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I
I
77-11,618
BECK, John Henry, 1949STATE AID AND EQUAL EDUCATIONAL
OPPORTUNITY IN MICHIGAN.
Michigan State University, Ph.D., 1976
Economics, general

Xerox University Microfilms,

Ann Arbor, Michigan 48106

STATE AID AND EQUAL EDUCATIONAL
OPPORTUNITY IN MICHI G A N
By
John Henry Beck

A DISSERTATION
Submitted to
Michi g a n State University
in partial fulfillment of the requirements
for the degree of
DO C T O R OF PHILOSOPHY
Department of Economics
1976

ABSTRACT
STATE AID AND EQUAL EDUCATIONAL
OPPORTUNITY IN MICHIGAN
By
John Henry Beck

In an effort to make education expenditures inde­
pendent of school district wealth, many states including
M i c h i g a n have adopted variants of "percentage equalizing"
state aid formulas.

Under such formulas all districts

are guaranteed equal dollars per pupil for each mill
levied regardless of the size of the local tax base.
There is a "matching" effect in that an increase in local
tax levies will increase state aid as well.
In districts receiving matching aid the marginal
"price" to local voters of one dollar of per pupil educa­
tion expenditures is less than one dollar.

Theory pre­

dicts that non-residential shares of the property tax
base are also factors in the "price" of school expendi­
tures although the stimulative effect may be less than
that of the matching rate if voters believe that some of
the taxes on non-residential property w i l l be shifted to
themselves.

Theory also predicts that the marginal impact

of family income on education expenditures should be equal

John Henry Beck
to the m a r ginal impact of a r e s i d e n t ’s share of noncategorical,

lump-sum aid.

This study uses regression analysis of the d e t e r ­
minants of education expenditure levels to test the above
hypotheses.

The results are used to predict the effects

of changes in the Mich i g a n school aid formula on the level
and distri b ution of expenditures wi t h i n the state.
The stimulative effect of non-residential property
is found to be significantly greater than,
less than,

that of the matc h i n g rate.

rather than

There is some indi ­

cation that this stimulative effect is greater in m e t r o ­
politan areas where there is less fear of loss of jobs
from raising taxes on industrial property or higher prices
from increasing levies on commercial property.
The marg i n a l impact of lump-sum aid is greater
than the m a rginal impact of family income,
to expectations.

also contrary

The characteristics of the distribution

of income w ithin the school district had no significant
effect on per pupil expenditures.
A lagged adjustment process is derived in which
millage rates adjust with a delay,

allowing increases in

l ump-sum grants to temporarily raise expenditures above
the new e q u i l i b r i u m level.

The estimated lag is long,

with only about half of the difference bet w e e n actual and
desired m i l lage rates being eliminated wi t h i n two years.

John Henry Beck
When inequality of expenditure levels is measured
by the Gini coefficient,

the change to percentage e q u a l ­

izing in M ichigan is found to have reduced inequality.
«

The remaining inequality in expenditures still is p o s i ­
tively related to state equalized value per pupil.

If

the c u r rent m a x i m u m on the local levy subject to matching
aid is removed,

predicted expenditures show an increase

in inequality as measured by the Gini coefficient but a
decrease in inequality associated w i t h differences in SEV
(state equalized valuation)
Recapture provisions,
we althy districts,

per pupil and in family income.

imposing negative matc h i n g rates on

only partially offset the increase in

inequality from lifting the ceiling on matc h i n g aid, but
further reduce the inequality associated w i t h SEV per
pupil and family income.

Contrary to studies based on

Massachusetts data, unlimited percentage equalizing with
recapture would not lead to a negative relationship
between SEV per pupil and expenditure levels in Michigan.
While inequality in per pupil expenditures would
have been greater under the 1972 foundation aid plan than
under any of the three variants of percentage equalizing,
a foundation plan w i t h higher levels of aid w o u l d result
in a more equal distribution of educa t i o n expenditures as
measured by the Gini coefficient.

The ranking of the five

aid formulas considered is u n a f fected by the use of the
Atkin s o n inequity measure rather than the Gini coefficient.

ACKNOWLEDGMENTS

I am grateful to D r . James L. Phelps for the
opportunity to participate in meetings of the School
Finance Research Group and to T o m Nicol, research analyst
with the M i c h i g a n Office of the Budget for assistance in
the use of the school district data tape.

Eileen Healy,

of the Office of Revenue and Tax Analysis, provided
access to data on the composition of the property tax
base by civil divisions,

and Pam Ma r v e l and Jacqueline

Grossman of the Michigan State University Department of
Agricultural Economics furnished preliminary estimates of
the portions of civil divisions falling in school d i s ­
tricts .
M y greatest thanks are to Professor Byron Brown,
chairman of my dissertation committee.

TABLE OF CONTENTS
Page
LIST OF

T A B L E S ......................................

vi

LIST OF

F I G U R E S .......................................... vii

Chapter
I.

INTRODUCTION

................................

The Case for Equal Educational
............................
Opportunity
The M i c h i g a n State A i d Plan
. . . .
Behavior Under Percentage Equalizing
.
O utline of the Following Chapters
. .
II.

R E V I E W OF STUDIES OF THE DETERMINANTS OF
E DUCATION EXPENDITURES .....................
T h e o retical Basis of Expenditure
D e t e rmination
.........................
The Dependent Vari a b l e
..................
Taste , In terest Group and Other
V a r i a b l e s ................................
Popula t i o n and Pupil Density and
Urbanization
.........................
Proportion of Public Students in
Secondary School .....................
Scale Economies and the Political
Effects of Larger Districts
. . .
"Interest Group" Varia b l e s
. . . .
Variables Reflecting Different Expec­
tations and Aspirations
. . . .
Other V a r i a b l e s .........................
The Price V a r i a b l e .....................
The Local and Residential Share
F a c t o r s ................................
Possible Perceived Shifting of
Non-Residental Taxes
..............
Problems in Identifying the M e d i a n
Voter's Share of the Tax Base
.
.
The Input Price Factor
..............
The Pupils Per Family Fa c t o r
. . .
Comparison of Estimates of "Price"
E l a s t i c i t y ............................
iii

1
2
7
17
24
26
27
31
34
35
38
39
44
54
58
59
61
65
70
71
73
76

Page

Chapter
Ability to Pay V a r i a b l e s ..............
Reasons for N o t Using Assessed
V a l u e Per P u p i l .....................
Estimates of Income Elasticity . . .
Variables Reflecting Permanent
I n c o m e ................................
Effects of the D i s t ribution of
I n c o m e ................................
The Effects of Non-Matching Aid
.
.
Comparison of the Effect of Block
G rants and Disposable Income . . .
The "Municipal Overburden" Issue
. .
The Functional Form of the Expenditure
E q u a t i o n ...............................
III.

82
83
89
93
98
100

106
Ill
113
117

RESULTS OF ESTIMATION OF THE EXPENDITURE
E Q U A T I O N ................................... 124
The Effect of the Price Variable . . .
Effects of N o n - M atching Aid and
Municipal Over burden
..................
Effects of Income and the Distribution
of I n c o m e ................................134
Effects of Other Variables ..............
Estimates of the Distributed Lag
R e s p o n s e ................................137
Comparison W i t h Estimates Based on
Earlier Years
.........................
C o n c l u s i o n ................................142

V.

79
80

PROCEDURES F O R ESTIMATING THE EXPENDITURE
E Q U A T I O N ....................................... 106
The Structure of an Hypothesized
Lagged Response .........................
A Test of the Equivalence of the Price
Effects of Non-Residential Property
and M a t c h i n g Aid
. . . . . . .
Threats to the Consistency and Effi­
ciency of OLS E s t i m a t e s ..................
The D a t a .......................................

IV.

79

THE DEGREE OF INEQUALITY IN ACTUAL
EXPENDITURES A N D IN PREDICTED E X P E N D I ­
TURES U N D E R AL T E R N A T I V E AID FORMULAS
.

.

The D i s t r ibution of Actual E x p e n d i ­
tures
................................... 143
Measures of the Distribution of Pre­
dicted S p e n d i n g .........................144
iv

125
131
135

14 0

14 3

Chapter

Page
Comparisons With Alternative Aid
P l a n s ....................................... 148
C o n c l u s i o n ................................151

VI.

SUMMARY A N D C O N C L U S I O N S ...................153

BIBLIOGRAPHY ..........................................

v

15 9

LIST OP TABLES
Table

Page

1.

Survey Results Regressed o n Allot t e d Tax
Base S h a r e s ....................................119

2.

Symbols and Definitions of Variables

3.

Regression Results for Expenditures Per
Pupil, 1974-75

126

4.

Other Regression Results

138

5.

Actual Expenditures in 1972-73 and
1974-75 .......................................

6.

.

.

.

.....................

121

144

Distribution of Predicted Expenditures for
371 D i s t r i c t s ....................................145

LIST OF FIGURES
Figure

Page

1.

Budget Constraints w i t h

2.

Individual Choice at Different Income
L e v e l s .......................................

vii

State Aid

.

.

.

.

15
87

CHA P T E R I
INTRODUCTION

In an effort to make education expenditures inde­
pendent of school district wealth, many states including
M i c higan have adopted variants of "percentage equalizing"
state aid formulas.

Under such formulas all districts

are guaranteed equal dollars per pupil for each mill of
local school taxes levied regardless of the size of the
local tax base.

The purpose of this study is to analyze

the degree to w h i c h the current Mich i g a n aid formula has
reduced inequality in per pupil spending and how m o d i f i c a ­
tions of the aid formula would affect the distribution of
e ducation expenditures.
This introductory chapter discusses arguments for
equalization of education expenditures,

the provisions of

the M i c h i g a n state aid formula designed to achieve equali­
zation,

and what other studies have shown about the

effects of similar formulas.

The concluding section out ­

lines the contents of subsequent chapters of the present
work.

1

2
The Case for Equal Educational
Opportunity
The desire to equalize educational opportunity has
led Coons,

Clune and Sugarman to advocate the normative

principle that "the quality of public education m a y not
be a function of wealth other than the total w e a l t h of
the state."

Stating the principle raises the question

of why state government ought to follow the proposed norm.
One answer to this question is simply that the
state c o n s titution requires it.

This was the ruling of

2

the California Supreme Court in Serrano vs. P r i e s t .

A second possible reason for adhering to the p r o ­
posed n o r m is that it achieves a desirable distribution
of income.

The concern here is w i t h the d i s t r ibution of

income w i t h i n the future generation.

Providing equal e d u ­

cational opportunities presumably achieves the desired

John E. Coons, W i l l i a m H. Clune, III, and Stephen
D. Sugarman, Private Wealth and Public Education (Cam­
bridge, Mass.":
Harvard University Press, Belknap Press,
1970), p. 304.
2
Cf. Advi s o r y Commission on Intergovernmental
Relations, Finan c i n g Schools and Property Tax Relief:
A
State Responsibility (Washington, D . C . : Govern m e n t Printm g Office, January 1973), pp. 101-102, for a brief sum­
mary of r e levant court cases, and R. Stephen Brow n i n g and
David C. Long, "School Finance Re f o r m and the Courts after
Rodriguez," in John Pincus, e d . , School Finance in Tran­
sition:
The Courts and Educational Re f o r m (Cambridge,
M a s s .:
B a llinger Publis h i n g C o . , 1974), pp. 81-105, for
a more e x t ensive discussion.

3
income distribution b y affecting the future earning power
of s t u d e n t s . 1
A third reason depends on the existence of e x t e r ­
nal benefits of education extending be y o n d the boundaries
of school districts.

Children may later move out of the

district and the quality of their previous education wil l
affect their new neighbors.

For example,

a good e d u c a ­

tion will enable t h e m to participate as informed citizens
in the democratic processes of their c o m m u n i t i e s , but a
poor education may prevent them from getting jobs and
leave them a burden on the wel f a r e rolls in their new
location.

Without state or federal corrective action,

the existence of externalities results in a socially suboptimal level of public education being provided by local
school districts.
If the marginal external benefits of education
are greater in those districts w i t h lower expenditure
levels,

it is optimal for the state to give a larger

stimulus to raise expenditure levels in those districts.
However,

an alternative assumption that marg i n a l benefits

are larger in high

socioeconomic

districts w h e r e e x p e n d i ­

ture levels are already higher implies that state aid,

1Cf. Gail R. Wilensky, State A i d and Educational
Opportunity (Beverly Hills, C a l i f . : Sage Publications,
1970), pp. 26-29.

4
following an efficiency criterion,

should be allocated in

a manner increasing the disparity in expenditure levels.^"
Nor need the assumption that marginal external
benefits are greater in low socio-economic districts imply
that all differences in educational expenditures should
be eliminated.

Exceedingly high expenditures may be for

school services that are private goods providing no e x t e r ­
nal benefits to those outside the district.

There is

no efficiency argument for state aid bringing expenditures
in poor districts up to such high levels.

This provides

a rationale for upper limits on percentage equalizing
aid.

Equalizing expenditures beyond the level w h e r e m a r ­

ginal external benefits are zero m u s t be justified as a
preferable method of achieving desired redistribution of
income.
A llowing inequality in spending levels m a y have
beneficial effects in the long run.

High expenditure d i s ­

tricts can experiment w i t h innovative educational methods
that may later be adopted by other districts.
A c hieving equality by a one hundred percent state
funding system as in Hawaii eliminates the freedom to
choose expenditure levels in accordance with local
tastes.

Even aid formulas designed to compensate for

wealth differences while allowing variations due to tastes
1 Ibid., pp.

24-25,

127-128.

5
may be regarded as penalizing residents of districts pr e ­
ferring low expenditure levels because they will not get
"their share" of state aid financed by their state tax
dollars.

On the other hand, wea l t h y districts desiring

high expenditure levels are "penalized"
if "recapture" provisions

for their tastes

take a share of their local tax

revenues for the state aid fund.

The recapture provision

in the W i sconsin aid plan is currently b e i n g contested in
the courts.
Rich residents of districts subject to recapture
might put their own children in private schools and vote
for low levels of public school support,

leaving children

from lower income families in these communities with
inferior public education.^
Plans that provide for m a t c h i n g aid to education
may distort choice to the detriment of other public serv­
ices if the stimulus to education spending results in
reductions of other expenditures.

2

There is also an

incentive to include as many services as p o s s i b l e — recre ­
ation,

libraries,

transportation— under the school budget

in order to receive matc h i n g aid.

cation

^ C o o n s , Clune, and Sugarman, p. 278.
2
Charles S. Benson, The Economics of Public Edu­
(Boston:
Houghton Mif f l i n C o . , 1961), p ~ . 245.
3
Coons, Clune, and Sugarman, p. 212.

6
Some writers have questioned the relationship
between equal educational opportunity and equal dollar
expenditures per pupil.
Expenditure differences may fail to reflect
the true variation in educational quality or even
in amounts of real resources devoted to education
because of the differences in the efficiency w i t h
w hich school districts operate, the differences
in the prices they must pay for equivalent goods
and services, and the differences in the e d u c a ­
tional tasks confronting them.l
Some opponents of equalizing expenditures have argued that
equalization wo u l d result in inferior educational oppor­
tunities in urban areas b ecause of the greater need for
compensatory education and the higher costs of inputs in
central cities.

However,

it is quite possible to make

allowances for such considerations in aid formulas.

For

example, Minnesota counts each AFDC child as an additional
half pupil unit in calculating state aid.

This presumably
2
reflects the need for compensatory education.
Lastly,

there is the ques t i o n of whe t h e r exp e n d i ­

tures have any effect on schools'

output.

Some scholars

claim they do:
. . . as might be expected logically because all
the foregoing components [affecting student p e r ­
formance] translate into dollar costs, we find

Robert D. Reischauer and Robert W. Hartman,
Reforming School Finance (Washington, D . C . : Brookings
Institution, 1973), p. 60.
2
Advisory Commission on Intergovernmental R e l a ­
tions, Financing S c h o o l s , pp. 104-105.

7
that measures such as expenditures per pupil and
teachers' salary levels are correlated signifi­
cantly w i t h pupil achievement m e a s u r e s . 1
Even those taking an opposing v i e w do not claim that
increasing spending will have no benefi c i a l effect.
. . . the teacher characteristics w i t h the g r e a t ­
est effect on pupil achievement are not those
that are actually purchased.
Under such circumstances it is only to be
expected that money per se has a small influence
on the results of schooling.
Yet this does not
mean that additional spending, if properly
directed, w o u l d not b ring about some improvement
in pupil achievement.
Having recognized the weaknesses in m e a s u r i n g
educational opportunity by expenditure levels,

the prese n t

study nevertheless takes per pupil spending as the measure
of educational quality.
The Mich i g a n State Aid Plan
One me t h o d of realizing "equal educational o p p o r ­
tunity" is for the state to provide all funds for public
education and distribute these funds to districts on the
basis of equal per pupil expenditures.

However,

this

would eliminate local choice regarding the level of
expenditures.

The me t h o d advocated by Coons, Clune and

Sugarman to make educational expenditures independent of
w ealth and yet allow varia t i o n in expenditures according
^James W. Guthrie et al. , Schools and Inequality
(Cambridge, Mass.:
M I T Press, 1971), p. 81.
2
A dvi s o r y Commission on Intergovernmental Rela­
tions, F i n ancing S c h o o l s , p. 248.

8
to local tastes was

"power equalizing" state aid.

simplest f o r m of power equalizing,
the ratio of matc h i n g state

aid^

In the

"percentage equalizing,"
to the sum of m a t c h i n g

aid and local revenues is given by the formula
»« _ -i
w
x

local w e a l t h
key district wea l t h

*
U.-U

where w ealth is me as u r e d in terms of assessed v a l u a t i o n
per pupil.
B eginning w i t h the 1973-74 school year,

the State

of M i c higan distributed aid to local school districts
according to a modi f i e d percentage e q u a lizing formula.
For that year "key dist r i c t wealth"
per pupil.

2

in

(1.1) was $38,000

The law differed from formula

(1.1)

in sev ­

eral respects:
1.

It granted matc h i n g state aid only up to a

local levy of 22 mills in 1973-74.
2.

Districts had the option of r e c e iving the

amount of aid received in 1972-73 adjusted for changes
in state equalized valuation per pupil.

^■"Matching aid" refers to aid w h i c h increases in
amount as local tax rates are i n c r e a s e d .
2

This formula only applied to opera t i n g levies.
Millages for retiring operating deficits are included in
operating levies.
A separate provision, Section 27 of
the State School Aid Act, took effect in 1974, p r o v i d i n g
for equalization of buil d i n g fund and d e b t r e t i r e m e n t
millages conditional on a reduction in such local levies
equal to the amount of aid.

9
3.

Districts were guaranteed no decline in total

aid for two years
4.
use,

following annexation or consolidation.

Districts

levying less than 20 mills could

for purposes of computing aid,

their actual millage

plus two-thirds of the difference bet w e e n 20 mills and
the actual millage.
5.

There were no "recapture" provisions.

Dis­

tricts above the key district w e a l t h did n o t make payments
into the state school aid fund.
For districts not falling under any of the above
exceptions in 1973-74,

M 73

1

formula

(1.1) gives

38,000

(1.2)

where W 73 Is state equalized valuation per pupil for
1973-74.

For districts levying operating millages above

the 22 mill limit,

there was no m a t c h i n g aid but a per

pupil block grant B 73 °f the amount
B 73 = .022

(38,000 - W 7 3 )

(1.3)

F or districts falling under the "grandfather
clause" p r o t ecting districts from a decline in aid c o m ­
pared to the amount received in 1972-73 there was no
matching aid and all aid was a block grant.
B ?3 = m a x { [B?2 - .020
[B72 - r 72

(W?3 - W ? 2 )]

(W73 - W 7 2 )J}

10

where r ?

M7

3

= 0

2

was

(1.4)
operating tax rate in 1972-73.

The annexation guarantee also had the effect of
making all aid a block grant in cases in w h i c h the guar­
antee was operative because the amount of aid was the
amount received prior to annexation regardless of the
local millage rate.
For districts

levying less than 20 mills,

there

was a block grant independent of the millage rate and
matching aid w h i c h increased as local levies were raised.

M 73

b ? 3

3
W 73
38,000 + 2 W ?

1

= ^

3

^

3

(38,000 - W ? 3 )

(1.5)

The matc h i n g rates derived above w e r e modif i e d by
the provision for municipal overbu r d e n aid.

If total

property tax rates in the district levied by any taxing
agency, e x cluding school operating levies,

exceeded 125

percent of the statewide average for such tax rates,

the

v aluation of the distr i c t for purposes of compu t i n g aid
was reduced by the percent by wh i c h the tax rates exclud ­
ing school operating levies,
the statewide average,

t.

t, exceeded 125 per c e n t of

However,

there was a limit on

the total amount of m u n i cipal overbu r d e n aid disbursed by

11

the state so that the amounts received were some fraction
<Ji of the amount to w h i c h districts were otherwise entitled,
Thus, if none of the special provisions appl i e d , 1 the
amount of state aid per pupil was
S = r (38,000 -

fl - <f> t- 1,f 5 t j
t

y

(1.6)

'J

Then the sum of matching aid and local revenues was
S + r W ? 3 , so the matc h i n g rate was
S
73

38,000 -

S + r W ?3

[l-<t> t~ 1|-2 5 t ] W ?3

38,000 + <f>

25t

W73

= 1 " ------------ t_i 251---------------38,000 + <f>
i
t
'J
Therefore M increases as t increases.

(1*7)

The amount of

municipal overburden aid per pupil was

S 0 = j,

r W 73

(1.8)

S0

,,

Therefore
* t-1.25t „
♦ ------ 1 -------

73 “ —

U .9)

30r if a district SEV per pupil exceeded $38,000
but
[1 _ t~ 1 v2.
5.
t ] w?3 < 38,000

12

and the matching rate can be expressed as

^73

«73 - 1 ------ ST

(1-10>

38,000 + ™
r
For districts

levying less

the municipal

overburden

S =

[r + ~

than 20

provision

(. 020-r) ] (38,000 -

mills

the effect of

was

£l-(f> t~ 1 v2^ -] w ? 3 >

= (f + ‘°3Q) (38,000 - [1—^•
t ~ 1i 25^ ]

W 73>

(1.11)

The m a t ching rate and the block grant were

m

73

^ (38,000 - l l ~ 4 > t" 1 *2 5 t l W
}
= __ _______________________ s_______ L ± _______
~

3

(38,000 -

[1-$ t~ 1l 2-5 t 3 W--,} + rW_,
t

73

7.

s0

38,000 + - p + 2 W ?3

B73 =

E38'000 +

“ w 73l

C o m paring equation

(1.10)

(1.12)

for districts receiving

municipal overburden aid and levying between 20 and 22
mills with equation

(1.2)

for other districts levying

between 20 and 22 mills, and comparing equation

(1.12)

for districts receiving munic i p a l overburden aid and

13
levying less than 20 mills with equation
districts levying less than 20 mills,

(1.5)

for other

one sees that the

municipal overburden provision effectively increased "key
district wealth" by an amount S^/r.

Note that S^/r is

added to 38,000 in the denominators of the expressions
for the matching rate in

(1.10)

and

(1.12)

and is also

added to 38,000 in the bracketed factor in the expression
for block grants in

(1.12).

The provisions for 1974-75 were similar except
that the "key district wealth" was raised to $39,000,

the

maximum local levy subject to matching aid was raised to
25 mills, and there was no longer any protection from a
decline in state aid from the amount received in 1972-73.
The provision for districts levying less than 20 mills
allowed the use of the sum of actual operating millage
and o n e - third the difference between 20 mills and the
actual millage.
ing to

(1.10)

Thus,

and

the formulas for 1974-75 c o r r e s p o n d ­

(1.12), respectively, were
W

M

74

1

74

39,000 +

M 74

0
r

3 W,
74
S
0
78,000 + 2
r

1

B 74 " T

(1.13)

S

1

+ w 74

t39'000 + T T - W 7 4 ]

14
The effect of the 1974-75 school aid formula on
the opportunity set of school districts is shown in Figure
1.

Assume:
1.

The school district has a state equalized
value per
pupil of $19,500.

2.

All taxes
district.

3.

There is no federal or state aid other
than member s h i p aid provided according to
the aid formula.

4.

Disposable income per pupil wo u l d be $5,000
if school taxes were zero.

If there were

are paid by residents

of the

no state aid provisions, the budget

constraint wo u l d be the dashed

line AB w i t h

For each additional dollar of school spending,
posable income w o u l d be reduced by one dollar.

a slope of -1.
local dis ­
A tax

levy of 40 mills w o u l d be required to finance education
expenditures of $780 per pupil.
Under a simple percentage equalizing formula such
as

(1.1), the budget constraint w o u l d be the line AE wit h

a slope e qual to
t-t
_
(1 - M)

However,

19,500 _
39,000

1
2

(1.15)

the m a x i m u m of 25 mills subject to matc h i n g aid

and the special provisions

for districts

levying less than

20 mills give the budget constraint shown by the solid
line segments GCDJ.

