-'"»• i. ... XT-TT Tr*»

OEC-0- 71-2859

HIE PROCESS OF FUNDS ALLOCATION

UNDER TITLE I OF THE ELETENTARY AND

SECONDARY EDUCATION AG' OF 1965

Sung Kim

Elsie Clark

John Donaldson

Joseph Jordan

Margery King

Eugene McDowell

Technical Analysis Division

National Bureau of Standards

Washington, D.C. 20234

March 1973

Second Interim Report

Prepared for

U.S, Office of Education

Washington, D.C. 20202

TABLE OF CONTENTS

1.0 OVERVIEW

Page

1.1 Introduction 1

1.2 Background 3

1.3 Distributional Issues and Alternative Possibilities.... 13

1.4 Formula Alternatives 33

2.0 EVALUATION OF THE PRESENT FORMULA AND GENERATION OF ALTERNATIVES

2.1 Criteria for Formula Evaluation 35

2.2 Overall Formula Structure 36

2.3 The Eligible Children 39

2.4 The Cost Factor 58

2.5 Adjustment for Underfunding (Reduction Procedure) 77

3.0 ALTERNATIVE ALLOCATIONS AND THEIR EFFECTS

3.1 Methodology 84

3.2 Cost and Concentration Effect 92

3.3 Reduction Procedure and the Floor Effects 108

APPENDIX A

SPECIAL GRANTS BASED ON THE CONCENTRATION OF POOR

CHILDREN: Part C of Title I -A-l

APPENDIX B

ENUMERATION UPDATING B-l

APPENDIX C

STATE ALLOTMENTS BASED ON ALTERNATIVE FORMULAS C-l

i

LIST OF TABLES

Table Page

1.3.1 State Allocations Resulting from Three Different

Enumerations of Eligible Children 15

1.3.2 FY73 State Allocations Resulting from

Modified Methods of Enumeration 21

1.3.3 State Shares of Poverty Children in FY73

Under Five Alternative Estimations 22

1.3.4 Average Per Pupil Expenditure for Elementary

and Secondary Schools by State 27

1.3.5 Comparison of Allotment Per Pupil: Alternative

Concentration Effects with $300 Per Pupil Cost .. . 30

2.3.1 Definition of Alternative Enumerations 56

2.3.2 Number of Eligible Children in FY73: Five

Alternative Enumerations 57

2.4.1 Average Per Pupil Expenditure for Elementary

and Secondary Schools by State 61

2.4.2 The Five Highest and Five Lowest Per Pupil

Expenditures at the LEA Level Within the States

of Delaware, Illinois, Maryland, Mississippi and

Pennsylvania 63 „

2.4.3 Concentration Ratios of Poverty Children 72

2.4.4 Concentration of Poverty Children in Forty-eight

Selected Counties 74

3.1.1 Components of the Title I Allocation Formula . . 86

3.1.2 Distribution of Poverty Children by County

Quintiles 90

3.2.1 Comparison of Allotment Per Pupil: $300 vs. SAPPE 94

3.2.2 Comparison of Allotment Per Pupil: $300, MAX, SAPPE 94

3.2.3 Comparison of Adding the Same Concentration Factor

to Different Initial Costs 96

ii

LIST OF TABLES (Cont'd.)

Table . " Page

3.2.4 Comparison of Allotment Per Pupil: Alternative

Concentration Weights with $300 Per Pupil Cost . . 99

3.2.5 Program Participation Rates for Alternative

Concentration Weights 105

3.2.6 Allotment Per Child: City—Suburb- -Rural Comparison;

Concentration Weight: Moderate 106

3.3.1 Number of States Supported by the Floors .... Ill

3.3.2 Distribution of Allotment Changes Among States;

K2 Substituted for Ki 112

3.3.3 Distribution of Allotment Changes Among States;

K5 Substituted for 112

7
I
LIST OF FIGURES

Figure Page

2.3.1 Comparison of Alternative Poverty Data 49

3.2.1 Comparison of Dollars Alloted Per Child;

Concentration Weight: Low 100

3.2.2 Comparison of Dollars Alloted Per Child;

Concentration Weight: Moderate 101

3.2.3 Comparison of Dollars Alloted Per Child;

Concentration Weight: High . . 102

iv

Chapter 1

OVERVIEW

1.1 Introduction

Tins chapter is intended as a self-contained report

indicating the background of this study, describing the nature

of the Title I provisions regarding the distribution of funds,

and summarizing the highlights of Chapters 2 and 3 concerning

distributional issues and alternative possibilities. This

study is derived from the Congressional mandate for a study

of the various provisions involved with the Title I grant

determination and distribution process. The description of

Title I provisions emphasizes the process relating to the

allocation of funds for local educational agencies (LEAs)

The maximum LEA grant is described as the product of the

number of eligible children and the amount of the basic grant

per child; the allocation actually received by the LEA,

however, results from the application of a procedure that

reduces the amount of all entitlements to a sum that can be

covered by the appropriation. The practical problems of

identifying and counting the eligible children for annual

grant determination are defined. These include attempting

to maintain an accurate, comprehensive, and up-to-date data

base. In addition, some of the issues associated with the

selection of an appropriate grant per child are mentioned.

These include whether the basic grants should reflect regional

differences in the cost of education and/or whether they

should be adjusted for areas with special needs, e.g., high

concentrations of eligible children.

Consideration of alternative possibilities suggests

that the present enumeration of eligibles can be improved

by using the so-called Orshansky poverty data from the 1970

census and by using AFDC* data as a multiplicative ratio to

update the count of children annually. Inclusion of a term

in the basic grant per child to effect a concentration of

funds according to the concentration of eligibles is shown to

result in a distribution of funds at the county level that is

interpreted as more closely complying with the intent of

Title I than does the present distribution. Finally,

preferential funding practices employed while reducing

entitlements are questioned as being without adequate justification , while unconstrained proportional reduction of the

entitlements is presented as permitting a seemingly better

realization of the distributional intent perceived for Title I.

The summarization contained in this chapter excludes much

of the detail and almost all of the technical basis for the

statements made concerning the analyses. If the reader

desires a more thorough, technical understanding, he is

encouraged to read the entire report.

* Aid to Families with Dependent Children.

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1 . 2 Background

Title I of the Elementary and Secondary Education Act

of 1965 (ESEA) was enacted in recognition of poverty as a national problem requiring extensive action coordinated at

the Federal level. One among several national antipoverty

programs, Title I is intended to break the self -perpetuating

cycle of poverty and ignorance by providing supplementary

educational opportunities to so-called "educationally deprived"

children — preschool, elementary school and secondary school

children whose general and economic backgrounds put them at

a disadvantage, with respect to learning, as compared to the

majority of other children.

The declaration of National policy in Title I (Sec. 101)

identifies two underlying motivations, the special needs of

the children and the fiscal burdens of the educational

agencies serving these children. The proposed remedial •*•

approach is to provide Federal financial assistance to the

local agencies, not for general educational needs but for

supplemental programs designed to meet the specialized

requirements of educationally deprived children:

Sec. 101. In recognition of the special educational

needs of children of low-income families and the

impact that concentrations of low-income families

have on the ability of local educational agencies to

support adequate educational programs, the Congress

hereby declares it to be the policy of the United

States to provide financial assistance (as set forth

in the following parts of this title) to local

educational agencies serving areas with concentrations

of children from low- income families to expand and

improve their educational programs by various means

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(including preschool programs) which contribute

particularly to meeting the special educational

needs of educationally deprived children.

Beyond the statement of National policy, the legislative

intent is evidenced in the principles embodied in the law and

in the legislative history. For maximum impact, the Title I program is aimed at educationally disadvantaged children in

poverty. Many studies* have shown a strong relationship

between educational attainment and family personal income.

It is thought possible therefore to approach the problem of

selection of eligible children from the point of view of

either educational attainment or level of income. However,

the absence of accepted Nationally uniform measures of

educational achievement** limits the program to the selection

of eligible children based on economic measures available on

a National scale. The provisions of Title I therefore provide

for using economic measures as the basis for determining the

grants to be made to educational agencies on behalf of the

eligible children.

* See, for example, Coleman's Equality of Educational

Opportunity (1966) or its later extension by Mosteller

and Moynihan , On Equality of Educational Opportunity (197 2) . ** This measurement deficiency as it relates to the development

of Title I is discussed in House Report 89-1814, Part 2;

August 22, 1966, pp. 28-33. The status of an evolving effort

to remedy the situation, the National Assessment of Educational

Progress, is reported in the February 1972 issue of Compact

(Vol. 6, No. 1), a publication of the Education Commission

of the States. It is noteworthy that the assessment has as

one of its goals "to make available the first comprehensive

data on the educational attainments of young Americans."

The present study examines the provisions that determine

the size and distribution of these grants. Public Law 91-230

in Section 102 calls for "a study of the allocation of sums

appropriated for the purposes of Title I. . . and of the

effectiveness of the various provisions of such title in

making funds available to State and local educational

agencies . . . .

The required study, as it has been pursued, has had

three facets. First, it has been concerned with the identification, description, and evaluation of the allocation

mechanisms and procedures used for the distribution of

Title I monies from the National level to the local level.

Second, it has sought to address and review the implementation

of the law and its administration as it relates to distributional matters. Third, the study has considered alternatives

to existing processes and procedures that might improve

existing approaches and resolve present problems. The first

two facets of the study were completed previously and have

already been reported.* The last facet has been the main

focus of the analysis effort during the past year and is the

subject of this interim report.

* "The Process of Funds Allocation Under Title I of the

Elementary and Secondary Education Act of 1965," An

Interim Report submitted to the U. S. Office of Education

by the Technical Analysis Division in March 1972.

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Further analysis of alternatives is still in progress

and is expected to be completed with the issuance of a

final comprehensive report in June 1973. This interim

report, presenting tentative findings from the analysis of

alternative procedures, has been prepared to provide

information which might be of value to Congressional committee

discussions of Title I now in progress. The findings

presented here have been limited to those associated with

the use of different provisions for determining grants and

with the use of different data from the 1970 census.

To this end, this chapter of the report presents a brief

review of the relevant provisions of Title I, and a discussion

of the issues and problems concerned with the distribution of

Title I funds. This discussion identifies open questions and

indicates the results of analysis where these are suggestive

of possible answers or resolutions to the issues raised. The

last portion of this chapter introduces and explores alternative legislative provisions for the determination and

distribution of Title I grants. Subsequent chapters of the

report deal more thoroughly with these subjects. Chapter 2

discusses the present grant determination process in detail

and includes in-depth consideration of problems associated

with it. Chapter 3 presents alternatives to various aspects

of the present process and examines in detail consequences

of their introduction in terms of the distributional effects

created

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1.2.1 Description of Grant Determination Provisions . Title I

contains three parts relating to authorizations for grants:

Part A, the Basic Grant; Part B, the Special Incentive Grant;

and Part C, the Special Grant for Urban and Rural Schools with

Highest Concentrations of Children from Low-Income Families.

Using the grant formulas, the U. S. Office of Education (USOE)

computes the allotted amount of Title I funds for each state

and for each county or county equivalent political subdivision.*

The distribution of funds to school districts within each state

is then computed by the state educational agency (SEA) , using

the most appropriate data and methods in the particular state.

A fourth part (Part D) defines administrative procedures

including the reduction procedure in case of underfunding

It also provides for reimbursement of the states for their

administrative expenses.

1.2.2 The Basic Grant Formula. The formula specified in the _—

——————— ___ ^ legislation for Part A is simple in concept. Each state may

receive (for its local educational agencies and for its stateoperated institutions) a maximum grant equal to the number of

* Continual change in the make-up and number of the Nation's

school districts has made annually determining grants to the

local level a practical impossibility for the USOE. For

example, while in the fall of 1967 there were 22,010 school

districts, by the fall of 1970 there were 17,995 districts —

4,015 had "disappeared" in only three years. Thus, although

the law stipulates school districts as the basis for grant

determination, neither the USOE nor the analysis of this

report considers a National distribution below the county

level

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eligible children multiplied by a cost factor per child:

Maximum grant - (No. of eligible children) X (cost factor

per child)

The formula includes two groups of eligible children: one

group administered by the local educational agencies (LEAs)

,

and the other served by various state-operated institutions.

The first group, administered by the local agencies,

includes children 5 to 17 years old in families having total

annual income less than a specified low- income factor,

those in families receiving annual AFDC payments of more

than the low-income factor, those living in local institutions

for neglected or delinquent children, and those who are being

supported in foster homes on public funds.

The second group covered by the grant formula for Part A

is composed of the children served by state - operated institutions and programs. These include neglected and delinquent,

handicapped, and migratory children. The formula for this

group is the same as for the first group. A discussion of

state programs will be a part of the final report and is not

covered in this report.

The low-income factor refers to a threshold level

defining poverty in terms of annual family income. The

legislation sets it at $2,000 for FY66 and FY67; $3,000 for

FY68 through FY72; and $4,000 for FY73. The low-income

factor is subject to modification, however, depending on

the amount of the appropriation, and, in fact, has remained

at $2,000 since FY66.

The cost factor is made up of two parts: (1) the average

per pupil expenditure (APPE) and (2) the Federal percentage.

The first is defined as the annual aggregate expenditures of

all the LEAs in the particular state plus any direct current

expenditures by the state for operation of such agencies,

divided by the average number of children in daily attendance.

This computation is done for each state and also for the

United States as a whole. To compute the maximum grant for

a particular state, the average per pupil expenditure for

that state or for the United States, whichever is greater, is

used

The Federal percentage is the figure representing a portion of the APPE deemed large enough to provide for a sufficient remedial effect on an eligible child to carry

out the intent of the Act. This percentage, established

by the legislation at 50 percent, has never been changed. ^ Approximately 85 to 90% of Title I appropriations, or

in the last few fiscal years, about $1.35 billion, is

allocated to LEAs under Part A. As such this is the core

of the Title I program and is also the focus for this report.

The tabulation and computation for determining the maximum

entitlement for this group is illustrated as follows:

Using FY73 data for the state of Delaware, the

enumeration of the eligible children in each

category for each of Delaware's three counties

is shown in the following table.

Low

Income AFDC Foster

Families Families N £j D* Homes Total

Kent

New Castle

Sussex

Total

1159

4 204

2059

7422

689

4161

861

5711

0

76

0

76

224

618

157

999

2072

9059

3077

14208

* Institutions for the neglected and delinquent

The appropriate cost factor is selected: 501

of the state APPE is $498 and 50% of the National

average is $429; therefore, the state APPE value is

used. The maximum grant to which the LEAs in

Delaware are entitled is $7,075,584 which is obtained

by multiplying the total number of eligibles, 14,208,

by the cost factor $498.

Part B of Title I provides for a special incentive grant

under which a state may qualify for additional funding if the

"state effort index" exceeds the "national effort index."

The state effort index is defined as the ratio of the total

expenditure of all non-Federal funds in the state for

public elementary and secondary education to the total

personal income in the state. The National effort index

is the ratio of total non-Federal expenditures in all states

to the total personal income in all states. The effort

indexes are expressed as percentages.

The formula for Part B specifies that the maximum

entitlement for a state shall be $1 per eligible child for

each 0.01 percent by which the state effort index exceeds

the National effort index. As an example, if a state had

an effort index of 6.501 and the National effort index

were 4.501 that state would be entitled to a maximum grant

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under Part B of $200 for each of the children counted as

eligible under Part A. There is a limitation that no single

state may receive more than 15 percent of the funds available

for the Part B grants.

Part C is a special grant for urban and rural school

districts serving areas with the highest concentrations of

children from low-income families. This part incorporates

two features. The first feature primarily benefits the rural

schools by qualifying an LEA if it has eligible children, as

counted in Part A, amounting to at least 20 percent of the

total of children of school age. The second feature

primarily benefits the urban schools by qualifying an LEA

if it has at least 5,000 eligibles who constitute at least

5 percent of the total of children of school age. An LEA

qualifying under either feature may receive a maximum special

grant under this part equal to 40 percent of what it received

under Part A.

The states are to be reimbursed for administrative

expenditures involved in the proper and efficient performance of their duties under Title I. Each state is to

receive 1 percent of the amounts received under Parts A and

C, or $150,000, whichever is greater. The funds required

for these administrative grants are deducted from the LEA

grants

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1.2.3 Reduction Procedur e. The allocation rules provide for

the maximum grants or entitlements which any SEA or LEA may

receive if the program is fully funded. Only in the first

year of the program, FY66, were the funds sufficient to meet

all entitlements. Every year since then the funding has been

less than the entitlements, and the disparity has been

increasing. The Act includes a section in Part D covering

the procedures by which the grants are to be reduced when

the appropriation is less than total entitlements.

The grants for the SEAs are to be paid fully. The grants

for the LEAs are to be recomputed with the low- income factor

reverting to $2,000. The sum for the LEAs is then ratably

reduced taking into account certain complexities involved with

ratable reductions for Parts B and C. With the present level

of appropriations, this provision restricts Parts B and C to

an extremely small share of Title I funds. In view of thejr

minor role, these parts are not considered further in the

discussion that follows.* Thus, after the SEAs have been

fully funded, the remaining appropriations are distributed

among the entitlements of the LEA grants of Part A, the state

grants of Part B, and the LEA grants of Part C.

Part B of Title I is discussed in detail in Appendix B of

the previously referenced report of March 1972. Part C is

reviewed in Appendix A of the present report. The extent

of the limitations identified in both appendices suggests

that these parts of Title I would be less than satisfactory

even if they were to receive more funds.

12 -

Although the Part A LEA grants are reduced below their

entitlement, each state must receive at least some specified

minimum (its floor value) for its aggregate Part LEA allotment.

If any state's grant is below the floor, its allotment must be

brought up to the floor value by proportionately reducing the

allotments to all the other states to make up the difference.

The Act, as it now stands, contains a floor provision

guaranteeing that each state shall receive Part A LEA grants

totaling at least what it received in FY67. The annual

appropriation legislation usually contains an overriding

provision of a different floor year to be used. For example,

for FY71 the floor year specified was FY68

1,3 Distributional Issues and Alternative Possibilities

1.3.1 Time for Change . The enumeration of eligible children

depends upon the decennial census. It is time to replace "the

1960 census base with the 1970 census which became available

in December, 1972. The total number of eligible children as

determined from the 1960 census was 4,947,525. This was the

number in families with incomes under $2,000. The comparable

figure from the 1970 census is 2,645,838 children (in families

with incomes below $2,000). When a $3,000 income level is

used, the number of children increases to 4,211,888. The

comparable totals when the appropriate AFDC data from 1972

are added are:

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(1) 8,216,712, from 4,947,525 children in families v/ith

incomes below $2,000 (from 1960 census) plus 3,269,187

children in AFDC families above $2,000;

(2) 5,915,025, from 2,645,838 children in families with

incomes below $2,000 (from 1970 census) plus 3,269,187

children in AFDC families above $2,000;

(3) 6,268,776, from 4,211,888 children in families with

incomes below $3,000 (from 1970 census) plus 2,056,888

children in AFDC families above $3,000.

These values highlight the obsolete quality of the 1960 data,

which suggests that some abrupt changes are likely when the new

data are substituted for the old in the allocation process.

This impression is ^reinforced by reference to Table 1.3.1

which lists the Part A LEA allocations by state using the data

associated with enumeration possibilities (1), (2), and (3).

The allocations arc those that result from a total appropriation

of $1.5 billion for SEAs and LEAs under Part A when there are

no protective floors. These conditions result in allocations

directly reflective of the changes in the National distribution

of the eligible children which may be expected regardless of

the income level used to determine eligibility. This state of

affairs, in which many changes are likely to occur, suggests

that this may be an opportune situation in which to give

consideration to making a variety of adjustments in recognition

of problems previously experienced. Much of what follows is

offered accordingly.

There has been discussion and public controversy over the

identification of the target population for Title I. Issues

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Table 1.3.1

State Allocations Resulting from Three

Different Enumerations of Eligible Children*

1960 Census

$2000 Income

ALABAMA ; ALASKA

A H J ZONA ' arkansas

c a l i forn j a Colorado

connect i cut

delaware

Florida

G£0RG I A HAWAII

IDAHO

ILLINOIS

INDIANA

IOWA

KANSAS

KENTUCKY

LOUISIANA

MAINE

MARYLAND

MASSACHUSETTS

MICHIGAN

MINNESOTA

MISSISSIPPI

MISSOURI ~ MONTANA

NEBRASKA

NEVA-DA NEW HAMPSHIRE

NEW JERSEY

NEW MEXICO

NEW YORK

north carolina

north dakota

Ohio - Oklahoma

Oregon

Pennsylvania

Rhode island

south carolina

south dakota

tennessee

TEXAS

UTAH

VERMONT

VIRGINIA

WASHINGTON

WEST VIRGINIA

WISCONSIN —

WYOMING

DJST, OF COLUMBIA

34 354954 .

" 2287?72

BOM&ON I

20846714. — 110996*30.

! 0 I 60379

,

I 167 1A70,

2 19 4 0 7 5,

2397 1 1 93.

4034 7 t 50.

3584785.

2 5 9 1 « 3 0 » 69.1 65777,

I 8665«92 . 14520*39.

9056*03 . 32033704.

31 I H 8 1 62.

55 I H* I a,

I 92 7 t MB . 247544 fl0 . S | 4 7 7 " 6 0 .

'" 207801 46,

357227 97

23236A99,

2 7 H 0 I 7 4 , 7 0 7 8 P 4 7 . 781 «63,

1 8 70" 68 . 4398S°o7.

7289644 i

I 95 7 38 ? 8 I . 5 I 26574 7 . 3979^44 , 4 | 929700

I 6555" A J

8340>60.

64<,3Q B 01 • 47Si*72.

2968 4 "09.

" " 5349*27

,

3I 0987M . 67297B70,

3769^78.

1960*34,

3 I 340» 1 2 ,

I 33 701 8 2

17223*15.

|.72H2«2<t, — 10 301 1 4 . ^-joootnaa.

1970 Census

$2000 Income

1 8S37904

,

2926 >74

89 74 "79,

9923*36,

l492203|0.

I 2032*33.

19880 128 , 2568"69

,

.._ 24 1 82'' 28 . - 26492*1 4 . 44 79*08,

2S97 '69.

'—- 82704724.

( 84 4 3 1 7 5.

I 0083 1 4S

B 704 moo ,

... - 1 9 4 8 I ° 4 1 » - 254 I S7Q6 , 5827924.

23404 745.

3 I 9 I 8*7 1 . .. 5 9 9 4 2 " 2 I ,

I 7808? | 5 . -

I 8 5 6 3 4 h | , J868839I.

259 7 769.

598 7 127 ,.-

1 224 U6 , 2 280345 . ... 58044770,

7949926. _ 25B 7 680 | I , _ 26705P23, -

25 10 745.

47072 14 3 , -

1 3232747,

.— I 024 2 '55.

7 1 6 4 1 130 . 5696769.-

I 4503*42.

3457 3 05.

15749 158.

5 1 4 9 3 * 4 3 . . 4687333,

1 968"03. _ 23153171.

1 7 I 60*22 . _ 9722*06.

1 B062<>38, . 1022*52.

12932790.

1970 Census

$30 00 Income

27367«2B,

3 13 14 38.

8994729.

1 5 4 9 0 r- 0 8 ,

1 3 I 704"S4

,

1 O937980.

1 537 8"A5.

