa-
Tate formulas. The description in this case study refers to the formula
as it existed in March 1977, prior to any revisions.

<fnote>23 Intercensal surveys (such as the CPS) produce high-variance esti-
mates, even at the State level, and have until now not been con-
sidered adequate for Title I purposes. The Survey of Income and
Education (1976) was mandated to produce State estimates usable
in Title 1.

<fnote>24 Here, and in what follows, the term "errors" refers to expected
squared errors.

<fnote>25 It would, of course, be necessary to set a maximum that could
be met inbe met in all subdivisions, given the resources available for sampling.
 
<ftnote>26 Jabine, Thomas B., "Equity in the Allocation of Funds Based on
Sample DaSample Data," paper presented at the 136th Annual Meeting of the
American American Statistical Association, Boston, Massachusetts, August 25,
1976.

<fnote>27 Part I of Jabine, T. B. "Equity in the Allocation of Funds Based
on Sample Data", presented at the 136th Annual Meeting of the
American Statistical Association, Boston, Massachusetts, August 1976.

<fnote>28  Most of the assumptions are not met in real allocation problems,
but can probably be relaxed or removed without appreciably changing
the main result.

<fnote>29 Based in part on an invited paper by W. Smith presented at the
Annual Meeting of the American Statistical Association, Boston,
Massachusetts, August 1976.