The Flypaper Effect
Phuong Nguyen-Hoang and John Yinger
Draft, April 2017
The Flypaper Effect
 Introduction
 Over the last fifty years ago, many scholars have found that, in
per capita terms, the impact of $1 of state aid on public
expenditure is larger than the impact of $1 of household income.
 This phenomenon is known as the flypaper effect, and it has
been found to exist for many levels of government in many
countries. (The term was apparently coined by Arthur Okun.)
 Despite a voluminous literature (Inman 2008 found over 3,500
papers on the topic!), no scholarly consensus exists on
the flypaper effect’s magnitude or causes.
The Flypaper Effect
 Introduction, 2
 This paper reviews what has been learned about the
methodology required to estimate flypaper effects; uses the
Slutsky equation to show, for the first time, that flypaper effects
are not confined to lump-sum aid; and reviews behavioral
explanations for the flypaper effect.
 Based on the results for New York State in Eom et al. (2014) and
Nguyen-Hoang and Yinger (2016) and on new results for
“hidden” flypaper effects, we find support for the argument in
Hines and Thaler (1995) that the flypaper effect arises from
framing.
 We also show that the magnitude of this effect may reflect the
salience of events in the local public sector.
The Flypaper Effect
 Introduction, 3
 This presentation has two parts
 (1) A review of the literature on estimating flypaper effects, with a
focus on state aid to K-12 education.
 (2) The introduction of two new flypaper effects, one of which
applies to matching aid.
 (3) (If time) Tests of theories about the causes of flypaper effects.
The Flypaper Effect
 Early Studies
 Several studies in the late 1960s and early 1970s estimated an
equation of the form:
ln{E}  K   ln{Y }   ln{ A}   ln{ X }  
 where E is school spending, Y is household income, A is lump-sum
aid—all measured in per pupil terms.
 This equation was interpreted as a constant-elasticity demand
function, that is, as the school spending that was demanded by
voters in a district with income Y and state aid A, controlling for
other demand factors, indicated by X. (K is a constant.)
 The flypaper effect is defined to be ϕ/θ.
Estimating the Flypaper Effect
The Flypaper Effect
 Early Studies, 2
 An early review of the flypaper effect literature finds that “The
current expenditure response to revenue sharing is roughly five
times that of the response to private income” (Gramlich and
Galper 1973).
 A later review (Duncombe 1996) finds that the flypaper effect is
in the range of 2 to 5.
Estimating the Flypaper Effect
The Flypaper Effect
 The Fundamental Nonlinearity of Aid
 Let Z stand for spending on the composite good, H for housing
services, P for the price of housing services, and T for a property
tax payment. The value of a house is V = PH/r, where r is a
discount rate, and PH is the annual spending on housing.
 So the household budget constraint is:
Y  Z  PH  T
 Now let t be the property tax rate so that T = tV in a
homogeneous school district and the district budget constraint
is:
E  T  A  tV  A
Estimating the Flypaper Effect
The Flypaper Effect
 The Fundamental Nonlinearity of Aid, 2
 Solving the district constraint for t and substituting it into the
household constraint yields the combined budget constraint:
Y  Z  PH  ( E  A) or Y  A  Z  PH  E
 Hence the income term in the budget constraint is (Y + A), and
the corresponding variable in a constant-elasticity demand
function is ln{Y + A}.
 An estimate of the flypaper effect requires a separate
coefficient on each of these terms, or θln{Y + (1 + f )A}, where θ is
the income elasticity of demand for education and f is the
flypaper effect.
Estimating the Flypaper Effect
The Flypaper Effect
 The Fundamental Nonlinearity of Aid, 3
 This formulation is obviously nonlinear, which makes it difficult to
estimate.
 To obtain a close linear approximation, we can re-write the
above expression as

 A 
 ln{Y }   ln 1  (1  f )   
 Y 

 Because ln{1 + a} ≈ a when a is a small fraction and because A/Y is
a small fraction, this expression can be closely approximated by
 A
 ln{Y }   (1  f )  
Y 
Estimating the Flypaper Effect
The Flypaper Effect
 The Fundamental Nonlinearity of Aid, 4
 Replacing the formulation in the early studies with this
formulation leads to a new estimating equation:
 A
ln{E}  K   ln{Y }   (1  f )     ln{ X }  
Y 
γ
 Define the coefficient of the unlogged (A/Y) term as γ.
 Then the estimate of the flypaper effect is [γ /θ – 1].
Estimating the Flypaper Effect
The Flypaper Effect
 The Bradford/Oates Equivalence Theorem
 Bradford and Oates (1971) and Oates (1972) showed that the
value of $1 of aid to a voter depends on the voter’s tax price.
 With heterogeneous voters, the outcome is determined by the
median voter, and the budget constraint accounts for the
overall property value in the district.
 To be specific, let V be property value per pupil in a school
district. Then the district budget constraint is
E  tV  A
Estimating the Flypaper Effect
The Flypaper Effect
 The Bradford/Oates Equivalence Theorem, 2
 With this addition, the combined budget constraint becomes:
 PH 
 E  A  PH
Y  Z  PH  t 