22131 13.

29724 "27 . 2 8 2 1 I " 6 5 . 42S0 1 35 . 29Q4U75.

7 4 0 6 8 T 0 I .

1 5579 •> fl 7 , 10074*93,

8473*24,

228847^7,

"32464^06,

426 I A 95

,

20MOIH38,

29 1 63"06

57033750.

I 8 6 5 4 * 7 I . " 2727I02M,

1 084 4* J 6,

29397Q2

,

5899*65.

1243^11.

2 3 2 9 * 1 | . " 5398 1*2 1 • 7 907*4 3 . 2 42S334H9,

308 1 5763 . 29l47 4 2. 39865*6 1 . 13959*70.

1 0257<>i9 . 6 7 2 1 1 494 . 5 188762.

" 200 14*40.

4 108025.

2 4 1 2 I * l 5 , 58987*4 1,

4695750,

1 980750.

25590339,

_ 1 588844 1 .

1 I 1 49*35.

18682474,

991*04,

13178450,

^Assuming appropriation of $1.5 billion for SEAs and LEAs under

Part A and the absence of protective floors.

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of principle as to "who are the poor" and the like are mentioned

but are set aside in favor of more pragmatic questions. These

are the empirical problems that result from the requirement

that the enumeration be done on an annual basis; that it be

extensive, covering the entire nation; and that it be intensive,

being as detailed as possible. This can be translated into a

set of characteristics that might be used to evaluate the

suitability of various methods of enumeration. Desirable

attributes are: National uniformity, regional parity,

completeness, reliability, and currency (up-to-dateness).

National uniformity means that data are available and applicable throughout the Nation; regional parity means that data

are adjusted for regional differences in cost; and completeness

means that data contain all relevant information in the detail

desired and are without gaps. In the material that follows

these characteristics are taken into account as different

possibilities are considered for the data requirements of the

grant determination mechanism, hereafter referred to as the

"formula .

1.3.2 Enumerating the Eligible Children . The law in its

statement of intent cites children in low- income families as

the target population. The present formula calls for the use

of census data to identify the number of children in families

whose income is below a fixed amount. Based on the census,

these data are reasonably uniform, complete, and reliable,

- 16 -

but they become increasingly obsolescent (they are already

three or four years old when first put to use). The

obsolescence stems from geographic mobility, shifts of the

target population due to differences in birth rates, and

economic changes. Moreover, these data do not reflect

interregional differences in the cost of living. Additionally,

these data do not reflect differences in family circumstances,

e.g., family size, as these might have a bearing on poverty

level

The present formula relies on AFDC data as the basis for

maintaining currency. Up-to-dateness is the major advantage

of these data, which otherwise are deficient with regard to

the other attributes desired of the formula data. The AFDC

data for use by Title I are recorded for a single month every

year for programs that vary from state to state. In addition,

the data, are subject to annual perturbations within states^

and their statistical reliability is unverif iable

The combination in the formula of both the censusdetermined low- income family count and AFDC count, i.e.,

adding them together, is a potential source of problems.

First, it permits the possibility of double- count ing ; that is,

children counted during the census year as being in families

with incomes below the specified amount might in subsequent

years also be counted within the AFDC tally, as their family

status changes. Second, there are possible errors of omission.

17 -

For example, it is possible that a family whose income is

above the low- income level during the census year suffers

income reductions in subsequent years but fails to receive

AFDC payments above the low-income level, and thus children

in such families fail to be included in either data count.

It is not possible to estimate to what extent the errors of

commission (over-counting) balance the errors of omission

(under-counting)

There are some alternatives that might tend to ameliorate

some of these problematic conditions. First, instead of

adding the count of children in AFDC families, the updating

or annual adjustment effect can also be achieved by using a multiplying factor which is a ratio of the current year AFDC

data for the state divided by the census year AFDC data for

the same state. This would avoid some of the difficulties

derived from the additive method of combination and also -

tend to suppress the influence of interstate programmatic

differences. Another possibility would be to control the

entire updated total by limiting the national total to the

values estimated annually by the Census Bureau for the

national level of poverty in the United States.

The use of an AFDC ratio adjustment for the enumeration

data might be thought to accentuate the annual perturbations

evidenced by the AFDC data as they are currently collected for

- 18

*

Title I.* To overcome this difficulty, instead of relying

on the data collected for a single month, the data available

monthly at the state level could be averaged over a sufficiently large number of months, e.g., 24, to reduce

the likelihood of experiencing sizable fluctuations in AFDC

counts resulting from seasonal variations or year-to-year

program changes.

A more fundamental change is the possible replacement,

of the present basis for enumerating the children in poverty

with the count of children based on the use of the so-called

Orshansky index. This index is recognized as the official

Federal poverty measure and has the advantage that it

defines poverty according to family circumstances, e.g.,

the number of children in the family, and family subsistance

needs

* Reference to the AFDC data of three representative states, for

several years in succession, reinforces the notion of year-toyear variation. Idaho typifies states with relatively modest

percentage change over the years FY66 to FY72; New Jersey,

moderate change; and West Virginia, extreme change. The yearto-year fluctuations for each of these cases is evident.

Title I Fiscal Year

AFDC 1966 1967 1968 1969 1970 1971 1972

Idaho 2403 2372 1609 4165 3197 2815 5587

New Jersey 25496 42106 31283 64696 85992 129407 165912

West Va. 82 0 2 12205 10353 15661 14684

- 19

Introduction of these various changes has interesting

distributional consequences. Table 1.3.2 presents the

resulting allocations by state. The underlying conditions

as to the amount of the appropriation and the absence of

protective floors are the same as those underlying Table 1.3.1.

The first column is the same in both tables — for comparison

purposes — showing the allocation using the present method

of enumeration. The second and third columns of Table 1.3.2,

however, both reflect the use of the AFDC ratio adjustment

(instead of the present additive adjustment) and the use of

the National totals as control totals. Column two differs

from three in that it is based on 1970 census $3,000 lowincome data, while column three is derived from 1970 census

Orshansky- based data which total to 8., 383, 602 for FY73 after

adjustment. These two methods, although different in

principle, result in enumerations whose state -by- state •» distributions are remarkably similar for FY73. This is

readily seen by comparing the last two columns of Table

1.3.3 which lists percentages by state of the eligible

children for each of the five methods of enumeration. The

Orshansky- based enumeration appears to be advantageous in

terms of the desirability criteria mentioned earlier and

is used in the remainder of the analyses presented.

1.3.3 Grant Per Child and Concern for Concentration. The

20 -

Table 1.3,2

FY 7 3 State Allocations Resulting from

Modified Methods of Enumerat ion*

1970 Census

XJVU LtlloUj t** t r\ r\ r\ $3000 iy/0 Lensu

$2000 Income ursjiciiib Ky

Income ACL J US lgq uy A /I n 1 1 c t D n r\ ' AflJUS LcQ u n 1 M c A VT)C AFDC Ratio AFDC Ratio

ALABAMA 34354954.' 37194 P 3] . -1-70.01 oc:/i ALASKA 2287772, 307411 '114 . 0 1 ? * 1 ~ " 7 • ARIZONA - 80469H i

.

I2?.5ni ?3, 1 ot/ioni q J t

J * r t I V • ARKANSAS 200 4 6 ? 1

4

. ? 4

l1 7 5

r> n r>

.

CALIFORNIA - J 1 OV96n30 c "

'" 94 'M ?3H. Qi ifmnxi

COLORADO 10160*79-: ll r>c,n7nQ,'

CONNECT I CUT j 1 6 7 1 A70 r 1 0^0 1 ni| o , 07 1 M i 1 0 Delaware 2 1 94n7S, 3 n 't70ri r

)

,

J 1 1 n ' ' • Florida - 2397 1 1 vJ. t+ fS n qo i 7

.

(if.OPSOII

G£ 0 R G I A H03M7 1 SO. l)5 Qli'l l i 1ci. H r > 1 1 ' ? • H A W A J J 3S8H ?85. 3VfS^"V,.

Idaho 2S91 <>30c 3 1 5 R "VO. \ . 3'l0p707

.

ILLINOIS 69145777.. -- rfiflflli 1 m 597<V) ; >?;?

.

INDIANA » 1 B 6 6 5 « 9 2 ( 2o 5 0 07?7

,

IOWA — \ (\\ fif^T) P .

I 4520039, " •! 9 D c

i 0 f, P O , KANSAS 9056PQ3 950

5

0 0 °< • Q^r,?7"»"\

,

KENTUCKY ~_. 32033704. "''

r "~ ' p f, I n 0 7 <i r>

,

LOUISIANA 3 1 148 162. 4?5 1 1 >°7 . MAINE 55|4»<I8, — 5 5 ? 3 7 1 ft

.

f^q^pnoii , MARYLAND 1 92 7 1 M8 . ? 0 0 7 S 0 ~> ? . MASSACHUSETTS 24 754 M ft o, , 1 n 1 0 r, »/! f.

.

i [1 1 '1 Mil Michigan 5 1 4 7 74^,0. ( 0 t\ c "X ii nil t* 6 5 3 6 3 ^ U . mjnnesota — 207801H6, 1 / n ' 1 7

f M * •

- j^fir,^^

MISSISSIPPI 35722797

.

37 ,n I 373. -3(S't 0 ^ n, q S . Missouri 23236A99. 1*7*^1 1 n r*. ^ 27"li n, ?« 27 ^°'? r, 7^

,

MONTANA 2 7 H 0 I 7 H , 3010011,

NEBRASKA 7078OM7. , Ei7 3" ' n n

.

NEVADA 78 1453. 1 7 3 fi 3 Q I>

,

14

c.

1

1 1

i (1t «Jp 0. o NEW HAMPSHIRE"" 18 70468. "

"~ 2° ntl710,

NEW JERSEY H3905«»O7 . jd" ' n 1 n f; • ^ U 0 ft 1 ft 7 0 . NEW MEXICO - 7 269AM H , 9

u 75'i?'->

.

1 ij 1 if * • r> • NEW YORK l95730?8l

.

131 ftoop

,

NORTH CAROLINA' ~ - S 1 2657 S 7 , 14 3 ' " r> n n ] • 450 1 <i l ^ 1 . NORTH D A *, 0 T A 3 9 / 9 > 4 m , 3 ? 5 1 1 0 fi

.

371 ft^^f,. OH I 0 —_ HI92V700. 47^3° r ' 07. Il3ft70'inq.

Oklahoma 1 65554fl3

,

161 ^n 1 70. 1 r» 0 7 3 *> 0 ^ . Oregon 8340"<60»" """" "_ 1 omnorii g?(S3&,7(i . Pennsylvania 64630°0 I * 51 > 1 1 '1 ^'t

.

3 ^. 1 ..1 1

' 1 1 > . Rhode island - 4 7 5 I n 7 2 . 3<> 1 1 ns'i

.

SOUTH CAROLINA 296B4M09. 35

1

7 1

1 ^ 1 . ju»/. CLC.1 Jn 1 "(107f • SOUTH DAKOTA 5349"27

14 7 R 7 1 1 0 .

" 11 7 f. 1 n 0 0 TENNESSEE 3I 098 76J , 3&" nnntiO • "^7 ^ ^ 1 ?7t: .1 ( ' M r » t Texas • : — 67297070.

UTAH 3769A78. tl 1 'ill -//- f 1 7 3 p n 3

.

VERMONT I 9 6 0

r~ 3 4 . — " . 1 C^(*r ir.n

1 nr»(. 1 1 '1 • 1

<-> 1 n ft 0

.

VIRGINIA 3 1 3 4 0 * I 2 . 3 ; ^

,

371 n 5

fl

1

1 <

.

Washington 1 3 370 t 82. " ~. 1 3' f

> ' < " " 12'IP^3'i3.

WEST VIRGINIA |7223«IS. 13TS1 I'M . Ipoo2°'ift

.

WISCONSIN I7242A2H. 1Ro7U 1< c 7. 10^5n573.

WYOMING 10 30114. mofS"r,7. 1 3

r>HS'i ft . dist, or Columbia loooinaa, — 9P11949. 9 ^ 7 7 ft 1 H . Assuming appropriation of $1.5 billion for SEAs

and LEAs under Part A without the protective

floor provision.

- 21 -

Table 1.3.3

State Shares of Poverty Children in FY73

Under Five Alternative Estimations

K

l K

2 K3 K

4 K5

/\X d L> d Hid 7 j V o

iX . 6U AH %.^ 9 4 7 ?s ij . 7J . i 1

0 X X o

xj 1 -n c V 1 J\X d 5 K

X1 7L

1 c

i X 0 i X u

1 c 1 fi x u

y\ r l zona , fio Qy

7 0 7 Q i / y 1

U 4

11 . U J A I J\u 11 o d b

1X i ft n i Ro Ro1X • 7L . i r X D

7 x1 ^7 California Qy

X J . 1 X XX . 1 . A 7 7 A 7 Colo Tado $3 fi o 0 X . u 0

Q C y o • y D • y 4

ft ^ 1X . x1 7/ 1X • X L • 7 7 •fi fi dc x av. are 1 O

1 Q , i y X 0

9 T Z 1

7 7 Z Z rioriua 9Z . u o L , 1 X 0 X

1 O 7 y j

7J . y 4

7J . A4 ftO9L . i o o 9 4ft 7 Q 7 y oA4 . D4U 4 rlaWall 7 R i u

T.4

• 7 .1 Z 4 7 5 JLUaJlU T n }i a ?A Z7 7/ 79

ill UlUlo cD « CiR f,yj . 7 7 •J « 64 4 7Z X1 4 76

i J lu 1 a 1 1 ci 1X i 1x . 57 X < 7 X1 oX 2 1 5

1T nU n a 1X i 2 3 87 , 86 8 0 85

i\ UilJ Q J , 77 , 76 , 74 7 5 , 8 0 Kentucky 2

,75 1 . , 71 2..00 2

30 2

,17

F.oui S i ana 2

, 68 2, 26 2

, 87 7, 64 3

, 43

Ma ine .46 , 50 , 36 44 , 53

Marvl 1 * >-J- X 7 JL Ci- nndJ I VX 1

, 38 1

, 73 1

,48 1X 4 1

. 46

2

. 02 2, 71 2, 4 5 1X i 4 3 1 . 43

Mi rh i n^n X•J <i R(J RU 4 7 n 4 ( , 4 2

XJ • 3 . 4 0 Mi nno^ot^ 1X . 30 X < , 36 1J. ii X . 2 6 Mi ^ i ^ i nfi i 3 , 1

1 , 67 2 . 44 X+j . 29 S . 08

Mi ^ *^ n

nx j o v ui ti ai 1X • , 98 1 . 63 1 , 63 2Li 1 , 29 2 . 27

1*10 ii l a ii a 7 A i L 4 1 X 7 fi X A 7 7

1 1 U U I a d d 1 fil i OH . 0 L ^ 7 56

iNC V dUd > u / > XX > X 1 . X1 44 1 7 X -J New Hampshire . i y

7 7

. Z 0 • U7 4 New Je r s ey Z

Q 1 xjQ 7 7O . 0 0

7L X1 4H 7 .XX1 1 New Mexico fi 7

. / X

7 n S ^ . O J R ^ vu, . v ^ -v- i^- In ew iorK y

7 7

1 I

O A 1 -t 11 . yi 0 . J 4

CJ

q 7 nor in Laroi liid /i4 . 1

9 . j4 9 A Q . o y

7 \J o 3 . 7 6 INOr til JJaKOta t r

. O D 7 fi ? 7 . 5 2 Oh i r\ KJll X O

7O . D L

A4 n q 7J . X

7 9 ? 3 . 59

\J J\ X dilUJlld 1

J. a n 1X X H X

7 1 . 33 1 .34

fir \J 1 nC nnn £ U i 1 u x 7 fi 11 .71 . 66

P^nn * LilJlDqvY J.1 \rV un n111i a^ C 1X AH

c on 47 3 . 90 4 . 03

Rhode Island .37 .46 .41 . 29 . 28

South Carolina 2 . 57 1 .29 1 .78 3 . 04 5 .08

South Dakota .45 .29 . 35 . 38 .39

Tennes see 2 .68 1 .38 2 .13 3 .12 3 .13

Texas 5 .81 4 .60 5 . 23 9 .46 10 . 51

Utah .33 .42 .42 . 34 . 35

Vermont .17 .17 .17 .12 .16

Virginia 2 .65 1 .99 2 .20 2 . 95 3 .08

Washington 1 .05 1 .41 1 . 29

1

. 99

1 .95

West Virginia 1 .47 .85 . 97 .11 . 07

Wisconsin 1 . 28 1 .37 1 .42 1 .33 1 . 3 5 Wyoming .09 .09 .09 .12 .12

Dist. of Columbia .66 .89 .90 .60 .60

100.00% 100.00$ 100.00% 100.00"o 100.00%

scope of Txtle I program coverage is intended to be broad.

The programs sponsored by Title I funds are to provide for

the special educational needs of children living in poverty.

The programs are to supplement, not supplant, the regular

educational program. As such, the programs in some areas

provide for basic material needs of these children including

clothing, dental care, and the like. More often, however,

the funds are used to provide remedial programs in reading

and mathematics. Nevertheless, the children's needs vary,

and appropriate programmatic responses are diversified.

This tends to complicate the already complex matter of

ascertaining that adequate financial resources are being

stipulated in the amount specified for the basic grant per

child. Questions of program effectiveness remain a matter

of considerable discussion. Satisfaction of the need to

establish appropriate cost estimates must await their answer.

Additional problems complicate the cost issue. It is

desired to represent geographic differences in the cost of

education. These differences are evidently reflected both

in interstate and intrastate differences. Other difficulties

are introduced when it is suggested that cost differences

reflect not just differences in the cost of providing

education for a child, but that the differences in cost

reflect differences in quality as well. Finally, related

to this quality aspect of cost differences is the notion

23 -

that differences in cost are likely to result from local

fiscal capability. If reflecting cost differences reflects

relative differences in the ability of local areas to pay

for education, then for Title I to reflect differences in

the cost of (compensatory) education would be to work in

opposition to the intent of Title I.

The basic issue concerning the concentration of funds,

i.e., increasing the basic grant per child in selected areas,

is whether areas of greater need have a requirement for a greater share of funds than would otherwise result from a

pro rata share based on the relative numbers of eligible

children. A corollary issue is whether the degree of an

area's need is more clearly evidenced by its level of

poverty in terms of per capita income or in terms of the

concentration level of poor among the total resident population.

Unfortunately, generally accepted empirical evidence

which may be brought to bear in resolving these issues is

scanty. The legislation, as stated in Section 101, suggests

that such emphasis be given to areas serving high concentrations of disadvantaged children. The present implementation

of this intent at the National level has been largely restricted

to Part C, a relatively minor part of Title I. In Part C,

areas with special needs are defined as those with either a sizable number of eligible children or a significant fraction

of their total school age population consisting of eligible

children.

- 24 -

Before the amount per child can be adjusted for reasons

of concentration, it would be useful to have established an

appropriate grant per child based on relevant cost considerations. The breadth of program coverage, however, makes

the establishment of such a value difficult, especially in

view of the fact that, for some, any amount of funds is

viewed as being useful. It suffices to state, nevertheless,

that a critical amount has not been demonstrated such that

above this value the chances for effective programs are

considerably enhanced, and below, considerably reduced. It

is noted that $300 has gained some acceptance for this

purpose, but there appears to be little empirical justification for selecting this amount.

The importance of empirical information can be somewhat

overemphasized, and the matter can quickly become one of <^ principle. With appropriations of about $1.5 billion and a count of eligible children of about 8.4 million, the use of

cost factors above $165 per child results in LEA grant

entitlements which cannot be fully funded, and reduction of

the maximum grant amounts must occur. The issue then becomes

whether to divide the limited funds equally among all areas

or to discriminate among them according to some notion of

differences in costs or perhaps in needs.

Although equal distribution of the funds appropriated

for Title I can be achieved by specification of any basic

grant amount per child above $165, applied uniformly throughout

the United States, the sum of $300 is used for illustrative

purposes because of its somewhat general acceptance as a "reasonable" amount. The actual value chosen is significant

only because disadvantaged children administered to by SEAs

are currently allotted their maximum grant; it is the LEA

children in Part A that are ratably reduced. The effect of

this provision is to decrease slightly the amount allotted

for each disadvantaged LEA child from $165 to $159. (Note

that if protective floors from past distributions are

imposed, there is no way to achieve an equal distribution

on a per-child basis.)

The other extreme in distributional principles, based

on cost discrimination, can be effected by using 50 percent

of the state APPE, for each state, if it is assumed that it

represents state -by- state differences. The extent of these

differences is seen in Table 1.3.4 which presents state APPEs

Although it does reflect interstate differences, it is not

clear what differences are being represented. Because of

this difficulty, the present formula incorporates a compromise,

motivated by the recognition that low APPE does not mean

lower cost to provide the same quality of education or more

efficient use of resources, but probably signifies less

ability to pay for general education; the compromise is to

substitute 50 percent of the National APPE when that is

- 26 -

Table 1.3.4

Average Per Pupil Expenditure for

Elementary and Secondary Schools by State

1970-71 School Year

(Apply to FY73

Title J Allocations)

Ala bama $ 529 . 38

Ala ska 1452

.

28

t\T l zona 745 . 96

Ar kan s a s 518 . 64

Ca 1 i f o r n i a 855

.

44

Colorado 812

.

60

Conncc t icut 1009. 4 8 Del awa re 996

.

4 2 Florida 781. 36

Georg ia 644 . 72

i-l oi.ro t 1 flawa 1

1

983. 74

Ida no 610. 16

111 ino i s 992. 62

Indiana 783. 42

I owa 864

.

84

jv.an s a s 787. 22

Kentucky 571

.

88

Lou i s iana 716. 30

Maine 709

.

60

Maryland 985

.

5 2 Massachusetts 894

.

22

Michigan 972

.

08

\A *i y~\ s~\ c r~\ +• o

rl 1 11 11 C b O L d 1005 . 92

Mis sissippi 4 69. 60

Mi s sour i 722 . 12

Mo n t a n a 801

.

60

Nebraska O A *7 8 07. 2 8 Ncvad a TOO 7 88. 1 8 New Hampshire h n n

7 7 0. 9Z

New Jersey 1135. 26

New Mexico 689

.

08

New York 1487 34

North Carolina 611

.

7 2 North Dakota 685. 34

Ohio 762. 84

Oklahoma 623. 72

Oregon 957

.

12

Pennsylvania 909 56

Rhode Island 951 86

South Carolina 571

.

12

South Dakota 719. 04

Tonnes see 552

.

80

Texas 667. 80

U tan 664 . 8 Vermont 797 . 14

Virginia 738. 56

Washington 893. 96

West Virginia 644 . 10

Wiscons in 950. 56

Wyoming 882 . 00

Dist. of Columbia 1116. 94

National Average 859.,88

greater than 50 percent of the state value. This is a compromise in the sense that it is, in principle, between the

distributional principles of equal shares, i.e., constant

cost, and fully discriminating shares, i.e., variable state

APPEs.

The effect of these changes can be best observed when

the allocations per disadvantaged child are averaged for

the poorest and least poor counties in the United States.