The endpoint of the bu d g e t constraint

at G corresponds to the 10 mill m i n i m u m levy required to

15

Disposable
Income
Per Pupil

5800

5600

5400

5200
5078
5000

V I

4800

4600

4200

200
130

600
332

I 800
780

1000
975

1200

1400

Expenditures
Per Pupil

Figure 1.— Budget Constraints with State Aid.

16
receive the full amount provided by the state aid formula.
The segment GC represents the constraint for the district
if it falls under the special provisions for districts
levying less than 20 mills.

From

(1.14), one sees that,

for a district with SEV p er pupil of $19,500,
„ _
M
A

B = *°^°

3 x 19,500
_ 2
78,000 + 19,500 ~ 5

(39,000 - 19,500)

Thus, GC has a slope of -

3

= 130

(1.16)

and the h o r i zontal distance

AF equals the block grant of $130 per pupil.
The segment DJ is the constraint if the district
levies more than 25 mills.

It is parallel to AB, w i t h

the slope of -1 mea n i n g that each additional dollar of
educational spending reduces disposable income of resi­
dents by one dollar.

The block grant for a district

with $19,500 SEV per pupil is
B = .025

(39,000 - 19,500)

- 487.50

(1.17)

This is the h o r i zontal distance bet w e e n AB and DJ.
Figure 1 also allows a comparison between the
opportunity sets under percentage equalizing and under the
old foundation plan.
equal to

A i d for 1972-73 was a block grant

17
'644 - .016 W

if

W >

17,750

715 - .020 W

if

W < 17,750

B =
(1.18)

Thus, a district w i t h $19,500 SEV per pupil w o u l d receive
a block grant of $332.

The budget constraint for such a

district is shown as the line segment IK, w h i c h is p a r a l ­
lel to AB.
The above equations were used to calculate the
matching rate, M, used as a variable in the regression
analysis in Chapter IV.^
Behavior Under Percentage Equalizing
The percentage equalizing formula in
antees that all districts

(1.1)

guar­

levying the same millage will

receive the same per pupil revenues.

But does school

district behavior under such a formula truly achieve
"equal educational opportunity"?

Coons,

Clune and Sugar-

man recognized that it might n o t .
. . . the socioeconomic characteristics of a d i s ­
trict count in its ability to translate attitude
about education, what e v e r that may be, into

The provisions of the 1973 school aid law dis­
cussed above are contained in Public Acts Numbers 101 and
160.
State of Michigan, Legislative Service Bureau,
Public and Local Acts of the Legislature of the State of
Michigan Passed at the Regular Session of 1973, pp. 303313, 638-646.
The provisions of the 1972 foundation aid plan
are found in Public Act Number 258.
Public and Local
Acts of the Legislature of the State of Mich i g a n Passed
at the Regular Session of 1972, p p . 644-66 8.

18
results at the ballot box; and the socioeconomic
characteristics of a district condition its atti­
tude toward e d u c a t i o n .
F eldstein restated the rule that "educational
spending not be a function of local wealth" as the more
precise n o r m "that the elasticity of local educational
spending per pupil w i t h respect to the value of local
taxable property per pupil be z e r o . "

2

He showed that

power equalization does not in general satisfy this rule.
Consider the expenditure equation linear in the
logarithms ,
In E. = 8 a + 3 . I n W . +
3 . 0
1
r

In P. +
2
i

K
J

6. In X.. + e.
I1
i
(1.19)

where W is we a l t h per pupil,
matching rate,

P equals one minus the

and the X^ are other variables.

Feldstein

defined the elasticity of spending with respect to wealth,
, to be equal to

“ l = ^1 + B2YP W +

1= 3

BjYX . W
J

(1.20)

j

where 'Y'xjw is the elasticity of X^ w i t h respect to W.

Let

K
BW = B1 +
1

Coons,

BjYX_.W

Clune,

and Sugarman,

(1.21)

p. 278.

2
M artin S. Feldstein, "Wealth Neutrality and Local
Choice in Public Education," Ameri c a n Economic Review 65
(March 1 9 7 5 ) :77.

19
Then a price formula of the form

pi = k W± Y PW

(1.22)

would achieve wealth neutrality
=

0 ) 1

(in the sense that

if
-**w

YPW

fTJ

(1.23)

Percentage equali z i n g formulas,

in the pure ver­

sion w i thout mini m u m and m a x i m u m limits on aid and other
special provisions,
Yp^ = 1.

Thus,

are of the form P^ = kW^,

i.e.,

such formulas will be we a l t h neutralizing

only in the special case
Empirically,

$ 2

=

Feldstein took the value of

esti ­

mated from
In E. i

4

In P. = b rt + b.
i

0

1

In W.
x

(1.24)

To the extent that the Xj are' taste variables,
Feldstein*s inclusion of
K

jl3

;W

in
is a departure from the normative position of Coons,
Clune and Sugarman that variation in expenditures accord­
ing to local tastes should be allowed.
Feldstein has
ruled out those variations in expenditures due to tastes
which are correlated with wealth.
An aid formula meeting
Feldstein*s criteria w o u l d eliminate w h a t Grubb and
Michelson call de facto correlations bet w e e n property
value and e x p e n d i t u r e s , as opposed to de jure correlation
which is only concerned w i t h property values as a direct
argument of the choice function.
Cf. W. Norton Grubb and
Stephen Michelson, States and Schools (Lexington, Mass.:
D. C. Heath, 1974), p. 173.

20
as an estimate of 3W -

From his various estimates of

8

W,

Feldstein calculated that with “price" proportional to
wealth or

=

1

, the elasticity of spending w i t h respect

to wealth, a^, would be between -.630 and -.832.

He con ­

cluded:
. . . power equalizing grants w o u l d not neutral­
ize w ealth but could create a stronger (but nega­
tive) relation between we a l t h and spending than
currently exists.^
The negative correlation bet w e e n we a l t h and
expenditures per pupil under percentage equalizing was
also found by Grubb and Michelson,

but Gini coefficients

measuring the inequality of expenditure levels increased
in their simulation of a percentage equalizing formula.
The correlation between expenditures and income levels in
2
the same simulation was reduced but remained positive.
In contrast to Feldstein,

Stern found:

. . . power equalizing would produce a pattern of
taxing and spending in which per-pupil expendi­
tures remained substantially higher, on average,
in w e a lthier school districts.
From the particular preference function Stern used, he
derived a marginal rate of substitution of expenditures,
g, for tax rate, t,
^"Feldstein, p.
2

3

8 6

.

Grubb and Michelson,

pp.

163-165.

David Stern, "Effects of A l t e r native State Aid
Formulas on the Distribution of Public School Expenditures
in Massachusetts," Review of Economics and Statistics 55
(February 1 9 7 3 ) :91.

21

I
? = n
at
n Ut
— a
g

(1.25)

where n and u are taste parameters depen d i n g on d e m o ­
graphic variables,

u reflecting homeownership and n

reflecting socioeconomic status.

Under percentage e q u a l ­

izing the budget constraint is g = kt.

Equating the m a r ­

ginal rate of substitution to the slope of the budget
constraint and substituting for g

n ut
- kt = k
or
t = —
u + k
Stern's estimates

(1.26)

led to the conclusion that percentage

equalizing wo u l d reduce but not eliminate the disparities
in per pupil expenditure associated w i t h property values
but w o u l d increase the disparities associated w i t h socioeconomic status.

1

In criti c i s m of Stern's work,

Feldste i n

argued that the
. . . price effect in Stern's analysis . . . is
essentially imposed by the form of the function
and not estimated from the s a m p l e . 2
Inman analyzed the effects of various school aid
formulas in a general e q u i l i b r i u m framework allowing for
relocation of family residence and move m e n t into or out of

1

2

Ibid., pp.

95-96.

Feldstein,

p.

85, n.

25.

22
private schools in response to public educa t i o n e x p e n d i ­
tures and taxes.

He den o t e d the decisive voter's net

taxes by Trrb, where i is a factor reflecting federal and
state income tax credits and deductions, b is the indi­
vidual's taxable base and the tax rate is

r = ^

( 1

B

- m) - z
(1 + e)

q

with k(E) b e i n g costs per child for service level E;
lump sum aid per child; m,
on family income)
value per child;
aid

the m a t c h i n g rate

for E S E A Title I aid;

2 7

)

z,

(which depends

B, the assessed

and e, the percentage rate of tax effort

(presently applicable under revenue sharing to local

income taxes).

Thus,

the marginal tax cost,

assuming

changes in E have a negligible effect on public school
enrollment,

is
tt

t

where

0

(1 - m) b k' (E)
(1 + e)
+

------------------ B

. db
dE

7rr0

fl
(1.28)

is the percentage of the tax base that is indus­

trial or commercial p r o p e r t y .

1

Percentage equali z i n g guarantees each dist r i c t a
per pupil base B

.

For a district in w h i c h B

than the previous tax base,

is greater

the implementation of such an

1

Robert P. Inman, "Optimal Fiscal Reform of M e t r o ­
politan Schools:
Some Simulation Results w i t h a General
Equilibrium Model," October 1975.
(Mimeographed.)

23
aid plan initially lowers x and thus increases the desired
level of E.

But,

in response to this change,

land values

will rise as families migrate into the district.
more, as r is reduced,

Further­

housing consumption is stimulated.

Thus b increases, w h i c h increases r, possibly undoing mu c h
of the initial effect of the aid and returning expenditures
to near the initial level.

While the initial impact on x

of a perce ntage equalizing plan is equalizing,

the sec­

ondary impact of capitalization and investment on x will
be unequalizing.

Inman concluded from his simulation

results:
For our sample cities, these unequalizing longrun adjustments in fact dominate! . . . the
e q u i l ibrium effects of a DPE plan in this economy
with its strong capitalization effects is to
spread rather than condense the distribution of
school spending.
Finally w e note that DPE and
DPENC m u s t both attempt to control for drop-out
in the EXIT ALL O W E D economy.
This is accomplished
by increasing B*.
Drop-out only reduces further
their ability to equalize educational s p e n d i n g . 1
Ibid., p. 43.
"DPENC" refers to a dist r i c t per ­
centage equalizing plan wit h o u t "recapture."
The long-run effects of an aid pro g r a m through
the capitalization of tax advantages in property values
will not be considered in the present study due to two
problems,
James M. Buchanan and Charles J. Goetz, "Effi­
ciency Limits of Fiscal Mobility:
An A s s e s s m e n t of the
Tiebout Model," Journal of Public Economics 1 (April 1972):
25-43, have questioned the use of a Tiebout model that
ignores locational fixity in assuming all income is divi ­
dend income.
Inman's specification of the equation for
median home value does not provide an adequate means of
dealing w i t h the pro b l e m of locational rents in a state­
wide sample nor are any solutions to the p r o b l e m readily
apparent.
Furthermore, in studying a recent change in the
aid formula, there is a question of h o w rapidly tax adva n ­
tages will become capitalized in m a r k e t values and how
quickly assessed values w i l l reflect changes in m a r k e t
values.

24
The criterion Inman used to evaluate the degree
of equalization was the Atkinson inequity measure, E/E.
E is the average level of education services received by
all children and
P

1/y

I

E =

where

f=l

(1.29)

is the amount of education services received by

each family, F is the number of families and the value of
Y used was -. 5 .^
Even in the short run, w i t h no c a p i t alization or
exit to private schools Inman found that,

although a p e r ­

centage equalizing formula had an equalizing effect,

there

were foundation and "matching aid" proposals w h i c h domi2
nated it according to the equity criterion.
Outline of the Following Chapters
The pre s e n t study investigates the degree to whi c h
the "percentage equalizing" aid formula in Mich i g a n has
Inman, "Optimal Reform," pp. 33-34.
The use of a measure of equality as a n o r m goes
beyond the principle that expenditures per pupil be inde­
pendent of wealth to the egalitarian principle that
expenditures per pupil be equal.
Not surprisingly, Inman
found that his notion of equality of opportunity is inco n ­
sistent w i t h local autonomy in d e t e r mining expenditure
levels.
Cf. ibid., pp. 43-44.
2

Ibid., p. 42, n. 35.
Recall that Inman's "match­
ing rate" is a function of income, not assessed property
values.

25
reduced inequality in per pupil expenditures and the
effects on equalization of modifications of the current
formula.
Predicting responses to changes in the aid formula
requires m easuring the effect of the variables determining
the level of school expenditures.

Chapter II surveys p r e ­

vious studies of the determinants of education exp e n d i ­
tures.

Chapter III discusses problems associated with

estimating an expenditure equation,

and Chapter IV pre­

sents estimates of such an equation b a s e d on Mich i g a n data.
Chapter V discusses changes in the distribution of
actual per pupil expenditures bet w e e n 1972-73,
year under the foundation plan,

and 197 4-75,

year under percentage equalizing.

Also,

the last

the second

the levels of

state aid and total expenditures and the distribution of
per pupil expenditures are predicted under the assumptions
that the 25 mill max i m u m on levies subject to matching had
been removed and that districts above the $39,000 guaran ­
teed tax base had been subject to a "recapture" provision.
Chapter VI provides a summary and conclusion.

CHA P T E R II
REVIEW OF STUDIES OF THE DETERMINANTS
OF EDUCATION EXPENDITURES

Numerous empirical studies have been made of the
determinants of educational expenditures and of local
government expenditures in general.

These studies have

differed in the explanatory variables considered,

the

functional forms used, the theoretical assumptions about
how expenditure levels are determined,

the choice of

dependent variable in the regression equation and the nature
of the observations
vidual districts,

(state- or county-wide totals or indi­

cross-section or time series,

etc.).

M o s t of the studies reviewed here were considered
by D e n z a u . 1

Denzau's survey used specifications

from 13

empirical papers to estimate educational expenditure equ a ­
tions for a common set of observations,
districts in 1969-70.

Virginia school

This common data base allowed com ­

parison of the performance of the various specifications.
The following sections review the studies con­
sidered by Denzau along w i t h other related work.

Rather

^Arthur T. Denzau, "An Empirical Survey of Studies
on Public School S p e n d i n g , ” National Tax Journal 28 (June
1 9 7 5 ) :241-249.
26

27
than considering each study separately, we shall survey
the field of studies w i t h respect to

(1 ) the assumed the­

oretical basis for the determination of expenditure levels,
(2 ) the choice of dependent variable used in regression
analysis,
tastes,

(3) the various explanatory variables reflecting

interest group influences and political institu­

tional factors,

(4)

"price” variables,

reflecting ability to pay,

and

(5) variables

(6 ) the specification of

the functional forms estimated.
Theoretical Basis of Expenditure
Dete r m i n a t i o n
The variety of assumptions regarding the the­
oretical basis for the determination of expenditure levels
in empirical studies is remarkable in that, however much
studies differ in their assumptions at this level,
do not,

for the most part,

they

test the assumptions.

The approach used in the pres e n t w o r k is w h a t
Miner^ calls a "political a p p r o a c h . "

Politicians seeking

voter support w i l l be led to make decisions according to
the preferences of the med i a n voter.

This occurs because,

in a two-candidate election in w h i c h v o t e r s 1 preferences
can be m e a s u r e d along a single dimension and citizens vote
for

the candidate w h o s e position

is closest to their own

^Jerry Miner, Social and Economic Factors in
Spending for Public Education (Syracuse, N 1Y .:
Syracuse
University Press, 1963), p. 6 6 .

28
preferred point,

the candidate w h o takes a position clos ­

est to the median of the d i s t ribution of voters'
ences will w i n a majority of the votes.

prefer­

Citizen

preferences about school expenditures are even more
directly expressed in states where school boards must
submit tax levies to a referendum.

If the initial millage

proposal is at least as high as that preferred b y the
median voter,

if each citizen votes against millages

above his own preferred level and for millages that do not
exceed this level,

and if school boards incrementally

decrease the pr oposed millage after any defeats,

the

median preferred millage will be adopted.^In a "political" model,

then,

the explanatory

variables to be considered are those wh i c h influence the
median voter's preferred point.

Am o n g the studies

reviewed,

this approach was used by Davis, Barr and
2
Davis, and Ladd.
However, Ladd explicitly disclaimed
3.

Cf. Randall G. Holcombe, "Equilibrium in the
Public Sector:
Theoretical Models and Empirical Obs e r v a ­
tions," paper presented at the annual mee t i n g of the Pub­
lic Choice Society, Chicago, April 3-5, 1975.
2

Otto A. Davis, "Empirical Evidence of Political
Influences upon the Expenditure Policies of Public Schools,"
in The Public Economy of Urban C o m m u n i t i e s , ed. Julius Margolis (Washington:
Resources for the Future, 1965), pp.
92-111; James L. Barr a n d Otto A. Davis, "An Elementary
Political and Economic Theory of the Expenditures of Local
Governments," Southern Economic Journal 33 (October 1966):
149-165? Helen F. Ladd, "Local Public E x p e n ditures and the
Composition of the Property Tax Base" (Ph.D. dissertation,
Harvard University, 1974), and "Local Educa t i o n E x p e n d i ­
tures, Fiscal Capacity, and the C o m p o s i t i o n of the Property
Tax Base," National Tax Journal 28 (June 1975) :145-158.

29
her regression results as a test of the median voter
model. ***
In contrast, M i n e r followed w h a t he called an
"economic approach" despite his recognition of its limita­
tions :
Problems of ascertaining preferences and of giv­
ing equitable weights to divergent individual
preferences w h e n known make it impossible for
any government to achieve the goal of utility
maximization.
Still, m a x i m ization of the sum of
individual utilities is the basis of an economic
model of government behav i o r . . . .
This study uses the economic m o d e l of g o v ­
ernment behavior bec a u s e public spend i n g p r i m a r ­
ily influences economic welfare, and a model
based on economic rather than political p r i n c i ­
ples seems a p p r o p r i a t e . 2
A no t h e r approach,

taken by Henderson,

is to assume

that elected officials maximize a "social welfare"

func-

3

tion.

Similarly,

Stern assumed that

. . . local school authorities will show some
consistency in evalua t i n g different combinations
of local tax rates and total expenditure w h e n the
state aid formula changes.
. . . it is possi ble to impute a preference
function to the local school boards . . . .
The general form of this preference function is f[g(L);
t<L,V);

zj,

where L is local reimbursable expenditure per

^Ladd, "Public Expenditures," p. 58.
2
Miner, p. 67.
3
James M. Henderson, "Local Govern m e n t Exp e n d i ­
tures:
A Social Welfare Analysis," Review of Economics
and Statistics 50 (May 1968):156-163.
4
Stern, p. 91.

30
pupil,

g(L)

is perceived total resources per pupil,

t is

the current school tax rate, V is equalized assessed
property value,
ables.^-

and Z is a vector of demographic v a r i ­

In a similar spirit,

Inman assumed a group,

rather than an individual, preference function of the
2
Stone-Geary form.
G ensemer rejected both the notion of maximizing
community welfare used by M i n e r and the notion that offi­
cials' decisions reflect solely voter preferences,
although he acknowledged that these preferences influence
their decisions and the strength of such influence may be
greater with education than with other govern m e n t expend i ­
tures b e cause school boards are only responsible for a
single p ublic service.

Instead,

Gensemer adopted a

"pluralistic" a p p r o a c h :
A ny one fiscal policy decision may be influ­
enced by the elected officials' desires (1 ) to
satisfy general citizen demands, (2 ) to s a t ­
isfy the demands of lobbyists . . ., (3) to
follow their own consciences, (4) to follow
the advice of public administration pr o f e s ­
sionals or other "experts," (5) to insure

1

2

Ibid., p. 92.

Robert B. Inman, "Towards an Econometric Model
of Local Budgeting," Proceedings of the Sixty-Fourth
Annual Conference on T a x a t i o n , National Tax Association,
1971, pp. 699-719; and "The Local Decision to Tax,"
paper presented to the Econometric Society wi n t e r meeting,
December 27-30, 1974.

31
reelection, or (6 ) to protect the economic p o s i ­
tion of themselves or their f r i e n d s . 1
The necessity of voter approval of school millages
provides substantial reason for the present study's use of
the m edian voter model although problems involving voter
participation,

imperfect information and impediments to

marginal adjustment w h e n millage proposals offer an "allor-nothing" choice are recognized.
The Dependent Variable
One issue regarding the choice of dependent vari ­
able is w he t h e r it should include only current operating
expenses or should also include capital outlays and debt
service.

The former alternative was chosen in all

studies reviewed which dealt specifically with educational
expenditures.

The grounds for this choice were stated by

Miner:
Government capital outlays . . . are irregular and
may occur several years after an event w h i c h con­
tributes to the need for them.
. . . debt service as w e l l as capital outlay
reflect the influence of past events on local
school spending.
Since the analysis in the pres­
ent study seeks to determine relationships between
expenditures and current values of factors used as
independent variables, expenditure elements d e t e r ­
mined by values of these factors w h i c h prevailed in
previous periods w o u l d introduce unsystematic e l e ­
ments and confound the results.
Bruce Lee Gensemer, "Determinants of the Fiscal
Policy Decisions of Local Governments in Urban Areas:
Public Safety and Public Education" (Ph.D. dissertation,
University of Michigan, 1966), p. 13.
2
Miner, pp. 69, 70.

32
M iner recognized the pro b l e m w h i c h might be caused
by the omission of capital expenditures if capital can be
substituted for other inputs.

He tested the hypothesis

that larger amounts of capital reduce current outlays by
including insurable value of school capital per pupil as
an explanatory variable in his regression analysis and
found the hypothesized negative effect to be present but
of small importance.

He noted that larger amounts of

capital m a y reflect positive attitudes toward education
and that these positive demand factors may offset the
negative influence of capital in reducing current op e r a t ­
ing c o s t s .^
Similarly,

Gensemer included non-operating m i l l ­

age among the explanatory variables,

recognizing that this

variable m i g h t reflect heightened voter resistance to
expenditure increases

accompanying rapid enrollment growth

as w e l l as the reduced operating costs of a more modern
plant.

Although this variable was important in explaining

the varia bility in locally financed expenditures,

its

coefficient was not statistically significant in the total
current per pupil expenditure regression results.

Gensemer

interpreted this difference in the variable's influence in
the two equations as reflecting the influence of state aid
in compensating districts with greater debt burdens.

1

I b i d ., pp.

2

Gensemer,

83,
pp.

104.
120-121,

131,

151,

154-155.

33
Denzau suggested excluding one component of cur­
rent expenditures from the dependent variable, viz., bus2
ing expenditures.
In his regression results R s ranged
from .24 to .81 w h e n current expenditure per pupil was
2
used as the dependent variable compared with R s ranging
from .29 to .85, typically between

.5 and

pupil current expenditure less busing.

.6 , using per

Denzau inferred

that "different factors affect spending for bu s i n g than
affect other types of current expenditures."^
A nother question is whether to use expenditures
per pupil or per capita as the d e p e ndent variable.
the studies surveyed by Denzau,

Among

the per capita measure was

used in those originally concerned with general local
government expenditures,
son, and Barr and Davis.

i.e., Fabricant,

Brazer,

Hender ­

Am o n g the studies originally

concerned especially with educational expenditure, only
Miner used a per capita variable in addition to r e g r e s ­
sions run on per pupil expenditure variables.

Denzau's

regression results showed the performance of per capita

2

specifications to be clearly inferior, with R s ranging
2
from .05 to .48.
Denzau did not test the performance of
3

the expenditure-income ratio used by McM a h o n
^Denzau,
2

3

"Survey," p.

as a

2 46.

I b i d . , p. 245.

Walter W. McMahon, "An Economic Analysis of Major
Determinants of Expenditures on Public E d u c a t i o n , " Review
of Economics and Statistics 52 (August 1970):242-252.

34
dependent variable.
dependent variable,

Gensemer used a somewhat similar
"tax commitment" or the ratio of tax

levy per pupil to "economic strength"
under "Ability to Pay Variables").
R

2

(discussed below

His results gave an

of .7989 using this as the dependent variable compared

with an R

2

of

.9083 w h e n tax levy per pupil was used.

1

Zimmerman has shown that public goods theory ind i ­
cates a specification of the dependent variable as the
transfer rate rather than per capita expenditures in
2
studies of welfare expenditures.
similar reasoning sup­
ports the use of per pupil rather than per capita expend i ­
tures as the dependent variable in education expenditure
studies,

and this is consistent w i t h Denzau's empirical

results.
Taste, Interest Group and
Other Variables
Variables explaining expenditures can be classi­
fied in many ways.

Income, wealth or some other measure

of ability to pay is sure to be suggested as a determina n t
of expenditures.

Also,

inclusion of some variable analo­

gous to price in consumer demand studies seems appropri­
ate.

But these will not explain all the variation in

expenditures.

Preferences of citizens and/or officials,

"^Gensemer, pp. 131-132.
2
Dennis Zimmerman, "On the Relationship Between
Public Goods Theory and Expenditure Determinant Studies,"
National Tax Journal 28 (June 1975): 227-239.

35
political factors affecting how these preferences are
related to actions,

and factors affecting costs w i l l vary

between communities and influence the level of expendi­
tures .
Population and Pupil Density
and Urbanization
Denzau found population density to be among the
three "best" variables in his survey.