Z

PH




 r 
 V  r

V
or
Y




V

V
A

Z

PH




V

E

 In this model, the tax-price term, V / V , is, of course, what it cost
the voter to obtain another unit of E, but it is also a weight
applied to state aid.
 Adding a flypaper effect and the above approximation, the
expression for income augmented by aid, labeled Y , is:
 V  A 
ln{Y }   ln Y    1  f      .
V  Y 
Estimating the Flypaper Effect
The Flypaper Effect
 The Bradford/Oates Equivalence Theorem, 3
 This formulation appears in Inman (1979) and Fisher (1982),
although their terminology is somewhat different.
 These authors do not, however, provide the associated
estimating equation. This equation is:
 A  V
ln{E}  K   ln{Y }   (1  f )  
 Y  V
Estimating the Flypaper Effect

V 
   ln     ln{ X }  

V 
The Flypaper Effect
 A Switch to Student Performance
 Bradford, Malt, and Oates (1969) explain that voters care about
final outputs, not spending as such, and the costs that link
spending and output vary with a jurisdiction’s spending
environment.
 Let S be student performance and E{S} be its cost function. Then
the tax price of S is the product of the marginal cost of S, MC,
and the (re-labeled) tax share, V / V .
 Now the demand function is
 A  V
ln{S}  K   ln{Y }   (1  f )  
 Y  V
Estimating the Flypaper Effect
 V