When all the counties in the U. S. are divided into five

groups containing a like number of counties, based on per

capita income, the poorest group averages an allocation of

$125 per child when 50 percent of the state APPE is used,

$153 per child when the present (state or National) cost

choice is used and $165 per child when the same ($300) value

is used for all states. On the other hand, the (20 percent)

group of counties experiencing the highest per capita income

4k- levels receives on the average $192, $175, and $165 per child

respect ively. * Thus, there is a significant difference in

distributional outcomes experienced at the county level

according to the choice made for a representative grant

amount per child.

* These data result from analyses in which SEAs receive a reduced share, and protective floors are not imposed on

the aggregate of LEA grants.

- 28 -
\
Concentration of funds is simply a discriminatoryallocation of funds seeking to increase the amounts made

available per child based on considerations of need. That

this is necessary or desired is a matter for judgment. It

is the intent of the discussion that follows to indicate

what distributional results might be achieved if it were

judged to be desirable to intensify the concentration of

funds made available at the county level for Title I purposes beyond what is presently being accomplished by

Part C. For the purposes of this discussion the same

fraction or percentage definition as used to measure concentration in Part C is used here: the number of eligible

children divided by the total number of school age children

in the area. The basic grant per child is assumed as $300.

Some results of the analyses seeking to concentrate

funds in counties of greatest concentrations of eligible

a* children are shown in Table 1.3.5. The 3,113 counties of

the U. S. are divided into five groups according to per

capita income. In the lowest income group are counties

with concentrations of eligible children of up to 76 percent,

while for the highest income group of counties the concentrations of eligibles are generally below 10 percent. The

National average is 14.8 percent. The results are in sharp

contrast with those resulting from direct variations in the

cost factor described above. It would seem that if the

- 29 -

intent of the law with respect to the special needs of

arens serving high concentrations of eligible children

is to be reflected in the distributional outcomes achieved,

then the desirability of introducing into the formula a

means for accomplishing this type of funds concentration

is worthy of consideration.

Table 1.3.5

Comparison of Allotment Per Pupil: Alternative

Concentration Effects with $300 Per Pupil Cost

County Groupings

Based on Per

Intensity of Desired

Concentration Effect*

Capita Income None Low Moderate High

Lowest Income Group $165 $235 $271 $303

Second Group 165 187 201 212

Third Group 165 165 167 168

Fourth Group 165 159 158 156

Highest Income Group 165 142 133 123

1.3.4 Constraints Imposed by Appropriation Levels . The

total of the maximum grants determined by the formula has

always exceeded the amount appropriated except for the first

year. The condition of underfunding raises the question as

to whether there are those who should receive preferential

* The intensity of funds concentration — low, moderate, and

high effect — can be quantitatively illustrated. For a county with 15 percent concentration of eligibles, about

the National average, the low intensity effect corresponds

to a 37.5 percent increase in the basic amount authorized

per child; for the medium effect, the increase is 75 percent; and for the high effect, it is 150 percent.

- 30 -

treatment and be reduced less than others. At present two

such forms of special treatment are given. First, the grants

on behalf of the eligible children administered to by SEAs

are fully funded. Second, the previously discussed protective

floors are imposed on allocations made to states on behalf of

their LEAs. Possible motivations behind these special

considerations are that SEA children have unique needs, and

that floors are needed to assure continuity of benefits to

prior participants and to avoid wide shifts in distributions

from year to year.

The effect of fully funding SEA grants is significant

in terms of the difference in the grant per child realized

by SEAs as opposed to LEAs. In FY71 the difference was $368

per child in SEAs versus $175 per child in LEAs; the difference

increased in FY72 as an average of $413 was made available per

SEA child and $168 per LEA child. The difference is sizable,

and its magnitude appears to be without empirical justification.

Moreover, in some cases it is not clear that any difference is

justifiable. In particular, this is true of one group of

eligible children, those in institutions for the neglected

and delinquent, which are found under the jurisdiction of the

SEA in some instances and under the purview of the LEA in

others. In fact, for FY73 more than half (53 percent) of

the 129,929 of these children are in institutions administered

31 -

by LEAs . It would seem that if these children had special

needs justifying full funding at the state level, the same

would apply to those in LEAs; alternatively, the grants in

both instances could be ratably reduced. Children in other

groups administered to by SEAs remain special cases, each

to be decided on its own merits.

It is generally recognized that the presence of the

protective floors constrains the realization of distributional

outcomes according to national need as reflected in the

enumeration data and associated maximum grants, and thus

there is little need to emphasize the consequences of the

presence of the floors. Of greater interest, and more

pertinent, is the extent to which the floors are effective

in serving their purpose of continuity. First, it should

be noted that the majority of states are not generally at

their floor value and that great variations (both up and ^ down) can occur from year-to-year. Second, the floor value

applies to the state aggregate of LEA grants; grants actually

received by LEAs may still vary even when the state total

remains at its floor value. Third, when the floor becomes

effective for a state, the effect of the floor is rigid,

i.e., it is completely unreflective of current needs as

represented by the authorization. These three considerations

suggest that the floor provision, as presently implemented,

can achieve only limited success in assuring opportunity

- 32

easily set aside as being of little value, but many still

remain for analysis. A sizable number of these have been

considered; others have been arbitrarily by-passed for the

present time.

It may be desirable to achieve certain specified

distributional characteristics related to the distribution

of income and the concentrations of poverty at the county

level. The present formula can be improved upon with respect

to these characteristics. In particular, alternative formulas

created from

(1) the adjusted Orshansky-based enumeration method,

(2) either 50 percent of the state APPE or a constant

cost factor, in concert with moderate concentration

effect, and

(3) cither with floors at the 90 percent level or without,

might offer a direction for such improvements in resolving

some of the difficulties that have been associated with the

present formula.

- 34 -

for participant continuity and in reducing variations that

are inhibiting to proper planning.

There are some alternative responses possible regarding

preferential funding for special groups of eligible children

and for states which might otherwise suffer reductions in

their funding levels. First, some consideration should be

given to ratably reducing all groups on an equal basis

except where a special need can be demonstrated, so as to

avoid inconsistencies of the sort identified. Second,

consideration should be given to the possibility of setting

floor values at 80 or 90 percent of previous allocation

levels to avoid rigidity and to permit gradual reductions

that might, in the long run, maintain a more nearly

equitable share of the limited funds for each state. Finally

consideration might be given to establishing the floors at

the county level within a state when the floor comes into ^ effect for the state.

1.4 Formula Alternatives

The variety of possibilit i.es for enumeration of the

eligible children, the various means for representing the

cost per child of compensatory education, and the several

responses possible under conditions of underfunding all can

be combined to create many different alternatives to the

present Title I formula. Some of these possibilities are

- 33 -

Chapter 2 EVALUATION OF THE PRESENT FORMULA

AND GENERATION OF ALTERNATIVES

2.1 Criteria for Formula Evaluation

The fundamental purpose underlying Title I is the provision

of equal educational opportunity. This purpose is extremely

ambiguous. There is no universal agreement regarding what

constitutes equal educational opportunity. While no final

resolution of this ambiguity is attempted in this report, a manageable number of alternative interpretations are developed.

Equality in educational opportunity can be viewed from

either the input or the output end of the educational process.

Viewed from the input end, the concept attempts to assure

"equivalent" educational resources to each child. Viewed

from the output end, the concept attempts to assure that each

child, upon leaving the educational system, has attained some

standard level of achievement. Accomplishment of this concept

would require (1) concensus regarding achievement standards and

(2) knowledge of how to vary the resources to attain the

achievement level. These two concepts are the subject of

intense debate at present, and no attempt is made in this

study to resolve the problem. As a matter of fact, it is

not clear that the Title I allocation mechanism could be

formulated to implement the output concept of equality. The

present study thus is limited to the input interpretation of

equality

Alternative formulas are based upon the following

considerations

1. The formula should be simple.

2. The formula should be restricted to the use of

data that are: uniform, up-to-date, geographically

detailed, from official sources, accurate, and

administratively feasible.

3. The formula should produce no incentive extraneous

to the purpose of Title I.

4. The formula should permit timely allocations to

assure program continuity and avoid wasteful spending.

2.2 Overall Formula Structure

The present grant determination process has three major

divisions. Before concentrating on Part A as the main focus

of this report, Parts B and C are briefly discussed as they

relate to the formula structure.

Part B establishes a program of incentive grants. A

complete analysis of this program* suggests that Part B

j should be dropped from Title I for two major reasons: (1) it

promotes general education rather than the objectives of Title I,

and (2) in order to provide an effective fiscal incentive, it

* See Appendix B of the previous interim report submitted in

March, 1972.

, - 34 -

needs fcg-ular funding, independent of Title i constraints.

In addition, Part B contains several defects of sufficient

seriousness that it cannot, in its present form, fulfill its

underlying purpose.

Part C provides grants to LEAs with high concentrations

of poverty children.* The motivating concept of Part C is

that more dollars are required per child for compensatory

education where the concentration of poverty is higher.

There is no analytical basis with which to determine whether

this is necessary to achieve the objectives of Title I.

However, if this concept is acknowledged to be essential, a bonus factor for poverty concentration can be conveniently

integrated directly into the formula of Part A. The result

would be a single, unified new formula that would no longer

contain the separately defined and complex qualification rules

of the present Part C. Also, the bonus would be proportional

to the degree of poverty concentration, as opposed to the present

all-or-none bonus of Part C. From the practical standpoint,

this would greatly simplify the administrative problems of

Title I allocation, since it would eliminate the costly data

collection effort now required for Part C.

The foregoing considerations provide the groundwork for

developing a general structure for alternative formulas for

Title 1. That general structure is detailed in the remainder

i of this section.

n For discussion of both the practical and theoretical aspects of

Part C, See Appendix A.

- 37 -

First, the difference between a Title I "grant entitlement"

and the actual "allocation" of funds must be re emphasized. The

"grant entitlement" for each geographic region is determined

initially, as the product of the number of eligible children,

the cost factor or dollar amount per child, and an optional

concentration factor.* The sum of all grant entitlements

normally exceeds the funds appropriated by Congress for Title

I. These entitlements must then be collectively reduced in

some fashion so that the total amount of money to be distributed

matches the appropriation. Each reduced entitlement is referred

to in this report as an "allocation." The set of rules specified

in the Title I legislation by which the entitlements are reduced

to the appropriation level is referred to in this report as

the "reduction process."

Second, the geographic unit that becomes the basis for

calculating any entitlement must be defined. The present law

specifies that LEAs are to be the regional units for Part A*~

entitlements. However, administrative impracticality has resulted

in selecting counties as the regional unit.

Third, the question of currency of data must be resolved,

primarily for the enumeration of poor children.

a

The concentration factor equals the number of eligible children

divided by the total number of school-age children.

- 38 -

Proposed formulas are similar in structural aspects

to the existing Title I formula, with the major change being

the incorporation of a concentration factor. The use of the

county as the base regional unit remains the same. However,

this study has examined in substantial detail alternative

ways of enumerating target children, determining the cost

factor, and performing the reduction process.

The formulas considered contain the three components:

the number of eligible children (K) ; a cost factor (M) , including

a concentration factor; and a reduction procedure (R) . These

elements are components of the formula that may be varied

independently or in combination. It should be recalled that

the first two elements may be quantitatively defined, whereas

the third element is a complex set of rules. The development

of feasible variations for each element is considered in the

sections that follow.

2.3 The Eligible Children

It is important to recognize that the children eligible

to be counted for purposes of the Title I allocation need not

be identical to those who ultimately participate in Title I programs. Ideally, the two groups would be identical. However,

it is a recognized fact that no uniform measure of educational

disadvantage or deprivation is nationally available. Thus, the

allocation of Title I funds on the basis of economic disadvantage

has been accepted as satisfying the intent of the law. Various

- 39 -

counts of children from low-income families ("poverty data")

are available, some of which are now used for the Title I allocation.

The choice among several types of poverty data is a crucial part of the selection of a new Title I formula. This

selection directly affects the question of the fairness of

grant allocations among the states and among urban, suburban,

and rural regions as well.

There are three basic sources of poverty data that are

currently available for the Title I allocation. These are the

decennial census, AFDC data, and estimates of the national

poverty population made annually by the Current Population

Survey (CPS) of the Census Bureau.

Data on children participating in the USDA free lunch

program might at some future time be the most useful for

Title I, since both programs are directed at the same economically

disadvantaged children. In the past, school lunch data were

not uniform on a national basis; a recent amendment (PL 92-433)

should correct the problem. These data could produce an

incentive extraneous to the purpose of Title I; for example,

children could theoretically be added to the school lunch count

at samll cost to state resources in exchange for a possible

greater gain in the Federally provided Title I grant.

40 -

The decennial census data provide the number of school

age children at the county level below some specified income

level. A number of different ways of counting poverty

children are possible in the 1970 census, as described later.

AFDC data at the state level are published monthly by the

Social and Rehabilitation Service (SRS) of DIIEW and the data

at the county level may be obtained by a survey of state

welfare agencies. Such a survey is the current practice.

In the SRS publication, the data apply to all children under

21 whose families receive AFDC payments, whereas the current

Title I program applies to children between 5 and 17 (inclusive)

from families whose AFDC payments exceed $2,000.

The annual CPS estimate is confined to the national

aggregate of the poverty population under 18; estimates for the

state or county level are not available.

Each of these basic sources of poverty data lacks one of the

characteristics of uniformity, currency, or geographic detail,

as shown in the following tabulation:

Uniform Current Geographic Detail

Decennial census Yes No Yes

AFDC No Yes Yes

CPS Yes Yes No

The decennial census data are, of course, fixed for 10 years

at a time, although significant demographic and economic changes

take place in that length of time. AFDC qualification and

41 -

payment stand irds differ greatly in different states, and thus

AIJ 1)(1 data lack interstate uniformity as a measure of poverty.

The CI'.*! est i ma I e , /is noted above, i s onjy a national total.

The general approach of this analysis (as in the present

Title I allocation) is to enumerate the eligible children by

a two-stage process: first, beginning with "baseline" data and

second, updating them periodically. The decennial census is

the appropriate source for the baseline, since it possesses all

the desirable attributes except currency. The AFDC and/or

CPS data are then available for adjusting the baseline data

to keep the enumeration of children current.

There are, then, two main problems in the enumeration:

(1) the selection of the most appropriate baseline data

from the decennial census, and (2) devising the "best" method

of updating. This second problem requires a rather detailed

discussion, which is given in Appendix B. The remainder of

this section discusses the choice of the baseline and summarizes

the development of alternative updating methods.*

In the present allocation process, the children enumerated on the

basis of census and AFDC data are only 93% of the total eligible

children (according to the FY73 data). The other children are

the 258,917 institutional LEA children and the 380,413 SEA

children. These are included in Title I because they presumably

have educational disadvantages similar to children in low income

families; but, because many of them live in institutions rather

than in families, or live in migratory families, they would not

be represented in the census data for low income families. In

the development of alternative enumeration methods in this study,

these SEA and institutional LEA children have been considered a part of the total eligible group under any alternative. Since

they are enumerated by an annual survey of the states, they are

not involved in the census data nor in the method by which the

census data may be updated. Thus, they are not included in the

following discussion of alternative enumeration methods, although

they are of course included in the analysis of distributional

consequences in Chapter 3.

- 42 -

2.3.1 Baseli n e Data . The 1970 census offers several candidates

for the baseline data. (Until now the Title I a J locations have

been based on the 1960 census. In December 1972, the 1970 census

data pertinent to this study became available.) This study has

utilized the 1970 census data to identify the number of children

aged 5 to 17 years, inclusive, in families below some annual

income level representing a poverty threshold. The poverty

levels considered by this study are (1) the $2,000 threshold

(the threshold presently used in Title I allocations) , (2)

the $3,000 threshold and (3) the "Orshansky" poverty index.

The Orshansky index is a set of poverty income thresholds

developed by Mollie Orshansky of the Social Security Administration,

based on Department of Agriculture cost figures for basic

nutrition and on several family characteristics*. It was adopted

in 1969 as the official Federal definition of poverty by the

Executive Office of the President,** and it is the poverty

definition reflected in all poverty statistics from the Bureau

of the Census. In this report it is referred to as the "Orshansky"

Us For the concepts underlying the Orshansky poverty data, as well

as for detail, see Orshansky, M. , "Counting the Poor: Another

Look at the Poverty Profile," Social Security Bulletin , January,

1965, and Current Population Reports , Series P-60 , No . 86,

published by the Bureau of the Census.

** Executive Office of the President, Bureau of the Budget:

"Definition of Poverty for Statistical Purposes," Circular No. A-46,

Exhibit L, and Transmittal Memorandum No. 9, August 29, 1969.

- 43 -

index rather than the "poverty" index, to avoid confusion

with the several other measures of poverty discussed here.

The Orshansky index was designed to remedy some of the

defect s in t lie use of a fixed family income as a poverty

threshold. Hie principal defect regards family size. When

using a fixed threshold, for example, a family consisting

of one adult and one child has the same poverty threshold

as a family of three adults and twelve children. The Orshansky

index sets the poverty threshold at different income levels,

depending on the family size.

In addition to these three candidates for baseline data,

this study has used the 1960 census data with a $2,000 poverty

threshold, to allow comparisons with the present Title I allocation method. All four candidates (by state) are included

in Appendix B where methods of updating the baseline are

discussed in detail.

I! It is noted here that there is one shortcoming inhereftt

in both the fixed threshold data and the Orshansky data. They

do not represent regional variations in the cost of living (except

that the Orshansky index differentiates between farm and non-farm

families) . No interregional cost-of-living index is available

for this adjustment.*

The Bureau of Labor Statistics publishes two cost-of-living indexes,

but neither is suitable for this purpose. The Consumer Price Index

measures changes in the cost of living over time, but it is not

valid for interregional comparisons. The Bureau also publishes

a Geographical Comparative Index, but it applies only to urban

I families with specified characteristics. The Bureau cautions

that these indexes are not designed for appraisal of the economic

condition of population groups.

- 44 -

An important aspect of the allocation data is the level

of geographica 1 detail. Ideally the ultimate targets of Title

1 — individual children —would be identified by the data, but

that is clearly impracticable. Following the principle that

an allocation formula should channel the funds as near as

possible to the target children, it is reasonable to consider

making allocations to LEAs . As it turns out, even this is not

practicable, for the following reasons.

The census data and AFDC data are not collected according

to geographic units corresponding to the boundaries of LEAs.

USOE has developed a cross-reference file for translating LEA

areas into census geographic areas (e.g., tracts and enumeration

districts) . Although this file can produce data useful for many

purposes, it is not clear that the file is suitable for

producing the basic Title I allocation data. The file does

not apply to the 7 ,000 smaller LI. As in the U.S. Even if the

census data could be used for all LEAs, there is at present no

way to update those data at that geographic level.

There is a very large number of LEAs and their number

changes substantially from year to year (mostly through

consolidations) . From the autumn of 1967 to the autumn of

1970, the number of LEAs was reduced from 22,010 to 17,995.

Maintaining a current cross-reference file for so many LEAs,

although not impossible, will be a difficult job subject to

many kinds of error. Until its workability has been demonstrated,

it is possible that the errors that may gradually appear in the

file would outweigh the geographic precision that the file

- 45 -

is intended to provide.

Aside from these practical difficulties, the census data for

the less populous LEAs would not be a valid basis for determining

the grants to which those LEAs are entitled. The reason for this

is that the income data in the census are based on a random sample

of 20* of the population. For large populations this sample

provides a valid estimate of the income distribution. However,

for the populations found in the smaller LEAs, the statistical

sampling error can be so large as to invalidate the derived

estimates ot the poverty population.

If allocation to the LEA level is not practicable, the

next level to be considered is the county.* There are about

3,000 counties, and they undergo practially no change from

year to year. Census data are available by county, and [as

discussed in the next section) county-level data can be updated.

One can consider stopping the Federal allocation process at

the state- level, and allowing each state to subdivide its aggregate

grant to the lower geographic levels. However, federal allocation

by formula to the county level affords protection to those LEAs

n In this study, "county" means one of the county or county

equivalents defined by Federal Information Processing Standards

Publication 6-1, except that Alaska is represented as one

county. This definition includes the District of Columbia

and independent cities in a few states as counties, and it

subsumes Kalawao Co., Hawaii, under Maui Co. as explained in

that publication. The reason for aggregating Alaska (which

has no counties), rather than using the Alaska Census Divisions,

is that the Alaska data pertinent ,o this study are organized

by several irreconcilable geographic subdivisions. By this

definition there are 3,113 counties in the U.S.

- 46 -

that arc lesb influential in state politics. That is, if

each state is free to choose its own basis for intrastate

distribution, that choice will be subject to the political

pressures of LEAs that stand to lose or gain according to the

choice. Some LEA officials interviewed in the course of this

study have expressed concern that the intrastate distribution

would be inequitable if the allocation by the Federal formula

did not extend at least to the county level.

Two conclusions are apparent in the matters discussed in

this section. First, the Orshansky index appears to be the

most suitable poverty measure available in the census, because

it accounts for factors that are disregarded by a fixed income

threshold (principally, family size). Second, the county is

the most practicable geographic level for data to be employed

in the allocation formula.

2.3.2 Updating the Enumeration . There are two reasons for

updating the enumeration. The most obvious is that changes

occur in the geographic pattern of poverty. Families move

in and out of an area, and these two movements may not balance

each other. As time passes, children who were infants or

unborn in the census year enter the scnool age population,

while the older children become adults, and these two changes

may not balance. Further, the economic condition of a community can change for better or worse.

The other reason for updating is inflation. The income

level representing a poverty threshold in one year is too low

in later years

.

- 47 -

To adjust for these changes, the enumeration could be

updated annually, as is the present practice in Title I.

Less frequent adjustments might also be considered adequate,

and they would afford greater predictability to the allocations

with less administrative expense. This study lias assumed

that the enumeration will be updated annually. Any annual

updating method could also be applied, less frequently.

There arc at present two sources of data suitable for

updating the baseline enumeration data: AFDC and the CPS.

There are two aspects of the data to be considered in

determining how to use them. First is the ability of the

data to reveal the extent of poverty in different places

(counties or states); this is the dis tributional aspect.

Second is the ability of the data to be related to the actual

number of children enumerated in the census ; this is the scale

aspect. The scale aspect is illustrated by Figure 2.3.1.

According to the CPS Orshansky data, the number of poverty**

children under 18 decreased by about one-fourth from 1965 to

1971. (Two values are plotted for 1966 and two for 1969

because of changes in the CPS definitions in those years.)

A similar trend holds true for the number of children aged

5-17 in families with an annual income below $3,000 (in 1971

dollars).* Although the direction and proportion of the changes

j

The CPS gives the estimated number of families under $3,000.

That was multiplied by the average number ot children 5-17 in

such families, according to the 1970 census, to arrive at the

number of children plotted in this graph.

- 48 -

ty Children

Mi ] lions)

16

15

14

13

12

11

10

9

8

7

Orshansky (0 - 17 years)

(5

Title I

5

4

3

2

1

Total APDC

(0 - 20 years)

Under $3,000

(5 - 17 years)

65 '66 '67 '68 '69 '70 '71 '72 Year

Figure 2.3.1 Comparison of Alternative Poverty Data

. - 49.-

in these two measures are consistent, the actual numbers of

children arc different. This is referred to as a scale difference,

and before numbers from these two measures could be meaningfully

added, one measure would have to be scaled up or dov/n to

correspond to the other measure.

The other two plots in the graph involve AFDC data.