Its coefficient was

positive and significant for all six models in w h i c h it
appeared when estimated on the common Virginia school d i s ­
trict d ata.^

This is somewhat surprising in that the

coefficients were negative, but not usually significant,
in the original studies by Fabricant, McMahon,
and Davis.

Only Miner found a positive

Renshaw,

(but insignificant

in the total current expenditures per pupil regression)
coefficient.

2

Various rationales have been presented for the
inclusion of density.

Davis remarked that population

density was

1

2

Denzau,

"Survey," pp.

242,

245.

Solomon Fabricant, The Trend of Government
Activity in the United States Since 1900 (New York:
National Bureau of Economic Research, 1952), pp. 124, 127;
McMahon, p. 247; Edward F. Renshaw, "A Note on the
Expenditure Effect of State Aid to Education," Journal of
Political Economy 6 8 (April 1 9 6 0 ) :172; Davis, p. 104; and
Miner, p. 98.

36
. . . selected primarily because it has often
been considered an important explanatory variable
for municipal expenditures, but there is a (some­
what weak) rationalization for its inclusion here.
It m i g h t be presumed, for example, that population
density is positively correlated w i t h "urbaniza­
tion" and that in urban— as opposed to rural—
areas it is easier for individuals to recognize
educational benefits (consumption benefits as well
as such things as easier access to certain jobs,
and so o n ) . If the more the benefits are r e c o g ­
nized the greater are individual desires that the
upcoming generation be educated, then a rational
politician should respond to these desires and
there should be a positive relationship between
educational expenditures, as meas u r e d here, and
p opulation density.^
In c o n t r a s t , Fabricant a r g u e d :
. . . increased density, at given levels of income
and urbanization, acts to reduce expe n d i t u r e s —
presumably because w h e n public facilities can be
used more intensively the cost of meeting speci­
fied levels of public service per head is less­
ened .^
And M c Mahon c o m m e n t e d :
. . . density is also assumed to influence demand
because of the technical skills required for urban
employments, because proximity reduces the incon­
venience and private costs of travel, and because
it increases demonstration effects. . . . Density
shifts costs also, for apart from the economies of
scale that it tends to pick up, it first reduces
t ransportation costs and then increases them
because of racial problems as urban densities are
reached.
But total busing costs are quite small
relative to total expenditure.
In regard to the point that density affects transportation
costs,

it should be noted that the positive significant
^Davis, p. 95.
2

Fabricant,

3
McMahon,

p. 129.

pp.

244,

245.

37
coefficient appears also in Denzau's results w h e n current
expenditures less busing is the depen d e n t variable.'*'
Hirsch used a similar variable, average daily
attendance

(ADA) per square mile, and found a negative
2
but insignificant coefficient.
But again Denzau got a
positive and significant estimate for this coefficient in
two of the four regressions he ran using the Hirsch
model, 3
Fabricant also used a percent of population in
urban areas variable,

for w h i c h he found an insigificant

negative coefficient but w h i c h Denzau found to be signifi4
cant and negative in two c a s e s .
The differences in statistical significance and
sign of the coefficients between Denzau's results and the
other studies indicate the effects of the density and
urbanization variables may be peculiar to the sample.
This may be no surprise in view of the ambivalent the­
oretical effects of these variables.

1

Arthur T. Denzau, Appe n d i x to "An Empirical Sur ­
vey," Table 3.
(Xeroxed.)
2
Werner Z . Hirsch, "Determinants of Public Educa ­
tion Expenditures," National Tax Journal 13 (March 1960):
35.
3
Denzau, Appendix, Table 3.
4
Fabricant, p. 142; and Denzau, Appendix, Table 3.

38
Proportion of Public Students
in Secondary School
Another of D e n z a u 1s three best variables was the
percentage of public school enrollment in grades 9 through
1 2

, having significant positive coefficients in all four

models in which it appears w h e n estimated on the Virginia
data.

This result agrees with the significant positive

coefficients in the original work by Hirsch and Weisbrod
as well as the positive but insignificant parameter esti ­
mate in McMahon.

Miner's original results gave signifi­

cant positive coefficients in both per capita expenditure
regressions and in the regression for local per pupil
expenditures, but the coefficient in the total expenditure
per pupil equation was insignificant although positive.
Gensemer found an insigificant positive coefficient for
proportion of public enrollment in grades

1 0

through

1 2

.^

The usual rationale for the positive effect of
secondary enrollment is that secondary education is more
costly.

There is some evidence against this view.

2

Denzau, "Survey," pp. 242, 245; Hirsch, "Public
Education Expenditures," p. 35; Burton A. Weisbrod,
External Benefits of Public Education (Princeton:
Princ e ­
ton University, 1964), p. Ill; McMahon, p. 247; Miner,
p. 99; and Gensemer, p. 151.
Gensemer did not present t statistics but these
can be c alculated from the partial r 2 which he did show.
2
Reischauer and Hartman, p. 91, n. 34.

39
Shapiro suggested that a higher proportion of secondary
enrollment may indicate greater interest in e d u c a t i o n .

1

Scale Economies and the
Political Effects of
Larger Districts
The size of the district is typically measured by
average daily attendance

(ADA).

Denzau considered this

variable as reflecting
. . . the combined effects of scale economies,
price elasticity, and possible increasing voter
apathy w i t h their lessened ability to affect pub­
lic school o u t c o m e s . 2
He concluded from his empirical work:
The total effect, except for the Bishop model is
no effect at all.
If scale economies (or b u r e a u ­
cratic d i s e c o n o m i e s ) exist, they are apparently
either miniscule or improperly measured by A D A . 3
McM a h o n cited studies finding economies of scale
for larger school size but found a significant positive
coefficient for pupils per district in his expenditure
equation.

He attributed this result not to bureaucratic

diseconomies but to "the search for improved quality wh i c h
has apparently overridden the effect of economies of
scale.

" 4

Sherman Shapiro, "Some Socioeconomic Determinants
of Expenditures for Education:
Southern and Other States
Compared," Comparative Education Review 6 (October 1962):
163-164.
2
Denzau, "Survey," p. 247.
3

Ibid.

4
McMahon,

p. 24 9.

40
Different specifications have been used to test
for scale effects.

James, Kelly and Garins argued that

economies of scale,
. . . if they occur, are more apt to be linearly
related to a proportional change in size than to
an absolute change in size. . . . It therefore
seemed appropriate to use the logarithm of A D A as
a variable, rather than A D A itself.
Despite the hypothesized negative relationship with
expenditure levels,

their empirical study also produced

a positive but insigificant regression coefficient.

2

Hirsch used a specification involving both linear
and quadr a tic terms in A D A but concluded "the m o s t impor­
tant finding is the absence of significant economies of
scale in the school districts of the St. Louis City3

County area."

In contrast,

Hanson found economies of

scale did exist.^
Hirsch pointed out that a more desirable variable
to reflect scale economies m i g h t be school rather than
district size.

In a similar vein Gensemer argued:

H. Thomas James, James A. Kelly, and Walter I.
G a r m s , Determinants of Educational Expenditures in Large
Cities of the United States (Stanford:
School of Educa­
tion^ Stanford U n i v e r s i t y , 1966), p. 116.
2

3
4

Ibid., p. 140.
Hirsch,

"Public Education Expenditures," p.

36.

Nels Hanson, "Economies of Scale as a Cost Factor
in Financing Public Schools," National Tax Journal 17
(March 1964):92-95, cited by Barry N. S i e g e l , HOn the
Positive Theory of State and Local Expenditures," in Public
Finance and Welfare:
Essays in Honor of C. Ward M a c y , ed.
Paul L. Kleinsorge (Eugene:
University of Oregon Books,
1966), pp. 171-186.

41
The m o s t convincing arguments [for economies of
scale] appear to involve the size of the high
school rather than the size of the school district
as a whole or the size of primary schools.
It is
claimed that a "well-rounded" curric u l u m can be
offered by a small high school only at a very high
cost. . . .
Gensemer used three dummy variables for districts with
enrollments in grades 10 through 12 of 600-999,
1,999, and 2,000 and over.

1,000-

All three dummy variables had

insignificant negative regression coefficients, w i t h the
larger in magnitude being for the larger size classifi­
cations .2
S omewhat similar to the A D A variable is the p o p u ­
lation variable used by Henderson and Stern.

Stern found

this variable to have a significant positive coefficient
but he did not justify the use of this variable in terms
of economies or diseconomies of scale.

It was introduced

by Stern as "a proxy for the stronger organization and
power of t e a c h e r s ’ unions in large districts" which
"should be associated with more pressure on the school
3
board to spend."
H enderson specified population as a variable
affecting the

"social welfare"

function.

He found it to

have a s ignificant positive coefficient for the regession
for metropolitan counties and a significant negative
1

2

3

Gensemer, p. 142.
I b i d ., p . 151.
Stern,

p . 9 3.

42
coefficient in the regression for non-metropolitan coun­
ties.
manner,

When the counties were not stratified in this
it was not significant.^
Two remarks should be made about the use of v a r i ­

ables reflecting the size of the district.
has noted that A D A or population

First, Bahl

(as is used in studies

of other government expenditures w h i c h he reviewed)

do

not reflect economies of scale.
. . . a negative relationship between per capita
expenditures and popula t i o n size gives very little
information about the existence or non-existence
of economies of scale, i . e . , about the nature of
the production function.
Moreover, the statis­
tical analyses have been made on cross-sections
of data, therefore, any conclusions reached must
be based on the finding that at a point in time
larger government units in the sample spend sig­
nificantly less than smaller units.
It does not
necessarily follow that an increase in the popu­
lation of any given governmental unit will be
accompanied by a decline in per capita costs.^
Economies of scale exist w h e n unit costs
input combination)
increases.^

decline as the scale of operations

But the number of "units” of education per

■^Henderson, pp.

2

(with the optimal

154,

158,

161.

Roy W. Bahl, "Studies on Determinants of Public
Expenditures:
A Review," appendix to Selma J. Mus h k i n and
John F. Cotton, Sh aring Federal Funds for State and Local
Needs (New York:
Praeger Publishers, 1969), p. 190.
3
A ccording to Ferguson's definition, economies of
scale may stem from financial reasons and need not always
be attributable to the physical and technological charac ­
teristics of the production function as is suggested in
the q u o t ation from Bahl.
C. E. Ferguson, Microeconomic
Theory (Homewood, 111.:
Richard D. Irwin, 1972), p. 237,
K~. ITT

43
pupil may be varied.

Ignoring the multidimensional

nature of school output,

assume the cost of a "unit" of

education is lower in larger schools.

This does not imply

expenditures per pupil decline as the number of pupils
increases.

This w o u l d be the case if the demand for

units of education were inelastic.

But if the demand

were elastic the desired number of units of education per
pupil w o u l d increase by a greater percentage than unit
costs decline,

thus increasing expenditures per pupil.

With a unitary elasticity the number of units per pupil
would increase by the same percentage as the decline in
unit costs,

leaving per pupil expenditures unchanged.

No

relationship between number of pupils and expenditures
per pupil w o u l d be observed, b u t there w o u l d be economies
of scale!
Second,

as Bishop has noted,

inclusion of number

of pupils as a variable reflecting economies of scale
deviates

from the assumption that expenditures measure the

quality of educational services prov i d e d each pupil.^
Since this study does interpret the depen d e n t vari a b l e as
a measure of quality of education,

the inclusion of number

of pupils as an explanatory variable can be justified
only by a ssuming there are no economies of scale b u t that
1

George A. Bishop, "Stimulative Versus S u b s t i t u ­
tion Effects of State School Aid in New E n g l a n d , " Nation a l
Tax Journal 17 (June 1 9 6 4 ) :141.

44
this variable represents political apathy or union power,
as mentioned above.
"Interest Group" Variables
Davis classified explanatory variables into
"desire determining" variables w h i c h influence all indi­
viduals ' p referred levels of spending more or less uni­
formly and "interest group" variables w h i c h affect
spending levels because costs or benefits do not fall
1

equally on all segments of the population.

One such

interest group w h i c h shares disproportionately in the
benefits of public education is families w i t h children.
One variable wh i c h m i g h t indicate the strength of this
interest group is the proportion of the population aged
5 to 17.
D enzau found this variable to be insignificant.
In contrast, McM a h o n found this variable to have a
significant positive coefficient in both his cross-section
and time series a n a l y s e s .

Bowman found his

"per cent of

families with children under 18" variable to have a p o s i ­
tive coefficient significant at the

.05 level.

Gensemer's

young families variable, defined as the ratio of persons
18 or older mar r i e d with children under 18 to the total
number of persons at least 18, had an insignificant n e g a ­
tive coefficient.
1

Davis, p.

Brown and Saks found the fraction of
95.

45
familes with school-age children to have an insigificant
negative coefficient.

Inman used percent over age 62 as

a variable reflecting the number of families without
school-age children who w o u l d oppose education e x p e n d i ­
tures and found this variable to have the expected nega­
tive coefficient significant at the

. 1 0

level in his

ordinary least squares estimates but insigificant in his
two-stage least squares results.^"
Denzau reported that the percent of total popula­
tion in public schools was used in only one study and was
found to be an i n s i g nificant determinant in that case.
It was significant and negative in Davis'

original results.

Feldstein found pupils per capita to have an insignificant
positive coefficient and Ladd found the coefficient of the
2
same variable to be insignificant w i t h varying sign.
Ladd offered possible reasons for the ambivalent
effect of this variable:
On the one hand, the higher the proportion of
families with school age children, the stronger
the positive interest group effect on the e f f e c ­
tive demand for school spending.
In the other
Denzau, "Survey," p. 246; McMahon, pp. 246, 247;
John H. Bowman, "Tax Exportability, Intergovernmental Aid,
and School Finance R e f o r m , " National Tax Journal 27 (June
1 9 7 4 ) :170; Gensemer, pp. 115, 151; By r o n W. Brown and
Daniel H. Saks, "Income Distribution and the Aggregation
of Private Demands for Local Public Education," [1976],
p. 20 (mimeographed); and Inman, "Optimal R e f o r m . "

2
stein, p.
151.

Denzau, "Survey," p. 243; Davis, p. 104; Feld­
83; and Ladd, "Education Expenditures," pp. 150,

46
direction, if more pupils per capita reflect more
pupils per family, then family income per pupil is
reduced, implying a negative effect on education
expenditures.
Edelson gave another reason that the percentage
of families with school-age children may not be signifi­
cant :
Other voters have used public schools in the past
(couples with children over eighteen years of age)
or expect to do so in the future (couples with
children under six years of age and unattached
i n d i v i d u a l s ) . To the extent that these voters
feel part of an intergenerational social contract,
they will vote according to y^ [disposable income
and other governmentally provided goods and serv­
ices] rather than their current usage of public
schools. 2
Brown and Saks suggested a more selfish rationale;

the

quality of the school system will affect the ma r k e t value
of h o u s e s .^
Gensemer gave another reason that the variable
percent families with school children may be insignifi­
cant.

A l t hough adults wit h o u t children may oppose school

spending,

this opposition may not be politically e f f e c ­

tive because of greater apathy among this g r o u p .

In

support of this view, he cited a study w h i c h found that
Ibid., p. 150.
The possibility that pupils per
family is a price factor is discussed be l o w in the section
on "The Price Variable."
2

Noel M. Edelson, "Efficiency Aspects of Local
School Finance:
Comments and Extensions," Journal of
Political Economy 81 (January/February 1 9 7 3 ) :16 9.
3
Brown and Saks, p. 25.

47
adults w i thout children "were relatively infrequent voters
in Birmi n gham school elections.
Parents of children attending private schools may
constitute an interest group opposing public education
spending.

This v i e w is supported by surveys of indi­

vidual v o t e r s ' attitudes in which parents of children in
non-public schools,

like those wit h o u t children under 18,

give less support to millage proposals than parents of
2
public school pupils.
On the other hand, sending chil­
dren to private schools reduces the number w h o must be
educated in the public sector and m a y create a capacity
3
for larger per pupil expenditures in public schools.
Feldstein noted additional complications in that parents
may support high quality primary education and send their
children to private secondary schools or vice versa.
Thus, more use of private

education could be associated
4
with larger per pupil public school expenditure.
Denzau used the percent of school enrollment in
private schools as a variable in four models and found:
1

Gensemer, p. 139, n. 2, citing R. V. Smith et
a l . , "Community Organization and Support of the Schools:
A Study of Citizen Reaction to the Birmingham, Michigan,
Public Schools," Cooperative Research Project No. 1828
(Ypsilanti, Mich.:
January 31, 1964).
2
Smith et a l . , p. 116.
^Miner,

p. 103.

4
Feldstein,

p.

81,

48
The effect of the private school variable was
always significantly positive.
This suggests
that the elasticity of total spending with
respect to public enrollment is less than one.
Thus, the increasing public enrollment outweighs
the effect of increased political support for the
public school b u d g e t . 1
Also,

the percent of total school enroll m e n t in public

schools was used in the Weisbrod model by Denzau and its
coefficient was significantly negative.

However, Weis-

brod's original work had found an insignificant positive
coefficient for percent of school-age children in public
school.

McMahon had used percent of school-age children

not attending public schools,

thus including those not in

school as w e l l as those in private schools.

He found this

variable to have a significant negative coefficient in his
cross-sectional study.

Davis had originally used percen t

of total population in non-public schools and found it to
have a significant positive coefficient.

Ladd found the

same variable to have an insignificant negative sign,

and

Feldstein found the sign of this variable to be unstable.
James,

Kelly and Garms had originally used percent of e l e ­

mentary pupils in private schools and found it to have a
significant positive coefficient.

They compared this

result, based on "great cities" data to the results in
Evans

1

unpublished dissertation ba s e d on d a t a f r o m

8 8

districts with A D A bet w e e n 11,000 and 25,000 and found
that the private school influence was even larger in that
‘'‘Denzau,

"Survey," p.

247.

49
sample.

The proportion of students in non-public schools

had a significantly negative effect in Gensemer's study.'*'
The religious composition of the p o p u lation is
obviously related to private school enrollment.

One

small sample study of the San Franc i s c o Bay area found the
percent Catholics in the population to be positively related
to current expenditures per A D A w i t h a .20 level of sig2
nificance.
This w o u l d be consistent with the positive
relationship between expenditures per public pupil and
private school enrollment.

On the other hand,

Inman,

using p e rcent families Irish or Italian as a proxy for
Catholics,

found this variable to have a significant nega3
tive effect.
Theoretical models incorporating choice between

public and private school attendance have treated private
school enrollment as a function of the level of public
school expenditures.

4

If this is the case,

the private

^Denzau, Appendix, Table 3; Weisbrod, p. Ill;
McMahon, pp. 2 40, 2 47; Davis, p. 104; Ladd, "Education
Expenditures," p. 150; Feldstein, p. 83; James, Kelly, and
Garms, pp. 131-132, 140; and Gensemer, p. 151.
2
Ma r v i n C. Alkin, "Religious Factors in the D e t e r ­
mination of Educational Expenditures," Educational A d m i n ­
istration Quarterly 2 (Spring 1 9 6 6 ) :129.
3
Inman, "Optimal Reform," pp. 28-30.
4
Y o r a m Barzel, "Private Schools and Public School
Finance," Journal of Political Economy 81 (January/
February 1973):174-186.

50
school variables above would be endogenous and would
introduce simultaneous equations bias unless appropriate
estimation techniques were used.

Thus, Felds t e i n used an

instrumental variables technique w i t h private pupils per
capita among the variables treated as endogenous but
found no substantial change in the r e s u l t s .^
not treat this variable as endogenous,

Ladd did

justifying her

approach by citing Toder's findings that the level of
public spending did not affect private school enrollments
but that the characteristics of public school pupils
(such as race)

influenced the parents of non-public school

pupils. 2
People recently moving into the community may be
a group differentially affected by the costs or benefits
of public education.

M i n e r cited some possible reasons:

Recent arrivals cannot vote for some time, often
do not own property, and may not plan to be in
the community long enough to derive benefits
from h igher outlays on education.
On the other
hand, expenditures will be higher if an influx
of population reflects preferences for patterns
of life in a community that includes a strongly
supported local school system.
Denzau used percent of population living in
another county five years ago as a measure of in-migration.
It was significant in only one of the six models in whic h
■'"Feldstein, p. 84.
2

3

Ladd,
Miner,

"Education Expenditures," p.
p. 80.

150, n.

12.

51
he used it.

Percent population change was a significant

negative determinant in the one m o d e l in w h i c h he used
it.

In—m i gra t i o n into the state was not significant in

M c M a h o n 1s original r e s u l t s , and Miner found per c e n t movi n g
into the d istrict in the last five years to be insignifi ­
cant.

G e n s e m e r 1s percent of population w h o changed resi ­

dence b e t w e e n 1955 and 1960 was found to have an
insignificant negative e f f e c t . 1
Taxpayers in a dist r i c t with heavy out-migration
may share little in the benefits of education they finance
and thus may be more resistant to education expenditures.
Weisbrod was concerned w i t h benefit spillovers from out­
migration resulting in a suboptimal level of educational
expenditure.
. . . insofar as fiscal arrangements fail to bring
all of the beneficiaries of education wi t h i n the
d e c i s i on-making unit, spill-overs will affect the
level of education support.
The anticipation of
out-migration of locally educated children may be
expected to exert a depressing influence on e d u ­
cation expenditures, since m o s t of the benefits
from education will be lost to the origin a r e a . 2
. . . the model forecasts a negative correlation
b e tween public education expenditures per pupil
and "degree" of out-migration, other things being
equal.
. . . although the m o d e l forecasts that o u t ­
m i g r a t ion will tend to depress per-pupil e x p e n d i ­
tures on education, it does not necessarily
forecast the converse p r o p o s i t i o n — that
Denzau, "Survey," pp. 242-243; McMahon, p.
Miner, pp. 94, 98; and Gensemer, pp. 117-118, 151.
2
Weisbrod, p. 105.
1

249;

52
in-migration will tend to augment spending. . . .
In-migration to area A may, indeed, bring b e n e ­
fits from the education provided elsewhere; but
to the extent that these "spill-ins" are indepen­
dent of the education expenditures in A, the
spill-ins are a "fixed" benefit.
As such they
will not affect decisions at the margin.
The
conclusion is two-fold:
(1 ) anticipated out­
m igration tends to depress education expenditures
per student; but (2 ) anticipated in-migration has
no effect.^
Weisbrod was

limited to statewide figures and data on net

rather than gross migration.

However,

he found his p e r ­

cent change in population from net out-migration variable
to have a negative coefficient significant at the
level in accordance with his hypothesis.

. 0 1

Percent change

in population from in-migration had an insignificant
2
negative coefficient.
If renters do not believe that property taxes are
shifted fully to them,
group

which

they may constitute a special

would favor expenditure increases,

of which they do not expect to bear.

the costs

The variable Denzau

used in three models to reflect this effect was percent
of d w e lling units that are owner-occupied.

He found it

to have a significant negative coefficient in only one of
the three models.

The corresponding variable had an

insignificant negative coefficient in the original results
of James, Kelly and Garms and a significant negative

1

I b i d . , p.

106.

2I b i d . , p. 111.

53
coefficient in Davis'

results.

The original Barr and

Davis model, which gave Denzau his one significant result
for this variable, had not used this variable but the
number of owner-occupied residences in a county divided
by the number of registered voters.

They found this v a r i ­

able to have a significant negative coefficient as
h y p o t h e s i z e d .^
Stern used percent homes owner-occupied as a var i ­
able in one term of the denominator in his non-linear
specification for local expenditures.

Thus,

his estimate

of a positive coefficient for this term is consistent
with the other findings of an inverse relationship between
2
expenditure levels and percent of homes o w n e r - o c c u p i e d .
Peterson found percentage of renters among the
adult population to have a significant positive effect on
expenditures in estimates of demand based on district
data,

and a binary dummy for renter status had a positive

coefficient in an analysis of voting behavior.
Gensemer used percent of occupied hou s i n g units
renter-occupied as a variable and found it to have the
^Denzau, Appendix, Table 3; James, Kelly, and
G a r m s , p. 140; Davis, p. 104; and Barr and Davis, pp.
157, 158.
2
Stern, p. 94.
3
George E. Peterson, "Voter Demand for Public
School Expenditures," in Public Needs and Private Behavior
in M e t r o p o litan A r e a s , ed” John E. Jackson (Cambridge,
Mass.:
Ballinger Publishing Co., 1975), pp. 107-110.

54
expected positive sign;

however,

it was insignificant.

He rationalized this weak result by arguing:
It m a y be that renters do have the relatively
favorable attitudes toward local taxes which have
b e e n ascribed to them, but that their attitudes
have only a moderate positive influence on local
school taxes due to their frequent failure to
v o t e .^
And in further support of this view he noted:
A study of a Birmingham, Michigan, school millage
election revealed that although renters had p a r ­
ticularly favorable attitudes toward the school
tax a relatively small proportion of renters who
were eligible to vote actually did v o t e . 3
Variables Reflecting Different
Expectations and Aspirations
James, Kelly and Garins proposed that one explan a ­
tion for variation in educational expenditure levels is
"that the expectations for educational service held by
4
the p ublic differ among school districts."
But the
direct measurement of expectations with regard to educa ­
tion is most difficult.