   ln 

 V


 MC    ln{ X }  


The Flypaper Effect
 A Switch to Student Performance, 2
 One way to estimate this demand function is to assume that the
average cost of S (i.e. the cost per unit of output = AC) equals
MC and to multiply sides of the unlogged version of the above
equation by AC. Because E = (S)(AC), this results in:
 A  V 
ln{E}  ln{S ( AC )}  K   ln{Y }   (1  f )   
 Y  V 
V 
  ln    (   1) ln{ AC}   ln{ X }  
V 
 This approach is used by Rockoff (2010).
Estimating the Flypaper Effect
The Flypaper Effect
 A Switch to Student Performance, 3
 Eom et al (2014) estimate Rockoff’s approach using data from
New York State from 1998 to 2011.
 The control for cost factors and (following Rockoff) for district
fixed effects.
 This study considers the price effect of property tax exemptions
as well as the standard tax price.
 They estimate that the flypaper effect is 20.7.
 This study also rejects the assumption behind the Rockoff
approach, namely that AC = MC.
Estimating the Flypaper Effect
The Flypaper Effect
 Introducing a Cost Function
 The only way to eliminate the assumption that AC = MC is to add
a cost function to the model.
 And a cost function requires an analysis of school district
efficiency.
 We use the approach developed in Duncombe and Yinger
(2011), Eom et al. (2014), and Nguyen-Hoang and Yinger (2014).
 This approach involves estimating a new equation, namely,
C{S }
E
e
 where C is best-practices cost to deliver performance S and e equals
1 in an efficient district and is less than 1 in an inefficient district.
Estimating the Flypaper Effect
The Flypaper Effect
 Introducing a Cost Function, 2
 In this context, S is a specific measure of student performance
and efficiency measures not only waste but also spending on
other types of student performance, say S*.
 Because voters value S*, the efficiency component of this
equation is specified like the demand function, with some extra
controls to indicate factors associated with voter monitoring.
 This approach leads to a two structural equations, which can be
estimated with 2SLS; all of the parameters, including the flypaper
effect are identified.
Estimating the Flypaper Effect
The Flypaper Effect
 Introducing a Cost Function, 3
 Eom et al. (2014) estimate this model using data for school
districts in New York State from 1998 to 2011; NYC is excluded.
 The measure of S is an index of test scores and graduation rates.
 This study finds a statistically significant flypaper effect of 52.1.
Estimating the Flypaper Effect
The Flypaper Effect
 Accounting for Salience and Framing
 Hines and Thaler (1995) argue that the flypaper effect reflects
the behavioral economics concept of framing.
 In this context, framing arises when households put different sources
of revenue in different mental accounts with links to different types
of spending.
 The flypaper effect also might be influenced by the salience of
related features of a state’s school finance system.
 Salience is a behavioral economics concept that denotes visibility;
people are likely to have larger responses to school finance
changes that are more salient.
Estimating the Flypaper Effect
The Flypaper Effect
 Accounting for Salience and Framing, 2
 The STAR program in New York State provides a unique
opportunity to look for the role of salience and framing.
 STAR is state-funded property tax exemption from school taxes. It
is equivalent to an open-ended matching grant with a local
share equal to (1 – X/V), where X is the exemption amount and V
is a voter’s property value.
 The exemption amount varies across districts and over time.
 This STAR-based local share alters the value of aid to voters, so it
is part of the augmented income specification that identifies the
flypaper effect.
Estimating the Flypaper Effect
The Flypaper Effect
 Accounting for Salience and Framing, 3
 STAR leads to a test of framing, because basic STAR property tax
exemptions were supplemented by rebates in the 2007-2009
period.
 These two types of property tax relief are algebraically equivalent,
but the exemptions are framed as part of the property tax bill, which
links to the public spending mental account, and the rebates
arrived in the mail and are framed as unlabeled income.
 Nguyen-Hoang and Yinger (2016; henceforth N/Y) hypothesize that
voters will perceive the impact of the exemptions on the value of
state aid, but will not alter this perception when rebates are added.
Estimating the Flypaper Effect
The Flypaper Effect
 Accounting for Salience and Framing, 4
 STAR also leads to a test of salience, because STAR was phased
in and heavily publicized in its early years.
 High salience for STAR implies that voters are aware that STAR lowers
the value they receive from each dollar of state aid.
 N/Y hypothesize that this greater awareness will result in a lower
flypaper effect in the phase-in years.
Estimating the Flypaper Effect
The Flypaper Effect
 Accounting for Salience and Framing, 5
 The N/Y results support these hypotheses.
N/Y Flypaper Effects
Estimating the Flypaper Effect
f for year = 1999 (no STAR)
34.9***
f for year = 2000 (Phase-in Year)
35.8***
f for year = 2001 (Phase-in Year)
41.0***
f for year = 2002 (Phase-in Year)
54.4***
f for year = 2003-06 and 2010-11
56.2***
f for year = 2007 (Rebate Year)
57.2***
f for year = 2008 (Rebate Year)
52.1***
f for year = 2009 (Rebate Year)
42.8***
The Flypaper Effect
 Two New Flypaper Effects
 This analysis of flypaper effects leads to two new types of
flypaper effects:
 Efficiency flypaper effects, which are flypaper effects hidden in the
efficiency equation.
 Slutsky flypaper effects, which are flypaper effects hidden in price
elasticities but illuminated by the Slutsky equation.
Two New Flypaper Effects
The Flypaper Effect
 Efficiency Flypaper Effects
 Recall that one component of inefficiency is spending on school
services other than the ones specified in S, called S*.
 Recall that voters have a demand for S*, and that this demand,
like the demand for S, depends on, among other things, voter
income augmented by state aid.
 The Eom et al. approach (and the N/Y approach) therefore
estimate an efficiency flypaper effect as part of the first-stage
expenditure equation.
 To keep the two flypaper effects separate, we call the standard
flypaper effect f D and the efficiency flypaper effect f E.
Two New Flypaper Effects
The Flypaper Effect
 Efficiency Flypaper Effects, 2
 Intuitively, f D and f E are similar to a decomposition of the
traditional flypaper effect, which is based on school spending.
 Specifically, f D measures the flypaper effect associated with a
selected, and presumably central, index of school quality, S, and