First is the number of Title I eligibles which consists

of a fixed 1960 census component of 5 million children plus

a changing component of children in families receiving over

$2,000 per year from AFDC payments. The other plot represents

the number of children under 21 years old in families receiving

any amount of AFDC money. It is obvious that AFDC data measure

something different from what is measured by the CPS Orshansky

data, since their trends are in opposite directions. Presumably

this indicates that AFDC programs are covering an increasing

portion of the Orshansky population. For all future discussion,

AFDC "coverage" is defined as the ratio of the number of

children in families receiving AFDC payments to the number of

children in families below the Orshansky index.

in a formula where the cost factor (see Section 2.4) is

independent of the number of children and where the adjustment

for underfunding (see Section 2.S) is strictly proportional,

the only important aspect of the enumeration is the distribution

of the numbers of children (relative to each other). However,

if the cost factor depends on the concentration of eligible

I children or if the underfunding adjustment is non-proportional

- 50 -

(as in the present Title I allocation process), it is imperative

that the actual numbers of children be correct.

The AFDC data provide distributional information, i.e.,

a measure of poverty for each county (although, as mentioned

earlier, this measure is not uniformly applied throughout

the nation) . The annual CPS estimate is not distributional

since it is strictly a national total. However, the CPS

provides data in the same scale as the decennial census data,

i.e., Orshansky and $3,000 data. The AFDC data, on the other

hand, are out of scale with the census data. In fact, the

coverage ratio just defined is the factor that relates the

census scale to the AFDC scale, and the coverage differs

from state to state. These observations can be summarized

as follows:

Distributional Census Scale

AFDC Yes No

CPS No Yes

I This suggests that the AFDC data can be employed to indicate

distributional changes in poverty from year to year and that

the CPS data can be used to adjust the enumeration to the

proper scale. The distributional adjustment represents the

changing geographic pattern of poverty, while the scale

adjustment reflects inflation (among other things) . In

the case of Orshansky data, inflation is represented by

an annual adjustment of the various family income levels

, (for various family compositions) according to the Consumer

»

- 51 -

Price Index. In the case of the $3,000 data, data for

different years arc expressed as constant dollars (e.g., the

buying power equivalent to a dollar in 1971), again by

means of the Consumer Price Index.

Two ways of using AFDC data for updating the distributional

aspect of the enumeration have been considered in this study:

the method presently used in Title I and an alternative

method. For reasons detailed in Appendix B, the present

method does not make the best use of the data. Briefly,

this is because it adds together AFDC and census data that

are out of scale with each other, and because the AFDC data

are not uniform from state to state due to different coverages

in different states. The nonuniformi ty is aggravated by the

fact that, it only counts children in families receiving more

than $2,000 annually from AFDC.

The alternative method uses a multiplicative updating factor,

on the assumption that the change in the Title I eligible

population is proportional to the change in the AFDC data.

Thus the updated enumeration equals the original census enumeration

times the ratio of the most recent AFDC count to the AFDC

count in the census year.*

T

Another approach to the alternative method is to employ an

additive updating factor, on the assumption that the difference

in the Title I eligible population tor two years is equal to

the difference in the corresponding AFDC data when adjusted in

i scale by the coverage ratio of the respective state.

The mathematical equivalence of these two alternative approaches

is shown in Appendix B.

' It is possible that still other valid methods can be developed

to use the available data for updating the enumeration. Some

methods may result in smoother annual transitions for particular

states than do other methods. Such further alternative methods

are under investigation.

This method relics on the assumption that the coverage

ratio (winch the graph shows to be increasing for the nation

as a whole) increases proportionately in all states. This is

the weakest link in the rationale of the alternative, and

there is no wr ay to measure the coverage ratio tor a state

after the census year since the Orshansky and $3,000 data

are not available for states except in the decennial census.

If such estimates were available annually at the state level,

they could be employed directly and would, obviate the use of

AFDC data at the state level.

One improvement to the AFDC data used in the alternative

is the introduction of values that are 24-month averages.

To eliminate seasonal variations, data recorded over the course

of the year are used, and the use of two years tends to

smooth out year-to-year fluctuations.

A second improvement stems from the fact that the AFDC

data used in the alternative do not include that portion *~

relating to unemployed parents. The unemployed-parent component

is optional with the states, and about half of the states

participate in it. Thus one source of interstate nonuniformi ty

is removed by the exclusion of this component of the data.

After the distributional updating adjustment is accomplished

' by means of the multiplicative factor, the actual number of

children indicated is wrong. For example, the total number

of children is 10,533,295. The CPS estimate of the total

- 53 -

number is 8,383,602.* Therefore, Die adjusted number of children

for each county is multiplied by the ratio of 8,383,602 to

10,533,295. This adjusts the scale without affecting the

distribution, and this is referredi- to as normalizing the

data according to the CPS estimate.

As the previous paragraph indicates, the updating is applied

to each county's enumeration. In this study the distributive

adjustment was actually applied at the state level; that is,

a multiplicative adjustment factor based on statewide AFDC

data was applied to all counties in the state. For purposes

1 >of analysis it was unnecessary to compute the distributive

adjustment factor for individual counties, since AFDC

qualification standards are relatively uniform among counties

in the same state. However, for the actual allocation of

grants it would be more important to use county-level data

for the adjustment.

The practicability of obtaining such data at the county -

level is an important consideration. The only county AFDC

data available from DHEW are for February of each year, and

these data are available only in printed form. Data for the

other months are available only as state totals. In order

to obtain monthly data for counties, it would be necessary

TT~As explained in Appendix B, this number is derived from the

CPS data and the 1970 census data by a simple calculation,

rather than taken directly from a CPS publication.

. 54 -

to create a new survey of the states. (The present Title I survey collects only one month's data for each year, and those

data arc only for families receiving more than $2,000 per year

from AFDC.) In the first year, the 3,113 counties' data for

48 months would be required (24 months representing the base

year plus the 24 most recent months available nationwide)

.

This would result in about 150 , 000 items of data- - clear ly

a large data processing job for the states and the Federal

government. Even if the county-level adjustment factors were

recalculated only in every second year, a 24-month data span

would require that data be collected for every year. If

the factors were recalculated in every fourth year, data

for only two years out of every four would be required.

In order to construct specific enumeration alternatives,

several representative combinations of baseline data and

updating methods have been assembled. Each baseline candidate,

as well as each updating method, is used at least once.

The first enumeration, called K-^ , consists of 1960

census data tor the $2,000 level, updated by adding the AFDC

data above the $2,000 threshold. This is actually the

present Title I enumeration. The second enumeration, ,

is identical except that 1970 census data are used. Enumeration

is like except that the $3,000 threshold is used (for

both the census and the AFDC data). K, consists of 1970

census data for the $3,000 level (like K^) , updated by the

multiplicative AFDC factor, and normalized to the CFS

- 55 -

estimate for the $3,000 level. is based on the Orshansky

data from the census and, like , is updated by the

alternative method, i.e., the distributional aspect is updated

by the multiplicative AFDC and the result, is normalized to

scale by the CPS estimate for the Orshansky poverty level.

For a summary of these definitions, see Table 2.3.1.

Table 2.3.1

Definition of Alternative Enumerations

enumeration

lesignati on Baseline Data

K

K.

K,

K

K,

1960 Census Data,

families Below $2,000

Income Level

1970 Census Data,

Families Below $2,000

Income Level

1970 Census Data,

families Below $3,000

Income Level

1970 Census Data,

families Below $3,000

Income Level

1970 Census Data,

Orshansky Poverty

Level

Updating Process

Pis tribut ional

AFDC Data, Families

Receiving more than

$2,000

AFDC Data, Families

Receiving more than

$2,000

AFDC Data, Families

Receiving more than

$3,000

AFDC Data,

Multiplicative

Factor

AFDC Data,

Multiplicative

Factor

Scale

CPS Estimate

For $3,00U

Level

CPS Estimate

For Orshans.o

Poverty Level

The number of children, by state, for each of these enumerations

is given in Table 2.3.2.

- 56 -

Table 2.3.2

Number of Eligible Children in i'Y73

I

: ive Alternative Enumerations

K 1 K

i

K 73 K

4

K

5 Alabama 243 ,596 97 ,058 151, 759 14 2, 851 260, 764

Alaska 9 ,519 8 ,985 10, 144 6, 669 15, 031

Ari zona 56 ,475 46 , 952 49, 4 09 46, 527 86, 526

Arkansas 148 ,158 52 , 247 86, 114 96, 691 177 , 511

Cal if ornia 767 , 565 775 ,406 715, 255 342 , 112 626 , 408

Colorado 70 ,876 62 , 662 59, 67 5 43 , 207 79, 101

Connect icut 67 ,847 69 ,342 70, 449 32 , 622 55, 566

Delaware 13 ,133 11 , 267 10, 144 9 , 463 18, 694

Florida 168 , 005 126 , 165 165, 787 176

,

58 2 550, 585

Gcorg ia 2S5 ,784 139 ,134 155, 753 176 , 474 338 , 978

Hawa i

i

22 ,734 21 ,131 21 , 049 10, 982 20, 956

Idaho 18 ,827 13 ,967 16, 416 12, 158 24, 441

Illinois 417 ,910 374 ,181 354 , 4 60 189

,

065 356, 910

Ind iana 127 ,501 92 ,951 81, 573 95 , 74 2 180, 212

Iowa 100 ,8 63 51 ,555 54 , 102 35 91 8 69, 549

Kansas 63 , 274 45 ,144 46, 132 55 888 67 , 069

Kentucky 225 ,893 101 ,114 125 , 399 103 266 18 2, 017

Lou is iana 219 ,8 68 133 ,378 179, 749 163 370 287 , 654

Mai nc 38 ,129 29 ,788 22, 493 19 860 44, 516

Maryland 113 ,123 102 , 527 95, 055 68 845 122 815

Massachusetts 165 ,739 160 ,355 155, 371 64 322 119 511

Michigan 518 ,818 277 ,819 277, 079 160 54 6 285 284

Minnesota 122 ,434 77 ,059 85 ,084 54 106 105 824

Mississippi 254 ,903 98 ,695 152 ,715 147 ,836 257 860

Missouri 162 ,311 96 ,515 102 ,058 102 ,8 53 190 222

Montana 19 ,681 13 ,757 16 ,405 1 5 ,176 27 ,921

Nebraska 50 ,242 31 ,656 52 ,745 2 5 ,612 47 ,142

Nevada 5 ,665 6 ,591 6 ,85 5 6 ,394 11 , 047

New Hampshire 12 ,630 11 , 256 12 ,145 10 ,112 19 ,894

New Jersey 230 722 228 , 610 222 ,657 95 ,950 176 , 518

New Mexico 51 ,529 41 ,917 45 ,763 38 , 08 2 71 ,557

New YorJc 766 ,02S 760 ,554 746 ,328 271 ,103 496 , 644

North Carolina 362 ,152 138 , 280 168 ,451 165 ,116 314 ,927

North Dakota 28 ,496 13 ,215 16 ,191 1 2 , 240 26 ,421

Ohio 289 ,084 241 ,899 215 ,4 34 176 r\ a r ,04 5 300 ,742

Oklahoma 115 ,151 67 ,688 . 75 , 235 c o QIC , 0 1 J 112 ,264

Oregon 50 ,259 45 ,909 48 , 5S 9

7 1 J 1 , oil 55 ,707

Pennsylvania 4 22 ,339 348 , 98 5

T A 54 2 , V J>7 1 7 C 1 0 7 337 ,856

Rhode Island 30 ,391 27 ,115 2 5 ,8 90 1 7 n r> x

, U 0 0 23 ,495

South Carolina 23 1 ,199 76 ,405 111 , ol3 1 7 A1 3 0

7 7 0 ,3/0 258 , 591

South Dakota 37 ,24 9 1 7 ,300 2.1 ,9] K 1 7 ,2 54 32 ,822

Tennessee 220 , 048 81 ,832 3 3 3 ,221 14 0

o 0 n

, Z8 0 262 ,774

Texas 477 , 550 271 ,965 327 ,7 28 4H l*? AH ^ Q ^ 864 , 524

Utah 26 ,738 24 ,696 26 ,000 15 ,420 29 ,406

Vermont 13 ,533 9 ,814 10 ,429 5 , 530 1 3 ,066

Virginia 217 , 986 117 ,921 157 ,710 132 ,258 258 , 019

Washington 86 ,544 83 ,194 80 ,581 44 ,351 79 ,577

West Virginia 120 ,959 50 ,037 60 , 558 49 ,914 89 ,568

Wisconsin 105 ,137 81 ,27 0 88 ,688 59 , 531 111 ,548

Wyoming 7 ,621 5 ,527 5 ,656 5 ,332 10 ,090

Dist. of Columbia 54 ,494 52 ,721 56 ,371 27 ,014 50 ,685

8,216,712 5,915,025 6,268,776 4,489,525 8,585,602

- 57 -

In summary, this discussion of updating has described one

alternative updating method that improves on the method

presently used in Title I. The weakest part of this method

is its reliance on the assumption that the AFDCJ coverage

ratio changes in the same proportion in all states. Since the

coverage itself differs among the states, any assumption

regarding the rate at which the coverage changes in suspect.

This reveals a crucial need for more satisfactory data.

Such data might in future years be available from the school

lunch program. Another potential source is the CPS itself.

In order for the CPS to produce valid poverty estimates at the

state level, its sampling base would have to be expanded.

The cost of doing this would have to be weighed against

the benefits. The CPS has many users besides (potentially)

Title I. In Title I alone, $1.5 billion per year are distributed

without a truly satisfactory data base for updating the

interstate distribution of eligible children.

2.4 The Cost factor

The cost factor is the dollars authorized per child, representing

the cost of compensatory education. Ideally, this would be

derived from actual cost data, in which case there might be

different cost factors for different categories of eligible

children. Such data are lacking.

- 58 -

Lack of information, and hence the absence of knowledge

on the cost of compensatory education, does not mean that

compensatory education is unnecessary for the educationally

disadvantaged children. The lack of data indicates either

that information regarding compensatory education is not

well known as yet or that there still exists a considerable

uncertainty about the nature of the correct methods of

compensatory education. The methods may range from

restructuring the entire educational system (e.g., requiring

the complete equality of APPEs) to providing intensive special

instruction on an individual basis. In any case, programs

associated with Title I have mainly been providing supplemental

education within the existing educational framework. Thus,

the cost factor in the Title I allocation formula should be

interpreted as representing the necessary per pupil expenditure

for the supplemental form of compensatory education.

Given that the cost factor is to be viewed as the

necessary expense for compensatory education per pupil,

there still remains the major question of estimating its

value. One alternative is to ignore the cost factor and

divide the appropriation strictly in proportion to the

number of educationally disadvantaged children. This

simple method is based on the assumption that all eligible

children shall receive equal services. Unfortunately, a dollar does not buy the same educational service, e.g.,

-59-

teacher's time, across the nation. If the provision of

equal educational service is to be the goal, a more sensible

allocation method might be to apportion the money based on

general educational expenses - -more specifically, average per

pupil expenditure (APPE). The use of APPE provides the

perspective necessary to develop the most appropriate cost

factor

.

The efficacy of the APPE values, however, depends on

how they arc used. The APPE values contain at least two types

of biases: quantity and quality of educational services

delivered to the students. The quantity aspect refers to the

differences in the amount of school time given to the

students such as the number of school days in a year or

average hours per day spent at school. The quantity differences

in APPE values thus are amenable to adjustment by available

data.

The qualitative differences in APPEs , however, are more**

difficult to evaluate although the high correlation between

a region's income and APPE would appear to underscore the

general belief that wealthier areas provide better quality

education. It does not appear possible, however, to remove

; qualitative biases in the APPE values,

if - The APPE values for the states that were actually used

in Title I allocations are shown in Table 2.4.1 for the school

years 1963-64 and 1970-71 as well as the percentage changes

between the two periods. As can be seen in the table, the

- 60 -

'J'jiblc 1.4.] Average' I'ci iupjl Expenditure for Elementary and Secondary Schools by State

(1) (2) (3)

1963-64 School Year 1970-71 School Year Percentage

(Used in PY66 (Apply to FY73 Change of Tit le 1 A l

l

ocations) JJ 1 1 e 1 Allo c ations) (2) over ( 1

)

A 1 1 1 1 i i.i i /\JL u IJ O IW'I ^ Z O J

ftO 7£* C 7 O

$ d t y

X ft J 0

ft c, 0 J J 4 p A

A 1 , l 'i i ,1 . h tl ft 7 A 0 / 4

.7 A' 1 '1 ,) £

7 ft 1 1 c, A 1 J J J Ar i 7,01) n

A ft 4 U 0 \ U

7 ^ C / 1 ^ O ft ft n n 4 Arkiins ii s

i n c

.S \) ,} 0 0 CIO bin (i 4 7 n n n u u Co] ] lei i'n i

a

C-ft I JUJ o c r 0 J J 1 4

ft 0 o y

.

7 ft z o Co J o rado >1 7 7 4 / / n o ft 1 7 o 1 Z

ft n 7 0 0 4 Conn cc t ieu

t

508 1 2 10 0 9 4 8

n p ^ 7 Del a wa re C T 7 3 J . Z I) no/". y y o

A 7 4 Zft 7 7 1 Z 1 Florida 38 5

.

58 781

.

36 102 65 Geo r ia 31

1

46 644 7 2 107 00 Ha wa i i 4 2 2 4 0 98 3 74 132 8 9 Idaho 34 7 36 610 1 6 7 5 66

1 1 1 i no i s 531

,

38 992 62 8 6 80 Indiana 4 60 02 783 4 2 70 30 Iowa 460. 26 864 84 87 90 Kansas 468 90 787 2 2 67 89 Kentucky 311 34 5 71 88 83 6 8 Lou i si a na 381 0 0 716 3 0 8 8 01 Maine 37 9 90 709 60 86 7 9 Mary] ami 4 8-3 0 6 985 5 2 104 02 Massachuse 1 1

s

51 7 8 2 8 94 2 2 7 2 69 Mich i j'.an 47 6 68 97 2 08 103 93 Minnesota c. c: jj ii D U X U U j 0 7 y z

ft 7 0 Za n 4 u Mississippi 7 A ) Z 4 Z

a n 4 uA ft O h u yft n

9 J

7 t M i s s o u r i A\l ft 7 O Z

7 7 7 / z z1 7 1 Z 6 •> n t Mo n t a na 4 0/ ft n ft n i o U 1

ft 0 0 uft ^ D 4 4 u Nc b r a ska 4 UU ft ft ft n 7 7 ft Z 0

x ft J 0 Nevada 4Honft ft J 4

7 ft ft / 0 01 ft 1 0ft 7 0 z n n u u Now Hampshire 1 1 J

ftft o O7/ 7f nu Q 7 y zft c. 0 J jX 7/ New Jersey CTt 3 / .T ^ ft J O

IIIi JJu 7 ft Z 0 Q7y / 7 d Z 4 New Mcx ico 4 U (

i

O 'J ftDOft 0J u 0

4 7/1 \ X J New York 7 X 1 / O 1

7 ft Z O 114A 0/ft 7 ^ a j 4 1U J j 4 North Carolina T 7 \ A ft ftOil1 1 7 7 / Z

ft Q o y 1 1

in o i \ n Uti k o l a 4 1 r» 58 68 5 34 64 9

1

\ 1J 1 i U A A 1 'Jh J

ft ft o O7 ft 7 ft A 7 7

/ z

ft /i 04 Ok 1 a horn a jO < Q ft A 7 7 0 Z j

7 7 7 7

/ Z n 7 U Z Oregon 54 :« 6 0 9 57 1 2 7 5 4 3 Pcnn s/1 va n i a 4 7 'I / 8 909 5 6 91 5 6 Knotlc J s l a ncl 50 ? 1 2 951 86 8 9 5 7 South Caro] i na 265 96 571 12 114 74 South Dakota 43] 34 . 719 04 66 70 Tennessee 7 Q 7 7 2 JCMJ <- ft n ft ft o o ft c, O J Texas 389 98 667 80 71 24 Utah 417 22 664 18 59 19 Vermont 449 30 797 14 77 42

Vi rf: i n ia 358 20 738 56 106 19 Wash) nj;ton 501 86 893 96 78 13 West Virginia 319 12 644 10 101 84 Wisconsin 524 30 950 56 81 31

Wyoni l n^ 514 92 882 00 71 29 Dist. of Columbia 518 64 1116 94 115 36 National Average 460 . 32 859 .88 86. 80

Source: Data compiled from the SHAs by the National Center for

Educational Statistics, USOH.

61 -

interstate differences have persisted over the years.

In the 1963-04 sclioo] year, for example, the highest value

(New York) was three times greater than the lowest value

(Mississippi) and the same difference was maintained during

the 1970-71 school year. If anything, the gap has widened

slightly as New York's APPE increased faster than Mississippi's.

The interstate differences in APPE values are much

greater than the differences in cost of living. Although

the data are not strictly comparable, the "minimum" budget

regional cost of living for a four-person family as estimated

by the Bureau of Labor Statistics for 19 71* shows the New

York City minimum budget to be higher than that of Atlanta

by 12 percent. On the other hand, the APPE of New York State

is higher than that of Georgia by 131 percent. A less extreme

example is the difference between Maryland and Louisiana:

Baltimore minimum budget is higher than that of Baton Rouge

by 14 percent while the APPE of Maryland is higher than that"

of Louisiana by 38 percent.

The state APPEs , however, are misleading numbers since,

strictly speaking, APPEs should be defined with respect to

LEAs . It turns out that the APPEs for individual LEAs show

about the same degree of difference within a single state

as among the states. Table 2.4.2 shows the five highest and

the five lowest APPE values for selected states: Delaware,

Autumn 1971 Urban Family Budgets and Geographical Comparative Indexes , Bureau of Labor Statistics, U.S. Department of Labor, April 19/2.

- 62 -

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[X +-» 00 a.

CD 0) 1/1 Cl, ^ (/) r-> •H

•M l/l co C 10

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cn o to rH oo to CO CO

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v+H rH XPh o +->

!-> (/) 4-> co O C' rH CXI to to CD rH rsi IO LO •H ^ (B CD

+-> U) ^ M

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r-i D - 63 -

Illinois, Maryland, Mississippi, and Pennsylvania. The

average of the five highest to the five lowest values within

each state show ratios of 1.46, 3.33, 1.26, 2.19, and 2.26,

respective! y

.

In general, the larger the sizes of LEAs relative to the

sizes of counties within a state, the smaller the disparities

among the highest and the lower APPE values. Thus, the

difference between the highest and the lowest values, is

smaller for Maryland than Illinois and Pennsylvania: the

LEAs are coterminous with the counties in Maryland (24)

,

whereas the LEAs are highly fragmented in Illinois and

Pennsylvania (1,175 and 597 respectively). At the other

extreme is Hawaii which has only one LEA that encompasses

the entire state.

Unadjusted use of the APPE values, therefore, results

in giving more money to richer counties whose needs may be

smaller than poorer counties. Doing so may amount to

accepting the prevailing biases in resource patterns which

may be one important cause of educational disadvantage

among the poor. It should be admitted nevertheless that,

although the existence of qualitative biases in APPE values

is apparent, there appears to be no satisfactory way to

remove such biases objectively.