The practical solution in those

studies considered here
. . . has been to identify socio-economic charac­
teristics which logically are related to expecta­
tions for educational services.
For example,
adult populations which themselves have attained
a high level of education w i l l usually seek a
■'"Gensemer, p.

151.

^ I b i d ., p . 139.
3
I b i d . , p. 139, n. 1.
4
James, Kelly, and G a r m s , p. 25.

55
high level of educational services for their chil­
dren. . . . Thus, our approach has been to use
demographic measures reflecting socio-economic
characteristics w h i c h on a priori grounds appear
to be related to expectations for educational
s e r v i c e s .I
The original study by James, Kelly and Garms found
median years of school completed by the adult population
over 25 years of age to be an insignificant determinant
of expenditures as did Denzau in the two models in which
he used this variable.
three variables:

The original Davis model had used

percent of residents over 25 w i t h one

or more years of college,

percent completing at least

eighth grade but wit h o u t college,

and percent completing

at least first but not eighth grade.
2
had insignificant coefficients.

A l l three variables

Gensemer also found median education of adults
over 25 to have an insignificant effect.

The sole exce p ­

tion to these findings of insignificant influence of adult
educational attainments was Stern's non-linear estimation
which produced a positive coefficient for median education
of adults.^
Other variables which m i g h t reflect aspirations
for their children's education are the occupations of the
adult population.

1

2
Davis, p.
3

Stern used percentage of the labor

I b i d . , p.

28.

Ibid., p.
104

140;

Gensemer,

p. 151;

Denzau,

"Survey," p.

and Stern, p. 94.

243;

and

56
force employed as p r o f e s s i o n a l , technical or kindred
workers and found it to have a positive coefficient.

Ladd

used the same group as a fraction of the popula t i o n and
found it to have an insignificant positive coefficient.
Gensemer constructed a more complex index of the o c c u p a ­
tional status of employed m e n and found it to have a significant positive coefficient.
The racial composition of the population may also
reflect d iffering aspirations with regard to education,
but the expected effect of this variable is ambivalent.
It m a y be expected that non-white parents p e r ­
ceive education as the primary means by which
their children can escape the confines of the
m i n ority subculture. . . . If this view prevails,
non-whites m a y be expected to support education
more vigoro u s l y than others.
On the other hand, it has been suggested that
non-white adults perceive little value in e d u c a ­
tion due to their experience w i t h segregated and
inferior schools and w i t h job discrimination.^
Non-whites as a percent of population was found
insignificant in all five of the models in which Denzau
used it.

A m o n g the corresponding original empirical

studies only Renshaw found this variable to have a sig3

nificant coefficient, which was negative.

However,

this

result m a y not reflect differing attitudes toward
■^Stern, pp. 93-94; Ladd, "Education Expenditures,"
p. 151; and Gensemer, pp. 112, 151.
2
Gensemer, p. 113.
3

Denzau, Appendix, Table 3; and Renshaw,

p.

172.

57
educational expenditures among the races.
observations were statewide expenditures
for the 48 states.

Renshaw's
for education

Shapiro also looked at statewide

expenditures throughout the country separately for the
years 1920,

1930,

1940 and 1950.

He found:

The r acial variable h a d no important explanatory
value w i t h i n either region [South or n o n - S o u t h ] ,
but it was highly significant in all years for
the United States as a whole; thus it was serv­
ing as an indicator of regional trait c h a r a c t e r ­
istics rather than in its own right.^
Thus regional differences m a y explain R e n s h a w 1s result.
G ensemer used the percent non-white variable in
his study of Michigan districts and also found it to be
insignificant.

Brown and Saks used fraction of wh i t e s in

the student popula t i o n in M i c h i g a n districts and found a
significant negative effect on local education revenues
per family.^
Gensemer included an unusual variable in his
expenditure equations,

the percent of district residents

born or whose parents w e r e born in a foreign country
other than Canada or the United Kingdom.
sized to r eflect attitudes

This was h y p o t h e ­

favorable to public expenditure

in general and not restricted to a particular interest in

1

2

Shapiro, p.
Gensemer, p.

161.
151;

and Brown and Saks,

p. 20.

58
education.

The estimated coefficient was positive but

not s i g n i f i c a n t . 1
Other Variables
Some studies,

such as that of Hirsch,

have used

some m e asure of the quality of education as an explanatory
variable in the expenditure equation.

It is important to

recognize that when such a variable is included the coe f ­
ficients of the other variables then reflect "the impor ­
tance of different factors in relation to per pupil
expenditures for a given quality of education."

The

present study is concerned with the determinants of e d u c a ­
tional opportunities offered in different districts,

not

differences in the costs of education of given quality.
It is the difference in quality that is to be explained;
therefore,

it would be inappropriate to include this as

an explanatory variable.

That costs may vary for educa­

tion of a given quality is recognized as a weakness of
using per pupil expenditures as a measure of educational
opportunity.
A nother set of variables that w i l l be,
most part,

for the

disregarded here are variables reflecting dif­

ferences in political institutions.

The exclusion of

these variables is justified because the observations are

1

2

Genseraer, pp.
Hirsch,

118,

151.

"Public E d u c ation Expenditures," p.

33.

59
all w i t h i n a single state in which all school districts
face similar legal constraints.
One political variable that will vary within the
state is the social heterogeneity of the community.

Gen ­

semer argued that greater heterogeneity would reduce
expenditures:
If preferences are substantially dissimilar among
individuals or groups in the community, consensus
is difficult to obtain and elected officials find
it difficult to respond to the challenges of
growth and change in a decisive manner.
Community
h e t erogeneity may thus be expected, ceteris pari­
bus , to introduce a downward influence upon the
level of public service expenditures and taxes.^
Gensemer used a measure of educational heterogeneity of
adult males but found this variable to have an insignifi2
cant effect.
The Price Variable
In an indivualistic model in which collective
choice is assumed to result in the selection of the median
voter's preferred level of expenditures,

one must consider

the price of government services which the median voter
perceives.

Assume that among the arguments of the voter's

utility function is educational services per pupil,

E.

The "price" of such services to the individual is the
amount he believes it will cost his household if educa­
tional services per pupil are increased by one unit.
^ G e n s e m e r , p . 21.
2

I b i d ., pp.

70-71,

151.

60
If one unit of educational services is produced
by one unit of a bundle of inputs,

one factor in the

voter*s price w i l l be the input price index,

Pi.

The

total cost of increasing per pupil educational services
will be Pi * Pu, wh e r e Pu is the number of public school
pupils.

But this cost will be shared among the F fami­

lies in the school district,

so F appears in the denomi n a ­

tor of the voter's price variable.
district is on a matc h i n g basis,

If state aid to the

such that state aid wi l l

pay a fraction M of any increase in total operating
expenditures,

one dollar of additional education expend i ­

tures will cost the district only $(1 - M )
the price term includes the factor

. 1

(1 - M ) .

Therefore,
Furthermore,

voters may believe they bear only that share of the tax
burden w h i c h is levied against residential property.

In

this case the price term will also include the factor R,
the fraction of the local tax base which is residential
property.

Finally,

the median voter's share of the cost

of education will be more or less than the average cost
Hm
per household as ?=— , the ratio of the median voter's
r l 3.

assessed residential property to the average assessed
residential property per household,
than one.

is greater or less

The resulting price for the me d i a n voter is

■^This definition of M corresponds to that used by
Feldstein, p. 78, and is different from the m defined in
Ladd, "Education Expenditures," p. 148.

61

P = Pi ~

(1 - M)

R g—

(2.1)

How successfully have previous studies incorpora­
ted these factors among the determinants of educational
expenditures ?
The Local and Residential
Share Factors
In his estimations of the Davis and Wilensky
models, Denzau used a "taxprice" equal to "the median
house value divided by tax base per pupil."'1'

The results

for both models gave significant negative coefficients
for this

taxprice

term but insignificant coefficients

for another

"taxprice" consisting of the ratio of median
2
house value to the tax base.
The latter variable would
be appropriate if the voter's utility were a function of
total, rather than per pupil,

educational services.

The closest thing to a taxprice term in the
original Davis study was per capita industrial property,
which had a significant positive coefficient in Davis'
regression results.

Similarly, Wilensky's percent indus­

trial property variable had a significant positive coeffi­
cient.

From this estimate of the elasticity of expendi­

tures w i t h respect to the proportion of the property tax
^Denzau,
2

"Survey," p.

Denzau, Appendix.

24 6 .

62
base w h i c h is industrial,

she approximated the price

elasticity by m u l t i plying by the ratio of residential to
industrial property taxes.
was -.51.

The resulting price elasticity

In G e n s e m e r 1s results the industrial proportion

of the tax base had a positive b u t insignificant coeffi­
cient. ^
Feldstein found the omission of match i n g rates
among the explanatory variables to be pervasive in p u b ­
lished work prior to his own with the exception of Inman
2
and Stern.
In part this is due to the pervasiveness of
foundation plans in which aid was not on a matching basis.
Feldstein's specification was log linear and had
separate terms for the logarithm of the residential frac­
tion of the tax base,

In R, and the logarithm of the local

share of marginal expenditures,

In

(1 - M ) .

His estimates

of the elasticity of expenditures w i t h respect to

{1 - M ) ,

which he referred to as the "price elasticity," ranged
3
from -.940 to -1.599.
Theory leads one to expect In R
to have the same coefficient.

Feldstein's results did

not agree with this expectation and he explained that

^ D a v i s , p. 10 4; Wilensky, pp. 151-152; and G e n ­
semer, p. 151.
2
Feldstein, p. 80.
Reference is to Inman, "Econo­
metric Model," and "Four Essays on Fiscal Federalism"
(Ph.D. dissertation, Harvard University, 1970), and Stern.
3

Feldstein, p . 82.

63
although measurement error m a y have biased this
coefficient toward zero, it seems safe to infer
that the true elasticity is actually less than
the price elasticity; this implies that voters
assume that a significant part of the nonresidential tax is shifted to residents in the long run.l
Feldstein's estimated elasti c i t y w i t h respect to
the residential fraction of the tax base may differ from
the elasticity with respect to
reason.

( 1

- M)

for an additional

He included total assessed w e a l t h per pupil among

his explanatory variables.

In an individualistic model

the appropriate w e a l t h variable is residential wealth.
Thus, it wo u l d be necessary to mult i p l y the total assessed
wealth v a riable by the residential fraction of the tax
base variable,

R.

Ladd showed that the correct comparison

of her results w i t h Feldstein's was bet w e e n Ladd's elas­
ticity w i t h respect to R, w h i c h was bet w e e n -.30 and -.31,
and Feldstein's elasticity w i t h respect to R, which was
-.09, minus his elasticity with respect to total wealth
per pupil,

.23.

Thus,

Feldstein's results reinterpreted

by Ladd give an elasticity w i t h respect to R of
-.09 -

.23 = -.32,

quite close to Ladd's own estimates.

1

I b i d . , p.

3

83.

2

Of. Ladd, "Public Expenditures," p. 92,
"Education Expenditures," p. 148.
^Ladd,

"Public Expenditures," pp.

and

110-112.

64
As an additional comparison w i t h this adjustment
of Feldstein's results,

note that Barlow found the elas ­

ticity w i t h respect to the non-industrial fraction of the
tax base to be -.34 when income per pupil but not total
wealth per pupil was included as the other explanatory
1
variable.
Like Feldstein,

Grubb and Miche l s o n found signi f i ­

cantly d i f f erent elasticities w i t h respect to

( 1

- M) and

R, the residential fraction of the tax base, but they also
included assessed value among the explanatory variables.
Another unusual result from their study was that the
elasticity with respect to

(1 - M) was found to be nega ­

tively r e lated to the school tax rate.

For example,

in

their log-linear specification they found the elasticity
of local revenue with respect to

(1 - M)

to be

1.352 - .0643 r
(.778)
(.029)
where r is the school tax rate and standard errors are

2

shown in p a r e n t h e s e s .

Robin Barlow, "Efficiency Aspects of Local
School Finance," Journal of Political Economy 78 (Septem­
ber/October 1970):1034.
2
Grubb and Michelson, pp. 124, 127.

65
Possible Perceived Shifting
of Non-Re srdentxal Taxes
Determining the effect of differences in the
composition of the tax base was one of the principal
objectives of Ladd's dissertation.

Since we are inter­

ested in the effect on expenditures, w h a t matters is the
perceived incidence of taxes on commercial and industrial
property.

We need not estimate the actual incidence of

taxes on these components of the tax base.
Rather than using the residential fraction of the
tax base as an explanatory variable,

Ladd used

R* — 1 - aC - 01,

(2.2)

where C and I are commercial and industrial fractions of
the tax base,

respectively,

foe estimated.^-

and a

and

0

are parameters to

The estimates of a and 0 w e r e made by

searching over plausible values and choosing those that
minimized the sum of squared r e s i d u a l s .
If voters believed they bore none of the burden
of taxes on commercial and industrial peoperty,
would be equal to one.

a and

0

Under "modern" theories of

property tax i n c i d e n c e , 2
1

*

The expression actually used for R also accounted
for v acant land and the ratio of realty to the total tax
base.
Ladd, "Public Expenditures," p. 150, n. 11.
2
E.g., Peter Mieszkowski, "The Property Tax:
An
Excise Tax or a Profits Tax?"
Journal of Public E c o n o m ­
ics 1 (April 1972):73-96.

66
. . . it is argued that while the burden of a
u n iform rate national tax on all property will
fall on owners of capital, the burden of local
differentials will be borne by local residents
either as landowners, consumers, or relatively
immobile workers, as mobile capital flows from
high rate districts to low rate districts.^
Assume the owners of both commercial and indus­
trial p r o perty are not voters in the dist r i c t or are so
small in numbers and influence as to be politically
irrelevant.

Residents considering the effects of such

relocation of capital on the size of the future tax base
would then perceive some burden from increasing current
taxes on non-residential property.

Since industrial might

be more m obile than commercial firms, w h i c h are tied to
local markets, we would expect the commercial property
tax incidence parameter, a, to be greater than the indus­
trial tax incidence parameter,

g, w i t h both b e i n g less

than o n e .
Under the traditional v i e w of property tax inci­
dence, the tax is passed on to consumers in the form of
higher prices.
sizes of a

In this case we mi g h t expect the relative

and 3 to be reversed because the local indus­

trial firms, p r o d ucing for a wider market, w i l l not have
the power to raise prices and because a smaller pr o p o r ­
tion of local industrial output is sold locally than that
of commercial firms.
1Ladd,

"Public Expenditures," pp.

21-22.

67
When Ladd's equations were specified as log-linear
and e s t i mated by minimizing the sum of squared residuals,
the estimates of the commercial tax incidence parameter,
a, ranged from

.71 to .74 and those of the industrial

tax incidence parameter,

3, from .39 to .41.

This is con­

sistent w i t h the "modern" view of property tax incidence,
assuming industrial firms are more mobile.
the coefficients of In R
an estimate of

*

and In

.79 for a and

stein's results,

(1 - M)

.45 for 0.

Constraining

to be equal gave
Contrary to Feld-

Ladd reported the hypothesized equality

of the coefficients of In R

and In

(1 - M)

cannot be

rejected accor d i n g to an F test.'*'
Among the threats to the validity of Ladd's
approach is the conjecture that assessment ratios for
business might be varied in response to millage rate
changes, ma k i n g revenues from business property equivalent
to a lump sum grant.

Edelson rejected this assumption

as being unrealistic in view of the uniformity provisions
2
of state constitutions.
Non-residential property m i g h t affect voter demand
for p ublic education in ways other than its effect on the
perceived price.

Omission of variables reflecting these

considerations from the specification w o u l d bias the

1

2

I b i d . , pp.

105,

Edelson, p. 160.

123.

68
*

estimates of a,
these lines,
property:

and the coefficient of In R .

8

Along

Ladd noted two potential effects of business

(1 ) an "externalities effect," w h i c h alters the

production function and thus the cost of public services,
and

(2 ) a "direct demand effect," w h i c h refers to the

reduction of r e s i d e n t s 1 disposable income to finance p u b ­
lic services benefi t i n g business but not residents,

at

least not d i r e c t l y .^
In regard to the direct demand effect,

if it is

assumed that b u s i ness-related expenditures are determined
by characteristics of business property,

etc., but are

independent of the level of r e s i d ent-related services,
the specification can be adequately modi f i e d by including
the level of business-related expenditures as an explan a ­
tory variable.

This is discu s s e d b e l o w w i t h the municipal

overburden argument.

Only if services to business are

dependent on the level of services to residents is the
,
*
price factor, R , affected.
To make the appropriate modification in the R

*

factor,

it would be necessary to know

the exact relationship between business- and residentrelated public services.

2

Ladd did not incorporate the externalities effect
in the price term but considered this to be reflected in
^Ladd,

"Public Expenditures," p.

^ I b i d . , pp.

43-55.

10.

69
the influence of the same variables r e p r e senting direct
1
demand effects.
Ladd also considered the p o s s i bility that indus­
trial property might be correlated with omitted taste
variables.
. . . a high positive correlation bet w e e n the
fraction of local residents w h o work in blue col­
lar jobs and the fraction of the tax base that is
industrial combined w i t h a negative effect of
resident blue collar workers on the local demand
for education would bias downward the estimated
parameter 3. This hypothesis is tested and r e j e c ­
ted in equation 4 in w h i c h the number of residents
who w o r k in manuf a c t u r i n g jobs divided by the
total resident population (BLUE) is added to the
e ducation demand equation. . . . the variable BLUE
(in log form) is statistically insignificant and
has little effect on the other parameters includ­
ing the relationship of a to 3 .
Ladd suggested further research into the effects
of the composition of the property tax base mi g h t inves­
tigate w h e t h e r these effects are diffe r e n t outside m e t r o ­
politan areas where the potential effect on jobs from
firms relocating m i g h t be greater but, on the other hand,
3
firm m o b ility mi g h t be reduced.

Ibid., pp. 61, 125, n. 31.
Cf. Nunn's criticis m
on this point in James R. Nunns, "Discussant," Proceedings
of the Sixty-Seventh Annual Conference on T a x a t i o n ,
National Tax A s s o c i a t i o n , 1974, p. 609.
2

Ladd,

"Public Expenditures,

3 I b i d . , p.

192.

pp.

118-119.

70
Problems in Identifying the
Median Voter's Share of
the Tax Base
Ladd's assumption

"that all residents are h o m e ­

owners and that the hou s i n g and location decisions of
all families have already been made"'*' is questionable.
Renters m a y not believe they b e a r the full burden of
property taxation of their residences;

this will affect

the identify of the median voter and his perceived price.
In her analysis of non-school expenditure,

Ladd included

the p e rcent renters variable as a separate explanatory
variable but did not incorporate it into the price term
2
as w o u l d be theoretically desirable.
Ladd also considered the
term.

na

factor in the price

She assumed the me d i a n voter's residence had a

value equal to the median hou s i n g value in the district.
This involves problems related to those arising from the
assumption that the me d i a n voter has me d i a n income which
are d i s cussed below.

Furthermore,

there w e r e problems in

calculating the ratio from Census of Housing data.

Lastly,

there was small v a r i ation in the calculated value of the
ratio across communities.

Given these problems,

it is

not surprising that in the one regres s i o n w h i c h Ladd

^ I b i d ., p . 14.
2

Cf. Nunns, pp.

609-610.

71
showed using this variable it was i n s i g nificant and had
the w r o n g s i g n . 1
The Input Price Factor
A lthough an input price index was included in the
price term in Ladd's theoretical development,

she did not

include any such explanatory variable in h e r regressions.
She argued that this omission could
. . . be parti a l l y justified on the assumption
that the observations come from a single market
area in w h i c h the prices of factor inputs are con­
stant across communities. . . . While it w o u l d be
desirable to include an index of teacher salaries
as an explanatory variable, difficulties arise in
defining an index fully corre c t e d for quality d i f ­
ferences .2
Feldstein remarked on his failure to find an input
price variable which had a significant effect:
In some estimates not reported in the paper, an
educational input price index was included and
found to be insignificant and sometimes to have
the " wr o n g ” sign; this suggests that much of the
price variation reflects qual i t y differences and
therefore local c h o i c e . 3
It was not surprising that Feldstein's price index
picked up quality difference effects because it was a
weighted average of average teacher salaries and the
wholesale price index, w e i g h t e d accor d i n g to the shares
^"Ladd,

"Public Expenditures," pp.

93,

105,

10 8 ,

202-204.
2

Ladd,

"Education Expenditures," p.

3
Feldstein,

p.

81, n. 10.

149, n. 10.

72
of teacher salaries and of other costs in current expen d i ­
tures .

The use of the wholesale price index for the price

of non-teacher inputs in all districts was justified on
the grounds that these inputs were bought in a single m a r ­
ket by all districts.'*'

M i n e r pointed out the error of

using average salary as an input price index and suggested
an alternative which controls for quality:
Average salary is not a determinant of spending
but the consequence of a decision about the
quality of the educational services to be p r o ­
vided, based, probably, on preferences and
capacity to pay. . . . While the over-all
qu ality of education varies from one school sys­
tem to another, it is probably true that the
productivity of beginning teachers w i t h u n d e r ­
graduate B .A. degrees is not greatly diverse.
. . . Most salary differences among teachers
appear to be the result of state and local finan­
cial circumstances coupled w i t h strong p r e f e r ­
ences by teachers for particular geographical
locations.
An index of begin n i n g teachers' sala­
ries under these circumstances is a mea s u r e of
the cost of obtaining a homogeneous input in
various school s y s t e m s . 2
Gensemer extended the argument for the use of
beginning teachers' salary levels:
. . . in hi r i n g begin n i n g teachers school boards
cannot judge teaching skill. . . . For this rea­
son beginning t e a c h e r s ' salaries cannot be used as
a tool with which to attract high quality t e a c h ­
ers, and these salaries are accordingly determined
by labor m a r k e t conditions rather than by school
board decisions concerning the qua l i t y of teacher
d e s i r e d .^
1

Ibid.,

p.

82, n. 15.

Miner, p. 78,
3
Gensemer, p. 123.
2

73
Miner's regressions

for a nationwide sample of

observations resulted in positive coefficients on the
salary v a riable in all four expenditure e q u a t i o n s .

This

is consistent w i t h a price inelastic demand for educa­
tional services.

However,

his analysis for a sample of

Michigan districts found a negative coefficient for the
salary variable.

This contrasts w i t h a positive but

insignificant coefficient for this variable in Gensemer's
results,

also based on Mich i g a n data."*"
Brown and Saks used another approach to control

for teacher quality.

They regressed average teacher

salary in a district on average years of experience and
proportion of teachers with master's degrees
form).

(in quadratic

The residual average teacher salary in each dis­

trict was then taken as a measure of cost differences
between districts and included as an explanatory variable
in their equation for local revenue per family.

The

estimated coefficient was negative and insignificant.

2

The Pupils Per Family Factor
Ladd omitted the factor

PU

public school pupils

per households,

wh i c h is included in the price term

derived above.

She assumed that educational services c o n ­

sumed by the voter's family was an argument of his utility
^Miner, pp. 105, 119; and Gensemer,
2
Brown and Saks, pp. 17-18, 20.

p.

151.

74
function.

She apparently adopted Edelson's assumption

that the v o t e r ’s demand for public education depends only
on his own children and ignores external benefits that
may arise from the education of other children.^"

Ladd

argued that the ratio of the number of public school
pupils in the median voter's family to the average number
of pupils per family should theoretically be a factor in
the price term but can be ignored because it is likely
2
to be relatively constant across districts.
If we made an assumption analogous to that adopted
by Zimmerman in his study of welf a r e expenditures,

that

the "transfer rate" is an argument of the voter's utility
3

function,

public education services per pupil w o u l d be

an argument of the voter's preference function and pupils
per household w o u l d be a factor in the price term as it
4

is in

(2.1)

above and as Peterson

specified it.

Barro used a district preference function rather
than an individualistic m o d e l but, because he included
expenditures per pupil and tax bu r d e n per household as
arguments of the preference function, he also concluded
1

Edelson, p.
2
3
4

Ladd,

163.

"Public Expenditures," p.

Zimmerman,

pp.

17, n. 13.

227-239.

George E. Peterson, "The Demand for Public
Schooling:
A Study in Voting and Expenditure Theory"
(Washington, D . C . : Urban Institute, 1973).
(Mime­
ographed. )

75
that pupils per household should be a factor in the price
term.

However, he considered two possibilities that mi g h t

lead to a different result:
1.

One m i g h t include pupils per household as a

separate argument in the preference function reflecting
taste differences in communities w i t h more families with
children and/or larger families.

This leaves pupils per

household as a factor in the price term but it also
appears as a separate term in the expenditure equation.
2.

