Full text of Economic Review (Federal Reserve Bank of Cleveland) : 1985 Quarter 2

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ECONOMIC REVIEW
FEDERAL RESERVE BANK
of CLEVELAND
QUARTER II

t 'V ,
-f. V-

IS

Economic Review
Federal Reserve Bank
of Cleveland
Quarter II 1985

Vector Autoregressive Forecasts
of Recession and Recovery:
Is Less More? ..............................................2
Vector autoregressive systems provide a simple
means of explaining or predicting the values
of a set of economic variables at any given
date. One merely looks at the values that the
variables took in the immediate past. It might
appear that the more historical data one uses,
the more accurate one’s forecasts would be.
However, research assistant Gordon Schlegel
shows that, at least for forecasts made at the
beginning either of a recession or of a recov­
ery, the exact opposite may be true; forecasts
can become less accurate as more explanatory
data are used.
Revenue Sharing and
Local Public Expenditure:
Old Questions, New Answers .............

13

The future of the general revenue sharing
program is uncertain, and it is appropriate to
examine how cutting off these funds would
affect local governments. Revenue sharing
seems to generate a disproportionate amount
of additional government spending compared to
the effect of local private income increases.
This pattern has come to be known as the fly­
paper effect. Paul Gary Wyckoff reviews the
economic literature on the impact of revenue
sharing on local government expenditures,
offers a critique of previous explanations of
this pattern, and presents a summary of a new
bureaucratic theory of flypaper effects.
Economic Review is published quarterly by the
Research Department of the Federal Reserve Bank
of Cleveland, P.O. Box 6387, Cleveland, OH 44101.
Telephone: 216/579-2000.
Editor: William G. Murmann. Assistant editor:
Meredith Holmes. Design: Jamie Feldman. Type­
setting: Lucy Balazek.
Opinions stated in Economic Review are those of
the authors and not necessarily those of the Fed­
eral Reserve Bank of Cleveland or of the Board of
Governors of the Federal Reserve System.
Material may be reprinted provided that the source
is credited. Please send copies of reprinted materi­
als to the editor.
ISSN 0013-0281

Gordon Schlegel is
a research assistant
at the Federal Re­
serve Bank o f Cleve­
land. The author
would like to thank
K.J. Kowalewski,
Owen Humpage,
Mark Sniderman,
James Hoehn, and
William Gavin fo r
their helpful com ­
ments and sugges­
tions.

1. One cannot,
however, perform
policy simulations
using vector auto­
regressive models.
Lucas (1976) pointed
out that under alter­
native policies, agents
will have different
views about the way
exogenous shocks
affect the system.
Therefore, one can­
not use the same set
o f parameters fo r
all alternative poli­
cies one may wish
to examine. This
implies that the co­
efficients obtained
through in-sample
estimation may not
accurately reflect
policy changes.

Vector Autoregressive
Forecasts of Recession
and Recovery:
Is Less More?

racy employed in the comparison. Section IV
looks at the estimation results for the speci­
fied models, while section V considers a more
recently developed VAR technique. Finally,
section VI sums up the overall results of the
study and mentions several cautions concern­
ing the interpretations of the results.

by Gordon Schlegel

I. VARs: Why and How?

Economic forecasts are valuable tools for
decision makers in many different areas.
When used with discretion, forecasts can
help guide the strategic plans of businesses
and corporations. A reasonably sharp picture
of the future is also important in the forma­
tion of sound fiscal and monetary policy.
Forecasts are particularly important when
the economy has just entered a recession­
ary or expansionary period. Policies that are
useful in expansionary periods must often
be adjusted before and during contractions,
and vice versa. To get an idea of the degree to
which policies must change, one needs to fore­
cast the extent of the expansion or contrac­
tion to come.
Many economists are turning to the use of
vector autoregressive (VAR) models for fore­
casting. A number of studies have indicated
that VARs forecast as well as, if not better
than, many large structural models; one such
study is that of Lupoletti and Webb (1984).
However, the forecast periods used in these
studies are not differentiated into expansion­
ary and recessionary periods. An economist
using VARs might want to ask the question;
“ What VAR specification will do the best job
in predicting the length and intensity of
recessions and recoveries?”
This paper provides a possible answer to
this important question. The first section dis­
cusses the reasons that VARs are gaining in
popularity among forecasters and describes the
methodology of VARs. Section II discusses the
pros and cons of VARs. Section III describes
the various model specifications compared in
the study and the measures of forecast accu­