- 64 -

The disparities in the APPE values among a i

1 the LEAs

arc considerable, much more so than among the state APPli

values that arc the basis of the cost factor in the present

Title I allocation formula. The fact that the LEA-specific

APPE values are not presently used in the Title I allocation

process means that the strict adherence to the concept of

APPE value in estimating the cost factor is not maintained.

Furthermore, two adjustments are made on the APPE values

before being incorporated into the present grant allocation

formula. The net effect of both is to reduce the presently

existing disparities among the APPE values.

The first adjustment is assigning the national average

per pupil expenditure (.NAPPE) whenever a state's value is

less than the NAPPE. This may be viewed as a half-way measure

of interstate cost equalization. The second adjustment is less

apparent, although its equalizing effects can be greater than

those of the first type. It is the use of a state average...

per pupil expenditure (SAPPE) rather than individual APPEs

of respective LEAs. Since variations of APPEs among the

LEAs in many states are as great as the variation of state

APPEs, the second form of APPE adjustment amounts to an

intra-statc equalization of the costs of education.

It may be concluded, then, that the use of APPE values

in the present allocation formula is not entirely consistent

with the assumption of proportional costs between regular and

compensatory education. In fact, the effect may be viewed

- 65 -
(
as more nearly consistent with the assumption of equal cost

of compensatory education for all disadvantaged children.

During the 1970-71 school year, for example, the number of

stales above the NAPPE was 19, less than half the states.

The natural extension of the argument leads to the use

of one uniform cost of compensatory education in the allocation

formula. This would amount to extending the cost averaging

adjustment, which presently applies within a state, to apply

among the states as well.

The actual merits of the assumption of a uniform cost

from the educational standpoint cannot be resolved here.

Nevertheless, it is possible to pursue the logical implications

of such cost factors. A caveat must be stated that although

the numerical examples chosen in the following discussions

are not entirely devoid of empirical meaning, no significance

should be attached to the specific numbers beyond their

use for illustration.

For a uniform cost factor, $300 per pupil is used. (Again,

no special significance should be attached to the $300 value

which is 35 percent less than one-half of NAPPE of the 1970-71

school year.) The $300 may be assumed to consist of two parts,

$250 for teacher cost and $50 for supplies such as books and

pencils. It will be assumed that the overhead costs such as

the costs of building and transportation are zero since

compensatory education of Title I consists mainly of programs

supplemental to the regular curriculum.

- 66 -

The teacher cost component can be related to per pupil

cost in the following equation:

Per pupil \ /Teacher 1 s \ /Teacher- pupil | /.Proportion of

cost ) / salary per | (ratio j *

J pupil's school

year j

\ JI time given to

\ / \Title I program (

In other words, the per pupil cost is the product of three

items on the right-hand side of the above equation. This is

an accounting equation that must hold true when appropriate

values of per pupil cost, on the left side, and annual

teacher's salary, on the right side, are specified; the

adjustments must be made to the teacher-pupil ratio and the

proportion of pupil's time in order to maintain the equality

between the two different dollar amounts.

For ease of subsequent discussion, the items of the equation

will be simplified as

(Cost) = (Teacher's salary) x (Teacher-pupil ratio) x (Pupil's

4ime)

.

The national average teacher's salary of all teachers in

public schools in 1971-72 was estimated to be $9,690.*

For ease of illustration, the average teacher's salary is set

at $10,000 per year. Since per pupil cost is assumed to be

T~

Rankings of the States, 1972, National Education Association,

Washington, U. C, 1972 . Table 41, p. 25

It is possible that average teacher's salary is not the right

datum since salaries of educational specialists would be more

expensive, while salaries of teacher aids would be less

expens ive

.

- 67 -

$250, 40 pupils can be assigned to one teacher. The Title I programs are unlikely to be full time programs; hence, three

combinational possibilities between the teacher pupil ratio

and pupil's time can be listed as follows.

Teacher-pupil ratio Pupi 1

' s time

A 1/10 1/4 (quarter time)

B 1/20 1/2 (half time)

C 1/40 1 (full time)

Given the fixed amounts of per pupil cost and teacher's

salary, only. one of the possible combinations can be chosen.

For each combination, improving the teacher-pupil ratio must entail

a reduction in child's participation time. In the case of A, for

example, if the teacher-pupil ratio is to improve to 1/5,

the pupil's time must be reduced to 1/8 or one-eighth of

his school time. It is instructive to view the teacher-pupil

ratio as a qualitative, and the pupil's time as a quantitative,

aspect of the compensatory education program. Then, it is

clear that, if the available budget is fixed, quality and

quantity are inversely related.

The discussion of fixed cost in terms of a simple accounting

relation should be interpreted carefully. First, the equation

is not meant to be an empirical cost equation; it is used

as a convenient explanatory device relating the logical

implications of a fixed cost factor. It does not consider

for example, the possible mix of teachers and teaching machines,

- 68 -

although the cost of using the machines can be translated to

teacher cost. Second, the equation may be used to calculate

roughly the minimum necessary cost of compensatory education

since the teacher's service is necessary for the purpose. Third

a school or an LEA can control the teacher-pupil ratio and pupil

time; i.e., the quality and quantity of compensatory education

are controllable if "average" teachers are provided to the

schools. It is clear that the teacher's salary, or the choice

of teachers, becomes the crucial part of the equation; however,

schools or LEAs cannot have much control over them. That is,

teacher's salary is a given datum to LEAs.

If actual averages for teacher's salary are used in the

above equation, LEAs with a high average for teacher's salary

must sacrifice either quality or quantity of compensatory

education if the fixed cost per pupil is to be maintained.

An alternative is to assign a nationally uniform teacher-pupil

ratio and pupil's time and let per pupil cost vary. Such an

alternative is subject to the same criticism as that of the

use of unadjusted APPE values; namely, qualitative differences

are not removed. Another alternative is to simply specify a uniform value for teacher's salary and justify such a choice

on the basis that every child should receive the same quality

of compensatory education. It can be seen that a choice for

teacher's salary cannot be based on empirical information

available. It can, at best, be based on some ethical

principles such as fairness. Finally, the analysis with the

- 69 -

cost equation docs nut invalidate the consideration of APPE

or teacher's salary in estimating the cost factor. The main

question still remains how to relate them.

Another possible equalization method, besides a uniform

cost factor, would be to assume the costs of compensatory

education to be inversely related to APPEs , i.e., providing

more money per pupil where the expenditures for regular

education are lower and, conversely, less money per pupil

where the expenditures are higher. A possible means of

implementing such a goal is to provide more money per child

where the concentration of eligible children is high

since such a concentration ratio and APPE show a high inverse

relationship. The idea underlying such an adjustment has

already been incorporated in the present Title I allocation

formula whereby LEAs with a high concentration of poverty

children are assigned additional grants (part C of the

present formula) . ^

The rationale for such an adjustment is presumably based

on the fact that it costs more to achieve a particular goal

of compensatory education when an LEA has a high proportion

of poverty children. The per pupil cost would be higher

because a child's educational disadvantage is compounded

by an impoverished school environment. It is argued by

many educators that peer group influence is crucial in a child's education process. If the peer influence is

unsatisfactory because of the high concentration of poverty

- 70 -

children, it may be argued that children in such an environment

need more educational resources to overcome the compound

educational disadvantage. Moreover, high concentrations

of poverty arc, as a rule, accompanied by low APPE values at

the LliA level.

What is the relative difference in concentration ratios

of poverty children? Table 2.4.3 compares concentration ratios

among the states as well as the counties. Ideally, poverty

concentration ratios should be compared at the individual

school level, but the necessary data are not readily available

even at the LEA level. The state and county comparisons

nevertheless should be illuminating.

As Table 2.4.3 shows, the proportion of poverty children

in a geographical area varies greatly both among the states

and within individual states. The first column compares the

poverty concentration ratio (percent of Orshansky poverty

children between ages 5 and 17) for the states, using the

1970 census data. Although the national average value of

concentration is 14.81 percent, the state average values

range from a low of 7.65 percent for Connecticut and New

Hampshire to a high of 40.51 percent for Mississippi. In

the case of Mississippi, nearly half the school age children

belong to the poverty class. As can be observed, the southern

states as a group belong to the higher concentration ratio

category

.

- 71 -

ouiii. i' Ji 1 1 a i lull i\ai.j.ua ivvi.il/ uiii-iui

Extreme Count y Values * State

Averag e L owest Hig h est

Alabama 28 76 % 15 . 4 7 % 72 3 5 % Alaska 14 24 N. A. N A.

Ari zona 1 7 5 2 10. 85 56 ] 6

Arkansas 30 66 12. 8 5 5 9 52

Cal i f ornia 12 42 6. 03 25 02

Colorado 12 42 0 53 .12

Conncc ticut 7 65 4. 68 10 . 24

Delaware 11 99 9. 68 16 r84

Florida 18 76 10. 31 49 .26

Georgia 23 56 6. 92 63 . 81

Hawaii 10 10 8. 43 12 .01

Idaho 12 48 3. 36 27 .58

Illinois 10 82 2. 40 52 .13

Indiana 9 14 3. 97 19 .67

Iowa 9 95 5. 18 24 . 70

Kansas 11 79 2. 34 25 . 24

Kentucky 24 33 8. 89 71 . 54

Louisiana 29 42 11

.

51 66 .19

Maine 14 09 8. 47 23 .71

Maryland 11. 26 3. 89 27 .40

Massachusetts 8 69. 5. 92 18 .31

Michigan 9. 50 4 . 80 33 . 33

Minnesota 9 35 3 8 7 30 . 98

Miss i ss ippi 4 0 51 14 7 7 7 6 . 37

Missouri . 1 4 6 3 7

.

25 5 2 . 24

Mori l.a na J 3 0 7 0 3 4 . 28

Nebraska 12 0 2 0

A 1 4 3 .

'I 3 Nevada 8 89 0 1 7 . 8 0 New {lamp shire 7 65 6 04 11 . 90

New Jersey 9

.

06 3 05 1

6

. 30

New Mexico L 0

l r 1 O 1 .5 y i> Z

1 r New York 1 L

A O

4 y 3 81 I 1 0 c. O D North Carolina L L y 6

o8 96 5,5 . 3 0 North Dakota 15 71 7

A H 4 7 4 3 . 57

Ohio 9. 86 3 95 33 . 56

Oklahoma 19. 30 7 46 52 . 56

Oregon 10 58 5 . 03 19 . 56

Pennsylvania 10 74 3 .79 21 .87

Rhode Island 11 58 5 . 90 14 .67

South Carolina 28 01 13 . 37 59 . 23

South Dakota 18 50 . 8 . 01 51 . 34

Tennessee 24 11 12 .40 73 . 53

Texa s 21 34 2 .42 70 .87

Utah 10 45 2 .47 41 .14

Vermont 11 14 7 . 30 22 .61

Virg inia 17 62 3 .44 51 .47

Washington 9 65 6 . 32 22 .61

West Virginia 23 77 7 .05 47 .58

Wisconsin 8 73 4 .29 43 .86

Wyoming 11 .63 4 .68 18 . 65

Dist. of Columbia 22 41 N .A. N .A.

National Average 14.81

* County values arc not available for Alaska and the District

of Columbia. In this study Alaska was treated as a single

county

.

Source: 1970 census of population.

The not two columns show the lowest and highest ratios

among the counties in each state. As to be expected, even

greater disparities of poverty concentration exist at the

county level. It should be noted that the lowest values for

some states such as Alabama and Mississippi are greater

than the highest values of other states like Connecticut and

New Hampshire. Since LEAs are smaller and as a rule more

economically homogeneous than counties, the poverty concentration

ratios can be presumed to show even greater disparities at

the LEA level. The second and the third column ratios may

be viewed as a gross picture of economic disparities existing

among the LEAs. In view of such a large disparity, the

need for some form of cost adjustment to the high concentration

areas appeals necessary.

Another way of looking at the > disparity of the concentration

ratios is comparing the values for some specific county

characteristics. One such display is the comparison in

**

terms of city- suburban- rural counties as shown in Table 2.4.4.

It is seen in the table that the large cities have uniformly

high concentration ratios, the suburbs have low ratios, and

the rural counties are generally high, but with extreme

variability. In spite of the recognized economic difficulties

of the large cities, the truly high concentrations of poverty

are found in the rural areas

.

- 73 -

Table 2.4.-1

Concentration of Poverty Children

in Forty-eight Selected Counties*

City

New York City, NY

Bronx, NY

Kings, NY

New York, NY

Queens, NY

Richmond, NY

Philadelphia, PA

Bait j more (city)

,

Richmond, VA

Denver, CO

Orleans, LA

St. Louis (city)

,

San Francisco, CA

Sub urb

Westchester, NY

Nassau, NY

Montgomery, PA

Bucks, PA . Montgomery, MD

Baltimore, MD

Henrico, VA

Fairfax, VA

Jefferson, CO

Arapahoe, CO

Jefferson, LA

St. Bernard, LA

St. Louis, MO

Jefferson, MO

Marin, CA

San Mateo, CA

MD

MO

Cone

.

Ratio

2 0. 44%

(27.85)

(23. 88)

(25. 36)

(8.17)

(5.81)

19.13

2A . 39

23. 87

15.48

34.71

26.27

16. 94

5.45

3.81

3.79

4.55

89

51

93

77

12

67

11 . 51

9.93

68

01

33

Cone

.

IVRiUi vi- aC4- JL1 Ratio

Al 1 e p anv NY 9. 96

Columbia, NY 10. 40

Cort ] and NY 10 . 08

Crawford JL. C*. » V J_ \J JL, \J. y PA1. 4. X. 11

.

84

Greene , PA 21

.

22

Wa vn e PA 10. 99

Garrett, MD 26. 78

Calvert. MD 24 . 09

Caro line , MD 22 . 96

Augusta, VA 15 . 79

Greene , VA 22

.

38

Halifax, VA 39

.

4 2 Cone j os , CO 43

.

53

Prowers , CO L 1 . Logan, CO 11. 14

Fast Carroll, LA 66. 19

DeSoto, LA 50. 13

St. Mary, LA 26. 52

Pemiscot, MO 48 . 80

Camden, MO 27. 27

Adair, MO 14. 41

Humboldt, CA 11

.

46

Merced, CA -19. 84

Yuba, CA 18. 02

5.61

*In each state, one county was chosen that was also a large city (the five boroughs of New York City were

treated as a single county) , then two suburban counties

of large cities were chosen, and finally three rural

counties were chosen.

Source: 1970 census of population.

- 74 -

If the diverse effects of high poverty concentration

on educational disadvantage are to be acknowledged, the question

still remains as to what concrete form cost adjustments

should take. (It should be stressed that the necessity

for such an adjustment is not an established fact; hence,

the relationship between the cost of compensatory education

and the poverty concentration cannot be formulated in terms

of any accepted basis.) One ready solution would be to

raise the per pupil cost. For example, any one of the

three items on the right-hand side of the cost equation

discussed earlier in this section, may be manipulated

singly or in combination. Thus, better teachers may be

provided, lower pupi 1- teacher ratios may be specified

or more pupil time may be assigned under compensatory

education. The net effect of these possible adjustments

is to raise the per pupil cost factor, but the exact form

of such adjustments cannot be prescribed v with presently

available information.

Although many possibilities of adjustment can be entertained,

the relationship adopted in this study is a simple one of

assuming some fixed weight for concentration ratios, i.e., each

county is given a bonus that is proportional to the size of

its concentration ratio. Because of the absence of knowledge

of this subject, the weight of the concentration factor

- 75 -

vis-a-vis the cost of compensatory education must be a highly

subjective choice.* Also, the effect of the concentration

ratio on cost is not applied at the state level because

the averaging among the counties would dilute the concentration

effect. Needless to say, it would be desirable to apply

the concept at the LEA level.

In summary, due to the absence of information on the actual

costs of compensatory education, three broad configurations

of cost of compensatory education may be assumed in comparing

the costs among arcal units. These are: (1) postively

related to the costs of regular education, (2) uniform

throughout the nation, and (3) negatively related to the

costs of regular education. The choice among them, however,

The relationship between the cost of compensatory education and

concentration ratio was formulated in the following linear form

M = M« (1+aC)

where M' represents the cost per child without considering the

poverty concentration effect, C the concentration ratio, a the

weighting constant, and M the adjusted cost of compensatory

education. Four values of the constant a were used in the

course of this study (0, 2.5, 5, and 10), and the results

are reported in Chapter 3.

The concept of concentration does not apply to the SEA grants.

When a concentration effect is applied, the LEA authorizations

are increased. In a proportional reduction process the SEAs

would therefore suffer a greater reduction than when the

concentration effect is not applied. To prevent this, when

there is a concentration effect and a proportional reduction,

the authorizations for SEA grants are increased in proportion

to the overall increase in the LEA authorizations.

- 76 -

must rest not on an empirical basis but on matters of

principle. The situation is different from that facing

the choice among the data for enumerating eligible children.

For that purpose, the problem is choosing among the

available data on the basis of the criteria of uniformity,

currency, accuracy, etc. Because of the different nature

of decisions required in the choice of a cost factor for

the formula, the numerical analyses of grant allocations in

Chapter 3 are concerned primarily with comparing the

possible distributional outcomes among the arcal units

under differently assumed configurations of regional costs.

2.5 Adjustment for Underfunding (Reduction Procedure)

Except in the first year of implementation, Title I

has consistently faced the problem of appropriation levels which

are lower than the levels of entitlement. This condition,

known as underfunding, shows no signs of diminishing. It

is possible to eliminate underfunding by reducing the cost

factor. This would produce an artificial situation wherein

the entitlement would be determined after passage of the

appropriation. Since there is no advantage of such contrivance,

the following discussion assumes the validity of predetermined

entitlement levels and the resulting need for a reduction

procedure

.

- 77 -

The underlying consideration in a reduction procedure is

equity: Should all eligibles be reduced in the same proportion

or should some receive preferential treatment? In the present

Title I allocation procedure, SEA children arc fully funded,

whereas the LEA children are partially funded. As the extent

of underfunding grows, this disparity grows also. The following

table shows that the average allotment per SEA child has

increased about 70% since FY67, while average allotment per

LEA child has been relatively constant.

Average Dollar Allotment Per Child

FY66 FY6 7 FY6 8 FY69 FY 70 FY 71 FY 7

2

SEA Program $243 239 263 297 328 368 413

LEA Program $206 164 168 149 170 175 168

At the national level, the consequence of this non- proportional

reduction is small for most children. In a completely

Do proportional reduction, the average allotment per eligible

child (SEA and LEA) in FY72 would have been $178. This

represents a 6 percent increase for the LEA children and a

57 percent decrease for the SEA children. It is questionable,

nevertheless, that SEA chidlren who constitute only 4 percent

of the eligibles should receive nearly 10 percent of the funds.

The consequence of underfunding can be viewed as either

(1) a reduction in the funds available for each eligible child

or (2) a reduction in the number of children who can be benefited

at the level indicated by the cost factor. These observations

- 78 -

lead to two potential rationales for the form that a reduction

procedure should take.

First, any reduction in the funding per child should be

based upon knowledge of benefit-cost functions for the various

groups of eligible children. For example, if it were known

that a 10 percent reduction in funding for one age group would

result in a 5 percent reduction in benefit, and that a 10

percent reduction in funding for a second age group would

result in a 20 percent reduction in benefit, then the second

group would merit preferential treatment.

Second, any reduction in the number of eligible children

to be served would probably rely on intuitive argument.

For example, the migrant children might be viewr cd as

especially disadvantaged because, although impoverished,

their mobility prevents them from qualifying for welfare

programs . ^ Since detailed knowledge of benefit-cost functions in

compensatory education is beyond the state of the art, the

first kind of justification for preferential treatment cannot

be sustained. Whether a justification of the second type can

be supported is entirely a matter of judgment, and not a matter

that can be finally resolved here. Thus, the equity consideration

seems to require proportionally equal reduction for all children.

However, there are several examples of inequity which

should be acknowledged and resolved. Neglected and delinquent

children may participate in cither LEA or SEA programs,

- 79 -

depending on whether the institutions serving them are

administered under local or state auspices. In the enumeration

for FY73, 68,865 neglected and delinquent children were

counted as eligible for the LEA program, and 61,004 for the

SEA program. Obviously, the latter group receives a significantly higher level of funding. This result is

due solely to an accident of administrative arrangement.

A parallel example would be the funding for handicapped

children. Title I funds are limited to those children in

state-operated institutions. Thus, no money is provided

to many handicapped children who are served by LEAs . * It

should also be mentioned that programs for handicapped

children are given additional grants through the Education

of the Handicapped Act (PL91-230, formerly Title VI of ESEA) .

While these considerations may not apply directly to the

reduction procedure, they substantiate the inequity of

fully funding Title I grants for the handicapped.

One factor which attempts to ameliorate any inequities

due to under funding is the "floor" provision. The floor

guarantees some minimum level of funding for each state.

In theory, the floor is intended to insulate the eligible

child from the vicissitudes of funding levels. In practice,

n The Bureau of Education of the Handicapped, in USOE , estimated

for FY72 that there were 6.5 million handicapped children in

the nation, of whom 2.8 million were being served in some

program. The Title I formula identified 130,782 handicapped

children

.

- 80 -

however, the floor applies at the state level. One result is

that some LEAs receive substantially higher allocations (in

proportion to their entitlement) than others. In FY72, the

majority of the states (those supported at the floor level)

received 39 percent of their entitlements, while New Mexico

(supported by a floor level) received 47% of its entitlement.

The need for the floor provision arises when the

entitlements of some states increase more rapidly than the total

appropriation. Any increase in a state's entitlement depends

upon two factors: (1) the increase in APPE and (2) the

increase in the AFDC counts. Although the effect of APPE

increases has been relatively small, the effects ot differential

increases in the AFDC data have been the principal cause of

the need for the floors . Any lessening of interstate biases in enumerating the

eligible children should, therefore, lessen the need for

the floors and reduce the gap between the floor and the

actual allotment levels. In particular, changing the

enumeration method from the additive AFDC of the present

formula to multiplicative AFDC components, as considered

for the alternative formula possibilities, should lessen

the need for the floor provision. The use of a uniform

cost factor would supplement this effect.

81 -

Chapter 3

ALTERNATIVE ALLOCATIONS AND THEIR EFFECTS

The allocation of Title I funds to the county level is a responsibility of the USOE. The official allocation is computed annually.

Although the computational task is a laborious and lengthy process, a

mixture of computer and manual procedures has proved to be satisfactory for program requirements. Early in this study it became

apparent that a great many alternative allocations should be examined.

In some formula grant programs, it would have been possible to do this

by analyzing a small portion of the system. This cannot be done in

the case of Title I. It is not possible to simulate the allocation

with any sample, because the reduction procedure must work on the

total allocation. Accordingly, a major initial effort of this study

was spent in developing a computer system which duplicates the official

allocation procedure.

The examination of numerous alternative allocations, and the *-

analysis of their effects on the distribution of Title I funds, has

been carried out by use of the computerized system. Each computer

simulation of the allocation process involves the following:

1. Selection of poverty children data for each of 3,113 counties,

from census data.

2. Updating of census data with current AFDC data.

3. Designation of cost values to be used.

4. Determination of concentration of poverty children for each

county (only when concentration effects are calculated).

- 82 -

5. Computation of the entitlements for SEAs and counties.

6. Reduction of the computed entitlements as required.

7. Aggregation of final county results for presentation.

To facilitate analysis of the proposed allocations, an arbitrary

"standard allocation formula" was developed. This standard formula uses

the Orshansky data from the 1970 census for the base enumeration of

poverty children. To update the 1970 data, the standard formula then

multiplies each county's initial value by the change in AFDC data for

that respective state. The county enumerations are then normalized

according to the CPS estimates of the national total.

