Public Finance Seminar
Spring 2015, Professor Yinger
State Aid
State Aid
Class Outline

The Education Finance System

Types of State Aid

Research on State Aid
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The U.S. Education Finance System

State elected officials make the rules for elementary and
secondary education.

State elected officials also design the education finance
system:
◦ State aid (~50% of total in average state)
◦ Property taxes and perhaps other local taxes
◦ Compensation for homestead exemptions

The federal government provides a little funding (< 10%), tax
breaks for property taxes, and some incentives (through
NCLB).
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EDUCATION FINANCE
IN THE U.S.
Authority
Revenue
Local Property
Taxes
Local Voters
School
District
State Regulators
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Federal Aid
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The Education Finance System, 2

The broad rules are laid out in a state constitution,
which has phrases such as “a system of free public schools’
or “a sound, basic education.”

Elected officials design a system that meets their
objectives, which usually (but not always!) do not involve
much re-distribution.

People in low-performing districts bring suits into the
state courts, and the state courts rule on the
constitutionality of the system designed by elected officials.
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The Role of the Courts

1971: Serrano decision by California Supreme
Court rejected California’s education finance
system based on U.S. and California Constitutions.
◦ It is unfair, the court said, for a child’s education to
depend on the wealth of his school district.

1972: Rodriquez decision by the U.S. Supreme
Court ruled out education claims based on U.S.
Constitution.
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The Role of the Courts, 2

Since 1971:
◦ 43 state courts have heard challenges to their state’s education
finance system.
◦ 20 more education finance systems have been declared
unconstitutional by a state supreme court.
◦ Court decisions have led to major education finance
reforms in many states, including California, Kentucky, New
Hampshire, New Jersey, Texas,Vermont.
◦ Several states have implemented major reforms without a
court mandate, including Kansas, Maryland, and Michigan.
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Educational Disparities

What the courts are responding to are enormous
disparities in both resources and student
performance across school districts within a state.

This disparities arise because districts vary widely in
both available resources and educational costs.

Large cities, which often contain many poor families,
have particularly low student performance.
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Sources of Student
Performance Gaps
Demand
Supply
Disparities in
Income &
Wealth
Poverty, Limited
English, Wages
Gaps in
Education
Resources
Gaps in Student
Performance
Gaps in
Education Costs
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8th Grade Test-Score Gaps
Between Big Cities and States, 2001
State
City
Reading
Math
California
Los Angeles
38.0%
42.9%
Oakland
44.0%
44.9%
Colorado
Denver
44.4%
64.9%
Illinois
Chicago
27.3%
50.0%
Louisiana
New Orleans
58.0%
63.6%
Maryland
Baltimore
63.0%
70.2%
Massachusetts
Boston
38.8%
41.2%
Michigan
Detroit
48.3%
44.4%
Minnesota
Minneapolis
35.4%
41.7%
Missouri
St. Louis
67.6%
60.0%
New Jersey
Newark
43.9%
61.4%
New York
Buffalo
48.9%
59.0%
New York City
26.7%
41.0%
Rochester
44.4%
71.8%
Ohio
Cleveland
18.7%
53.4%
Pennsylvania
Philadelphia
61.7%
68.6%
Wisconsin
Milwaukee
49.3%
79.5%
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Proficiency and Graduation Rates in New York, 2013
90
80
70
60
50
40
30
20
10
0
NYC
Buffalo
Grades 3-8 ELA
Rochester
Syracuse
Grades 3-8 Math
Yonkers
Graduation Rate
Rest of State
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Key Questions in Education Finance Reform

1. What is the best way to measure the
education provided by a school district?
◦ What do we want schools to provide?

2. What is the appropriate equity standard?
◦ How would we recognize a fair outcome if we saw
it?
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Measuring Education, 1

Spending per pupil is a poor measure of
education
◦ Easy to measure, but hard to interpret
◦ Rejected by most courts

Spending ignores variation in the cost of
education due to
◦ Concentrated disadvantage among students
◦ The high cost of attracting teachers to some districts
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Measuring Education, 2

Pupil performance, such as test scores and dropout rates, provides a better measure of education
◦ It corresponds with what parents want
◦ It is consistent with the trend toward setting higher standards
◦ It is consistent with accountability programs (discussed next
class)

An education cost index provides a bridge
between performance and spending
◦ An equivalent approach is using higher “weights” for
disadvantaged students
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Educational Adequacy

Adequacy is the equity standard emphasized in most
recent court decisions and by most policy makers:
◦ Every student should be in a school that delivers an adequate
average student performance.