In their never-ending search for the perfect
crystal ball, economic forecasters try to obtain
high forecast accuracy and, at the same time,
use as simple a technique as possible. This
is particularly true of business economists who
work under significant time and resource con­
straints which, in turn, limit the degree of
sophistication they can apply to their forecasts.
However, the forecasts must still be accu­
rate enough to give a fairly sharp picture of
the environment that firms and consumers
will be facing in the immediate future. A fore­
cast is, obviously, not useful if it does not
predict with an “ acceptable” degree of accu­
racy. However, even if the technique exists to
produce a perfect forecast, the method is worth­
less if it is too complex for a practitioner to
apply properly.
VAR techniques have been proposed as a
means through which one can have the best
of both worlds: simplicity and accuracy.1In
a VAR system with n lags, each variable being
forecast is regressed against its own values
in each of the n preceding periods, against the
values in each of the n previous periods of
all of the other variables being forecast, and
against a constant term. For example, a VAR
system with three variables, X, Y, and Z, and
with two lags would consist of the following
equations:
X = c\ + a\\X_\ + d2\X-2 +

+ b2\Y-2

+ c\\Z.\ + C2 \Z_2 + e\,
Y = C2 + CL12X -1 + 022^-2 + ^12^-1 + ^22^-2
+ CtfZ-i + C22Z-2 + #2>
Z = C3 + 013^-1 + #23^-2 + bizY-i +
+ C13Z-I + C23Z-2 + €3 ,

6 23 K 2

2. The in-sample
fits o f the various spe­
cifications are not
considered. We only
want to predict f u ­
ture values o f the
variables in the sys­
tem, not explain their
past values.

where
X .n = the value of X n periods before
the current period,
er = the error term of equation r, dis­
tributed as a normal random
variable with mean 0 and con­
stant variance, and
cr = the constant term of equation r.
The equations are estimated individually
to yield estimates for all parameters and con­
stant terms. One can then calculate the
reduced form of the system and predict the
values of all variables in the current time
period. These values can, in turn, be used as
regressors in predicting the next period’s
values for the variables. The process can be
continued indefinitely, enabling one to pro­
duce dynamic, out-of-sample forecasts as far
into the future as desired, given the infor­
mation available in the present period.
The regression equations are commonly
estimated in one of two ways. With ordinary
least squares, the parameters are completely
unconstrained and can assume whatever val­
ues best fit the data. Bayesian techniques
enable a forecaster to explicitly include, in the
model, subjective judgment or other objective
evidence concerning the values of the param­
eters, as well as the degree of confidence he
has in his judgment. A general discussion of
the techniques is given in Todd (1984), while
Litterman (1979) approaches the topic from a
more technical basis.
In this paper, we first search for the optimal
ordinary least squares (OLSQ) specification,
where the “ optimal” specification is the one
that provides the most accurate forecasts, the
measures of accuracy being described below.2
We then compare this specification to one
derived through a Bayesian procedure.

II. Advantages and Disadvantages
of VAR Models
VARs have a number of characteristics that
make them convenient for those who make
economic forecasts on a regular basis. Of