A uniform cost factor of $300 per child is used for the standard

formula. The reduction procedure in the standard formula assumes no

floors, and proportionally reduces all SEA and county grants from the

calculated entitlement to the appropriation of $1.5 billion for the

51 states under Part A. The "standard" entitlement of $300 per child

then becomes an allotment of $165 per child.

The distributional results of each proposed alternative are compared

to that of the standard formula. Subsequent analyses are presented in

terms of change with respect to the standard.

Presentation of actual results for 3,113 individual counties would

be impractical. For simplicity, three different methods of displaying

results are used. These are:

1. Aggregating all results into 51, equal size, groups of counties

(the first and last groups contain 62 counties, the remainder

have 61). All counties are ranked in terms of either per

- 83 -

capita income (highest to lowest) or percent of poverty

children (lowest to highest).* Results for the first 62

counties are then summarized into the first "pseudo-state,"

or group. This process continues until all 3,113 counties

are aggregated into 51 groups. It should be emphasized,

there is no geographic basis of distribution; therefore,

each group may contain counties from all over the nation.

2. The same process is carried out at a higher level of aggregation,

five equal -size county groupings. Hie word "quintile" is

used in this text to describe these groups.**

3. Summarization by states.

The computer system developed for this study is being maintained

through FY73 in anticipation of its subsequent use for other analyses

which may be desired.

3.1 Methodology

3.1.1 Conceptual Framework for Analysis . The purpose of the following

analysis is to evaluate the allocation effects of the factors that make

up the proposed Title I allocation formula. Such evaluations, by

showing the numerical magnitudes of the effects, would be valuable in

reformulating grant allocation procedures for compensatory education.

The effects of the formula are analyzed singly and in various combinations.

*Three other criteria were considered but not used. They were income

per school enrollment, number of poverty children, and total income

deficit. The first criterion is almost identical to per capita income,

whereas the latter two were almost identical to each other. The number

of poverty children and total income deficit were not used because they

were dependent on the county sizes and hence would result in aggregating

counties according to population sizes—not a very useful result.

**The term "quintile" is commonly used to denote the end point of a range of one- fifth.

- 84 -

The factors that make up the formula are the following:

1. Enumeration of the eligible children.

2. Cost of compensatory education.

3. Concentration of poverty children.

4. Differential funding between LEAs and SEAs.

5. Presence or absence of the floors.

Each of the factors can be varied, independent of the others, and

effects analyzed. The second and the third factors in the above list

pertain to the cost of compensatory education, and the fourth and the

fifth pertain to the reduction procedure. For ease of presentation,

therefore, the five factors have been consolidated into three components:

(1) number of eligible children; (2) cost factor incorporating the concentration effect, and (3) reduction procedure. The three components of the

formula are designated, respectively, as K (Kids), M (Money), and

R (Reduction procedure)

.

The variations of the three formula components are defined in Table

3.1.1. The first variation of the number of poverty children (K^) should

be read as follows: the number of children from families whose income was

below $2,000 in the 1960 census plus the number of children from families

receiving AFDC payments above $2,000 as of January 1972. For I^, the

number of children below $2,000 family income is replaced by the newer

data from the 1970 census. For K^, the number of children represents

those whose family income was below $3,000 according to the 1970 census,

which necessitated the change in the number of AFDC children to those

- 85 -

Ta&le 3.1.1

Components of the Title I Allocation Formula

K (Number of Poverty Children]

$2,000 (60) + AFDC (72) above $2,000

$2,000 (70) + AFDC (72) above $2,000

$3,000 (70) + AFDC (72) above $3,000

$3,000 (70) x AFDC Ratio I adjusted for CPS estimates]

Orshansky (70) x AFDC Ratio I adjusted for CPS estimates]

M (Cost: S0% of APPE When Applicable)

MAX (SAPPE, NAPPE); Concentration Effect: none

MAX (SAPPE , NAPPE); Concentration Effect: low

MAX (SAPPE, NAPPE); Concentration Effect: moderate

MAX (SAPPE, NAPPE); Concentration Effect: high

SAPPE; Concentration Effect: none

SAPPE; Concentration Effect: low

SAPPE; Concentration Effect: moderate

SAPPE; Concentration Effect; high

$300; Concentration Effect; none

$300; Concentration Effect; low

$300; Concentration Effect; moderate

$300; Concentration Effect; high

R (Reduction Procedure)

Nonproportional Reduction; Floors for LEA grants

Nonproportional Reduction; No floors for LEA grants

Proportional Reduction; Floors for LEA £~ants

Proportional Reduction; No floors for LEA grants

- 86 -

receiving annual family assistance above $3,000 payment level. For

and Kr, the children below the $3,000 family income and the Orshansky

family income levels, respectively, are multiplied by the changing rates

of AFDC children of all payment levels (i.e., not confined to those

receiving payments above $2,000 or $3,000 per year) between 1970 and

1972.

The variations of the cost component are the combinations of three

costs and four concentration effects. The three costs are:

1. 50 percent of whichever is greater—state or national

APPE: MAX (SAPPE, NAPPE).

2. 50 percent of state APPE: SAPPE.

3. $300 per eligible child: $300.

The concentration effects are classified as none, low, moderate, and

high.

The variations of reduction procedure are composed of (1) proportional

or nonproportional reduction and (2) the presence or absence of the floors

for the LEA grants. The nonproportional mode of reduction fully funds

the SEAs while ratably reducing the LEA grants, and the proportional mode

ratably reduces both the SEA and LEA grants.

The formula cannot be exercised until the appropriation level and

the LEA floor value are specified. The two appropriation levels assumed

are $1.5 billion and $1.6 billion. The three floor values for LEA grants

are assumed at 80, 90, and 100 percent of FY72 grant level for LEA

children

.

*The numbers of poverty children for Kj. used for analysis in Chapter 3

do not exactly match the of Chapter 2, for technical reasons. The

analytical results presented, however, are only minimally affected.

- 87 -

The selection of the two appropriation levels is based on finding

an amount close to the FY 7 2 level which was $1.6 billion. The selection

of the three floor values is based on finding suitable values that are

consistent with the assumed appropriation levels. When the floor value

is defined as 100% of the FY72 grants, the $1.5 billion appropriation

level is insufficient to satisfy the floor requirements for the LEAs if

the SEAs are fully funded. Hence, 80 and 90 percent values are also

included.

In the present analysis, the number of variations assigned to each

of the items is as follows:

Enumeration of children 5

Cost of compensatory education 12

Ratable reduction 2

Appropriation level 2

Floor values for LEA grants 4

The total number of possible formula variations is the product of the five

numbers, or 960. Computing and analyzing the grant allocations for all

the possible variations would be impractical. Through an a priori

selection, therefore, 150 variations have actually been computed and

analyzed.*

Such a selection process, as well as the selection of the values for

the three formula components, involves some subjective judgments on the

part of the analysts, a fact that should be kept in mind in interpreting

the analysis results.

*The 16 allocation results presented in Appendix C match the K,. value of

Chapter 2. All of the computed allocation results are available for

inspection.

- 88 -

When the first variations of the formula components, i.e., K,, M^,

and R^, are confined, the result is the present Title I allocation

mechanism. It, however, is not used as the standard case against which

formula variations are compared because doing so would obscure the

various allocation effects that are to be analyzed and evaluated. It

is for this reason that the standard case is the combination of Kr, Mq,

and Rj. It is a simple case in the sense that every eligible child is

allotted an equal amount, the specific level depending solely on the

appropriation level and the particular K value. It is equivalent to

dividing the appropriation equally among all the eligible, children of

any particular enumeration, but disregarding all other considerations

such as the floors, differential costs, or differential needs. The

choice of the standard case thus satisfies the purpose of this study

analyzing the factors affecting the allocation of Title I grants and

evaluating their numerical significance.

3.1.2 Aggregation of Counties . The analysis of the effects of different

Title I allocations might be made at any of three levels:

1. State.

2 . County

3. LEA.

The analysis of the impact at the school district (LEA) level is

ruled out, however desirable it may be, since poverty children data are

not yet available for LEAs. In some ways, the state level is desirable

for analysis , because the state is readily identifiable and because APPE

values and floors apply at the state level. In this study, however,

- 89 -

most of the analysis is conducted with respect to counties. This is

because counties are more homogeneous units and more closely reflect the

conditions of the LLAs. Also, the concentration effect of poverty

children is more meaningful at the county level.

As explained earlier, the presentation of results aggregates

counties on the basis of two characteristics of relevance to Title I:

1. County per capita income.

2. County per cent of poverty children in its school age population.

These two characteristics are in general inversely correlated. That is,

a county with a high per capita income tends to have a low concentration

of poverty children, and vice versa.

It is of interest to note how the total population of poverty

children is distributed among county quintile groups. On the per

capita income basis, the distribution is highly skewed; on the percent

poverty children basis, it is not. These distributions are compared in

Table 3.1.2:

Table 3.1.2

DISTRIBUTION OF POVERTY CHILDREN BY COUNTY QUINTILES*

Quintiles Ranked Percent of All Quintiles Ranked Percent of All

By Per Capita Poverty Children by Concentration of Poverty Children

Income In This Group Poverty Children In This Group

1. Lowest Income 16% 1. Highest Concentration 19%

2. 11 2. 23

3. 10 3. 16

4. 17 4. 23

5. Highest Income 46 5. Lowest Concentration 19

All Counties 100% All Counties 100

*The data used to rank and group the counties are from the 1970 Census.

- 90 -

This table shows, first, the large numbers of poverty children are

found in areas with high per capita income. Such an apparent anomaly

merely reflects the fact that many of the large counties fall into the

highest per capita income quintile. Along with high per capita income,

these counties have concentrations of poverty children. That is, some

of the large counties in the highest per capita income quintile are not

in the lowest quintile ranked by concentration of poverty children.*

(These instances should not be viewed as invalidating the notion of the

existence of a basic inverse relationship between the two rankings.**

The calculated allocation results are more generally presented in

terms of the per capita income ranking of counties only because:

1. The county rankings by per capita income and percent poverty

children show a high degree of inverse correlation.

2. Per capita income is a more unambiguous economic measure.

3. Allotment per pupil is sensitive to a county's economic conditions

•but not to its number of eligible children per se.

In general, counties can not be neatly classified as cities, suburbs,

or rural. Thus, the two county statistics do show the distributional

consequences among the counties in terms of economic measures but not the

effects among the cities, suburbs, and rural regions. To this end, 48

*For example, three boroughs of New York City—Manhattan, Brooklyn, and

Bronx—all belong to the quintile having highest per capita income but

also belong to the quintile having the second highest percent of poverty

children.

**In the case of the 24 counties in Maryland with Washington, D. C. treated

as a county, the rank-order correlation coefficient of the two measures

was -0.7192. When Washington, D. C. , and Baltimore City were excluded

the coefficient increased in absolute size to -0.8834.

- 91 -

comities from 8 states are selected and their allotment levels are

evaluated. Differences in the distributional effect among cities,

suburbs, and rural nrcas are accomplished only when the concentration

factor is added to the cost factor.

3.1.3 Presentation Measure . In most of the analyses, the allotment per

eligible child is a more graphic comparison among counties than the total

dollars. This is because the allotment per child :

1. Directly relates to the cost of compensatory education.

2. Removes size differences (in terms of the count of poverty

children) among counties.

For example, this type of analysis permits a direct comparison of allocation

consequences among large urban and small rural counties.

However, when comparing effects of using different means of counting

poverty children (values for K) , the allotment per child statistic can be

misleading. For example, Table 2.3.2 shows that the five population

totals vary from roughly 4.5 million to 8.4 million. A change in K can

make a proportional change in the dollars per child allotment while the

total allotment to a county unit might be unaffected.

3.2 Cost and Concentration Effect

Because the real cost of compensatory education and its pattern of

regional variation are not known, the cost factor in the allocation

formula lias been interpreted as the incremental resources necessary (per

pupil) to carry out supplemental compensatory education. Three broad

regional cost configurations based on APPE values are discussed in

Section 2.4, and their concrete forms are assumed to be

- 92 -

(1) 50 percent of state APPE (SAPPE)

;

(2) uniform cost of $300; and

(3) additional money in proportion to the size of povertyconcentration.

The presently used cost factor (larger of the state or national APPE) is

an intermediate case between (1) and (2) above, and will be treated as

such in this analysis.

The main purpose of the numerical analysis of the cost factor is to

compare the allocation effects of alternative cost assumptions. Since

the main focus of the earlier discussion on cost dealt with the regional

disparities of APPE according to income measure, the following analysis

is concerned with the manner in which economically different regions

are affected by alternative cost factors.

3.2.1 Comparison of Costs without Concentration Effect . The first

comparison deals with the distributional consequences of using (1) SAPPE,

(2) $300 per pupil or (3) MAX (SAPPE, NAPPE), as the cost factor. First,

the comparison of allotment per pupil by county quintiles between SAPPE

and the $300 value is shown in Table 3.2.1.

The per pupil allotments demonstrate, as expected, the income bias

of using SAPPE values. Only the highest income quintile (i.e., 20 percent

of the counties) benefits by using SAPPEs rather than a uniform cost

factor. This results from the fact that 46 percent of the poverty

(Orshansky) children, in terms of the 1970 census enumeration (see

Table 3.1.2), reside in the counties belonging to the highest income

quintile. The results, therefore, may be interpreted to imply that by

- 93 -

Tabic 3.2.1

. COMPARISON OP ALLO'IMENT PP R PUPIL: $300 VS. SAPPP

Quint ilcs Ranked

by Per Capita

Income $300* SAPPE % Difference**

1. Lowest income $165 $125 -24%

2. 165 136 -18

3. 1.65 149 -10

A4

.

16b T C A 154 -7

5. Highest income 165 192 16

Table 3.2.2

COMPARISON OF ALLOTMENT PER PUPIL: $300, MAX, SAPPE

Quintiles Ranked

by Per Capita

Income $300 . MAX (SAPPE, NAPPE) SAPPE

1. Lowest income $165 $153 $125

2. 165 155 136

3. 165 157 149

4. 165 159 154

5. Highest income 165 175 192

*The $165 per pupil allotment under the $300 cost factor is achieved for

any other constant cost so long as it is greater than $165. When the

reduction procedure is proportional and no floors apply, the formula

merely divides the total appropriation equally among the eligibles. The

neutrality of a uniform cost carries over if concentration effects are added so long as the reduction procedure is proportional and no floors

are applied. In this sense, the choice of any particular uniform cost

value is arbitrary.

**Thc percentage values do not sum to zero since (1) the per child allotment

values incorporate the total allotments and the number of children and (2)

the quintiles contain unequal numbers of children.

- 94 -

choosing a uniform cost, a large majority of counties would receive

higher per pupil allotments. Moreover, the additional amounts to be

gained vary according to the economic status of each county group.

The presently used cost factor, MAX (SAPPE, NAPPE) , is a compromise

case between the use of a uniform cost and SAPPEs. Since income levels

and APPE values show close association (i.e., they show high positive

correlation), the allocation results of using MAX (SAPPE, NAPPE) as the

cost factor are intermediate between the uniform cost and SAPPE results.

Such results are presented in Table 3.2.2.

It should be noted that when MAX (SAPPE, NAPPE) is used as the cost

factor, the effect of NAPPE results in relatively equal per pupil allotments for four of the quintile groups. It may be inferred that the

main beneficiary of using MAX (SAPPE, NAPPE) as the cost factor instead

of a uniform cost is the top 20 percent of the counties measured in

terms of per capita income. •

3.2.2 Concentration Effect . The purpose of incorporating the concentration effect into the cost factor is to channel more funds to the

areas with high concentration of poverty children. This amounts to more

funds for low income areas. The effect of concentration would be even

greater if the initial cost factor favored low income areas. Accordingly,

the allocation results should show the greatest monetary increase for

low income areas when the concentration effect is incorporated with

the uniform cost factor. Table 3.2.3 shows results of adding the

same concentration effect to the initial cost factors of $300 per pupil

and SAPPE.

- 95 -

Table 3.2.3

Comparison of Adding the Same Concentration Factor to

Different Initial Costs

Quintiles Ranked

by Per Capita

Income

1 . Lowest Income

2.

3.

4.

5. Highest Income

I. $300 Per Pupil

Without

Concentration

$165

165

165

165

165

With

Concentration

$271

201

167

158

133

% Difference

64%

22

1

-4

-19

II. SAPPE

1. Lowest Income

2.

3.

4.

5. Highest Income

$125

136

149

154

192

$214

171

156

151

163

71%

26

5

-2

-15

- 96 -

Three significant points should be noted in Table 3.2.3.

(1) The larger percentage increase in the lowest income quintile

relative to the highest income quintile: results from the unequal distribution of poverty children in the respective quintiles. If the distribution

of poverty children were uniform for all quintiles, the relative changes

in the allotment per pupil among the quintiles would exactly cancel out.

(2) 'Die relative strength of concentration effect is similar for

both values of initial costs. That is, the distributions of "% Difference"

column appear quite similar.

(3) The purpose of the concentration effect is to reallocate the

grant money among economically different counties ,. This phenomenon is

not something intrinsic in the way the concentration effect operates;

rather, it results from having to divide a fixed amount of grant money.

If the supply of total grant money were unlimited, a quite different

outcome would occur. Specifically, every county would receive a higher

allotment per child compared to the initial situation when the concen-

*- tration effect is absent; the sizes of additional amount would be

proportional to the sizes of concentration ratio. When the supply of

total grant money is fixed, introduction of concentration effect is

equivalent to a reallocation of the grant money from richer to poorer

counties

.

3.2.3 Intensity of Concentration Effect . The specific consequences of

incorporating a concentration effect into the cost factor were described

in the preceding section. What was not described is the possible change

in allocations in response to varying the intensity of concentration

- 97 -

effect. More specifically, the importance or relative weight of the

concentration effect vis-a-vis a given cost factor can be varied freely

so that such consequences should be studied.

The question naturally arises what weight should be attached to the

concentration effect. The allocation results of alternative weights

given to concentration effect are shown in Table 3.2.4. The table

represents the outcomes using three different concentration weights

(low, moderate and high) with the $300 per pupil cost and compares them

to the results derived from the same cost without any concentration

effect. The designations, low, moderate , and high are arbitrary; what

matters is that their relative rankings are maintained.* The $300 per

pupil is chosen because changing allocations are thus easier to compare by

quintiles, but similar effects would result for the other costs.

*More specifically, the concentration effects can be defined in terms

of the cost formula discussed in Section 2.4,

M = M' (1+aC)

where M is per pupil cost incorporating concentration effect,

M' is cost,

C is concentration ratio of poverty children, and

a is the weighting constant.

The four cases of concentration effect are defined in terms of the

weighting constant as,

none: c = 0

low: a = 2.5

moderate: a = 5

high: a = 10

It should be stressed that the choice of the specific values for the

weighting constant is an arbitrary and subjective one, depending on a preference for desired outcomes.

- 98 -

Tabic 3.2.4

COMPARISON OP ALLOTMENT PER PUPIL: ALTERNATIVE CONCENTRATION

WEIG1 ITS WITH $300 PER PUPIL COST*

Qiiintiles Ranked

By Per Capita

Income

Concentration Weight

None J_AJW High

1. Lowest Income $165 lP / J. $303

2. 165 187 201 212

3. 165 165 167 168

4. 165 159 158 156

5. Highest Income 165 142 133 123

In the above table, noticeable changes are confined to the first,

the second, and the fifth quintiles, while the third and fourth quintiles

are affected only slightly. Still, these numbers are not sufficient to

determine what the "appropriate" weight should be. However, numbers

like these may be used to choose a desired weight, if the resource needs

can be determined independently for those counties belonging to different

income categories.

The same information that is presented to Table '3.2.4 is shown in the

following three sets of graphs in a more disaggregated form. Each graph

compares the percentage difference in allotment per pupil for each of

the 51 homogeneous county groups when concentration effect is added to

the cost. That is, each point (designated by the integer 1) represents

the difference in allotment per pupil (as expressed in percentage value)

for those cases with varying levels of concentration versus one without

concentration effect. The 51 county groups are placed along the horizontal

*The concentration effects in terms of SAPPE and $300 per pupil costs

presented in Table 3.2.3 correspond to the case of moderate weight.

- 99 -

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102

axis according to the size of per capita income (increasing from left

to right). Thus, county group 1 has the lowest average per capita

income and county group 51 lias the highest average per capita income.

The graphs reveal dramatically the reallocation consequences among

the counties when concentration effects are added. 'Die beneficiaries

of the concentration effect are the counties with lower per capita

income. Their gains are offset by the losses of those counties with

higher per capita income. It should be pointed out, again, that the

unequal distribution of eligible children among the county groups, i.e.,

more at the higher income end, gives the impression that there are more

gains than losses. Such an impression can be counteracted by noting

that the measure compared in the graphs is allotment per child, not

total allotment to the counties.

3.2.4 Alternative Interpretation of Concentration Effect . Heretofore,

the interpretation attached to the concentration effect has been that

the resource needs for compensatory education may be different accoi?ding

to a pupil's educational environment. As the environment becomes

unfavorable, the need for resources increases, i.e., the cost of

compensatory education rises. The pupil's educational environment is

measured by the concentration of poverty children at the county level.

An alternative interpretation of the concentration effect is to

assume that the costs of compensatory education are actually known, at

least the minimum levels that are necessary to administer some specified

form of compensatory education. The concentration effects, under this

interpretation, are used to channel more money to specific areas

- 103 -

or counties so that more eligible children can participate in the

compensatory educational programs.

If the cost factor is viewed as some minimum necessary cost which

is greater than the average allotment per pupil, the number of eligible

children being able to participate in the Title I program in any county

must be less than the total number of eligible children so long as

underfunding of Title I prevails. The maximum number of children that

can be accommodated by a given level of allotment to a county can be

calculated and be expressed as the program participation rate. As the

allotment level rises, so would its participation rate.

The critical assumption regarding this interpretation of the concentration effect is that the cost factor is actually known. The use of the

minimum necessary cost concept may prove to be helpful in estimating the

cost operationally. For example, a particular program may specify a

reading specialist for five disadvantaged children at one-quarter of

their school time. The salary of the specialist then becomes the minimum

necessary cost for the administration of this particular program.

Table 3.2.5 illustrates the distributions of participation rates

for the county quintiles. The same four concentration weights are used

and the cost factor is $300 per pupil.

Three observations may be made from the table.

(1) Relatively small losses by the higher income counties can

provide more than proportionate benefits to the lower income counties.

As in the case of allotment per pupil, differences in the distribution

- 104 -

Table 3.2.5

PROGRAM PARTICIPATION RATES FOR ALTERNATIVE

$300 Per Pupil

Quint iles Ranked

by Per Capita

Income None Low Moderate High

1. Lowest Income 55% 73% 901 101%

2. 55 63 67 71

3., 55 55 56 56

4. 55 53 53 52

5. Highest Income 55 47 45 41

of eligible children among the quintiles make possible the trade-off of

a smaller sacrifice in terms of participation rate by the highest income

quintile with a large gain by the poorest two quintiles.