An adequacy standard does not eliminate all disparities:
◦ Districts are allowed to provide above-adequate educations if
they can.

Adequacy is achieved by a foundation aid program
(discussed below).
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Other Equity Standards

Access Equality
◦ The education provided by a district should depend only on its property
tax rate.
◦ Refers to fairness for taxpayers, not students.
◦ Is achieved by power-equalizing aid (discussed below)
◦ Was the main issue in Serrano.

Wealth Neutrality
◦ Educational outcomes should not be correlated with school district wealth.
◦ Difficult to achieve.

Equality
◦ All school districts should provide the same level of education.
◦ May require state provision, as in Hawaii.
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The Foundation Aid Formula

40 states use a foundation aid formula, designed to
achieve educational adequacy.

The foundation aid formula is
Aj  E*  t *V j
◦ Aj = aid per pupil to school district j.
◦ E* = foundation spending per pupil (state-selected; the same in
every district).
◦ t* = minimum required property tax rate (state-selected; the
same in every district).
◦ Vj = actual property tax base per pupil in district j.
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The Foundation Aid Formula, 2
Spending
per Pupil
Spending Above
Foundation Level
Foundation
Spending
Level
E*
Required Local Taxes
Aid
Vmin
Vmax
Tax Base per Pupil
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The Foundation Aid Formula, 3

A foundation aid formula can easily be adjusted for
educational costs (that is, focused on performance):
Aj  S *C j  t *V j
◦ S* = foundation spending level per pupil in a district with average
costs
◦ Cj = educational cost index for district j.

Pupil weights can also be used.

This formula is equivalent to offsetting fiscal disparities across
schools.
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The Foundation Aid Formula, 3

A foundation formula must address four issues:
◦ 1. How much spending is “adequate”?
◦ 2. Should the foundation level be adjusted for variation
in education costs across districts?
◦ 3. Should a minimum local property tax rate be
required?
◦ 4. How should burden of funding an adequate
education be distributed?
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Foundation Aid without Minimum Tax Rate
Requirement
Spending
per Pupil
Spending Above
Foundation Level
Foundation
Spending
Level
E*
Spending
Lost
without
Required
Minimum
Tax Rate
Local Taxes
Aid
Vmin
Vmax
Tax Base per Pupil
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Power-Equalizing Aid

Power-equalizing (or guaranteed tax base,
GTB) aid, is the main program in 3 states and a
supplementary program in 10 others.

The idea behind GTB aid is that a district’s
spending should depend on tax effort, not tax
base:
E j  t jV

*
where V* is a policy parameter set by the state.
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Power-Equalizing Aid, 2

To determine the associated aid formula, note
that
E j  Aj  t jV j  t jV * or Aj  t j (V * V j )

Combining this with the GTB formula leads to:
 Vj 
Aj  E j  1  * 
 V 
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Power-Equalizing Aid, 3

GTB is matching aid; the state share of spending
decreases with Vj.

If V* < maximum Vj, then matching rates are negative in
rich districts.
◦ This is called recapure.
◦ Vermont is an example.

Raising V* raises the cost of GTB aid.
◦ To offset this effect, set matching rates at a fraction of the value
in the above formula
◦ That is, flatten the line in the following picture.
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Power-Equalizing Aid, 4
mi = (1 – Vi /V*)
Matching
Rate =
State
Share
Recapture
0
Vmin
V*
Vmax
Tax Base per Pupil
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Power-Equalizing Aid, 5

GTB aid can be adjusted for costs (but rarely is):
 S *C j V j 
Vj 

Aj  E j  *  *   E j  C j  * 
 S C V 
V 




Using GTB as a supplement to foundation aid is
misguided:
◦ Foundation aid already requires poor districts to set
tax rates above their desired level.
◦ Adding GTB aid will not induce any further tax rate
increases.
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Comparing Foundation & GTB Aid

GTB aid is often thought to be more equalizing than
foundation aid.