these characteristics, the following five seem
especially worthy of note:
1) It is relatively easy to write a computer
program to perform a VAR. A programmer
with a moderate amount of skill and a pack­
age of standard regression techniques should
be able to implement such a program without
much trouble.
2) The commands needed to perform an
OLSQ VAR can be implemented in virtually
any programming language. This would make
it unnecessary to buy a specialized package
to run VARs and would enable a forecaster to
avoid this type of expense. The Bayesian VAR
can be implemented with a little more effort,
provided that matrix capabilities are available.
3) Since VARs can be programmed fairly
easily, it might not be necessary to buy fore­
casting services from an outside data vendor.
Subscriptions to the major econometric fore­
casting services can cost from $16,000 to
$20,000 per year, no bargain if, as Lupoletti
and Webb (1984) suggest, the simpler VAR
models can perform as well as, or better than,
the large models.
4) Because VARs only use a relatively small
number of variables, it is easy to update and
revise the data series as needed.
5) In their pure form, VARs require no sub­
jective add factors. Large models contain a
number of arbitrary constants that a forecas­
ter might be unable to estimate sufficiently
well for his purposes, due to a lack of neces­
sary specialized information or expertise. The
VAR gets around this problem by avoiding it.
No forecasting technique, however, is with­
out its problems. VAR models have two major
disadvantages:
1) Since most aggregate economic time
series are highly correlated with their own
previous values and with present and past
values of other time series, multicollinearity
can become a serious problem as more and
more series and lagged values of series are
added to the model. As the system expands,
it can become very difficult to separate the
effects of the explanatory variables, and the

parameter estimates can become highly sensi­
tive to the combination of variables used in
the model.
Also, a high degree of multicollinearity will

Fig. 1

make it difficult to determine which explan­
atory variables are significant, since the
standard errors of the coefficient estimates
will tend to be large. A forecaster considering

Dynamic Out-of-Sample Root Mean Squared Error
Error

Error

Error

Error

Lags

Lags
Real GNP ( Y)

_______ Unemployment (U)

GNP deflator (P )

---------- AAA bond rate (r)

3. We choose the
growth rate o f real
G NP instead o f a
measure o f the level
o f this variable. This
implies that we are
interested in the pat­
tern o f G N P growth
over our forecast
horizon, not ju st the
proportion by which
output will have
grown seven or eight
quarters hence.
4. Implicit in this
methodology is the
assumption that
turning points are
recognized when they
occur. In practice,
there may be a time
lag o f several months
between the occur­
rence o f a turning
point and its recog­
nition by forecasters.

a certain lag structure might want to ask if
certain lagged variables can be dropped from
the system without sacrificing forecast accu­
racy. A detailed discussion is found in Intriligator (1978), among others.
As far as the forecasting aspects of multicollinearity are concerned, Christ (1966)
points out that if the joint distribution of the
regressors changes during a forecasting
period, multicollinearity between regressors
will affect the accuracy of the forecasts.
Given the increasing volatility of aggregate
measures of economic activity over the past
10 years, particularly interest rates, it would
appear that such changes have taken place.
Multicollinearity, therefore, seems to present
a problem for VAR forecasting.
2) As the number of variables of a VAR
model increases, the number of parameters to
be estimated goes up rapidly If a variable is
added to the model, each equation has n more

Table 1 Rankings of Root Mean Squared
Errors of Dynamic Out-of-Sample Forecasts
Forecast
period

Variables

Number of lags

l

2

3

4

5

6

7

8

1973:IVQ1975:IIIQ

P
Y
r
U

1
6
2
8

2
4
1
7

3
1
3
4

4
7
4
6

6
5
6
3

7
8
8
2

8
3
7
1

5
2
5
5

1975:IIQ1977:IQ

P
Y
r
U

1

2
2
4
2

5
7
1
4

4
4
3
3

6
3
5
5

3
6
6

7
5
7
7

8
8
8
8

2
3
1
2

3
5
2
6

8
1
6
3

5
4
5
5

4
6
3
4

6
7
7
7

1
8
8
8

8

7
3
3
4

6
2
2
1

8
5
4
2

5
4
5
3

2
7
8
6

4
6
7
5

3
8
6
7

47

49

55

72

75

86

94

98

1981:IIIQ1983:IIQ

1983:IQ1984:IIIQ

Total ranking

P
Y
r
U
P
Y
r
U

1
2
1

7
2
4
1
1

1
1

6

coefficients to be estimated, where n is the
number of lags for each variable.
If a lag period is added, each equation has
r more parameters, where r is the number of
variables in the system. As the number of
coefficients increases relative to the amount
of available data, random events of the past,
as well as systematic relationships, are
increasingly reflected in the coefficients. If
these coefficients are used in out-of-sample
prediction, a set of future random events that
differs from the shocks of the past would be
expected to result in less accurate forecasts.
This problem is discussed in Todd (1984).