(2) The program participation rate is 101 percent for the lowest

income quintile under the high concentration weight. In other words,

more than the enumerated eligible children can participate in the programs.

It is clear that an upper limit can be set on the size of concentration

weight by observing the resulting highest value of participation rate.

In this sense, the determination of concentration weights is not completely

free.

(3) Since the program participation rate is a more operationally

usable concept than allotment per pupil, it may be used as a guideline

for fund allocation. For example, some particular level of participation

rates may be specified as the program goal for some or all of the county

quintiles. The same procedure may be used to find the combinations of

- 105 -

cost factors and concentration weights that best achieve the specified

goal, provided that the alternative cost factors to be considered are

reasonable estimates of minimum necessary costs.

3.2.5 Concentration Effect: Comparison Among City- Suburb -Rural Counties .

The concentration effect is brought out more dramatically in terms of

comities in city—suburb—rural comparisons. The following table lists

the mean value, as well as the highest and the lowest values, of the

allotment per child in each of the classes from the specially selected

48 counties.

Table 3.2.6

ALLOTMENT PER CH

I

LP: CITY—SUBURB—RURAL COMPARISON

CWCT-NTRAT I ON WE I GHT : MODERATE"

City Suburb Rural

Average $169 $100 $190

Highest Value 196 117 309

Lowest Value 144 91 ' 114

The allotment per pupil is uniformly $165 for all counties when the

concentration effect is absent. The substantial decreases for the suburban counties are to be expected. Even the highest value for the suburbs

is about the same as the lowest value for the rural counties and well below

the lowest value for the cities. Although the highest value comes from

the rural counties, the rural county values have greater variation than

the city values. In other words, the cities, although representing

various geographical regions, are characterized by uniformly high degree

of need whereas the needs of the rural areas are more varied.

*The list of counties is shown in Table 2.4.4 of Section 2.4.

- 106 -

3.2.6 Summa ry . Although concrete data on the costs of compensatoryeducation arc lacking, the foregoing analyses bring out certain

gencralizablc patterns in the intercounty allocation effects associated

with the alternative assumptions of the cost factor. The main findings

are summarized:

1. The allocation effects measured by the allotment per pupil show

substantial changes among the counties when the definition of the cost

factor is changed.

2. The present version of the cost factor- -MAX (SAPPE, NAPPE) --

equalizes the per pupil allotment level for about 80 percent of the

counties rather than one half as might be expected.

3. If a uniform cost is to be used when underfunding exists, its

particular level does not matter. Both 50 percent of NAPPE ($429) and

$300 pupil cost factors give essentially the same allotments per pupil

to all counties.

4. The concentration effect becomes a redistribution effect when

the appropriation level is fixed. Funds are shifted from richer to

poorer counties while the intermediate counties are relatively unaffected.

5. Even when using SAPPE, a large enough concentration weight can

bring about a significant redistribution of funds among the counties.

6. If minimum necessary costs can be roughly estimated, allocations

may be made to satisfy prespecified levels of program participation rate.

7. The concentration effect shifts funds from suburban areas to

larger urban and poorer rural areas.

- 107 -

3.3 Reduction Procedure and Floor Effects

3.3.1 Differential Funding Kates for SEAs and LEAs . Hie number of

children administered by SEAs is relatively small in the Title I program.

In FY73, they constitute about 4 percent of the total eligible children.

Because of their small relative number, the allocation differences of

fully funding or ratably reducing the SEA grants have a small effect

on the LEA grants. Thus it is easy to overlook the fact that differential

funding rates appear to constitute an important inequity in the present

Title I funding procedure.

The actual level of appropriation was roughly 40 percent of the

authorization in FY72. Since the SEAs were fully funded while the LEA

grants were ratably reduced, the SEA share of the total appropriation

was about 10 percent, i.e. two and a half times as much per child as the

LEA share.

An alternative formula using a uniform $300 cost factor and full

funding of the SEA grants allocates $300 per SEA child and bout $160 per

LEA child. If the SEA grants are proportionately reduced, all children

are allocated about $165 each.

The problem of differential funding rates cannot be resolved in

terms of analysis results. It is sometimes argued that the necessary

data for resolving the problem are, once again, the respective costs of

compensatory education. It may be stated, nevertheless, that unless

some presumption exists for needing the differential funding procedures

between the two groups (e.g., in terms of perceived costs), the present

procedure is unnecessarily discriminatory.

- 108 -

If a new policy is to be adopted for a uniform reduction rate,

however, some form of floors appears necessary for the SEA grants

since the required reduction in SEA grants is so large relative to

their present share. For example, the aggregate of SEA grants in a

state (like the aggregate of LEA grants) could be given a floor of 90%

of the previous year's aggregate grant.

3.3.2 Floor Effects . As a general principle, it is reasonable to

assume that participation in Title I programs should depend on actual

need, not the vagaries of fund availability. Over the years, the

funding level of Title I has become progressively lower when compared

to the increasing needs expressed by the authorization formula, even

though in absolute dollar terms the funding level has increased. The

floor provision, therefore, performs the task of protecting the ongoing

programs that are threatened by a lower funding level. Since the SEA

grants are fully funded by law, the present floor provision applies only

to the LEA grants. *~

The extent of undcrfunding was so severe in FY72 that 18 states

had to be supported by their respective floors. As a result, the

formula was ineffective for about one-third of the states.

The major defect of the floor provision as it is defined at present

is that the floors are superficial; they do not offer protection to

units below the state level, i.e., to counties, LEAs, schools, and

individual children. The floor values are defined in terms of state

aggregates of allotments for LEAs, but the data used to allocate below

- 109 -

the state level may change. Allotments to LEAs, for example, may change

considerably. Logically, it would be preferable to apply the floors at

lower geographical levels than the states, for example, the counties.

The practical implications of doing so have rot yet been worked out.

The analysis of floors presented in this section is done with

respect to the states, not counties, because the existing floor provision

applies to the states. Effects to be analyzed are the numbers of states

supported by their floors, as a result of (1) the appropriation level and

and the floor values and (2) the choice of enumeration methods for eligible

children. Since the FY73 appropriation level and the definition of floor

values arc still undetermined, the following three cases are assumed

for the purposes of analysis.

Appropriation Floor

Case I $1.5 billion 80 percent of FY72 LEA allotments

Case II $1.5 billion 90 percent of FY72 LEA allotments

Case III $1.6 billion 100 percent of FY72 LEA allotments

When the five enumerations of eligible children for FY73 as defined

in Section 3.1, are alternatively substituted in the present allocation

procedure (i.e. with MAX (SAPPE, NAPPE) as the cost factor, and with SEAs fully

funded) the number of states supported by the floors can be tabulated

as follows. Except in Case I using (the present enumeration), the

number of states supported by the floors is large. This demonstrates

that unless the floor level is much smaller or the appropriation level

much higher than those listed here, the substitution of new enumerations

- 110 -

Tabic 3.3.1

NUMBER OF STATES SUPPORTED BY THE FLOORS

Enumeration Methods

Case K

l K2 K3

K

4

K

5

I 1 24 21 14 16

II 20 33 31 31 31

III 29 38 38 39 41

of eligible children can be negated by the floor. Conversely, those

who should be entitled to higher allotments cannot receive their proper

shares

.

Another way of assessing the influence of the floors is to compare

the state aggregate allotments that result with and without the floors.

Since the purpose of such a comparison is only to assess the influence

of the floors, this demonstration uses Case II of the appropriation and

floor levels, and enumeration changes from to 1^ and from to K^.

Tables 3.3.2 and 3.3.3 show that the applications of the floors restrict

the changes in allotment levels for the states. Described in another

way, changing the method for enumerating poverty children does not

effect the expected changes in allotment levels so long as the influence

of floor provision is retained in the allocation procedure.

- Ill -

Tabic 3.3.2

Pis tr ibut ion ol Al l otmcnt Changes Among States

K~ Substituted for K

Change in Allotments

(in absolute values)

With

Floors

Without

F 1 nnT^

n - If)?; AR 12

11 - 201 3 17

21 - 30% 0 8

31 - 40% 0 7

41 - 50% 0 7

51 - 60% 0 0

61 - 70% 0 0

Total 51 51

Distribution of

Table 3

Allotment

.3.3

Changes Among S t a t p 9

K

5

Substituted ior

Change in Allotments

(in absolute values)

With

Floors

Without

F -1 nnT^

0 - 10% 38 J. V

11 - 20% 8 J. D

21 - 30% 3 13

31 - 40% 2 4

41 - b0% 0 1

51 - 60% 0 2

bl - 70% 0 2

Total 51 51

112

Appendix A

SPECIAL GRANTS BASED ON THE CONCENTRATION

OF POOR CHILDREN: Part C ot Title I

Part C of Title I authorizes bonus grants for LEAs that

have a concentration of eligible children equal to 20% of the

school age population, or that have at least 5,000 eligible

children who constitute a 5% or greater concentration. The

underlying assumption of this program is that more money per

child is necessary where the concentration of eligible

children is higher. The following analysis addresses two

aspects of Part C: practical considerations, such as administrative problems and the effects of the program in terms of

the resultant allocation of funds, and the theoretical or

conceptual foundations of the program.

A.l Practical Considerations

A. 1.1 Technicalities . The administrative process for Part

C at the Federal level (interpretation of the law, collection

and validation of data, and computation of allotments) is

extremely burdensome. The computational process itself is

considerably more complicated than that for all the rest of

Title I. An example of the technical problems is found in

the "marginal" LEAs that are eligible pursuant to Sec. 131

Ca) (2) . These are the LEAs that are not eligible for Part C

grants under the defined conditions of the number and percentage

A-1

of eligible children, but that "would be eligible" for such a

grant if there were "a relatively small increase" in the number

of such children, but only provided that the LEA meets

unspecified criteria of "urgent need" for financial assistance.

In reducing the grants from the authorization level to the

appropriation level, each part of Title I affects the others.

Part C makes no reference to the grants to SEAs for

administrative expenses, and the provisions for those

administration grants in Part D do not distinguish between

the regular Part C grants and those to the marginal LEAs

.

Nonetheless, legal opinion has established the practice

that the Part C grants to marginal LEAs are to be disregarded

in computing the administrative grants, in spite of the

fact that the SEA's administrative burden is greater, not

less, for grants to marginal LEAs since special justifications

in terms of tax effort and other measures of urgent need arjs

required in those cases. Because of this exception, the

!j already complicated reduction procedure for underlunding is

made considerably more complex.* The total amount of money

Although the extent of the complications will not be apparent

to the casual reader, no detailed example is provided here.

Such an example, together with its explanation, would be longer

than this appendix. The complexity of the reduction procedure

results in part from a logical circularity in which the administration grants aepend on the actual allotment levels of the

other grants (under Parts A and C) , while at the same time

j the money available for those allotments depends partly on

I the administration grants. If the administration grants were

proportional to the others, the solution would be relatively

simple. However, this is not the case, and since the reduction

procedure comprises a set of logical rules as well as mathematical relations, there is no strictly mathematical solution.

A description of the reduction process has been provided in the

previously cited Interim Report of March 1972.

A-2

that was redistributed in FY71 as a consequence of this

exception was $1700. Eleven states were affected, so on

the average the administration grants were reduced by about

$150 per state. Certainly the effect of this technical

nicety, in monetary terms, did not justify the complications

it added to the administration of the Part C grants.

The previously cited Interim Report of March 1972 stated

(p. C-10) that problems of interpretation have been generally

settled, although some still arise intermittently. Since that

report was written such problems have arisen, one of them in

conjunction with Part C. In FY71 and FY72 the funds for

administration grants corresponding to Part C grants came

from the aggregate Part C allotment and those for Part A

came from the aggregate Part A allotment. The practice in

FY73 was changed to make the funds for the administration grants

for Part C come oft the top of the Title I appropriation, £hus

affecting' the amounts available for Parts A, B, and C.

However, no change was made in the funding of Part A administration

grants. The amount of money involved in this change is less

than 1% of the aggregate Part C allotment. In addition to

further complicating the allocation of funds, this new

exception required that the amount reserved for FY73 Part

C administration be an es timate , since the amounts of the

Part C grants themselves were not yet known.

A3

A. 1.2 Data . The pervasive problem in the administration or.

Part C, at both the Federal and state levels, is the collection

and validation of the required concentration data. Two sets

of data seem on first reading to entail no problem, but in

fact have been very difficult and expensive to obtain: these

are the number of resident children of the LEA and the Part

A authorization of the LEA. Generally the only source of

hard data on resident children is the decennial census; until

now that meant the 1960 census. Thus USOE and the SEAs were

faced with the choice of using badly outdated data or estimating

the number of resident children in each LEA, for example,

from some formula based on enrollment. The fact that

LEAs do not in general coincide with census geographic areas

means that using the census (either 1960 or 1970) for LEA

population data requires costly transformations and is often

impracticable. The census mapping project currently underway

at USOE will help in this regard, but its coverage excludes

about 7,000 of the smaller LEAs.

Obtaining the Part A authorization for an LEA (from which

to calculate its Part C authorization) is a problem because,

in the allocation of Part A grants, authorizations are only

computed to the county level, not to the LEA level. The

Part A allotments at the LEA level are computed on a different basis from that used at the county level; the LEA

allotments are determined from the county allotments (not

from authorizations) by the several SEAs, each according to

its chosen method of subcounty allocation. Thus, USOE must

A-4

rely on a survey of the states to obtain the data from which

it can compute Part A authorizations corresponding to the

allotments at the LEA level. Needless to say, the collection

and correction of such a volume of data from so many sources

produces many mistakes and misunderstandings that must be

detected and corrected through a long process.

A. 1.3 Resul ts . As a result of these and other data problems,

months are required for the allocation of Part C funds.

For FY71 (the first year of Part C) , the allocation was completed

on June 30, 1971, the last day of the fiscal year. The FY72

allocation was completed on August 31, 1972, two months

after the fiscal year had ended.

Aside from the tardiness of the allocation, the size of

the Part C allotments shows some ridiculous results. While

some LEAs do receive sizable grants from this program in

FY71 (the largest grant went to New York City: $2.3 million),

the average grant (in FY71) was $3,868, and 223 LEAs received

grants of $100 or less (in two cases only $2). Although the

average grant is far short of the amount needed to hire an

additional teacher, it could provide an aide or some additional

equipment. However, many of the grants are so small that not

only do they provide a useless amount of money for intensifying

a program to compensate for the high concentration of poverty,

but the administrative cost to the recipient LEA consumes the

grant. If the LEA accepts the grant, its personnel must

A5

tamiliarize themselves with the regulations and guidelines

regarding Part C; they must account for Part C tunds separately;

and they must prepare a comprehens ive plan for the use of

the Part C grant, setting forth specific objectives and the

criteria and procedures to be used for an annual evaluation.

Even if the LEA wishes to decline its grant, it incurs

some expense in exchanging correspondence with the SEA.

Because of the small size of many of the grants, some

states encourage the LEAs entitled to small grants to relinquish

them so they can be consolidated into one or more grants of

a reasonable size. Consequently the distribution of the Part

C grants to LEAs actually can require several months beyond

the final allocation by USOE. This additional process in

the allocation of grants (which is required not by the law

but by reasonableness in using such small grants) represents

a substantial cost to the SEAs and LEAs. Some SEAs and LEAs

have complained that the administrative burden is costly

compared to the relatively small grants involved. Two states

in FY71 and four in FY72 declined to participate in Part C,

presumably because they felt it was not worth the effort

and expense.

In summary, the practical considerations regarding Part

C show that the computational complexities and the difficulties

of the data collection process have resulted in an administrative

nightmare. The grants have finally gotten to the recipients

after the fiscal year was over. The administrative burden

A-6

at the Federal, state, and local levels has been costly and

out of proportion to the amounts of money being distributed;

there are instances where the cost to the recipient agency

has exceeded the value of the grant itself.

A. 2 Theoretical Considerations

There is no body of knowledge that establishes clearly

the costs of providing educational services; therefore, there

is no factual basis on which to establish whether there is or

is not a relation between the needed dollars per child and the

concentration of poverty.

Second, if it were assumed that there is such a relation,

the direction of the relation is not known, nor even whether

it is unidirectional. It can be argued that the needed funding

is greater where the concentration is greater, because the

children have an additional problem of a worse general social

environment compounded with their individual problem of

educational deprivation. The same point of view can be

argued on the basis that the school faces higher than normal

costs in the form of teacher salary bonuses or repairs for

vandalism. On the other hand it can be argued that a high

poverty concentration leads to reduced costs due to economies

of scale and to homogeneity of the school population, while

poor children in places with low concentrations are social

outcasts, unable to keep up with, their peers, and handicapped

by futility. One might even adopt both arguments, resulting

A7

in the view that places with very low and very high concentrations

need more money per child than places with medium concentrations.

In the third place, if it were assumed, for example, that

the needed funding per child increases when the concentration

increases, one still would not know whether it increases by

the same rate at both ends of the range of concentrations, i.e.,

whether it is a linear relation.

Finally, if the shape were assumed to be linear, the rate

(slope) would not be known, even approximately; it could be

0.1, 1 or 10.

The conclusion indicated by these theoretical considerations

(apart from practical problems, which migh'c be corrected)

is that there does not appear a factual basis to justify altering

the distribution of funds according to the concentration of

poverty, much less to indicate in what way to alter the

distribution. A less harsh judgment is possible if one is

willing to make several assumptions. Some possible implementations

of such a judgment are examined in Chapter 3.

The primary assumption that is expressed by Part C is

that the per child allotment should be higher in places with

high concentrations of eligible children than in places with

low concentrations. The present implementation of this concept

is crude. An LEA either does or does not qualify; that is,

the per child bonus does not reflect varying degrees of

concentration. Further, the qualification rule is a "step

function" (in mathematical language) , involving an abrupt

A8

change at a certain point; an LEA with 4,999 eligible children

would need a concentration of 20 ?

o in-order to qualify, but

with one more eligible child it could qualify with a concentration of only 5%. The alternative formulation of a concentration-based grant developed in this report applies

in concept to all LEAs and relates the size of the bonus to

the degree of concentration.

A-9

Appendix B

ENUMERATION UPDATING

This appendix provides technical detail in support of Section 2.3.2,

concerning the updating adjustments in the enumeration of eligible

children. It is presumed that the reader of this appendix is familiar

with that section, which provides a coherent exposition of the concepts

of updating. This appendix addresses four topics that require more

detailed discussion than is appropriate in Chapter 2. The first section

examines a different general approach to updating than that developed

in this study, and explains why this alternative approach, although

conceptually plausible, is technically impracticable. The second section

analyzes the major flows in the present Title I updating methods, because

these are some of the important pitfalls that an alternative method shall

avoid. The third section is the detailed documentation of the alternative

updating method described in Chapter 2. The fourth section discusses the

updating of the total school age population data required when a concentration factor is employed in an allocation formula.

B.l General Approach

The general approach to updating in this study has been to make an

adjustment of some base year enumeration in terms of changes in AFDC

data. Another approach, that has been considered and rejected, is to

adjust for population changes and changes in the income distribution.

The population changes would be in-migration, out -migration, births,

deaths, and aging of the population (such that young children become

B-1

adults). An adjustment for changes in the income characteristics

requires projected values of income distribution parameters (such as

a median and probit slope, if a log-normal form is used).

Projection models for population and income estimations are

necessary in this approach because there is no comprehensive and

detailed survey other than the decennial census Itself.* Of course,

there are some current data, such as CPS data, that can be used to

calibrate the projection methods. The Census Bureau, the Bureau of Economic

Analysis (Department of Commerce) and several other Federal agencies

are concerned with such projections. Even at the state level (not to

mention the county level) projections are more in the nature of model

development than of standard economic indicators. 'Die state of the

art of detailed economic projection at the subnational level is not yet

sufficiently advanced to be seriously considered as a basis for allocation

of grants. This is particularly so when the required estimate represents

one extreme of the income distribution (poverty)

.

It is for this reason that Title I updating must continue to rely

on some direct measure of the poverty population, i.e., AFDC data and,

potentially, school lunch data.

*Due to the acceleration of social change, the desirability of having a comprehensive census every five years (instead of ten) has often been

suggested. Of course, that would be expensive. Title I funds allocation

is an example of a Federal function that could be improved with data

from such a census.

B-2

B.2 Flaws in the Present Method

An analysis of the faults of the present updating method not only

shows why it should be discontinued but also suggests the ways improvements can be made.

B.2.1 Data Incompatibility: Non- complementarity . One flaw is that the

two principal categories of children -- those from low- income families

and those counted under AFDC -- are not complementary groups; that is,

one does not begin whore the other leaves off. That is illustrated by

the following two example's , one in which a poor child would not be counted

and one in which a child would be counted twice. The first child's

family has an income of $200 from AFDC and $1900 from other sources.

Since the total income is greater than $2000, the family is not counted

in the census low- income component of the Title I formula. But since

its income from AFDC is less than $2000 it is not counted in the AFDC

component either. Hie second example involves a family whose total

income reported in the census was below $2000, thus causing the family

to be counted by the Title I formula in every year. In some year after

the census year, however, the family's income from AFDC alone has risen

above $2000, thus eventually qualifying the family under the AFDC

component of the formula as well. These examples point to the desirability

of updating the count of eligible children in a way that does not rely

on adding together two incompatible measures.

B-3

B.2.2 Data Incompatibility: Scale Disparity . The use of an additive

adjustment for updating involves another flaw in that the numbers of

children measured by the updating variable are not necessarily on the

same scale as the numbers of children measured by the baseline variable.

That is, each variable involves a measure of poverty, and there is no

guarantee that the two measures are consistent, particularly if one

measure (AFDC) is subject to change during the intercensal years and the

other (census) is not. One way to avoid this flaw is to use a multiplicative adjustment,* such as a percentage change. To use the census

and AFDC data as an example , the percentage change in AFDC might be taken

as an estimator of the percentage change in census data that would be

observed if the census were redone in the current year.

B.2.3 Geographic Bias . The present method of updating by adding AFDC

data to census data is also invalidated by the large interstate bias in

the AFDC data, due to differing qualification standards. (There is also

an intercounty bias within some states, but this is less pronounced^

than the interstate bias.) One way of indicating the interstate bias

empirically is by means of the coverage ratio defined in Chapter 2, i.e.,

the ratio of all school age AFDC children to school age poverty children

(based on the Orshansky index). Table B.2.1 shows the coverage ratios

for all states, arranged by state median income. (South Carolina is the

*A different approach, involving an additive adjustment, is developed

below, in Section B.3.2; it is shown to result in a form mathematically

identical to the multiplicative adjustment that was presented in

Chapter 2 and that is detailed in Section B.3.1.

B-4

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lowest, and New York is the highest.) As noted in the table, the actual

values shown there are inflated since the available AFDC data cover a

larger age span (0-20) than "school age" (5-17). As it turns out, this

is of no consequence in the way that the age span enters into the proposed

updating method, since an age span adjustment factor would cancel out of

the updating equation. (This is explained in Sections B.3.1 and B.3.2.)

A large part of the interstate bias in the AFDC data used in the

present updating method is due to the fact that AFDC children are counted

only in families receiving more than $2,000 a year from AFDC. When all

AFDC children are counted, without regard to the level of payments, the

changes over a period of time are more uniform among the states. In

Table B.2.2, the first column shows the percentage increase in the number

of Title I AFDC children from 1965 to 1971, (used for the FY66 to FY72

allocations) . The second column shows the corresponding increase in

the total number of AFDC children, aged 0-20. Since these are percentage

changes, the difference in age spans should not be important. The degree

to which the two statistics differ for each state is the degree to which

the two statistics measure different things. One way to see the interstate variation in the practical difference between these two measures

is to examine the ratio of one measure to the other, in the last column.