Using education services per household as an

argument of the preference function eliminates pupils per
household as a factor in the price term.

It m a y remain

as a separate term in the expenditure equation if it is
incorporated as a "taste" variable in the preference
function.^
Including percent families w i t h children as an
interest group variable

(as discussed above)

m i g h t allow

a test of whe t h e r pupils per household has a price effect
alone or whether family size reflects a difference in
tastes for education or has an income effect.

Stephen M. Barro, Theoretical Models of School
District Expenditure Determination and the Impact of
Grants-in-Aid (Santa Monica, C a l i f . : Rand Corporation,
1972), pp. 23-25.

76

Comparison of Estimates of
"Price" Elasticity
Inman's tax price was equivalent to R(1 - M)

r

lia

except that he also included a factor to reflect federal
and state tax deductions and credits for local property
taxes.

His estimates of the price elasticity w e r e -.34

and -.41.

These can be compared to Ladd's estimated

elasticities with respect to R*(l - M ) , w h i c h ranged from
-.6320 to -.6529,

and Feldstein's estimates of the elas­

ticity w i t h respect to
to -1.599.

(1 - M) , w h i c h ranged from -.9 40

Inman's lower price elasticity may be because

most of the variation in his data was in the residential
share of the tax base, which is an inappropriate price
factor if there is some p e r c eived shifting of nonres idential t a x e s .^
These price elasticities of educational spending
can be compared to estimates of the "price" elasticities
of other public expenditures.

Ladd examined the demand

for all non-school municipal expenditures with the price
variable simply the residential share of the tax base and
found elasticities ranging from -.4915 to -.30 46.
When
*
she used the R variable allowing perceived shifting of

Ladd, "Education Expenditures," p. 151,
"Public Expenditures," p. 105; Feldstein, p. 82;
Inman, "Optimal Reform," pp. 47-48.

and
and

77
non-residential taxes,

the estimated elasticities ranged

from -1.015 to - . 5 0 6 0 . 1
Bergstrom and Goodman did not consider the price
effects of matching aid an the grounds that little revenue
for the services studied came from other g o v e r n m e n t s .
They used a "tax share" variable w h i c h was the ratio of
the m edian assessed house value to the total property
tax base.
states,

Pooling observations of municipalities in ten

they found tax share elasticities for general

expenditures, police expenditures,
ation expenditures of -.23,

and park and r e c r e ­

-.25 and -.19, respectively.

But the estimated elasticities va r i e d w h e n based on
observations in only a single state.
only M i c h i g a n data,

For example, using

they estimated tax share elasticities

for general expenditures,

police expenditures,

and recreation expenditures of -.41,

and park

-.76 and +.25,

respectively.

The positive elasticity for parks and

recreation was

statistically insignificant.

Gramlich and Galper used a price term consisting
of the relative price of inputs m u l t i p l i e d by one minus
the m a t c h ing rate.

Using pooled cross-section data for

ten large urban governments

from 1962 to 1970,

they found

1

Ladd,
2

"Public Expenditures," pp.

65,

83.

Theodore C. B e r g strom and Robert P. Goodman,
"Private Demands for Public Goods," Ameri c a n Economic
Review 63 (June 1973):280-296.

78
elasticities of total discretionary expenditures with
respect to the "prices” of public safety services,

of

social services and of urban support services to be -.71,
-.74 and -.92,

respectively.

They found the price of

education to have no significant substitution effect.
These estimates are difficult to compare with others
because they measure the elasticities of total city
expenditures w i t h respect to the prices of particular
public services and because the concept of discretionary
expenditures excludes expenditures required to match
closed-end categorical aid.'*'
Despite the difficulties in comparisons w i t h the
Gramlich and Galper results,

it seems safe to say that

these three studies of non-school local government
expenditures are similar to the studies of education
expenditures in showing the elasticities w i t h respect to
the m a t ching rate factor and w i t h respect to the modified
residential share of the tax burden,
shifting of non-residential taxes,

allowing perceived

to be larger than the

elasticities with respect to the median voter's share of
the p r o perty tax b a s e .

Edward M. Gramlich and Harvey Galper, "State
and Local Fiscal Behavior and Federal Grant Policy,"
Brookings Papers on Economic Activity (19 73:1), pp. 4243.

79
Ability to Pay Variables
The desired level of education services should be
a function of ability to pay.

The single best measure of

ability to pay is probably family income.

It is not then

surprising that Denzau found me d i a n family income to have
a significant positive coefficient in seven of the nine
models in w h i c h he used this variable,

and the two e x c e p ­

tions can be explained by m u l t i collinearity w i t h equalized
assessed value per pupil, which was also included as an
explanatory variable in these models.'*'
Reasons for Not Using Assessed
Value Per Pupil
It was briefly mentioned above that it is inappr o ­
priate to include total assessed wealth per pupil as a
measure of ability to pay in an individualistic model.
The n on-residential component of total assessed value has
a price effect as discussed above but does not represent
the w ealth of individual voters.
There are also simultaneous equations problems
when assessed value is included as an explanatory variable
because it is an endogenous variable, w i t h taxes and p u b ­
lic expenditures both affecting property values.

Thus,

Reischauer and Hartman argued in favor of family income

1Denzau,

"Survey," pp.

242,

246.

80
. . . as an alternate measure of fiscal capacity
that avoids some of the problems of the per-pupil
property value index.
In the first place, it
does not exhibit such unrealistic variations in
school district capacities.
It also avoids the
problems arising from the possible capitalization
of tax advantages into housing costs because it
assumes that if two neighboring districts house
families of similar incomes they w i l l have equal
fiscal capacities irrespective of their property
tax bases.
Estimates of Income Elasticity
While income is generally acknowledged as a sig­
nificant explanatory variable,

the magnitude of the elas­

ticity of education expenditures with respect to income
is disputed.

Feldstein found the elasticity to be around

.48, but he also included total assessed value per pupil
among the explanatory variables.

Ladd found income elas ­

ticities in a range from .42 to .45; however,

she included

residential wealth as an explanatory variable and argued
that the total income elasticity should be taken as the
sum of this partial income elasticity and the product of
the elasticity of education expenditures with respect to
residential property value and the income elasticity of
demand for housing.

This gave an income elasticity for

education expenditures close to the lower limit of the
2
.85 to 1.35 range found by Peterson.
1Reischauer and Hartman, p. 70.
2
Ladd, "Public Expenditures," pp. 109-110.
The
reference is to Peterson, "The Demand for Public School­
ing ."

81
Ladd's estimates were based on Massachusetts
data.

Inman's estimate of the income elasticity, with

no property value variable included, was

.60 based on

1

Long Island data.

Hirsch's income elasticity estimated

on St. Louis county cross-section data was also on the
low side at .519 but this also had assessed value per
pupil among the variables.

2

His time series study did

not include such a variable and found an income elasticity
of 1.09, the higher elasticity having been expected from
3
time series analysis.
It is possible that these differ­
ences may be explained by different effects of socio­
economic variables in different areas similar to Shapiro's
finding that per capita personal income was a highly sig­
nificant determinant of expenditures outside the South
but was insignificant in that region.^
Not all of these studies have used median family
income as did Denzau.
income,

For example,

Davis used per capita

and Rens h a w used income per capita and per school-

age child, both of which w o u l d pick up possible income
effects from the children per household variable.

When

1

Inman,
2

Hirsch,

"Optimal Reform."
"Public Education Expenditures," pp.

38-39.
■^Werner Z. Hirsch, "The Costs of Public Educa­
tion," in The Economics of E d u c a t i o n , ed. Charles S.
Benson (Boston:
Houghton Mifflin, 1963), pp. 156-157.
4
Shapiro, p. 163.

36,

82
Renshaw used income per child and school-age population
as a percentage of total population as explanatory vari­
ables in the same equation,
negative coefficient

the latter variable had a

(indicating a price effect rather

than an interest group effect?)

and the relationship wit h

the income variable was not as strong as that w i t h income
per capita.
Variables Reflecting
Permanent Income
A nother variation in the income variable used
arose from the desire to use a variable reflecting perm a ­
nent income.

Fabricant used average income for the pre­

ceding five years.

Ladd rationalized the inclusion of

residential property per pupil on this basis,

although it

is not clear why this is in per pupil terms when her
income variable is family income.
permanent income rationale,

In addition to the

she argued exclusion of the

residential wealth variable w o u l d bias the estimate of
2
the price elasticity.
The unemployment rate had a significant positive
coefficient in McMahon's time series analysis and in the
cross-section study by James, Kelly and Garms.

In the

time series analysis this is explicable as reflecting the
^Renshaw,
2

p.

173.

Fabricant, p. 122, n. 9; Ladd, "Education Expendi
tures," p. 148, and "Public Expenditures," p. 92, n. 7.

83
difference between current and perma n e n t income.

This

explanation does not seem as valid for the cross-section
results.

Because such a significant coefficient was not

found in other studies not using a large city sample,
James,

Kelly and Garins speculated that in the large school

districts

"certain rigidities in the institutional

arrangements for education kept the level of services
high even after some of these socioeconomic indicators
had turned downward.
Gensemer used an "economic strength" variable
defined as family income per school child plus imputed
local property income per public school pupil.

The

latter c o mponent of economic strength was calculated by
assuming the market value of property was twice state
equalized value and using an average rate of return on
property of ten percent.

Economic strength was one of

the three significant determinants of operating expendi2
tures per pupil in Gensemer's results.
Effects of the Distribution
of Income
The use of median family income in expenditure
equations implicitly assumes that other characteristics
of the community income distribution do not affect
1

2

James, Kelly,

and G a r m s , p.

Gensemer,

46,

pp.

109,

151.

112.

84
expenditures.

In a me d i a n voter m o d e l this is appropri­

ate if the med i a n voter has the me d i a n income.

Ladd

justified the use of median income in her expenditure
equation by a theorem given by B e r g s t r o m and Goodman
allowing the use of median income alone under certain
assumptions.

However,

Ladd claimed too much for the

Bergstrom-Goodman theorem in stating that
. . . it has been shown that the use of median
family income to represent the income of the
me d i a n voter in cross sectional analysis can be
justified even if the demand for education is not
a m o n ot o n i c function of income as long as income
distributions across communities m e e t certain
regularity a s s u m p t i o n s . 1
B ergs t r o m and Goodman discussed demand functions
that are not monotonic functions of income as one condi­
tion that may lead to the median voter not being the
citizen with me d i a n income, but because the proof of
their T h e o r e m 1 assumes constant price and income elas­
ticities of demand and constant income elasticity of tax
share

(which means demand ijs a monotonic function of

i n c o m e ) , they explicitly stated:
If there were frequent and substantial v a r i ­
ations of this kind, our procedure would not be
e xpected to give reasonable estimates of the
income elasticity of d e m a n d . ^
Differences in the tax share functions for d i f ­
ferent segments of the population m a y also create a
^"Ladd, "Education Expenditures," p. 148.
2
B ergs t r o m and Goodman, p. 2 86.

85
situation in w h i c h the voter w i t h median demand is not
the citizen w i t h median income,

and it is in this case

that their Theorem 1 justifies the use of median income
in the expenditure equation.

The theorem allows the use

of m edian income in the expenditure equation "even though
there may be differences in tastes or in tax share sched­
ules w i t h i n c o m m u n i t i e s . "^
more restrictive than this.

But the conditions are even
The the o r e m explicitly

requires that the tax share function,

although differing

among d i f ferent segments of the popula t i o n
have a "proportional"

income d i s t r i b u t i o n ) , m u s t have an

equal constant income elasticity.
itly stated,

(which must

Alth o u g h not ex p l i c ­

any "differences in tastes" must not affect

the price and income elasticities of demand since these
are taken as constants in the proof.
Brown and Saks developed an approach that can be
used when the median voter does not have the me d i a n income
and demand is not a monot o n i c function of income.

There

are two factors that m a y cause individuals with different
incomes to prefer d i f f erent levels of expenditure for
public education:
1.
given tax price,

The utility function m a y be such that,
individuals desire to spend a larger or

smaller fraction of their income for public education at
different income levels.
^Ibid.

for a

86

2.
levels.

The tax price may vary at different income

If people with different incomes face different

"prices" for a public good,

they will have diffe r e n t views

about increasing the level of expenditures even if the
marginal rate of substitution between public and private
goods were the same.
As an example of the effect of the second factor,
assume assessed residential property values are proportional to income.
R
i

Hi
th

Then the "price" to the i

th

voter is

Pn
(1 - M) -p- f where Hi is the assessed value of the
voter's residence.

This "price" is an increasing

function of i n c o m e .
The combination of these two factors m a y result
in U-shaped fractional Engel curves for public education.
The poor may want to spend a larger fraction of their
income on public education because of the low price and
the rich may favor higher tax rates because utility func­
tions incorporate greater
income levels.

" p u b l ic-regardingness" at higher

1

This is illustrated in Figure 2.
three voters w i t h incomes
assessed values

, Y 2 / and Y^ and homes with

, and

.

each voter are given by

1

Brown and Saks, p.

Assume there are

8.

The

"prices"

faced by

87

Y

Y

3

2

Y
1

0

E„ E

E

Figure 2.— Individual Choice at Different Income Levels.

88

p± = R H
and home value,

( 1

■ M> ¥ ■

<2-3)

Hi, increases with income

Y 1 < Y2 < Y 3
H,

< H2

< H3

(2.4)

Assume all three individuals have identical utility func­
tions, represented by the indifference curves drawn in
Figure 2,

However, each faces a different budget con­

straint,
Y i = Yd +

(2.5)

where Yd is disposable income after school taxes.

Thus,

the b udget constraint is steeper for higher income levels
because of the difference in price.
The middle income voter prefers expenditure level
E2

1

w h i c h is smaller, both in absolute size and as a

share of personal income,

than the expenditure levels

and E^ preferred by the low and high income voters.
B rown and Saks showed that using an expression
involving median income alone results in biased estimates
of the Engel curve.

The bias is a function of median

income, Y, and the Gini coefficient,

G.

Specifying the

local revenue per family equation in the form

89

L = 0O + &iY + ^ 2

+

,
fr-GY* +
5

K
I
i=

+

y 2

6

3GY + B4G

y 2

B.X.
6

1

f 2 .6 )

1

they found the bias, measured by the terms involving GY,
2
3
GY , and GY
to be statistically significant at the
level.

.05

The unbiased estimated Engel curve was U-shaped

with a m i n i m u m at about $10,300 while the bia s e d curve
was m o n o t onically decreasing.^The Effects of N o n - Matching Aid
In addition to the private incomes of the resi­
dents of the district,

another contribution to ability to

pay comes from state and federal aid.

A i d that is on a

matching basis is considered in the price variable but
aid that is independent of the level of local revenues
must also be considered.
A frequently discussed question with regard to
such block grants or lump-sum aid is to what extent it
stimulates expenditures for the aided function and to
what e xtent it merely substitutes for locally financed
expenditure.

Match i n g aid w o u l d be expected to have a

^Brown and Saks, pp.

18,

23.

90
more stimulative effect because its effect on price has a
i
substitution as well as an income effect.
If the dependent variable is total expenditure per
pupil and aid per pupil is among the independent variables,
a coefficient for the aid variable less than one indicates
that part of the aid substitutes for locally financed
expenditure.

This is consistent w i t h Brazer's estimate
2
of this coefficient of .29
and Renshaw's estimate of .16.
However,

Renshaw's estimate increased to

.38 w h e n mandated

revenue required to participate in the aid p l a n was con­
sidered and to .51 w h e n income per school-age child,
rather than per capita, was used in the equation.^
The results from L a d d ’s log linear specification
gave a m a r g i n a l impact of non-matching state aid on total
expenditures of about 50 cents for each dollar of aid.
But Ladd included categorical state aid in a separate
term w i t h federal aid and found this variable to have a
marginal impact of about $1.10.
was

She argued this result

"consistent w i t h the view that these grants are for

"^Although the difference may be small for m a t c h ­
ing and n o n - m atching plans when both have very large
grants.
Cf. James A. Wilde, "The E x p e n diture Effects of
Grant-in-Aid Programs," National Tax Journal 21 (September
1 9 6 8 ) :343.
2
Harvey E. Brazer, City Expenditures in the Un i t e d
S t a t e s , Occasional Paper No” 6 6 (New York:
National
Bureau of Economic Research, 1959), pp. 54-55.
3
Renchaw, pp. 17 2-173.

91
specialized purposes on w h i c h local communities w o u l d have
spent less than the allotted amount in the absence of
aid.

This is also consistent w i t h Denzau's results that

" 1

the coefficient of federal aid is not significantly dif2
ferent from o n e .
Feldstein also separated state block grants from
a federal grants variable which included state grants for
special programs.

The elasticity of the former variable

was usually much less than that of the federal grants
variable, as expected.

The ordinary least squares esti­

mate of the state grant elasticity based on 1970 data
implied a marginal impact of about 60 cents for each
dollar of aid.

Felds t e i n argued this was biased upward

because block grants were endogenous,

going only to towns

that passed the limit of m a t c h i n g aid in 1970.

The 1965

equations

(when all aid was a block grant under a founda ­

tion plan)

showed an unbiased estimate not significantly

different from zero but w i t h o u t significant change in the
other coefficients.

Felds t e i n reported, with o u t remark,

that an instrumental variable estimation based on 1970
data treating state block grants as endogenous gave an
expenditure elasticity with respect to state grants

1

Ladd,
2

"Education Expenditures," p.

Denzau,

"Survey," p. 2 47.

150.

92
of .127 compared to that with respect to federal grants
of .124.1
Stern expressed total educational resources avail­
able per pupil as
g = c ^

+ qc2

(2.7)

where c^I» is the sum of local revenues and matching
grants, L

being local revenues,

and

the local

share of local plus matc h i n g

amount of

block grants is c 2

parameter

to be estimated reflecting

the reciprocal of
revenues.

The

and the coefficient q is

a

a discount factor

school boards apply to block grants because such aid is
not a perfect substitute for local revenue or matching aid.
One r eason for this lack of substitutability is that such
grants are often categorical, w i t h restrictions on their
use w hich may make them less valuable according to local
preferences than unrestricted moneys.

Ano t h e r reason is

the uncertainty about the size of block grants w h e n school
budgets are made.
which,

The estimated value of q was

for Stern's specification,

.601,

implied a reduction in

^"Feldstein, pp. 81-84, nn. 11, 12, 18.
Barro, Theoretical M o d e l s , pp. 58-61, shows that
whether categorical or unrestricted lump-sum aid has the
larger m a r ginal impact on total education expenditures
depends on whether expenditures for functions receiving
categorical aid and other expenditures are complements
or substitutes.
When they are complements, theory p r e ­
dicts that categorical aid has the larger marg i n a l impact
on total expenditures.

93
locally financed expenditure of about 45 to 55 cents in
most districts.

Since the smaller the value of q, the

less block grants reduce locally financed expenditure,
Stern argued:
. . . the uncertainty and limited substituta­
bility of block grants, as measured by the esti­
mate of q, could conceivably offset the greater
incentive of matching grants for some school d i s ­
tricts. . . . the important implication for
policy is that the recipients of aid are sensi­
tive to the way grants are appropriated and
administered.
Because theoretical models have
ignored such institutional complications, they
may predict behavior i n c o r r e c t l y . 1
The dy namic mo d e l discussed in the next chapter
addresses the issue of uncertainty and the separation of
categorical from general block grants as was done by
Feldstein and by Ladd addresses the effect of restrictions
tied to categorical aid.

Thus, we avoid the problem

implicit in Stern's discussion,

that institutional changes

would affect the value of q and require re-estimation of
its value before Stern's model could be used for pr e d i c ­
tive purposes.
Comparison of the Effect of
Block Grants and Pisposable Income
Stern's model was based on a school board p r e f e r ­
ence function, not on the preferences of the median voter.
Use of such a model has implications for the specification
1S t e r n , p . 9 4.

94
of the aid term in the expenditure equation.

Inman also

used a leadership preference function approach and had
hypothesized that community income and exogenous grants
should be combined in one variable.

However, he found

that an increase in exogenous aid w e n t entirely into
expenditure increases whereas the marg i n a l propensity to
consume public services out of income was about .04.
explanation of this unexpected result,

Inman argued:

One hypothesis to account for this pattern
argues that additional exogenous grants enter the
budget constraint with "prior claims" for their
a l l o c ation— claims that are distinct from those
expressed through the usual budget channels for
tax and debt funds.
For example, much of the
exogenous aid for cities w i t h responsibility for
education comes via closed-ended educational
matching grants or foundation (per pupil) assist­
ance . It is easy to imagine the educational sys­
tem m aking a strong claim to these outside funds
as "supplemental money for education."
Given the
likely bargaining power of this bureaucracy in
the city budgeting process such a claim may be
hard to deny.
If this is, in fact, the case our
previous arguments that service-specific exoge­
nous aid would lead to an equivalent release of
tax dollars from that s e r v i c e 's budget for allo­
cation as general revenue will not be observed.
The argument here says cities treat exogenous aid
as supplemental or transitory to their usual tax
and debt r e v e n u e s , and as such there may be quite
d ifferent allocative pressures w h i c h come to bear
on its disbursement.
Patronage (as in the case
of sanitation or parks and r e c r e a t i o n ) , charity
(as w ith w e l f a r e ) , the constitutional structure of
the political process, or perhaps even the name of
the aid program may all be possible special d e t e r ­
minants of the [exogenous aid] a l l o c a t i o n . 1
Elsewhere Inman argued:
i

Inmaii,

"Econometric Model," pp.

711-713.

In

95
The differences in the impact of [exogenous aid
per capita] and private income on [taxes per
capita] is a small bit of evidence in favor of
the leadership-bureaucracy m o d e l as opposed to
the median voter model.
Bradford and Oates (1971)
have shown that the me d i a n voter m o d e l predicts
that a dollar increase in income to the median
voter should have the same budgetary impact as a
dollar increase in exogenous aid.i
In fact, Bradford and Oates did not reach such a
conclusion but rather found that
. . . for the simple models . . . the gift to a
member, which is identical in effect to the gift
to the club, is equal to his tax share times the
total amount of the gift to the c l u b . 2
Intuitively,
lows:

this result can be explained as fol­

A grant-in-aid to the local government is e q u i v a ­

lent to the potential increase in the individual's private
disposable income that would be achieved if all of the
grant w e r e used to reduce local taxes.

If the reduction

in tax rates must be uni f o r m over all taxpayers,
and non-resident alike,

resident

the individual's share in such

potential tax reduction will not be the amount of per
capita aid but the total aid times his tax share.
Mathematically,

the individual voter's preferred

level of educational services per pupil w i l l be determi n e d
by m a x i m i zing U(Y<j, E) , where Yd is disposable income
1

Inman,
2

"The Decision to Tax," n.

23.

David F. Bradford and Wallace E. Oates, "The
Analysis of Revenue Sharing in a New Appro a c h to Co l l e c ­
tive Fiscal Decisions," Quarterly Journal of Economics 75
(August 1971):430.

96
after all federal and state taxes as well as local educa­
tion levies and E is per pupil educational services.
N eglecting other local tax levies and assuming education
expenditures are more than the m i n i m u m required to
receive block grants,

E =

Y

“

the budget constraint is

-— — + B,

(2.8)

where B is block grants per pupil, Y is disposable income
before education tax levies, P is the cost to the media n
voter of an additional unit of educational services per
pupil as derived in

(2 .1 ) above,

cost one dollar per unit.

and education services

Rewritten in the more familiar

form of a budget constraint,
Yd + PE =

(Y + PB) ,

(2.9)

where P is the "price" of education per pupil,
of private expenditures is one,
This is similar to Edelson's y^,

the price

and the budget is

(Y + PB) .

"tax adjusted income per

child for a voter in tax class i ," except that he took
income per child rather than per household as the relevant varxable.

1

The me d i a n voter's preferred level of education
expenditures is that which maximizes utility subject to
his b u d g e t constraint.
^Edelson, pp.

F r o m the Lagrangian
162-164.

97

(2 .1 0 )

L a U(Yd , E) + X [Y + PB - Yd - PE],

the first order conditions

3L

for utility m a x i m i z a t i o n are

(2 .1 1 )

Y + PB - Y d - PE = 0

The equivalence of a block grant of amount B to
an increase in disposable income before school taxes of an
amount PB can also be demonstrated graphically by refer­
ence to Figure 1 in Chapter I.
families ratio is one.

Assume the pupils to

Then in the example illustrated

in Figure 1 for a district levying less than 20 mills the
budget constraint is GC, having a slope of P =

.6 .

per pupil block grant is $130, or the distance AF.
ever,

The
How­

the extension of the budget constraint GC intersects

the income axis $78, or

. 6

x 130, above the $5,000 level

of private income.
Ladd's empirical work,

although developed from an

individualistic median voter model,

did not incorporate

(Y + PB)

as the income variable because she did not include
i
block grants in the me d i a n voter's bu d g e t constraint.
1

Cf. Ladd,

"Education Expenditures," p.

146.