III. Model Specification
The model contains four variables: the growth
rate of the GNP deflator (P ), the growth rate
of real GNP ( Y ), Moody’s AAA corporate bond
rate (r), and the civilian unemployment rate
(U)? All variables are expressed as percen­
tages—the growth rates being annualized.
We wanted to examine how well the various
model specifications estimate the scope of the
expansion or recession to come because, as
mentioned before, once an expansion or con­
traction begins, an economist needs an idea of
how long the new phase of the business cycle
will last.4
One-quarter- and eight-quarter-ahead, ex post,
dynamic, out-of-sample forecasts were pro­
duced from two cyclical peaks: the fourth quar­
ter of 1973 and the third quarter of 1981, and
from one cyclical trough: the second quarter of
1975. For the period beginning in the first
quarter of 1983, a cyclical trough, a sevenquarter-ahead forecast was made rather than
one for eight quarters ahead, since revised data
for the fourth quarter of 1984 were not avail­
able at the time this paper was written.
The first step in our estimation process
was to perform a multivariate time series anal­
ysis on the four variables for each in-sample
period. Using the techniques described in Box
and Jenkins (1976) and Tiao and Box (1981),

it was found that, in each period, an AR(1) or,
at most, an AR(2) specification provided an
adequate in-sample fit.5 Since these models
contain no moving average or lagged error

Fig. 2

One-Step-Ahead Errors (Absolute value)

Error

Error
20
1975:IIQ-1977:IQ

1973:IVQ-1975:IIIQ

Error

Error
5

1981 :IIIQ-1983:IIQ

1
—_

2
.

terms, they closely approximate a standard
VAR with one or two lags of each explanatory
variable.6 This makes our use of VAR tech­
niques to solve the model under consideration

3

4

Real GNP (K )

5
Lags

6

7

8

BVAR

_______ Unemployment ( U)

1

2

3

4

______ GNP deflator (P )

5
Lags

6

7

8

________AAA bond rate (r)

BVAR

however, be signifi­
cant moving average
terms in the A R IM A
specification which
provides the best
out-of-sample fit.
6. Box and Jenkins
(1976) show that,
fo r moderate or
large samples, the
ordinary least
squares estimates
o f the parameters
o f a VAR equation
differ only slightly
from those obtained
through the YuleWalker equations
used in A R IM A
type analyses.

justified by these more general time series
analysis procedures.
Each specification of the model consists of
four OLSQ regressions. In the equations, each
variable at period t is regressed against the
values of all four variables at times /-I through
t-n, as well as a constant. For this paper, the
lag length n ranged from one to eight. Despite
the multicollinearity problems and estimation
difficulties mentioned above, OLSQ estima­
tion has been used in such seminal VAR models
as that of Sims (1980). Our goal is to compare
the different lag specifications to see which
size of OLSQ VAR model provides the best outof-sample forecasts of recession and recovery.
Comparing Forecast Accuracy
There are many measures of forecasting
accuracy that one may use to compare differ­
ent models that propose to explain the same

Table 2 Rankings of Absolute Values
of One-Step-Ahead Forecast Errors
Forecast
period