Since this ratio differs among the states, it matters whether the first

or second measure of increase is used.

Still another source of geographical bias, as well as irregularity

over time, is the unemployed-parent component of AFDC. This program is

optional with the states; about half of the states participate in it.

B-6

Table D.2.2

Percentage Increase in AFDC , 1965 to 1971

Percentage Increa.se In

(1) (2)

APDC All

above $2,000 AFDC (1) ~- (2)

Alabama 116% . _ * Alaska 459% 110 4 . 2 Ari zona 216 59 3 . 7 Arkansas 108-

California 455 168 2 . 7 Colorado 345 112 3 .

1

Connecticut 456 70 6 . 5 Delaware 99

Florida 138 m _ Georg ia 261 *. — Hawaii 371 121 3.1

Idaho 133 76 1.8

Illinois 156 95 1.6

Indiana 804 150 5.4

Iowa 194 70 2.8

Kansas 417 95 4 . 4 Kentucky — 73

Louis iana 6153 127 48 .

5

Maine 536 184 2.9

Maryland 472 97 4.9

Massachusetts 523 169 3.1

Michigan 608 134 • 4.5

Minnesota 239 96 2.5

Miss iss ippi 61

Missouri 214 37 5.8

Montana 280 153 1 ! 8 Nebraska 2082 131 15.9

Nevada 251 173 1 . 5 New Hampshire 415 208 2 . 0 New Jersey 551 291 1.9

New Mexico 252 96 2.6

New York 454 131 3.5

North Carolina 594 38 1.5.6

North Dakota 173 60 2.9

Ohio 345 82 4.2

Oklahoma 158 50 3.2

Oregon 341 195 1.8

Pennsylvania 270 89 3.0

Rhode Island 325 87 3.7

South Carolina ~ ~ 137

South Dakota 367 75 4.9

Tennessee 127

Texas 277 _ _ Utah 455 63 7.2

Vermont 904 186 4i9

Virginia 1292 155 8.3

Washington 277 88 3.2

West Virginia 17807 - 15 -1187.1

Wiscons in 239 123 1.9

Wyoming 171 81 2.1

Dist. of Columbia 419 198 2.1

*Dash indicates that there were no APDC children counted at the $2,000 level in 1965.

Thus in these cases the percentage increase is either infinite or indeterminate.

The past four years' data for New Jersey, shown in the following tabulation,

exemplify the irregularity of the unemployed -parent data.

AFDC Children

February of: Total Of Unemployed Parents (1)- (2)

1969 151,000 11,600 139,400

1970 214,000 36,200 177,800

1971 312,000 69,900 242,100

1972 272,000 272,000

Between 1969 and 1970 the number of children in the unemployed-parent

component in New Jersey more than tripled; in the following year it

nearly doubled again. In 1972 the program was dropped in New Jersey.

The total number of children shows a large increase in 1970 and 1971, and

a decrease in 1972. However, the number of AFDC children, exclusive of

the unemployed-parent component (in the last column), shows a comparatively

moderate increase in each year. Obviously, the loss of nearly 70,000

children from the AFDC cound in 1972 does not reflect a decrease in

poverty. New Jersey was chosen here as an illustration. The unemployedparent AFDC data for all participating states are given in Table B.2.3.

In general, it seems that the variation in the unemployed-parent

component does not reflect the trend in the number of children needing

compensatory education. Children of the chronically unemployed do relate

to the objectives of Title I, and these children are identified in the

census data and to a large extent, in the main AFDC component. Thus, one

source of interstate variation in the AFDC data can be removed by excluding

the unemployed-parent component.

B-8

Tabic B. 2.3

Number of Children (aged 0 -20) in

Unemployed--Parent Component of AFDC*

Feb. '69 Feb. '70 Feb. '71 Feb . '72

California 104 ,000 119,000 19 7,000 146,861

Colorado 3,800 3,300 6,700 6,652

Connect icut 850

Delaware 320 190 500 436

Hawaii 1,000 980 1, 600 2,801

Illinois 15, 300 16,400 37,300 58 , 7 74

Kansas 1,100 1,100 2,900 2,305

Maine 100 520 2,600** 431

Maryland 720 1 ,300 2,600 2,778

Massachusetts 3,300 10,900 6,200 6,871

Michigan 5,500 8, 200 24 , 700 38 ,920

Minnesota 2,400 4,934

Missouri 450 660 1,700

Nebraska 280 290 690 634

New Jersey 11,600 36,200 69,900

New York 63,400 47,200 64,400 28 ,142

Ohio 10,200 8,400 18,800 34,409

Oklahoma 1,800 980 1,000 1, 531

Oregon 8,100 16,000 18,800 13, 515

Pennsylvania 16,400 9,500 10,800 10,989

Rhode Island 1,200 1 , 200 2,300 2,688

Utah 4,200 4,200 5 ,700 6,527

Vermont 340 7on i x n n 1 , jUU 1 A ? ^ Washington 6,500 9,200 14,400 17,863

West Virginia 20, 200 i/i c n n 1 4 , b 0 U

i a Ann *~ 14 , 6 UU 0,14/

Wiscons in 3,900 7,255

District of Columbia 640 3, 298

Total 284,000 311,000 509,000 408 ,186

Number of States

Participating 25 23 25 24

*Blank indicates that the state elected not to participate in that

year. States not listed did not participate .In any of these years

**Apparently an error.

B-9

'4

B.2.4 Updating the Poverty Standard . Another part of the updating

process is the revision of the definition of poverty, to reflect

inflation. The present Title I provisions attempt to accomplish this

by changing the $2000 low income factor to $3000 in FY68 and to $4000

in PY73. However, under conditions of under funding the factor reverts

to a lower level, as provided elsewhere in Title I, and in fact the

low income factor has remained at $2000 throughout the history of Title I.

Consequently, in the census data used for Title I allocations, there has

never been an adjustment for inflation. Furthermore, if such an adjustment had materialized, there would have been substantial distributional

shifts. This undesirable side effect was explained in the previously

cited Interim Report of March 1972, beginning on page C-10.

These considerations point to the need for an effective but smooth

inflation adjustment such as the built-in Consumer Price Index adjustment

in the CPS data.

B.3 Alternative Method

B.3.1 The Multiplicative Factor . Chapter 2 describes an alternative

method of updating, which uses a multipicative adjustment factor on the

assumption that the "true" change in the Title I eligible population in

each county is best approximated by the ratio expressing the change in

the local AFDC data. Symbolically,

W

c Kc

= K

b x WT > b

B-10

where K is the number of eligible children in a county,

W (for "welfare") is the number of AFDC children in

the same place,

the subscript c means current, and

the subscript b means as of the time represented by the

baseline (census) data.

This avoids the principal objection to the concept of an additive adjustment as presently used in Title I, namely, that the AFDC data as a whole

are out of scale with the census data and that the AFDC data for the

several counties or states are out of scale with each other due to

different coverage in different places. Except for coverage changes

that may occur after the base year, the intercounty (and interstate)

variation in coverage is eliminated in the ratio W* /W, •; that is, each

county's current AFDC datum is compared only with the same county's base

AFDC datum, and not directly witli that from any other county or state.

However, if the AFDC coverage changes in that county, W reflects

a different coverage than W^, and thus the ratio W /W, is biased in

proportion to the coverage change. Chapter 2 observed that at the

national level the coverage apparently has been increasing. The normalization process (discussed in detail in Sections B.3.3 and B.3.4) adjusts

for the national trend in coverage. But since this adjustment is applied

to each county, each county's normalized value is only partially corrected

for coverage changes. That is, each county value is still biased in

proportion to the ratio of its own coverage change to the national

coverage change. Therefore, this residual bias is the major weakness

in this updating procedure.

B-ll

As explained in Chapter 2, the A3 DC data used in this method represent

children aged 0-20 in all AFDC families, except those in the unemployedparent component. The bias due to the broader age of the AFDC data (as

opposed to the census data) is cancelled out by the W /W, ratio.

As noted in Chapter 2, the AFDC data used in this study are 24 -month

averages of state totals. The months used for W

c were September 1970

through August 1972, and those for W, were January 1969 through December

1970 since the census data represent the 1969 incomes of persons enumerated

in 1970. The monthly data at the state level are available from the SRS

publication cited in Table B.2.1. Data by county are available only for

February of each year.* In order to obtain monthly data by county it

would be necessary to institute a survey of all the states.

B.3.2 An Additive Approach . As noted in Chapter 2, a different approach

to the alternative updating method is to use an additive adjustment, based

on the assumption that the arithmetic difference in a county's Title I

eligible population for two years is equal to the difference in the

(a. corresponding AFDC data when adjusted in scale by the local coverage

ratio. Symbolically,**

K = K, + (W - W, ) ~ . c b

v c b Wb

^Recipients of Rib "lie Assistance Money Payments and Amounts of Such

Payments, by Program, State, and County , NCSS Report A- 8 Social and

Rehabilitation Service, National Center for Social Statistics, DIIEW,

published annually.

**To update county Orshansky data, 24 -month averages of state AFDC data

can be applied to the multiplicative method by assuming the constancy

of the county shares within a state. Practically, however, only the

February AFDC data can be used for the additive method as applied to

counties at present.

B-12

The ratio at the end multiplies the AFD.G increment by the reciprocal of

the local coverage in order to adjust it to the scale of K. Since W

appears in both the numerator and the denominator of the additive term,

no adjustment for the larger age span of W is necessary, i.e., it would

cancel out anyway.

But this equation is actually the same as the equation in Section

B.3.1 using the multiplicative adjustment. Manipulating the right side

of the present equation,

W - W, ebb W, . b

W W, K

c

- K

'b

c 1 + wf - w>

b b

W

c b Hvu

b

which is the multiplicative adjustment.

B.3.3 Normalization . The updated distribution is normalized to a

national total estimated from the CPS. Since the sampling basis of**the

CPS is different from that of the decennial census, estimates from those

two sources are not strictly comparable. Therefore the actual value

derived from the CPS should not be used to normalize a distribution

based on the decennial census. On the other hand, the rate of change

in the CPS data is applicable to such a distribution since the populations

measured by the CPS and census data can be assumed to change at the same

rate. Thus the current total of a poverty population can be estimated

B-13

by multiplying the decennial census total by the ratio of the current

CPS total to the CPS total for 1969. The CPS data labelled 1969 correspond

to the 1970 census data since the former refer to the 1969 income of

families enumerated as of March 1970, while the 1970 census data refer

to the 1969 income of families enumerated as of April 1970.

To scale a distribution up or down such that the resulting distribution has a desired total, it is necessary only to multiply each element

by a ratio whose numerator is the desired total and whose denominator is

the actual total. The normalization procedure is illustrated in the

sample calculations in B.3.4.

B.3.4 Sample Calculations . This section illustrates the alternative

updating method and provides data examples and data source citations.

Table B.3.1 shows the state totals of the census data used (at the

county level) in this study. The sources of both the 1960 and 1970

census data were special tabulations produced by the Census Bureau under

contract to the National Center for Educational Statistics, USOE. Jji the

1970 census, data on children 5-17 years old in families below the $3,000

level are also available from the Fourth Count computer tapes, a standard

census product available to the public. Those data do not exactly match

the special tabulation data because the Census Bureau made certain

corrections to its basic records (the common source of the Fourth Count

and the special tabulation) after the Fourth Count was produced and

before the special tabulation was.

B-14

Table B.3.1 Children S - 17 Years Old in Families

Below Specified Annual Income Levels

1960 1970

$2 000 $2,000 $3,000 Orshansky

Alabama 242 , 522 95,984 151 ,759 7 7 7 1 & A 1 1 O Alaska 4, 796 4,262 6.4S6 1 7 1Q7

I J 7 J Ari zona 38 , 851 . 29,328 46,092 Q A O 4

r\i a

, U 1 4 Arkansas 148, 158 52,247 86,114 19ICC9 , 1 J J Cal ifornia 206, 572 214,413 331, 209 J " J , / O J Colorado 33, 581 25,367 39,618 7 i 7 C A Connecticut 20, 731 22,226 32,918 c r

;> 5 net , Uo J Delaware 7, 422 S.5S6 8,951 1 1 771 Florida 142, 533 100,693 162,886 c y y

C 1 C

t J / J Georgia 239, 789 93,139 155,733 293 ,8 71 Hawaii 8, 832 7,229 10,384 1

9

,465 Idaho 12, 257 7,397 12,009 2 3

7 1 A

, / 1 O Illinoi- 147, 518 103,780' 163,013 302 ,311

Indiana 76 386 41,836 66,780 • 1 AO a a a 4 O 4 Iowa 71 789 22,459 37,830 7 1

, 000 Kansas 40 263 22,133 34,770 64 ,621

Kentucky 193 559 68 ,780 120,390 2 08 ,4 62 Louisiana 201 090 114,600 178, 5S2 O U 0 orn Maine 18 408 10,067 16,489 36 308 Maryland S3 716 43,120 66, 73S 116 ,9 51 Massachusetts 47 065 41 ,679 64 ,045 116 90 0 Michigan 124 712 83,713

' 126,146 2 2 0 4 8 5 Minnesota 77 280 31.885 51,491 98 936 Mississippi 254 903 98,695 152,715 261 ,679

Missouri 125 159 59,163 95,193 172 955 Montana 14 106 8,182 13,831 24 998 Nebraska 34 417 15,831 25,413 4 5 9 5 2 Nevada 3 238 3,964 6,417 1 A 8 90 New Hampshire 5 ,932 4,538 7,392 1

4

7 Q A too New Jersey 59 ,845 57,733 86.14S 15 5 690 New Mexico 37 ,554 27,942 43,763 8 0 5S9 New York 200 ,060 194 ,566 292,498 526 402 North Carolina 323 ,096 99,224 166, 80S 312 545 North Dakota 2 3 346 8 06 5 12 899 27 354 Ohio 1S1 |310 104 ',125 162,'993 273 542 Oklahoma 84 , 7 79 37,316 66,465 122 548 Oregon 23 ,933 19,583 31 ,382 S3 953 Pennsylvania 175 ,394 102,040 160,892 304 8*5 Rhode Island 12 ,083 8 ,805 13,857 24 482 South Carolina 206 ,638 71,844 111,118 206 985 South Dakota 30 ,712 10,763 18,095 33 815 Tennessee 220 ,048 81,832 133,221 245 157 Texas 398 ,224 192,639 318,420 636, 776 Utah 11 ,680 9,638 16,438 30, 796 Vermont 7 ,208 3,489 5,627 13 062 Virginia 167 ,844 67,779 111,847 214, 357 Washington 33 ,072 29,722 45,577 80 172 West Virginia 106 ,406 35,484 60,468 106, 3S9 Wisconsin 58 ,446 34,579 56,441 103, 89S Wyoming 5 ,4 08 3,314 5,408 10, 054 Dist. of Columbia 14 ,854 13,081 20,178 37, 193

4,947 ,525 2,645,838 4,211,888 7,700, 368

B-15

Table B.3.2 lists the AFDC ratios, i.e., the multiplicative factors,

used for the distributional updating adjustment. Multiplying the Alabama

factor by the number of children indicated in the $3,000 census data

yields an adjusted number of children:

1.20387 x 151,759 = 182,698.

Similarly, for the Orshansky data:

1.20387 x 272,146 = 327,628.

When this adjustment is made to every state (actually, to every

county), the national totals of the adjusted $3,000 and Orshansky data,

respectively, are 5,741,561 and 10,533,295. It is known in advance,

however, that these totals are greater than the respective totals of the

census data for two reasons, i.e., the multiplicative factor represents

two effects: (1) the slight general increase in poverty, as indicated

by the CPS data, and (2) the considerably greater general increase in

AFDC coverage. The normalization process retains the first of these and

excludes the second.

To generate the normalizing factor, it is necessary to know two

values: the scale from which to normalize, arid the scale to which to

normalize. The first of these is simply the sum of the distribution at

its present adjusted stage. The second is the current number of poverty

children, estimated from the CPS and census data.

For the $3,000 level the estimate is calculated as follows. The

Census Bureau's Current Population Report, Series P-60, No. 85, p. 31,

gives the income distribution for several years in terms of constant

B-16

Tabic H. 3. 2 Distributional Updating Factors

Alabama

Alaska

Arizona

Arkansas

California

Colorado

Connecticut

Delaware

Florida

Gcorg ia

Hawaii

Idaho

Illinois

Indiana

Iowa

Kansas

Kentucky

Louisiana

Maine

Maryland

Massachusetts

Michigan

Minnesota

Mississippi

Missouri

Montana

Nebraska

Nevada

New Hampshire

New Jersey

New Mexico

New York

North Carolina

North Dakota

Ohio

Oklahoma

Oregon

Pennsylvania

Rhode Island

South Carolina

South Dakota

Tennessee

Texas

Utah

Vermont

Virginia

Washington

West Virginia

Wiscons in

Wyoming

Dist. of Columbia

1. 20387

1.32104

1 . 29100

1. 43602

1. 32104

1.39479

1. 26744

1.35202

1. 38647

1.44927

1. 35262

1.29481

1.48333

1.83361

1. 21365

1.30400

1. 09.703

1.17019

1. 54042

1.31959

1. 28447

1.62567

1.34389

1.23808

1. 38185

1.40332

1.28896

1.27443

1.74959

1.42450

1.11290

1.18539

1. 26599

1. 21356

1.38135

1.15098

1. 29725

1.39261

1.20567

1.56967

1.21953.

1. 34670

1.70539

1.19969

1. 25677

1.51233

1.24396

1.05571

1.34897

1. 26087

1.71221

B-17

dollars. The most recent (1971) data are used for the "current" estimate.

Now, this CPS report does not give direct.]/ the number of children 5-17

years old. It gives the total number of families in the U.S. (53,296,000)

and the percentage of them below the $3,000 level (8.3%).* Multiplying

these gives 4,423,568 families. The corresponding number of families for

1969 (which corresponds to the 1970 census) is 4,150,197. The ratio of

these two numbers is 1.0658692; this ratio expresses the 1969-to-1971 growth

in poverty, as measured by the $3,000 income level. When this ratio is

multiplied by the 1970 census datum for children 5-17 years old in

families below the $3,000 level, the updated estimate for the national

total of such children results:

1.0658694 x 4,211,888 = 4,489,323.

This is the other value needed for the normalizing factor, which can now

be computed as

4,489,323/5,741,561 = 0.78189938.

*A1 though the percentage figure has only two significant digits, the

sampling error of the CPS limits the precision to about that amount, so there would be little point in going back to the unpublished CPS data

to get the number of families below $3,000 more directly. In the

ensuing calculations, nevertheless, enough significant digits are carried to avoid introducing additional errors in the intermediate

steps, since such errors are compounded through the course of the

computation. It is the end result of the computation that the accuracy

limitations should be reflected; ultimately this means in the grant

allotments

.

It is evident that the accuracy of the data, including the decennial

census and APPE data, may not justify all of the painstaking data manipulation procedures of the past. The implications of this, however, are not self-evident. The technical aspects of this problem are now being

investigated.

B-18

Multiplying the estimate previously derived for each county (from the

AFDC ratio) by this normalizing factor completes the updating process.

Illustrating with the total for Alabama:

182,698 x 0.78189938 = 142,851,

which is the number given for Alabama under enumeration in Table 2.3.2

in Chapter 2.

The normalization of the Orshansky distribution is somewhat simpler,

because the CPS publication (Current Population Report, Series P-60,

No. 86, p. 29) gives the number of poverty children under 18 years old.

Dividing the 1971 value by the 1969 value gives:

10,344,000/9,501,000 = 1.0887275

as the two-year growth in poverty, as measured by the Orshansky index.

Multiplying this by the 7,700,368 children indicated in the Orshansky

census data yields 8,383,602 as the current national total of such

children. Dividing this by the total of the AFDC-adjusted Orshansky

data (10,533,295) gives the normalizing factor of 0.7959145, which is

then applied to the AFDC- adjusted Orshansky datum for each county. Again

using the Alabama total to illustrate, the previously derived 327,628

multiplied by the normalizing factor yields the 260,764 listed for

Alabama under enumeration in Table 2.3.2.

B.4 Total School Age Population

When the concentration of poverty is an element of the cost factor

(see Section 2.4), one more updating problem arises. The concentration

is defined as the ratio of the eligible children to the total school age

B-19

population. In this study the total population data were taken from the

census but were not updated since no updating data arc presently available

However, such data will be available by late 1973 or early 1974 from a

new Federal-State Cooperative Program for Population Estimates being

implemented now under the auspices of the Census Bureau. This program

will provide total population data for each county. The population change

indicated by these data could be used to update the school age population

data. It is possible that age-specific population estimates will be

available annually at some later time. If so, these would provide a

more direct means of updating the school age population data by county.

B-20

I

Appendix C

STATE ALLOTMENTS BASED ON ALTERNATIVE FORMULAS

This appendix presents the allocations for each state as computed using sixteen variations of the formula components.

As noted in Chapter 3, there are 960 possible combinations

of formula components that might be considered. Of the 150

combinations that were analyzed, the resulting allocations

for sixteen are presented in this Appendix. These are among

the combinations suggested as providing the most potential

improvement over the existing formula.

The allocation results, which follow, are presented in

eight pairs of tables. In each pair, the combination of

formula components is the same except the first table shows

allocation levels based on the proportional method of

reduction and the second table reflects the nonproportiona-1

method (SEA entitlements are fully fundedj.

The specifications for the formula components, as used

for this presentation, are as follows (each of the eight

consists of proportional and nonpropor tional reduction)

:

C-1

Formula Components

Enumerat ion Cost Factor Concentration

— — 1 Floors

1 Orshansky with

AFDC Ratio

50% of SAPPE None 90% of FY 7

2 50% of SAPPE None None

7. ii 50% of SAPPE Mode rat

90% of FY72

4

,, 50% of SAPPE Moderate None

5

,, $300 None 90% of FY 7

6 $300 None None

:

$300 Moderate 90% of FY72

$300 Moderate

,

1 None

i

The computations are based on an appropriation level of

$1.5 billion, not counting Parts B and C or the outlying areas.

The allocations are presented as the computer printed the

results; for each state, the allocation is listed for LEA,

SEA, administrative grant, and total allocation.

For example, in Table C.l.l (formula variation number one,

proportional reduction) it can be seen that column one presents

total LEA allotment for each state, e.g., Alabama receives

$36,231,421. Column two, entitled "State agency", presents

the total SEA allotment for each state, e.g., Alabama receives

$584,692. Column three presents the administrative grant

and column four presents the total allocation (LEA + SEA

+ administrative) for each state.

I C-2

The tables contain four additional columns with headings,

Notes 1 through 4. Notes 1, 3, and 4 present information of

value only for internal accounting purposes and therefore,

should be disregarded. However, Note 2, which presents the

total allocation as a percentage of the authorization, should

be of interest to the reader.

For example, in Table C.l.l it can be seen, under

"Note 2", that the total allocation, $37,184,274, received

by the state of Alabama is only 51.91% of the authorized

entitlement. Thus, it may be inferred that if full funding

were to occur, Alabama would receive $71,632,198.

C-3

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