98
Like the individualistic model,

a theory based on

a district preference function such as B a r r o ’s predicts
the marginal impact of lump-sum

aid

of private income by the factor

( 1

sition of the tax base is ignored.

to differ from that
Dm
- M)
if the compor
The use of a district

preference function rather than an individual voter's
utility function then provides an additional reason that
private income and lump-sum aid effects may not be equiva­
lent i_f the district preference function treats decreases
in gross income differently than increases in taxes.^
The '’M u n ic i p a l Overburden"
Issue
The necessity of supporting other public services
might be expected to reduce the ability to pay for educ a ­
tion.

This is the controversial issue of "municipal

overburden,"

the claim that high local tax levies for

non-educational purposes reduce the ability to pay for
education.
Sophisticated definitions of m u n i c i p a l overburden
have restricted the concept to costs of pu b l i c services
which b e n e f i t people outside the local jurisdiction but
for w h i c h local residents m u s t pay.
include:

^Barro, pp.

15-16.

Such costs might

99
. . . local contributions to at least some forms
of p ublic welfare payments and to other func­
tions , the support of w h i c h involves costs
imposed by federal or state law, the openness of
the city, or its role as a place of residence for
new, culturally d i s a d vantaged migrants . . .
[but
should] exclude the costs of providing w h a t may
be called 'urban amenities.'^
Higher n o n - e ducation public expenditures resulting from a
taste for more public goods or from the fact that city
residents may purchase goods through the public sector
that others obtain through private expenditure should not
2
be considered as m u n i c i p a l overburden.
Two empirical studies that considered all noneducational local government revenues as a measure of
municipal overburden found it to have a strong positive,
rather than the expected negative,
expenditures.

eff e c t on education

The explanation offered was that educa­

tional and non-educational expenditures have m a n y of the
same determinants,

and this prod u c e d a spurious positive

3

correlation.

Grubb and Michelson produced results in

which local non-education revenues,
population,

in interaction w i t h

had the expected negative effect

(significant

Harvey E. Brazer, "Federal, State and Local
Responsibility for Financing Education," in E c o n o m i c F a c ­
tors A f f e cting the Finan c i n g of E d u c a t i o n , ed. Roe L.
Johns et al. (Gainesville, F l a . : Nati o n a l Education
Finance Project, 1970), pp. 249-250.
2
Reischauer and Hartman, p. 71.
3
Gensemer, p. 122; and McMahon, p. 249.

100
at the 7 percent level)

on eduation expenditures.^-

They

interpreted the dependence of this effect on population
to mean:
In large school districts, then, school e x p e n d i ­
tures . . . appear restricted by nonschool
expenses which are necessary for the maintenance
of the d i s t r i c t s ' integrity rather than expres­
sive of local preferences.
Ladd used a two-rstage least squares procedure
like Grubb and Michelson b u t not allowing for interaction
with population.

Including local non-educational revenue

per pupil in her log linear specification,

she found it

to have an insignificant positive coefficient.

As fur­

ther evidence against the municipal overburden hypothe­
sis, she used the major determinants of non-educational
expenditures— per pupil commercial and industrial workers
by location of employment and fraction of hou s i n g units
that are r e n t e d — directly in a reduced form education
demand function and found none to be significant, w i t h
3

one h a ving the

"wrong" positive sign.
The Functional Form of the
Expenditure Equation

The models considered by Denzau all were linear
in the variables.

However,

the expenditure equation need

^Grubb and Michelson,
2

pp.

127-128.

Ibid., p. 130.

2Lada,

"Public Expenditures," pp.

124-130.

101
not have this functional form.

Among the more unusual

function forms for the expenditure equation are ones
derived from a preference function of the form

U = ng - j

g 2

- J ut2 ,

where g is per pupil expenditures,

(2.12)

t is the millage rate

and n and u are functions of demographic v a r i a b l e s .

The

budget constraint is
g = c1tV + q c 2 ,

(2.13)

where V is assessed value per pupil,

c2

is block aid per

pupil, q is a parameter to be estimated reflecting the
discount factor applied to block grants,

and c^ is the

ratio of the sum of matching aid and local revenues to
local revenues,

or

^ M in the notation previously used.

From the Lagrangian

L = ng - ~ g 2

- ~

ut2

+ A ( c ^ V + qc2 - g) ,

(2.14)

the first order conditions for utility m a x i m ization are

§ i = n - g - A g = 0

■
y g* ~ — ut + Ac

“ o^tV + q c 2

—

0

— g = 0

(2.15)

102

This leads to an equation for local revenues of the form

„ = tV
L

n ~

q C 2

(2.16)

u
1

Stern and Grubb and Michelson used specifications
of this form but with different demographic variables
included in n and u.

Stern did not report the resulting

estimate of the price elasticity, but Grubb and Michels o n
found a "perverse" estimate of the elasticity,

implying

increasing the matc h i n g rate w o u l d not increase total
expenditures.

This was contrary to their other estimates

of the price elasticity w i t h different specifications as
well as contrary to their theoretical expectations.

They

attributed this peculiarity to the constraint imposed by
the estimated coefficient of income in their specification
where u = a ^ Y .
where u = a^O,

A similar constraint was imposed by Stern

1

0

being the percent of homes owner-occupied.

A nother preference function w h i c h Grubb and
Michelson used was, using Stern's notation,
U = a x In

(g-a2 ) + ^

In

(32 ~ t ) *
(2.17)

^Grubb and Michelson,

p.

122, p.

148, n.

17.

This resulted in the linear expenditure equation

L = a 2 32V +

(2.18)

The r e s u lting estimate of the price elasticity was

.85,

which was similar to other estimates from the same func ­
tional form but w i t h different demographic variables.
They concluded that
. . . the fact that the price elasticities are so
similar signals an important weakness:
the
linear expenditure system implies a price e l a s ­
ticity w h i c h is not responsive to parameter d i f ­
ferences and, like the utility function specifi­
cation, which depends critically on coefficients
not intended to measure price effects.^
Grubb and Miche l s o n also used a modi f i c a t i o n of
the linear additive form of the equation of local revenues
They specified

L

=

- 61mL - B2A

I

where A is non-matching aid, m =
aid.

(2.19)

M

and mL is matching

This resulted in a non-linear equation of the form
Eoc.X.

L

r

i

- 0_A

2

1 + 8^m

•''Ibid. , p.

103.

I b i d . , p.

125.

2

(2 .20)

104
Alth o u g h n o t as frequently used as the s p e c ifi c a ­
tion of the expenditure equation as linear in the v a r i ­
ables,

a log linear specification was used in studies of

educational expenditures b y Feldstein,
and Michelson.

Ladd,

and Grubb

Inman used a specification w h i c h was

basically log linear b u t included the perc e n t Catholics
and the percent elderly as linear terms and a t e r m c o m ­
posed of percent w i t h income be l o w $ 6

, 0 0 0

multiplied by

the log of voter turnout.
Ladd gave three reasons

for using the log linear

specification:
Such a formulation allows first of all for the
m u l t iplicative form of the price variables in
that

[log

R

(1-M) } j is equal to the sum of

the logs of each component taken separately.
Secondly, it is logical to assume that the total
price variable affects the desired level of e d u ­
cation expenditures in a m u l t i p l i c a t i v e fashion,
that is, w i t h constant elasticity rather than
w i t h constant margi n a l impact. . . . A n d finally,
the log-linear f o r m is convenient in that the
estimated coefficients are elasticities.
In support of the constant elasti c i t y rather than
constant marginal impact effect of the e x p l a natory v a r i ­
ables,

K urnow showed that the log-linear specification

gave a b etter fit than the linear in regression analysis
of state and local expenditures.

2

Inman found the

^Ladd, "Public Expenditures," p. 103.
2
Ernest Kurnow, "Determinants of State and Local
Expenditures Reexamined," National Tax Journal 16
(September 1963):252-255.

log-linear formulation to be superior to a linear speci­
fication w i t h the same variables under a criterion of
minimizing the residual sums of squares in predicting
e x p e n d i t u r e s .^

"'"Inman,

"Optimal Reform," p. 29, n.

25

CHAP T E R III
PROCEDURES F O R ESTIMATING THE
EXPEND ITURE EQUATION
The Structure of an Hypothesized
Lagged Response
F eldstein estimated two equations to test for a
distributed lag response by including the dependent var i ­
able lagged five years among the explanatory variables
and u s i n g an instrumental variables procedure.

His

results for the 1970 cross-section data gave an insignifi­
cant e s t i mated coefficient of
expenditure term.

In

(E_^).

.071 for the lagged
In contrast to this very

short e s t i m a t e d lag, his estimate of the coefficient of
In

(E_j-) based on 1965 data was

.653, indicating a sig­

nificant lag.^"
The use of lagged total expenditures w o u l d be
appropriate if it were to reflect the influence past
experience w i t h education expenditures in the community
has on tastes.
This was the rationale provided by
2
McMahon.
Such a specification w o u l d not seem appropri ­
ate if the lagged variable,

rather than representing an

^Feldstein, pp. 82-84.
2
McMahon, p. 244.
106

107
influence on tastes,

is to represent a delay in the

political process by w h i c h actual expenditures adjust to
some d e s ired level.

In such a model actual local millage

rates w o u l d be assumed to adjust to desired millage rates
according to a partial adjustment model since local
d ecision-makers will have to make any adjustment through
a change in local tax rates.

This results in a different

s pecification of the equation to be estimated.
Let M be the matching rate,

expressed as the

state share of the sum of local revenues plus matching
aid.

Total expenditures per pupil, E, are the sum of

block grants-in-aid per pupil,
m atching aid,

^^

M

^

B, local revenues, L, and

Combining the last two terms into

gives

E

nt

(3.1)

Desired local revenues are determ i n e d by
(3.2)

where E

it

is the desired level of total expenditures, w h i c h

is a function of the variables w h i c h have been used in
cross-section studies to explain the e q u i l ibrium level of
education e x p e n d i t u r e s .
1

In the following equations the subscripts n and
t are the indices of the school distr i c t and the year,
respectively.

Millage rates will adjust w i t h a lag as the
political process takes time to adjust to the new level
of local taxation preferred by the me d i a n voter.
a partial adjustment model,
rates is a fraction

1

Using

the change in actual millage

of the difference between the cur-

rent d e sired millage rate, ^n t / and the previous actual

or
(3.3a)

where

is a ra n d o m disturbance term.

To get this

equation in terms of local revenues per pupil, multiply
each term in

(3.3a) by

assessed value per pupil.

w

n,t-l nt
or

4. -.Wnt.
n,t-l
(3.3b)
Substituting

(3.2)

into

(3.3b) and

equation for actual expenditures is

(3.3b)

into

(3.1), the

In the model described b y

(3.4), an increase in

block aid w o u l d result in a delayed reduction in local
tax rates,

and therefore expenditures w o u l d be temporarily
A
above the new long-run equilibrium level, E . In the
second line of

(3.4)

this is seen in that the increase in
*

block grants would not only increase E

(since it is

included among the variables de t e r m i n i n g E ) but would
also increase the first term w h i l e the influence of the
lagged millage rate in the third t e r m w o u l d result in
local revenues and matc h i n g aid remai n i n g above the level
to w h i c h they will eventually fall w h e n part of the bloc k
aid is p assed on in tax reductions.
Such a temporary stimulative effect of block
grants was hypothesized by Wilensky,
*
.
in this m a thematical form.

1

although not stated

This effect is not allowed

by the lag structure used in Feldstein,

in which e x p e n d i ­

tures w o u l d be temporarily b e l o w the new eq u i l i b r i u m
value if block grants were increased.

Since expenditures

rather than tax rates adjust w i t h a lag in Feldstein*s
model,

school districts receiving increased block grants

would temporarily accumulate financial surpluses and/or
cut local taxes more than desired in the long run.
^Wilensky,

p.

116.

if

If the eq uation for desired expenditures,
log

linear,

E , were

the equation incorporating this lag structure

would be
K

n
i=l

X

to .
(1 - A )r
. ,w .
_ nt ,
1 n,t~l nt
------e
+ —
1
- M
int
nt

Cnt W nt
1-M,

(3.5)

nt

where
K
In E

nt

= In A +

I

i=l

y . In X. . +
i
xnt

(0

(3.6)

nt

Estimation of this equation w o u l d require trans ­
forming the equation to the form

In

En t - U - A )

n,t-lW ntl
B„ t +

X- M n t

J

= In

K
(XA) +
£ y. In X.
i=l
(3.7)

nt
and u sing a non-linear estimation of X and,

if R

rather

than R w e re included among the X^, of the perceived tax
*
incidence parameters in R . Another p r o b l e m w i t h this
specification is that € t is not a linear combination of
and

and thus the disturbance m a y have a compli­

cated distribution.
A n alternative w o u l d be to specify E
tive function of the X^.

*

as an addi­

In this form X, as well as the

perceived tax incidence parameters in R ,
mated w i t h o u t a search procedure.

could be esti ­

Desired expenditures

would be given by

K
(3.8)

Letting Cnt = X% t

+
nt
K

(3.9)

E quat i o n

(3.9)

can be estim a t e d wit h o u t resort to

non-linear estimation techniques and y e t incorporates a
lag structure in which the delay in the adjustment of
millage rates allows an increase in lump-sum aid to have
a temporary stimulative impact larger than its long-run
effect.

Estima t i o n results using this specification are

presented in chapter IV.
A Test of the Equivalence of the Price
Effects of N o n - Residential Property
and M a t c h i n g Aid
If we allow for some p e r c eived shifting of the
tax b u r d e n on commercial and industrial property and
*
PU
impose the r e s t r iction that the factors -p-,
•k
R have a combined price effect,

(1 - M)

and

through Xg , respectively,

the restriction on the effect

of the price factors implies

Y1 + Y 4 = Y 2 +

Y5 = Y3 +

Y 6

=

<3-1:L)

0

The p e r c eived tax incidence parameters a and 0 are identi­
fied and

cl

—

-

y 2
“
1

Y3
3 = - “

(3.12)

T 1

The test for a set of linear restrictions such as
(3.11)

in a standard regression model w i t h a normally d i s ­

tributed disturbance term is given in Theil.^
null hypothesis that the restriction holds,

Under the

the test st a ­

tistic is distributed as F(q, N - K ) , w h e r e q is the number
of linearly independent restrictions.

York:

^Henri Theil, Principles of Econometrics
John Wiley & Sons'i 19 71) , pp. 14 3-144

(New

113
Threats to the Consistency and
Efficiency of OLS Estimates
However,

the validity of this test of the

restrictions is threatened if the assumptions of the
standard regression model do not hold.
explanatory variable

(rn t - l ^ t *

^

1

In

(3.9)

the

- M nt^ may be cor"

related with the disturbance term,

Tiie inconsistency

of least squares estimates under these circumstances mi g h t
be circu m vented by the use of instrumental variables.
F urther problems arise if pooled cross-section
time series data are used.

This problem has been formu­

lated by Balestra and Nerlove.'*'
we might assume that

Modif y i n g their approach,

can be decomposed into two sta­

tistically independent components,

an individual effect

and a remainder,

wnt

(3.13)

^nt + Vnt

and that both components are independent of Cn t -

Further

assume
C

W

S t nt
1-M
nt

n 1t 1Wn 1t ’
1-M

n't1

a
0

'a

if n = n* and t = t'
otherwise

P. Balestra and M. Nerlove, "Pooling CrossSection and Time Series Data in the Estimation of a
Dynamic Model:
The Demand for Natural Gas," Econometric a
34 (July 1 9 6 6 ) :585-612.

cr
M

The

0

otherwise

Q 2

if n = n ’ and t = t'

0

otherwise

(3.14)

(Wnt.r n ,t— x
,)/(! - Mnt .) term in

(3.9)

is cor-

related with the disturbance because

iX in,t-x ** Bn,t-T^

(3.15)

and the

component appears in each of the £n t_ T *

Therefore,

least squares estimates of

inconsistent.

Even with o u t the lagged

(3.9) wo u l d be
term, ordinary

least squares estimates would not be efficient because
disturbance terms for observations of each district in
different years would be correlated since they all con­
tain the yn component.

However,

the m a x i m u m likelihood

method given by Bale s t r a and Nerlove cannot be applied to
our data because data for an insufficient number of years
are included.
Even wit h o u t the inclusion of the lagged response
term there is a simultaneous equations pro b l e m that
threatens the consistency of ordinary least squares e s t i ­
mates .

Because the state only matches revenues up to a

115
m a x i m u m millage rate

(25 mills in 1974-75),

rate is an endogenous variable.

the matchin g

The commonly used two-

stage least squares procedure is not a theoretically
satisfactory method of d ealing with this pro b l e m because,
although the expenditure equation can be specified in a
linear form,

the other relationship in the system is no n ­

linear and discontinuous.

Thus, there is no assurance

that an instrumental variable procedure will result in
estimates with desirable properties.
A no t h e r prob l e m with ordinary least squares est i ­
mates is that the disturbance term may be h e t e r o s k e d a s t i c .
While not affecting the unbiasedness or consistency of
ordinary least squares estimators,
efficiency of these estimators.

this does affect the

Brown and Saks argued

that the estimation of the me d i a n voter's demand for
public expenditures is analogous to the problem of esti­
mating individual de m a n d functions

for a private good

from grouped data w h e r e only the means of the quantity
demanded and of the explanatory variables of several
groups are observed.^"

The latter situation results in
2

the disturbance term having a variance of a /ng# where
n

is the number of individuals in the g
group, if the
y
disturbance term in each individual de m a n d equation has

1Brown and Saks, p.

18, p.

38, n.

21.

116
the same variance,

2
0

.

The procedure to obtain efficient

estimates is to w e i g h t each grouped observation by
However,

y
the pu b l i c expenditure level chosen by

the collective choice process is not the mean of the
individually preferred levels as is the dependent variable
in observations of grouped data.
ferred by the m e d i a n voter.

It is the level pre­

Altho u g h the public expend i ­

ture e q u ation is not produced by the same aggregation of
individual demands as in the grouped data problem,

it may

involve a disturbance term with a variance inversely
related to the size of the community.
ties the distribution of voters'

In larger commun i ­

prefe r r e d expenditure

levels may be "denser" in the sense that the distance
between one voter and the voter with preferences closest
to his own will be less.

If individual demand curves are

stochastic the identity of the me d i a n voter,

as w e l l as

that individual's preferred level of expenditures,
random variable.
tures, m e d {E^},

The me d i a n preferred level of expendi­
is to be distinguished from Em , the

level of expenditures preferred by the voter who,
his socioeconomic characteristics,
median voter.
skedastic, E

m

is a

from

is expected to be the

If individual demand equations are homowill have the same variance regardless of

^Jan Kmenta, Elements of Econometrics
Macmillan Co., 1971), pp. 322-336.

(New York:

117
community size.

But m e d {E^} may be expe c t e d to have a

smaller variance in larger communities because, w i t h a
"denser" distribution of voters, m e d { E ^ w i l l
closer to

E(Em ) .

tend to be

Therefore, w e i g h t i n g observations

according to the size of the school district, w h i c h may
be m e a s u r e d by the number of families in the district,
is a p p r o p r i a t e .
The Data
The National Center for Educational Statistics
has compiled the 1970 Census Fourth Count

(Population)

School D i strict Tapes giving census data by school dis­
trict.

Selected demographic statistics from this census

tape, various financial and personnel data for the 197273 through 1975-76 school years collected by the Michig a n
D epartment of Education,

and responses to a survey of

school d i strict superintendents in the spring of 1976 are
included in the School District Data Pile of the School
Finance Research Group of the Governor's Advi s o r y Task
Force on Property Tax Revision.

This was a principal

source of data for this study.
One important set of variables for w h i c h school
district data are not available is the c o m p osition of the
property tax base.

The survey of school superintendents

asked for an approximation of the percentages of school
districts'

total 1975-76 SEV falling into each of the

118
categories "commercial,"

"industrial,"

"residential,"

"agricultural," and "other."
Estimates of the fractions of the tax b a s e fall­
ing into the above categories were made for 1972,

1973

and 1974 by allotting the equalized prop e r t y values in
each category in each city or township
Tax Commission data)

(found in State

to school districts according to the

approximate fraction of the area of the city or township
falling in each school district.

There are several

sources of error in this allotment procedure.

The frac­

tions of each civil decis ion falling in the school dis­
tricts w e re estimated me r e l y by casual visual estima t i o n
from school distr i c t maps.

The allotment proce d u r e also

assumes that the different classes of property are homo­
geneously distributed throughout civil divisions.
exclude a pparent serious errors in this regard,

To

all school

districts for w h i c h the total of allotted p r o p e r t y value
deviated by more than ten per c e n t from the actual total
S EV for the di st r i c t w e r e excluded from the sample.
of 496 K-12 districts

Out

for w h i c h census data were avail­

able, the allotment procedure gave estimates w i t h i n the
ten p e rcent bounds

for 314 districts in 1974,

314 districts

in 1973 and 304 districts in 1972.
A n o t h e r indication of the accuracy of this p r o ­
cedure is the degree of agreement b e t w e e n the estimates
given by school superintendents in the survey results w i t h

119
the estimates derived by allotting the Tax commission
data for civil divisions.

Table 1 shows the results of

regressing the survey estimates for 1975 on the allotted
estimates for 19 74.
Perfect agreement w o u l d be indicated
o
by an R of 1.00, a constant term of 0.00 and a coeffi­
cient of 1.00.

The regressions for industrial and agri­

cultural fractions of the tax base per f o r m relatively
well by these standards.

Part of the deviation may be

explained b y changes from 1974 to 19 75.

The poor results

for commercial and residential prop e r t y may be due to
school superintendents not adhering to Tax Commission

TABLE 1.— Survey Results Regressed on A l l o t t e d Tax Base
Shares.

Constant

Coefficient of
Allo t t e d Share
of Tax Base

.032
(.009)

.748
(.061)

.3729

.939
(.037)

.7135

(.008)
-.017
(.033)

1. 003
(.064)

.4924

Agricultural

.036
(.0 1 1 )

1.108
(.050)

.6607

"Other"

.007
(.007)

.325
(.059)

.1057

Classification
of Property
Commercial
Industrial
Residential

. 0 2 0

*

R2

NOTE:
Standard errors are shown in parentheses.
Results are based on 255 observations.

120
definitions by which apartment buildings are classed as
commercial property.

The "other" classification in the

survey corresponds to timber and public utility property
in the Tax Commission data,

and the poor results in this

regression may likewise be due to school superintendents'
interpretations of this category.
possible data sample,

survey responses are used for tax

base composition in the regressions
tures.

Of course,

To obtain the largest

for 1974-75 expendi ­

the allotted tax base shares are used

in the regressions for 1972-73 and 1973-74.
Brief definitions of all variables used in the
regressions w i t h the symbols used m a y be found in
Table 2.

121
TABLE 2.— Symbols and Definitions of Variables.
Symbol

Variable Name and Definition

E

Operating expenditures per pupil.

Etr

Transportation expenditures per pupil.

Pu

Number of public school pupils; the number of
legally enrolled pupils at the close of school
on the fourth Friday after Labor day.

F

Number of families in the school district
according to the 1970 census fourth count.

B

Block grants per pupil; the sum of nonc a t e g o r i c a l , non-matching state aid, intermediate
revenues (collected from political subdivisions
other than school districts, the state or fed­
eral governments) and incoming transfers from
other districts per pupil.

M

Matc h i n g rate; the ratio of state aid to state
aid plus local operating revenues at the margin.

I

Industrial fraction of the property tax base;
1974-75 regressions used the school district
superintendent's estimate for 1975-76; regres­
sions for 1972-74 used the fraction of SEV in
this category estimated by allotting the prop­
erty values for 1972 and 1973 in civil divisions
to school districts according to the approximate
fraction of the area of the civil division fall­
ing wi t h i n each school district.

C
T or 0

Wr

Commercial fraction of the tax base; derived
similar to I.
Fraction of the tax base in the "other" category
in 1975-76 according to a survey of school
superintendents; 1972-74 regressions used the
fraction of tax base in timber and public
utility property as determined by allotting civil
division property values to school districts in
proportion to the area falling in each district.
Residential wealth; SEV per family multip l i e d
by the residential share of the property tax
base

122
Table 2.— Continued,
Symbol

Variable Name and Definition

Hs

Fraction of public school pupils in grades 9-12.

Pi

Input price; "adjusted salary" from the School
District Data File of the School Finance Research
Group; computed by weigh t i n g instructional staff
in units determined by the statewide average
salary increments for additional experience and
education and dividing average salary by this
"average staff weight."

Ca

Categorical aid per pupil; the sum of federal
aid, gifts and bequests, and state aid for trans­
portation, pregnancy programs, reading support,
special ed., compensatory education, vocational
education and "other" categorical aid.

Fc

Fraction of families with children under 18 p r e s ­
ent according to the 1970 census fourth count.

Pr

Fraction of students in private schools; the
fraction of kindergarten, elementary and high
school students in parochial or private schools
according to the 1970 fourth count.