f E measures the flypaper effect associated with all other school
quality measures or, to put it another way, with all spending not
directed to S.
 This comparison is not exact, however, because estimates of the
traditional flypaper effect, unlike estimates of f D and f E, require
the assumption of constant returns to quality scale. Estimates of f
D and f E are therefore more precise and more general than
traditional estimates.
Two New Flypaper Effects
The Flypaper Effect
 Efficiency Flypaper Effects, 3
 Efficiency flypaper effects were first estimated by Duncombe,
Lukemeyer, and Yinger (2008), although they did not focus on it.
 Eom et al. (2014) find that f E = 59.8, which is similar to their
estimate of the standard flypaper effect: f D = 52.1
 As shown on the next page, N/Y find that the time pattern is very
similar for the standard and efficiency flypaper effects.
 This evidence indicates that state education aid has a largerthan-income impact on the spending associated with many
types of school performance measures, not just those that are
highlighted in academic studies and state accountability
systems.
Two New Flypaper Effects
Standard and Efficiency Flypaper Effects
70
60
50
40
30
20
10
0
1998
2000
2002
2004
Standard
Two New Flypaper Effects
2006
Efficiency
2008
2010
2012
The Flypaper Effect
 Slutsky Flypaper Effects
 Open-ended matching grants are rarely used for state education aid, but
as shown by Rockoff (2010) and Eom et al. (2014), STAR is equivalent to this
type of aid; so STAR provides an opportunity to estimate the extent to
which voters respond to a change in the price of local education.
 From the perspective of this paper, STAR also makes it possible to estimate
a third type of flypaper effect, which is hidden in the price elasticity of
demand estimated by Rockoff and Eom et al.
 According to the Slutsky equation, the behavioral response to a price
reflects both a substitution effect and an income effect.
 This income effect could have a flypaper effect attached to it.
 So the behavioral response to the implicit income increase from the STAR tax
exemptions could be greater than the behavioral response to an equivalent
change in household income.
Two New Flypaper Effects
The Flypaper Effect
 Slutsky Flypaper Effects, 2
 The elasticity form of the Slutsky equation is
µ  µC – s
 where μC is the compensated price elasticity, s is education’s budget
share, and θ is the income elasticity.
 We argue that the income effect in this formula (the last term) may include
a price-linked flypaper effect, labeled f P, so that
µ  µC – 1  f P  s 
 We are working on a way to estimate f P using this equation.
 Any ideas!!??
Two New Flypaper Effects
The Flypaper Effect
 What Causes the Flypaper Effect?
 Theory 1: Deadweight Loss
 Jonathan Hamilton (1986) and Dahlby (2011) argue that the
perceived marginal cost of public services includes the
deadweight loss from the taxation required to fund it.
 Intergovernmental grants lower this MC at the before-grant level
of S and thus provide a price incentive, which does not arise with
income increases, to increase S.
 This theory requires implausible assumptions: (1) Voters select
private goods but the government independently selects the
level of S. (2) Each voter assumes that everyone else will act just
like she does, which implies that a voter’s selected level of the
taxed good can be treated as the tax base.
What Causes the Flypaper Effect?
The Flypaper Effect
 What Causes the Flypaper Effect?
 Theory 2: Citizen Misperception
 Courant, Gramlich, and Rubinfeld (1979) amd Oates (1979)
argue that voters think their tax share is not V / V but is instead
their property taxes divided by their jurisdiction’s spending.
 State aid lowers this ratio and is misperceived as a price
reduction.
 This theory is contradicted by the widespread finding that the
demand for S depends on V / V .
What Causes the Flypaper Effect?
The Flypaper Effect
 What Causes the Flypaper Effect?
 Theory 3: The Power of Public Officials
 Filimon, Romer, and Rosenthal (1982) argue that voters are
generally unware of aid. This ignorance allows public officials to
spend the aid money on their own preferred projects.
 This theory is contradicted by the widespread finding that voters
know enough about aid to adjust it for V / V , as in the
Bradford/Oates equivalency theorem.
 Wyckoff (1988) says that public officials have more bargaining
power than voters in the disposition of aid than in the income,
because aid stays in the jurisdiction when a voter leaves.
 This theory is contradicted by the N/Y finding that adding the
STAR exemption did not lower the flypaper effect (as predicted
by the loss of public officials’ bargaining power).
What Causes the Flypaper Effect?
The Flypaper Effect
 What Causes the Flypaper Effect?
 Theory 4: Politics
 Chernick (1979) and Knight (2002) argue that governments
wanting to increase spending lobby for more aid, which leads to
reverse causation and upward bias in the aid variable.
 For this to be a problem in studies with district fixed effects
(Rockoff 2010, Eom et al. 2014, N/Y), the unobserved district traits
that affect both A and S would have to vary over time, which
seems unlikely.
What Causes the Flypaper Effect?
The Flypaper Effect
 What Causes the Flypaper Effect?
 Theory 5: Framing (Adjusted for Salience)
 Hines and Thaler (1995) argue that the flypaper effect arises
because of framing.
 Changes in state aid appear in voter’s mental account for S,
where they have a disproportionate impact on the demand for
S compared to the impact of changes in household income.
 As shown by N/Y, the STAR rebates provide a natural experiment
to test this theory because the STAR tax exemption appears on a
voter’s tax bill, which is part of the mental account for S, but the
STAR rebate check arrives in mail as unlabeled income.
 The N/Y finding that the rebates have no impact on the flypaper
effect supports this framing hypothesis.
 N/Y also show that the flypaper effect varies with the salience of
the tax price in a given year.
What Causes the Flypaper Effect?
The Flypaper Effect
 Conclusions
 Dozens of studies find a flypaper effect.
 The magnitude of the flypaper effect varies enormously;
the studies with the best methodologies find the largest
values (≈ 50).
 Flypaper effects arise both for school performance
measures explicit in the demand function and for other
measures implicit in the cost function.
 Flypaper effects may arise with matching grants (or
equivalent property tax exemptions) through the income
term in the Slutsky equation.
 The evidence clearly points to framing as the best
explanation for the flypaper effect, with an adjustment for
salience.
Conclusions