In fact, however, price elasticities are small, so the
response to GTB aid is small, even for poor districts.
(See D/Y, NTJ, 1998.)

So:
◦ Foundation aid is much more equalizing at the bottom of the
property value distribution (and is the only way to ensure
adequacy).
◦ GTB aid is more equalizing at the top of the property value
distribution—at least if it includes recapture
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Comparing Foundation and
GTB Aid, 2
Spending
per Pupil
Initial Spending
Spending with Foundation Aid
Spending with Power-Equalizing Aid
With Required
Min. Tax Rate
Recapture
E*
Small Impacts Due to
Small Price Elasticity
Vmin
V*
Vmax
Tax Base per Pupil
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Wealth Neutrality

Wealth neutrality is defined as a zero correlation between
property wealth and performance outcomes.
◦ This is the same as a flat regression line for performance as a function
of wealth.

When it was first proposed, many people thought GTB aid
would lead to wealth neutrality.

But a famous paper by Feldstein (AER 1975) shows that this
would be true only by coincidence because outcomes depend
on the behavioral responses to the matching rates.
◦ A low response by low-wealth districts (which seems to be the case)
would lead an upward sloping line.
◦ A high response by low-wealth districts would lead to a downward
sloping line.
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Research on State Aid

The Oates Equivalence Theorem
 Recall that
V 
Y  Y  A 
V 
A
 The Oates theorem says that the impact of these two
components of augmented income on demand should
be the same.
 Other equivalence theorems arise in other models.
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Research on State Aid, 2

The Flypaper Effect
 Empirical studies find that the Oates theorem does
not hold.
 In the D/Y equations, f ≠ 1:

V
S  K Y  f A
V

*
*
  *
* 1  V
    C  e  
 
V
 There is no consensus about why this is true.



*
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Research on State Aid, 3

Matching aid
 The community budget constraint
 C{S}

 e


 A 1 m   tV


 The household budget constraint
Y
V
 A 
V



1 m  Z  PH
 C{S}   V
 

 V
e


 Tax Price
TP  MC V 1 m 

V



1 m
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Research on State Aid, 4

The matching rate
 Note that in this formulation, the matching rate is the
state share
S
m
SL
 Some studies use the state match per dollar of local or
 This leads to:
S
m* 
L
 C{S}  A   1 

 
  tV
e

 1 m * 
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Research on State Aid, 5

Matching vs. lump-sum aid
 There is a well-known theorem that matching aid has a
more stimulative effect than equal-cost lump-sum aid.
 This is an application of the classic microeconomic
theorem that price subsidies have larger effects (per
dollar) than cash grants.
 The relevant graph follows:
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Cash vs. Price Subsidy
Budget Line with
Cash Grant
Tangency Point
with Cash Grant
Clothing
Tangency Point
with Price Subsidy
I3
I2
I1
F1 F3
Cost of Both Programs
(in Units of Food)
F2
Food
Budget Line with
Price Subsidy
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Research on State Aid, 6

This theorem fails to consider three key
elements of the demand for public services
 Lump-sum aid has a flypaper effect.
 Matching aid alters the value of existing lump-sum aid
(and, to be specific, makes it less stimulative).
 Both matching and lump-sum aid may alter efficiency,
but these effects are not well understood.
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Research on State Aid, 7

The flypaper effect applies only to lump-sum aid.
 Even if the price elasticity is high for a government
service, the theorem applies regardless of the price
elasticity.

The theorem assumes no flypaper effect.

Hence, a large flypaper effect could reverse the
theorem.
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Research on State Aid, 8

Matching and lump sum aid
 With matching and lump-sum aid the household
budget constraint is
Y
V
fA 
V



1 m  Z  PH
 C{S}   V
 

 V
e





1 m
 Matching aid affects the value people place on lumpsum aid (because it alters their tax price),
 This effect could reverse the standard theorem
because it lowers the stimulative impact of matching
aid.
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Research on State Aid, 9

Aid and Efficiency
 Both types of aid appear in augmented income.
 Matching aid appears directly in tax price and both
types of aid affect tax price through e.
 Hence both type of aid may alter efficiency—and
this effect may reverse the standard theorem.
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