Pf

Professional, technical and kindred workers as a
fraction of all employed persons 16 and over
according to the 1970 fourth count.

Mg

Fraction of managerial personnel among employed
persons; salaried and self-employed managers and
administrators except farm managers as a fraction
of employed persons according to the 1970 census
fourth count.

SI

Fraction
of sales, clerical and kindred workers
among employed persons according to the 1970
census.

Fa

Fraction
of farmers, farm managers and paid farm
laborers and foremen among employed persons
according to the 1970 census.

Bl

Fraction
of population w h i c h is Black according
to the 1970 census.

123
Table 2.— Continued.
Symbol

Vari a b l e Name and Definition

Rs

Fraction of the population living in the same
residence for the p a s t 5 years according to the
1970 census.

Y

M e d i a n family income; for 1974-75 regressions
this is nominal income for 1969 as reported in
the 1970 census; for 1972-74 regressions this is
adjusted by the percentage growth in per capita
income by county betw e e n 1969 and 1972 or 1973
[Source:
"Per Capita Personal Income in M i c h i ­
gan Counties:
1969, 1972, and 1973 and Percent­
age Change, 1969-1973," Michi g a n State Economic
Record 17 (March-April 1975):4-5].

D

Dummy variable for districts in met r o p o l i t a n
areas; value is 1 for districts in an SMSA and
0
otherwise.

G

Gini coefficient for d i s t r i b u t i o n of family
income according to the 19 70 census.

Sk

Skewness in the d i s t r ibution of family income.

W

We a l t h as measured by SEV per pupil.

r — 2

AMbd

APu
Pu
P

Operating millage rate (taxes levied p e r dollar
of SEV) for 1972-73; used as a lagged variable
in 1974-75 regressions.
Change in b u i l d i n g site and d e b t retirement
millage rate (taxes levied per $1,0 00 of SEV)
between 1972 and 1974.
Change in number of public school pupils from
1972 to 19 74 as a fraction of 1972 membership.
"Price" of expenditures per pupil to a voter;
P = ^

(1 - M)

(1 - ctC - 01) .

All dollar quantities in the 1972-74 regressions
are d e f lated by the ratio of the average CPI for 19 72 and
1973, respectively, to the average CPI for 1969.

CHAPTER IV
RESULTS OF ESTIMA T I O N OF THE
EXPENDITURE EQUATION

Prediction of the effects of changes in the aid
formula on the distribution of education expenditures
requires knowledge of the behavioral response of school
districts to changes in variables determining the level of
expenditures.

While the discussion in Chapter II indica­

ted the log-linear specification of the expenditure equ a ­
tion m i g h t be preferable,

this specification does not

allow the constant marginal impact of categorical aid
that is expected and does not allow a test of the h y p o t h e ­
sised e q u ality of the marginal impact of Y and PB.
these reasons and to avoid non-linear estimations,

For
all

results presented are for specifications linear in the
parameters.

Tables 3 and 4 show estimates of various

specifications of the expenditure equation.
are discussed in detail below.

These results

The reasons for including

most of the variables are evi d e n t from the discussion in
Chapter II, and the restrictions tested are derived in
Chapter III.

More detailed definitions of the variables

may be found in Table 2.
124

125
The Effect of the Price Variable
In ad dition to allowing commercial and industrial
property to have a "price" effect,
used a llow the "other" category,
and timber property,

the specifications

including public utility

to have a "price" effect.

This is

justified by the probability that most owners are not
voters in the district.

The specifications do not allow

agricultural pr operty to have a price effect since most
owners are voters in the dist r i c t and studies indicate
little tax shifting.^
Equations

(l)-(7)

and

(9) in Table 3 show

weigh t e d least squares estimates of different specifica ­
tions of the expenditure equation based on data for 197475.

To o bt a i n the largest possible sample size school

s u p e r i n t e n d e n t s 1 estimates of the property tax base com p o ­
sition for 1975 w e r e used rather than the allotted esti ­
mates for 1974.
E quation

(9) is specified to include

as a fac­

tor in the price variable while the other equations omit
o
it.
A comparison of the R of .7670 in equation (4) wi t h
the R

2

of

.7204 in equation

p„

(9) suggests that omitting — =•
r

as a price factor gives a slightly better fit.
result tends to support Ladd's model,

This

in which expenditures

^E. C. Pasour, J r . , "The Capitalization of Real
Property Taxes Levied on F a r m Real Estate," American
Journal of Agricultural Economics 57 (November 1975):539w w . ------------ —

---------------------

TABLE 3.— Regression Results for Expenditures Per Pupil, 1914-75.

(4)

(7)

(1)

(2)

(3)

(5)

578* •
(136)

192**
(138)

512**
(152)

513“
(150)

413
(348)

602**
(140)

842*
(331)

-174**
(35)

-176**
(36)

-295**
(38)

-147.2**
(30.4)

-132.9**
(31.2)

-151.4**
(30.7)

B(l-H) ^

.484**
(.077)

.206**
(.063)

.444**
(.064)

.403**
(.075)

.397**
(.075)

BU-HJO

Y

-.505
(.384)

-.206**
(.063)

-.444**
(.064)

-.404
(.397)

B(1-M)C

y -

-1.745**
(.331)

-.206**
(.063)

-.444**
(.064)

Bll-MJI

~

-.915**
(.174)

-.206**
(.063)

Site of school district.
In Pu

6.800
(5.027)

Fraction in high
school, Hs

-4.7
(209.1)

Adjusted teacher
salary, Pi

(9)
467

667**
(167)

-144.1**
(31.3)

-121“
(33)

-269**
(47)

.385**
(.076)

.372**
(.076)

.396“
(.084)

.277**
(.0B6)

-.441
(.398)

-.312
(.405)

-.344
(.405)

-.367
(-426)

-.203
(.448)

-1.538“
(.342)

-1.525**
(.347)

-.563**
(.348)

-1.466**
(.353)

-1.93“
(.38)

-.654
(.359)

-.444**
(.064)

-.350**
(.178)

-.858“
(.180)

-.801**
(.181)

-.802**
(.182)

-1.19“
(.21)

-.746**
(.206)

-12.7
(9.0)

-32.6**
(10.0)

5.48
(9.19)

10.65
(9.60)

13.7
(9.1)

19.5*
(9.4)

26.2*
(10.3)

-1.25
(9.89)

-a.a
(219,5)

-15.7
(249.6)

-118
(215)

-5.58
(222.12)

46
(212)

84
(221)

-124
(230)

-155
(235)

.0144
(.0088)

.0198*
(.0092)

.0469**
(.0100)

.0221*
(.0089)

.0240*
(.0092)

.0177
(.0091)

.0181*
(.0092)

.00881
(.00934)

.0258*
(.0098)

Categorical aid, Ca

1.016**
(.115)

.999**
(.119)

1.216**
(.133)

1.098**
(.117)

1.096**
(.119)

1.094**
(.120)

1.076**
(.121)

1.109**
(.124)

1.198**
(.128)

Fraction of faailies
with children, Fc

-671**
(1411

-784**
(148)

-695“
(167)

-678**
(163)

-697“
(169)

-787**
(147)

-705**
(172)

-531“
(156)

-848“
(162)

Fraction of students
in private schools, Pr

-119
(92)

-87.2
(97.7)

5.7
(109.8)

-75.1
(94,7)

-89.6
(95.3)

-90.6
(96.5)

-94
(97)

-114
(102)

-46.5
(103.2)

Professional fraction
of labor force, Pf

641**
(162)

688**
(170)

860“
(189)

667**
(163)

684“
(178)

490**
(175)

719**
(177)

Managerial fraction
of labor force, Mg

15.8
(278.3)

-253
(2B8)

492
(326)

-125
(318)

-158
(340)

62.7
(269.2)

-37.0
(347.6)

Black fraction of
population, B1

-151
(95)

-142
(97)

-101
(109)

-143
(96)

-152.1
(99.5)

Constant
Pu
Pupils per faaily, —
F
Block Grant Teres

282**
(85)

262**
(89)

179
(101)

Residential wealth. Hr

,00255*
(.00117)

.00300*
(.00121)

.00628**
(.00133)

Median incone, V

.0263**
(.0051)

.0315**
(.0055)

.0362“
1.0063)

Y2

277**

(88)

278.3*'
(89.4)

-220*
198)

-170*
(102)

-144
(1051

119.5
179.5)

139
(82)

304“
(95)

269*
(97)

.0319*
(.0159)

.1017*
(.0501)

.0402*
(.0151)

.0498
(.0474)

.0000002
(.0000058)

-.OOOOOf
(.ooooo:

-.00000001
(.00000051)

-.00000422
(.00000283)

.0270**
(.0056)

.0529*
(.0171)
-.00000071
(.00000063

126

Fraction in sane
residence, Rs

-199.9*
(95.0)

Effects of Income Dis­
tribution, GY

GY3

sk
“Price Terms,“ I

518"
(77)

355**
(75)

462.2**
(B4.5)

562**
(59)

-.213
(.129)

-.2BS*
(.129)

.0000170
(.0000137)

.0000313*
(.0000133)

< 10-B
t - .143

>-i< io~B

46.5
(169.4)

12.3
(167.2)

560.9**
(59.6)

t - -.813

559.6**
(60.4)

566.3**
(60.6)

658**
(75)

*7

462**
(67)

c

675**
(140)

205
(114)

0

251*
(115)

182
(102)

C * D

328"
(117)

266*
(117)

100.5
(117.3)

I • D

163*
(72)

170*
(72)

-50.4
(70.1)

H

353"
(81)

97.2
(64.4)

411.9"
(63.2)

27 8 "
(721

259"
(75)

-355"
(75)

-462.2"
(84.5)

-109B"
(185)

-1114**
(185)

-1106**
(187)

-1123**
(187)

-2103"
(338)

-1758"
(337)

-1727**
(345)

-1824**
(344)

-1704"
(351)

-2106**
(449)

-1014*
(331)

-384
(391)

-345
(393)

-348
(398)

-339
(400)

-356
(445)

-237
(371)

MI

-997**
(255)

311.4*
(12B.3)
411.9**
(63.2)

MC

-1461**
(375)

-205
(114)

-311.4*
(126.3)

MO

-4B2
(386)

-1B2
(102)

-411.9**
(63.2)

CMC

-583
(421)

-266*
(117)

-100.5
(117.3)

EMI

-175
(324)

-170*
(72)

50.4
(70.1)

822**
(12B)

801**
' (130)

867"
(129)

805**
(132)

98 4"
(144)

401"
(125)

194
1116)

1B9
(116)

203
(118)

188
(119)

154
(127)

107
(130)

265.5**
(73.2)

241.7**
(75.3)

Change in debt retire­
ment revenues, WAm ^

304"
(87)

“7

1B2*
(69)

« T

-906**
(104)

.000330**
(.000116)

R2

.7850

.7498

.6732

.7670

.7708

.7556

.7609

.7204

R2

.7674

.7355

.6574

.7509

.7520

.7402

.742B

.7010

7.0147"

42.7720"

P statistic to test
restriction
described in text

1.417

NOTE: Observations weighted by J ? , F being the number of families in the district.
tures per pupil. Standard errors are in parentheses below coefficients.
•Significant at .05 level.
"Significant at .005 level.
tlnstrmental variables estimation with M, HI, MC and HO endogenous.

1.6899

The dependent variable is operating expendi­

H

to
-4

128
per family enter the utility function, over P e t e r s o n ’s,
in w h i c h expenditure per pupil is the argument of the
preference function.
Equations

(1) and

(4)-(7)

show the results when

no restrictions are imposed on the coefficients of the
terms in the price variable.

Equation

(1) includes inter­

action terms with D, a dummy variable for districts in
metropolitan areas, multiplied by C, I, MC and MI to
allow for Ladd's hypothesis that perceived tax shifting
may differ inside and outside metropolitan areas.
The results show all terms in the price variable
have the correct sign,

and Ladd's result that commercial

property stimulates expenditure more than industrial is
c o n f i r m e d .-1-

The interaction terms between D and C and I

are p o s itive and significant at the

.025 level or better,

indicating voters in metropolitan areas perceive less
threat of tax shifting through commercial businesses
raising prices and industrial firms lowering wages or
leaving the community.
But the results contradict the theoretical expec­
tation that the coefficients of I and C should be less than
or equal to the coefficient of M.

The stimulus of non-

residential property is apparently greater,
less, than the stimulus of matching aid.

rather than

Furthermore,

1The proportion of commercial property has not
been corrected to exclude apartments as Ladd did.

the

129
restrictions that the coefficients of block aid m u l t i ­
plied by the terms in the price variable should be of
equal m a g n itude and that the coefficients of I and MI, C
and CM, O and OM, DI and DMI,

and DC and DMC should be of

equal m a g n itude and opposite sign is rejected at the

.0005

level of significance with an F statistic of 7.0147,

as

shown in equation

(2).

However,

for any district with

much non-residential property the large coefficients of
the MI and MC terms so dominate the coefficient of M that
the effect of an increase in M is to reduce expenditures.
One possible source of downward bias in estimating
the coefficient of M is the simultaneous equations p r o b ­
lem w i t h the matching rate, w h i c h was noted in Chapter
III.

Because of the discontinuous non-linear relationship

between the level of expenditures and the matching rate,
two-stage least squares is not a theoretically appropriate
solution to this problem.

Nevertheless,

an attempt was

made to use an instrumental variables procedure.
equation

But

(8 ) shows little change in the relative m a g n i ­

tudes of the coefficients of the price terms w h e n this
procedure is used.
A second possible reason for the low estimated
coefficient of M is that voters are not aware of the m a t c h ­
ing provisions in the recently enacted state aid formula,
and thus it does not yet stimulate higher expenditures.
The survey of school superintendents inquired as to whether

130
the m a t ching provisions of the aid formula had been pub l i ­
cized in millage campaigns.

This was merely a yes or no

question and thus has the weakness of not measu r i n g the
intensity w i t h which the matc h i n g provision was publicized.
To incorporate the possible influence of such publicity on
the effect of the matc h i n g rate on expenditures,
regressions

(not shown)

some

included an interaction term

between the matching rate and a dummy variable having a
value of one if the superintendent reported matching p r o v i ­
sions were publicized in the millage campaign and zero
otherwise.

The correlation between this interaction v a r i ­

able and the matching rate was

.82205,

indicating that

superintendents in m o s t districts favored by the matching
formula replied that they did publicize it in the campaign.
This high degree of multicollinearity resulted in either
the m a t ching rate or the interaction term being insignif i ­
cant in the regressions in w h i c h the latter was included.
Thus there is no conclusive evidence that lack of infor­
mation o n the part of voters explains the small coeffi­
cient of M in the regression results.
In addition to the restrictions imposed in equa­
tion

(2), equation

(3) constrains the effect of non-

residential property in m e t r opolitan areas to be equal to
that of the matching rate.

The hypothesis that these

restrictions hold is rejected w i t h an F statistic of
44.7720.

Imposing the constraint makes the interaction

131
terms w i t h C and I and the m e t r o p o l i t a n area dummy insig­
nificant.

Alth o u g h these restrictions are rejected by

the P test, because of the implausible implications of
the unrestricted regressions the parameter estimates of
equation

(3) are used in Chapter V to predict the effects

of changes in the aid formula.
The input price variable,

Pi,

is a measure of

average teacher salary in the district adjusted for ed u c a ­
tion and experience, w i t h the weights of education and
experience determined by the statewide average salary
increments for these characteristics.

Pi is not included

in the "price" terms in the regression analysis as it was
in the theoretical derivation.
theoretical formulation,

While deviating from the

this allows a separate analysis

of the effect of this variable.

The positive coefficient

on this variable in the expenditure equation indicates a
price inelastic demand for educa t i o n inputs.
Effects of Non-Matching Aid and
Municipal Overburden
The categorical aid variable includes all federal
aid plus state grants for transportation, vocational ed u ­
cation,

special education, pregnancy programs,

tory e d u cation and reading programs.

compensa­

The estimates of the

coefficient equal or are greater than one,

agreeing wit h

other s t u d i e s ’ findings that categorical aids do not
result in a decrease in locally financed expenditure.

132
As theoretically derived in Chapter XX, the income
effect of non-categorical lump-sum aid is represented by
the variable PB, block grants multip l i e d by the
variable.

"price"

With block grants per family equal to B

and

the price
P =

- M)

( 1

R* =

- M)

( 1

( 1

- etc - BI - 5T)

(4.1)

if perceived shifting of non-residential taxes is to be
allowed,

then

PB = B(l-m)

^

- ctB(l-M)C

- 3B(1-M)I ~

- 6B(1-M)T ^
(4.2)

Note that the block grant terms should include the facPu
tor -p- regardless of whether or not the "price" variable
includes this factor because in either case the income
effect depends on block grants per family.
Thus the regression analysis should include the
four variables B(l-M) ^r, B(1 - M ) T

B(1-M)C

and

Dq

B( 1 -M)I -=- w i t h no restrictions on the coefficients of
£

these four terms.
ters a,

and

3

B (1-M) T ~ ,
r

6

If the p e r c e i v e d tax incidence p a r a m e ­

are less than one,

B (1-M) C ^

r

and B(1-M)I

the coefficients of
£

should be negative

and smaller in magnitude than the coefficient of
p„

B(1-M) -~=.

These equations are contradicted b y the results

shown in equa t i o n

(1 ).

133
In examining the impact of non-categorical block
grants,

attention is focused on equations

(2) and

because the unrestricted estimates in equation
lead to the implausible conclusion that,
with m u c h non-residential property,
grants reduce expenditures.

(3)

(1 )

in districts

increases in block

Non-categorical block grants

multiplied by the price variable w o u l d have a coefficient
equal to the coefficient of income if the political
process perfectly represented voter demands and such
unrestricted aid were equivalent to increases in personal
income.

Expressing Y in terms of 1969 nominal income

while other money variables are in nominal quantities
for 1974 should,

if anything,

coefficient of Y.
in equation
of Y.

give an upward bias in the
pn
The coefficient of B{l-M) r
(1-T-C-I)

(3) is clearly not equal to the coefficient

A l though such non-categorical aid apparently

results in some reductions in local school taxes,

its

stimulus to expenditure is greater than that of increases
in personal income,

indicating that education interests

exert a c laim on such aid that results in a greater
increase in school expenditures than local voters desire.
To measure the effect of municipal overburden it
would be desirable to consider only non-school local
government expenditures w h i c h provide benefits for or
which are imposed by persons outside the local govern­
ment unit.

However,

this b r e a k d o w n is not available.

134
When non-school local government revenue per family was
included in a regression equation
similar to equation

(not shown)

specified

(1 ), its coefficient was positive

and significant at the

.0005 level.

This crude test

supports other s t u d i e s 1 finding that "municipal o v e r ­
burden" does not reduce education expenditures.
Effects of Income and the
D istribution of Income
M edian family income and state equalized value
of residential property
nent income)

(which is taken to reflect p e r m a ­

have the expected positive coefficients in

all equations, both being significant at the
in equation

(3).

.0005 level

Evaluated at the sample means the p a r ­

tial elasticity of expenditures is
median family income and

.2958 with respect to

.0650 with respect to residen­

tial p r o perty value per family.

Follo w i n g Ladd's

assumption that one percent differences in residential
w ealth are associated with one percent differences in
income^" gives a total expenditure elasticity w i t h respect
to income of .3508.
B ut do the effects of the d i s t r ibution of income
make the use of only the me d i a n income variable inappro­
priate?

Equation

(4) specifies expenditures per pupil

as a quadratic function of median income.

Equation

tests for bias resulting from omitting other
^Ladd,

"Public Expenditures," p. 110.

(5)

135
characteristics of the income distribution by including
GY, GY

2

, GY

3

and Sk

(skewness)

as regressors.

The F

statistic to test for the significance of these addi­
tional regressors is 1.417, w h i c h is insignificant at the
10 percent level.

To eliminate any possible effects of

the occupation variables on the validity of this test,
equations

(6 ) and

(7) omit Pf and Mg from the regressors.
2
The F statistic to test for the significance of GY, GY ,
3
GY and Sk in equation (7) is 1.8899, still insignificant
at the 10 percent level.

The discrepancy with the Brown

and Saks results may be attributed to the fact that this
specification is in per pupil rather than per family
terms and includes total expenditures rather than only
local revenues in the dependent variable.
Effects of Other Variables
D

Public school pupils per family,

m

is included

in the e x penditure equation to capture the price effect
and possible per child income effects of the number of
public school pupils per family.

The negative and sig­

nificant coefficient found in all regressions conforms to
theoretical expectations.

The fraction of families with

children, Fc, intended to represent an interest group
favorable to education expenditures,

is found to have a

significant negative coefficient contrary to theoretical
expectations.

Perhaps this variable reflects some of the

136
same price and income effects as
In

Pu

The variable

(Pu), to reflect the varying political power of edu­

cation interest groups in different size districts,

is

found to have an insignificant coefficient of varying
sign.

Contrary to other studies,

the coefficient of the

fraction of students in high school is insignificant and
negative.

The fraction of school children in private

schools has an insignificant coefficient in all equations
but has the expected negative effect except in the con­
strained equation

(3) of Table 3.

Data on migra t i o n in and out of school districts
are not available but a related variable,

the fraction

of persons living in the same house for five years, has
a significant positive coefficient in all equations.
The taste for education of persons in professional and
technical occupations is reflected by the significant
positive coefficient of Pf.

The coefficient of the

fraction of the labor force in salaried and self-employed
managerial positions is insignificant and of varying
sign.

The fraction of Blacks in the population has a

negative effect on school expenditures b u t is statis­
tically significant only w h e n the occupation variables
are excluded or when an instrumental variables estima­
tion is u s e d .

137
Estimates of the Distributed
Lag Response
Equations

(1) — (3) in Table 4 incorporate the lag

structure developed in Chapter III.

All three equations

show there may be a significant lag in responding to
changes in the aid formula.
least squares estimates,

Equation

and equation

(1) shows ordinary
(2 ) shows estimates

imposing the constraint derived from the theoretical
development that the coefficients of B and
should be equal.
tion is 3.1623,

The F statistic for testing this res t r i c ­
indicating that the hypothesis that the

restriction holds is rejected at the
nificance.

(r_2 W)/(l-M)

.076 level of sig ­

The estimate of the lag parameter in equation

(2) indicates that only 49 per c e n t of the gap between
desired and actual mil l a g e rates is eliminated w i t h i n two
years.

The instrumental variables estimate indicates an

even longer lag, but the standard error of the estimated
lag parameter is large.
The coefficient of —yVL in these regressions shows
a significant negative impact of increases in number of
pupils on per pupil expenditures.
may have this effect because,
SEV per pupil,

Changes in enrollment

in addition to changing

they affect pupil-teacher ratios if there

is a delay in changing the number of staff in response to
enrollment changes.
The W

-

• AMbd term is included to estimate the

effect of changes in building and debt retire m e n t millages

TABLE 4.— Other Regression Results.

Constant
Pu
Pupils per family, —
F

tl)

(2)

<3) +

285*
(106)

260*
(106)

-88.7

-33.2
(30.2)

-7.93
(26.70)

11.9
(89.9)

(4)

(5)

(6)++

(7)
520“
(84)

171.4*
(74.7)

463.9**
(74.8)

364.2“
(75.1)

-242.4**
(31.8)

-494.6**
(52.4)

-534.0“
(52.1)

-406.5**
(57.8)

Block Grant Terms
.140*
(.056)

.115
(.374)

.529** .
(.081)

.5827**
(.0944)

.6316**
(.0948)

.407**
(.105)

B(1-H)T —
F

-.159
(.291)

-.182
(.292)

-.105
(.463)

-1.345“
(.255)

-1.170**
(-235) .

-1.252**
(.236)

-1.146**
(.280)

Bd-DC a

-.906**
(.253)

-.982**
(.250)

-1.04
(.69)

-1.152**
(.236)

-1.025“
(.259)

-1.022**
(.260)

-.656*
(.302)

BI1-HII ^
t

-.341*
(.134)

-.352*
(.134)

.474
(1.306)

-.894**
(.135)

-1.212“
(.172)

-1.250“
(.173)

-1.126**
(.201)

Site of school district,
In Pu

11.5
(6.0)

12.7
(6.8)

6.32
(13.00)

-22.35“
(5.50)

-11.4*
(5.6)

-8.90
(5.65)

-21.04“
(6.35)

Fraction in high school.
Ks

-60.2
(167.0)

26.9
(166.4)

214
(530)

218.4*
(99.7)

179
(103)

199
(103)

23.1
(119.6)

Adjusted Teacher salary,
pi

.00815
(.00673)

.00612
(.00665)

.0102
(.0098)

,0237**
(.0064)

.0245**
(.0066)

.0273**
(.0066)

.0284“
(.0074)

Categorical aid, Ca

1.018*
(.086)

.994**
(.085)

.869**
(.247)

1.445**
(.088)

1.437**
(.092)

1.360**
(.092)

1.411**
(.100)

Fraction of families with
children, Fc

-485**
(110)

-491**
(110)

-299
(318)

22.4
(71.0)

-89.6
(73.4)

-91.9
(73.8)

-73.3
(82.0)

-13
(991

-209“
(51)

-172.7**
(52.1)

-177.6**
(52.4)

-141.5*
(55.9)

459**
(81)

458**
(81)

407**
199)

—

■

Fraction of students in
private schools, Pr

-13.0
(71.3)

-18.1
(71.3)

Professional fraction of
labor force, Pf

215
(123)

218
(123)

-71.7
(491.4)

Managerial fraction of
labor force, Mg

-261
(201)

-256
(202)

-504
(518)

423**
(79)
-190
(130)

Sales, clerical fraction
of labor force, SI
209“
(102)

Farm fraction of labor
force. Fa
Black fraction of
population, B1

-2B.9
(72.0)

-14.2
(71.8)

138
(301)

-329*
(135)

-395**
(1351

-520“
(154)

34.6
(105.9)

151
(106) *

-27
(114)

291*
(111)

274*
till)

136
(115)

138

.256**
(.0B6)

Bll-K)

Fraction in same
residence, Rs

114
(65)

126
(663

47.0
(190.4)

Metropolitan area, □
i

Residential wealth. Hr

20.5*
(B.5)

27.1**
(8.9)

.00937**
(.00148)

.009997**
(.001627)

.0101**
(.0016)

.00716**
(.00175)

.01429**
(.00221)

.0143**
(.0022)

.0199**
(.0027)

.0202**
(.0039)

.0207**
(.0039)

.0118
(.0129)

.01717**
(.00212)

"Price 'Perms," 1

2oa**
(49)

224**
(48)

-209
(666)

616**
(561

C

510**
(94)

520**
(94)

532
(370)

969**
(104)

T

38
(87)

61
(86)

7.82
(160.94)

763**
(100)

M

170**
(54)

177**
(54)

156
(163)

-511**
(140)

-519**
(140)

HC

-1052**
(251)

KT

304
(290)

HI

Block grants per pupil, B

611.8**
(63.1)

661.2**
(63.3)

531.7**
(69.8)

S
Ti

695.6**
(94.8)

762.2**
(95.2)

552.1**
(99.6)

PU
F

595.3**
(78.7)

613**
(79)

573.5**
(94.8)

532**
(83)

u zn
" F

454.7**
(72.3)

493.7**
(72.7)

340.7**
(75.2)

1456
(2844)

-826**
(201)

Ml f

-1037**
(252)

-1980**
(429)

-1708**
(343)

-264
(291)

868
(940)

-1300**
(280)

.356**
(.093)

.5139**
(.0325)

.774
(.776)

Membership revenues with
r_2 W
lagged tax rate, --- —

.514**
(.032)

.5139**
(.0325)

.920
(.706)

Change in debt retirement
revenues, W A M ^

.000458**
(.000080)

.000462**
(.000080)

.000516**
(.000168)

Rate of growth in number
of students, APu/Pu

279**
(84)

5.2
(9.8)

-285**
(64)

I
1 F
f
f

MI —
F

-764**
(181)

-819**
(182)

-652**
(180)

-1302**
(304)

-1350**
(305)

-895**
(296)

-975**
(233)

-1026**
(234)

-928**
(239)

-229
(IB?)

R2

.8756

.8745

.6985

.6794

.711B

■6B52

S2

.8659

.8650

.6859

.6655

.6993

-664B

602

602

602

412

F statistic to test restric­
tion described in text
Number of observations, H

3.1623
371

371

371

NOTE: Equations (l)-(3) use operating expenditures per pupil in 1974-75 as the dependent variable; equations (4)-{7)
use per pupil expenditures for 1972-73 and 1973-74. Standard errors are shewn in parentheses.
•Significant at .05 level.
••Significant at .005 level.
tlnstrumental variables with M, Ml, HC, MO, (r_;W)/U-K) endogenous.
tt(E-Etr), operating expenditures less transportation costs, used as dependent variable.

139

Median income, Y

28.B**
(8.9)

on operating expenses.

Section 27 of the State School

Aid A c t provided "equalizing" aid to districts reducing
their b u i lding and debt millages in 1974.
tion of equations

The specific a ­

(1)— {3) in Table 4 does not explicitly

model the incentives offered by Section 27.

Rather,

the

equations include the change in per pupil building and
debt revenues as a determinant of operating expenditures
w i thout regard to whether Section 27 induced these changes
or o ther factors were involved.

Contrary to the expect a ­

tion that reductions in building and debt millage would
allow increases in operating expenses,

the estimated

coefficient of this variable is positive and statistically
significant at the .0005 level in all three equations.
Since surveys of districts participating in the Section 27
aid p r o g r a m indicate it has had a positive effect on
o perating millage election r e s u l t s , 1

apparently other

factors associated w i t h increases in building and debt
retirement millages w e r e also associated w i t h increases
in operating expenses.
Comparison With Estimates Based
on Earlier Years
Equations

(4)-(7)

in Table 4 show the results of

regressions on pooled cross-section time series data for
^State of Michigan, Governor's Advisory Task
Force o n Property Tax Revision, S u m m a r y ; Interim Report
to the G o vernor (July 1976), p. 53.

141
1972-73, the last year under the foundation aid formula,
and 1973-74,

the first year under percentage equalizing.

Qualitatively,

the m o s t notable differences from

the results in Table 3 are the larger coefficient of the
fraction of timber and utility property in the tax base,
T; the significant negative effect of the district size
variable,

In (Pu) ; the positive coefficient of Hs, the

fraction of pupils in high school;
negative effect of Pr,

and the significant

the fraction in private schools.

That the last variable has the expected interest group
effect in the 1972-74 sample but not in 1974-75 may
reflect the fact that it is based on 1970 census data and
thus would more accurately describe districts in 1972 than
in 1974.

Fa,

the fraction of the labor force w h o are

farmers or farm laborers,

is not included in the re g r e s ­

sions for 1974-75 but is shown in Table 4 to have a
significant positive effect on expenditures.
A comparison of equation

(6 ) with equation

(5)

agrees with Denzau's finding that opera t i n g expenditures
less transportation costs as the dependent variable gives
a better fit than total operating expenditures per pupil.
The higher

w i t h expenditures excluding transportation

was also found in other regressions not shown here.
i

The regression shown in equation

(7) attempts to

avoid the simultaneity problem with the m a t c h i n g rate by
excluding

"out-of-formula" districts

(levying m o r e than

142
22 mills)

from the sample.

Alth o u g h the m a t c h i n g rate is

an exogenous variable for districts in this sample, the
estimated coefficient of the m a t c h i n g rate term is still
smaller than the coefficients of the non-residential
shares of the tax base.
C onclusion
The regression results presented here lead to the
rejection of the hypotheses that match i n g aid has a
greater price effect than non-residential property and
that the voter's share of block grants has an effect on
school spending equivalent to that of private income.
Theoretical considerations lead to the choice of
equation

(3) in Table 3 to predict the consequences of

changes in the aid formula.

These predicted consequences

are d i s c ussed in the next chapter.

CHA P T E R V
THE DEGREE OF INEQUALITY IN A C T U A L E X P E N D I ­
TURES A N D IN PREDICTED EXPENDITURES
U N D E R A L T E RNATIVE A I D FORMULAS

This chapter discusses to w h a t degree the change
to a percentage equalizing formula has reduced the degree
of inequality in per pupil education expenditures in
M i c higan and predicts the effects on the distribution of
expenditures of modifications in the existing formula.
The analysis assumes equality of per pupil expenditures
within school districts.

Inequality at this level m a y be

an important obstacle to equal opportunity but is beyond
the scope of this study.
The Distributio n of Actual Expenditures
Consider first the distribution of actual per
pupil expenditures in 1972-73 under the foundation aid
plan and in 1974-75 under percentage equalizing.

To

maintain comparability w i t h later analysis of predicted
expenditures under modifications of the aid formula,
only the 371 K-12 districts for which all data are a v a i l ­
able are considered.

These districts had 81.7 percent

of the public school member s h i p and spent 82.9 percent
143

144
of the total public school operating expenditures in the
state during 1974-75.
Table 5 shows that for these 371 districts the
Gini coeff icient for the d i s t r i b u t i o n of operating
expenditures was

.089989 in 1972-73 and

.086988 in 1974-

75, indicating a slight reduction in the degree of
inequality of education spending under the "percentage
equalizing" formula.

TABLE 5.— Actual Expenditures in 1972-73 and 1974-75.
Total
Operating
Expenditures*

. .
Toiidi
.
..
HerabershiP

Gini Coefficient
for the Distribution
of Ejtpenditures

Sample 371 districts
in 1972-73

$1,733,300

1,792,528

.089989

Sample 371 districts
in 1974-75

2,112,025

1,745,927

.086988

All 602 districts
in 1972-73

2,085,335

2,193,270

All 590 districts
in 1974-75

2,548,499

2,135,867

*In thousands of dollars.

Measures of the Dist r i b u t i o n
of Predicted Spending
The first row of Table

6

shows m e a s u r e s of

inequality in the distribution of predicted expenditures
for the 371 school districts in the sample under the

TABLE 6.— Distribution of Predicted Expenditures for 371 Districts.

-it
U *0

5
&
0H

Under Michigan law

0J

Atkinson
Inequity
Measure

+)
c
0
•H
U
*H

o
“H rl
<a u
P -H
PM P
0
r-t 01
m o
+■
0 <t)

Atkinson
Inequity
Measure

<u *
-M cn
u 0
•H P
*0 0
0 +>
P -H
PM t
G
H Q)

to

8

& u

C
-H
o

■P c

<D 0
S5 £

y

=

-.5

y = -1.0

+j
UH
•H *rl
P Qi
+> 3
to PM
•H f-l
G
Q
*H P
ID
u tnp«
U Pw
3 0) M
<U T3
W P >i
PM O A

to

■P
u tp
*H 6
P O
+1 U
0) G
•H -rl H
GQ
•P
c
0 Oi (tJ
1 G -H
0 -H TJ
TJ P 0)
3 OE
o <a
to

P

N

ft o h

$2,090,350

$652,906

.076266

.013851

.018536

.034439

.026313

Without maximum on tax
rate subject to match­
ing aid

2,112,512

709,144

.081137

.015648

.020977

.033290

.017820

With "recapture"

2,107,483

660,268

.080587

.015503

.020802

.031119

.017253

Under 1972 foundation
plan

2,061,694

465,245

.080122

.015060

.020131

—

—

Under increased
foundation plan**

2,103,829

606,809

.074298

.012951

.017301

—

—

Without any aid

1,603,080

0

.109084

.030261

.040681

—

—

*Xn thousands of dollars.
**With a gross allowance of $728 per pupil for districts with an SEV per pupil above
$17,750 and with a gross allowance of $808 per pupil for districts with a lower SEV per pupil.

146
actual aid formula for 1974-75,
mates of equation

using the p a r a meter e s t i ­

(3) in Table 3 for predic t i v e purposes.

The Gini coefficient for the dis t r i b u t i o n of predicted
expenditures is

.076226, w h i c h is less than the Gini

coefficient of actual expenditures because predicted
expenditures exclude the varia t i o n unexplained by the
regression analysis.
A ltho u g h the Gini c o e f f icient is a common measu r e
of inequality,

other measures such as the coefficient of

varia t i o n and the standard d e v i a t i o n of logarithms are
also sometimes used.

All of these meas u r e s will rank

different distributions in the same order if none of the
corresponding Lorenz curves cross.

However,

curves do cross,

"inequality" of the

the ranking of the

if the Lorenz

distributions consid e r e d m a y depend on wh i c h m e a s u r e of
inequality is used.

This is because the vari o u s inequality

measures we i g h t parts of the d i s t r i b u t i o n differently.
The Gini coefficient wei g h t s the mid d l e of the d i s t r i b u ­
tion more, whereas the standard devia t i o n of logarithms
gives greater weight to the lower end of the distribution.
A tki n s o n defined a general class of inequity
measures given by

1

w here

=

1

-

4-

(5.1)

y

(5.2)

147
The value of the parameter y can be varied from +1.0 to -ro
to give d ifferent weights to different parts of the dis­
tribution.

As y becomes more negative, greater weight is

attached to the lower end of the distribution.
Atkinson found this measure with y

=

Thus

0.0 to give rankings

of income distributions similar to the rankings given by
the Gini coefficient, whereas the Atki n s o n inequity m e a ­
sure w i t h y = - 1

. 0

gave rankings similar to those given

by the standard devia t i o n of l o g a r i t h m s . 1
To explore the possibility that the choice of
inequality measure m i g h t affect the ranking of the d i s ­
tributions of educa t i o n expenditures predicted under d i f ­
ferent aid plans,

the fourth and fifth columns of Table 5

show the A t k i n s o n inequity measures with y
Y = -1.0, respectively.

= -.5 and

As can be seen from the table and

the following discussion, both of these measures and the
Gini c oefficient produce the same ranking for the d i s t r i ­
butions under the alternatives considered.
The sixth column of Table

6

gives a "pseudo-Gini"

coefficient derived by ranking pupils according to the
state equalized value per pupil with those with the lowest
SEV per pupil first,

graphing a "pseudo-Lorenz curve"

showing the fraction of total operating expenditures
1This discus s i o n on alternative measures of
inequality is b a s e d on Anthony B. Atkinson, "On the M e a ­
surement of Inequality," Journal of Economic Theory 2
(September 1 9 7 0 ) ;244-263.

148
spent on each fraction of the total school population,
and, as usual,

calculating the Gini coefficient as the

ratio of the area between the 45° line and the Lorenz
curve to the total area under the 45° line from the ori­
gin to the point

(1,1).

If there w e r e complete equality

in per pupil expenditures,

the pseudo-Lorenz curve would

coincide w i t h the 45° line and the pseudo-Gini coefficient
would be zero.

If less wealthy districts had lower

e x p e n d i t u r e s , the pseudo-Lorenz curve would lie b e l o w the
45° line and the pseudo-Gini coefficient would be posi­
tive.

However,

if low SEV districts had higher per pupil

expenditures, unlike the usual Lorenz curve,

the pseudo-

Lorenz curve w o u l d lie above the 45° line and the pseudoGini coefficient w o u l d be negative.

Thus,

the pseudo-

Gini coefficient in the sixth*column meas u r e s the
inequality in expenditures associated with inequality in
SEV per pupil.

Likewise,

the pseudo-Gini coefficient in

the seventh column of Table

6

measures the inequality in

per pupil spending associated with differences in median
family income for the district.
Comparisons W i t h A l t e r native Aid Plans
The second row of Table

6

shows the effects of

unlimited matc h i n g of local revenues above the 25 mill
ma x i m u m effective in 1974-75, g u a r a nteeing the same
$39,000 per pupil tax base.

All other variables including

149
categorical aid are assumed to have the same values in
1974-75.

Lifting the ceiling on matching aid would

increase the inequality in per pupil spending as measured
by the Gini coefficient or by either of the Atkinson
inequity measures.

But the inequality associated with

school d i strict wea l t h and family incomes w o u l d be
reduced.

There w o u l d be an

8 . 6

percent increase in total

state m a t c h i n g aid but only a one percent increase in
total expenditures.
The third row figures show that implementation of
recapture provisions, that is, requiring districts with
SEV per pupil above $39,000 to pay part of local tax
revenues to the state, w o u l d reduce but not completely
offset the inequality in per pupil spending caused by
lifting the ceiling on matching aid.

The inequality in

expenditures associated w i t h inequality in school d i s ­
trict w e a l t h and family income w o u l d be further reduced.
Total expenditures and net state matching aid to districts
would be reduced but not to the levels predicted under the
actual 1974-75 formula.

That recapture wo u l d n o t sub­

stantially reduce net state aid is not surprising since
97 p e rcent of all school districts had tax bases below
the guaranteed level in 1973.
F e lds t e i n had found that a pure percentage equal ­
izing formula with recapture and no limits on the amount
subject to matc h i n g w o u l d result in an inverse

150
relationship between SEV per pupil and per pupil expend i ­
tures.

The results in Table

6

contrast w i t h this in that

the pseudo-Gini for the relationship between the d i s t r i ­
bution of SEV and the distribution of expenditures for
"pure" p e rcentage equalizing remains positive, w i t h a
value of

.031119.

This difference might be attributed to

differences in the estimated price effect of matc h i n g aid,
but it could also be affected by differences between the
M i c higan and M a s s achusett s samples in the correlations of
wealth,

as meas u r e d by assessed value per pupil, with

income and other socioeconomic determinants of school
spending.
The fourth line in Table

6

shows the predicted

effects if the 1972 foundation aid plan had remained in
effect in 1974-75.

The distribution of predicted e x p e n d i ­

tures is more equal

(according to b o t h A t k i n s o n inequity

measures and the Gini coefficient)

than the distributions

under percentage equalizing w i t h no limit on matc h i n g aid
and w i t h recapture,

b u t it is less equal than the dis­

t ribution predicted under the law actually in effect.
The fifth line in Table

6

shows that by increasing

the gross allowances in the foundation aid formula by the
approximate change in the GNP price deflator from 1972 to
1974,

that is, by increasing the gross allowance from $644

to $728 per pupil for districts with an SEV per pupil
above $17,750 and from $715 to $808 for districts below

151
$17,750 SEV per pupil, the d i s t r i b u t i o n of predicted
expenditures is m a d e m o r e equal than the distribution
under the actual law.
All of the above comparisons are based o n the
assumption that federal and state categorical aids are
maintained at actual 1974-75 levels.

The last line in

Table 6 describes the predicted effect of eliminating all
of this aid as well as all

"membership aid" provided by ■

the percen tage equalizing or foundation formulas.

If

school districts w e r e forced to rely only o n local tax
revenues,

predicted total expenditures w o u l d be 23.3 per­

cent less than under the actual M i c h i g a n law with federal
and state categorical aids, and the d i s t r i b u t i o n of these
expenditures would be m u c h m o r e u n e q u a l , w i t h a Gini
coeffi c i e n t of .109084.
Conclusion
If state policy makers desire to reduce the relationship between differences in school expenditures per
pupil and differences in district we a l t h and family
incomes,

c hanging to a "pure" percentage equalizing

formula w i t h o u t a limit on local millages subject to
m a t ching aid and with "recapture" of a portion of local
tax revenues from wea l t h y districts w o u l d achieve this
goal.

But if they desire to reduce inequality in

expenditure levels per s e , the retention of the m a x i m u m

152
on m i l lages subject to m a t c h i n g aid is advisable.

This

ceiling on match i n g aid effectively makes the M i c h i g a n
state aid plan a foundation plan for those districts
levying above the m a x i m u m millage.
cussed in this chapter show that,
ture levels is the goal,

The predictions d i s ­
if equality in expend i ­

a sufficiently high level of aid

under a foundation plan will do better than even the
actual M i c h i g a n state aid law for 1974— 75 and m u c h better
than a pure percentage equalizing formula.

Comparisons

with the d i s t r ibution of predicted expenditures without
any state or federal aid show that all of the existing or
propo s e d aid plans significantly reduce the inequality in
expenditures that w o u l d prevail if all school spending
were financed by local taxes.

CHA P T E R VI
SUMMARY A N D CONCLUSIONS

Percentage equalizing aid formulas have a m a t c h ­
ing effect in that an increase in local tax levies will
increase state aid as well.

This means that in districts
I

receiving matching aid the marg i n a l

"price" to local

voters of one dollar of per pupil education expenditures
is less than one dollar.
T heory predicts that non-residential shares of
the property tax base are also factors in the "price" of
school expenditures.

Ladd hypothesized that the stimula­

tive effect of non-residential shares of the tax base is
less than that of the m a t c h i n g rate because voters believe
that some of the taxes on non-residential property will
be shifted to themselves.

She found this to be the case

in her study of M a s s a chusetts school and municipal
expenditures.
T heory also predicts that the voter's share of
non-categorical,

lump-sum aid will have an impact on

school spending equal to that of increases in family
income.

However,

those previous studies reviewed here

that a t t e m p t e d to test this hypothesis used an incorrect
specification w h i c h failed to account for the share of
153

154
lump-sum aid that should be apportioned to non-residential
p roperty owners and for interaction w i t h the matching aid
rate.
The empirical results in Chapter IV contradict
both of the hypotheses in the preceding paragraphs.

The

stimulative effect of non-residential property is sig­
nificantly greater than, rather than less than,
the m a t c h i n g rate.

Indeed,

that of

in districts with m u c h non-

residential property the interaction terms result in
increases in the matc h i n g rate reducing total per pupil
expenditures.

Correctly specified,

ginal impact of non-categorical,

the estimated m a r ­

lump-sum aid is greater

than the marginal effect of family income.

This evidence

might be regarded as refutation of the me d i a n voter model
in w h i c h voter preferences determine the level of public
expenditures.

There is, however,

a serious simultaneous

equations problem with the endogenous matching rate and
block grant variables that is not satisfactorily treated
because of the discontinuous relationships determining
the values of these variables.
The use of only the me d i a n income variable in the
expenditure equation is inappropriate if the demand for
public expenditures
income.

is not a monot o n i c function of

B rown and Saks tested for and found a significant

bias resulting from the use of only me d i a n income as a
determinant of local e d u c ation revenues per family.

155
However,

the present study finds no such bias in the

regressions for education expenditures per pupil.
Previous studies of the determinants of educa­
tion expenditures that have investigated a possible
lagged response to changes in these determinants have
simply used lagged expenditures as an independent v a r i a b l e .
The present study is unique in assuming a standard par­
tial adjustment model for determining millage rates whic h
results in an expenditure equation in wh i c h the effects
of the lag are represented by two t e r m s , bl o c k grants per
pupil and the lagged millage rate multiplied by current
SEV per pupil divided by one m i n u s the current matching
rate.

The effect of this specification on dynamic

behavior is that an increase in block grants will tem­
porarily increase expenditures above the new long-run
equilibrium level.

The estimates of the lag based on

this specification indicate that only about half of the
gap between the initial m i l l a g e rate and the long-run
desired rate is eliminated in two years.
Theoretically,

the existence of property tax

credits and deductions should affect voting behavior in
m i l lage elections.

Currently,

income tax return data by

school d i s trict is not available so the present study
does not investigate this effect.

This question is one

topic for further research into the determinants of edu­
cation expenditures if the necessary data becomes

156
available.

Another topic for further research if the

data becomes available is the effect of publicity campaigns
informing voters of facts which are relevant to voter
choice in millage elections such as the advantages of
m a t ching aid plans for the district.
The evidence in Chapter V shows that the "per­
centage equalizing" aid formula adopted by M i c h i g a n in
1973 has somewhat reduced the inequality in per pupil
expenditures in the state.

Inequalities in expenditures

associated w i t h differences in the tax base and in the
level of family income remain, but these two variables are
associated with only a fraction of the meas u r e d inequality
in expenditures.
The long estimated lag in response to changes in
the determinants of education expenditures may decline
further over time as districts adjust to the current per ­
centage equalizing formula.

However,

this might be off­

set by c a p i t alization in property values of the effects of
the aid formula.

The present study has made no attempt to

estimate these c a p i t alization effects.
The restricted form of the estimated expenditure
equation predicts that removing the m a x i m u m limit on
millages subject to m a t c h i n g aid would increase the
inequality in spending levels but reduce that inequality
w hich is associated w i t h differences in tax base and
family income.

Implementing recapture provisions tends to

157
reduce inequality in expenditures but, because of the
high guaranteed tax base, would not fully offset the
effect of lifting the ceiling on matc h i n g aid and would
not g r e atly reduce net state aid.
The results of this study disa g r e e with Feldstein's finding that percentage equalizing would so
stimulate expenditures in low tax base districts that
inequalities inversely related to SEV w o u l d arise.

The

possi b i l i ty that the simultaneity problem has not been
adequately treated suggests that the predictions of the
effects of removing the m a x i m u m on m a t c h i n g aid and
implementing recapture may understate the stimulus to
spending from the former policy and the depressing effect
of the latter policy.
W hile the distribution of predicted expenditures
under the actual 1974-75 state aid law is m o r e equal than
the distribution predicted under the 1972 foundation
plan, a foundation plan w i t h a higher level of state
support produces a m o r e equal pat t e r n of predicted
expenditures.
The policies recommended on the basis of the
above findings depend on the normative principles to be
followed.

If the objective is to impose greater equality

on the distribution of education expenditures within the
state,

the ceiling on millages subject to matc h i n g aid

should be retained.

This effectively makes the state aid

158
formula a foundation plan for districts levying millages
above this ceiling,

and greater equality in expenditures

could be obtained if a foundation plan w i t h high levels
of state support w e r e adopted.
However,

if the objective is to reduce the r e l a ­

tionship between expenditure levels and school district
w e alth w hile allowing inequality in expenditures caused
by other variables which,

at least in part, reflect dif ­

ferences in local tastes,

eliminating the foundation-like

m a x i m u m on millages subject to match i n g aid and adopting
a "pure" percentage equalizing formula w i t h

"recapture"

of a p o r t i o n of tax revenues from wea l t h y districts is
recommended.

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