1973:IVQ1975:IIIQ

1975.IIQ1977:IQ

Vari­
ables

2

3

4

5

6

7

8

P
Y

1

5

2

8

6

4

r

1

6
2

U

6

7

3
3
1

4
5
4

7
5
7
3

3

1

8
6
8

7
4
5

2
8
2

P
Y

5
1
1
1

3
3
3
4

7

8
2

6

4
7
5
7

2

1

5
7

8
8
8

3
4
5
1

r

U
1981:IIIQ1983:IIQ

P
Y
r

U
1983:IQ1984:IIIQ

P
Y
r

U
Total ranking

Number of lags

l

6
2

4

4

6

3

2

5

1
1
7

4
7

2

5

8

7

3
3

8
8

5

5
5
4

6
6

2

6
2
2
6

3

8

7

8
2

6

5

4
5

2

6

7
4
4
5

3

7

1
7

7

8
6
6

8

75

94

87

85

8

1
3
1
3

3

2

2

1

5
4

38

59

65

73

8

6

phenomena. For this study, the following
techniques were chosen:
1) To compare the one-step-ahead forecasts
for each lag specification, we simply com­
pare the absolute values of the one-step-ahead
forecast errors. Here, we assume that it is
just as undesirable to overestimate the actual
values of the variables being forecast as to
underestimate them, since either type of
error can cause problems. We only want to
know the degree to which the forecasts miss
the mark.
2) For the seven- or eight-quarter-ahead
forecasts, we look at the root mean squared
errors of the forecasts for each variable. This
seems to be an appropriate procedure, since
we are not directly comparing forecasts of
different variables.
Also, in business, as forecasts become more
inaccurate, the fallout from decisions based
on these forecasts increases even faster than
the inaccuracy of the forecasts. The more
inaccurate a forecast, the more sectors of a
business’ operation are affected by decisions
made on the basis of the incorrect prediction.
Thus, we seem justified in using a squared
error measure, as opposed to a measure based
on the simple difference between the actual
and predicted values. Again, this implies that
it is equally important to avoid overprediction
and underprediction.
3) It would also seem useful to know if the
longer-term forecasts consistently overesti­
mate or underestimate the actual values of
the variables we are interested in. If forecasts
constantly miss the mark in the same direc­
tion, the problems caused by the decisions
based on the forecasts will be compounded over
time, rather than being compensated for by
mistakes in the other direction. The measure
used here is the bias component of the Theil
U decomposition described in Theil (1961).
This bias component is calculated as:
Bias = (Y - Y )2/MSE,

where

Y = mean of the actual values
of Y, during the forecast
period, and

Y = mean of the forecast values
of Y,

Fig. 3

Theil U Biases

Bias

Bias

Bias

Bias

Lags

Lags
Real GNP ( Y)

_______ Unemployment ( U)

GNP deflator (P )

_______AAA bond rate (r)

and so on, the largest error or bias being as­
signed a rank of eight. If there is a tie, say, for
the third smallest error, the tied errors are
It must be noted that all of these measures
each given a rank of three, while the next larg­
of accuracy are subject to McNees’s (1975)
est error gets a five ranking. Since there are
comments concerning the use of ex post fore­
four forecast periods and four variables in­
casts to compare the predictive power of dif­
volved, we have 16 sets of rankings for each
ferent models. However, McNees’s critique
of the three accuracy measures.
does not apply to the VAR models examined
2) The 16 sets of rankings for each measure
here as much as it does to the large models he
are then added for each of the eight lag lengths.
studies. With VARs, we have no exogenous
We thus obtain the totals of all the ranks for
variables and no subjective adjustments—
each lag length, one through eight. The lag
two factors that McNees feels present a
length with the smallest total ranking is con­
strong case for the use of ex ante forecasts
sidered the one that forecasts the best, the
when judging the comparative performance
length with the second smallest total ranking
of econometric models. For our purposes, the
is considered the one that forecasts second
ex post forecasts would seem to be appropriate.
best, and so on.
To evaluate the rankings of the forecasts,
Several assumptions are implicit in this
we used the following techniques:
type of ranking scheme. We assume that all
1) For each variable in each forecast period,
variables and all time periods are equally
the smallest error or bias is given a rank of
important. We also assume that the quantita­
one. The next smallest is given a rank of two
tive differences in error measures between
forecasts are not important; we only want to
know which forecast does better. It must be
noted that even if two forecasts have different
Table 3 Rankin gs o f Theil U Bias Statistics
quantitative error measures, the difference
Number of lags
Forecast
Vari­
between the measures may not be statistically
period
7
8
ables
l
2
4
6
3
5
significant. Ashley, Granger, and Schmalen1973:IVQ4
1
P
2
5
6
7
8
3
see (1980) suggest a technique through which
Y
1
2
8
7
4
5
6
1975:IIIQ
3
one can test the squared errors of forecasts
r
4
7
2
8
1
6
5
3
from various models for such significance. How­
2
6
U
8
7
5
4
3
1
ever, our methodology generates only four
P
2
4
5
1
7
6
8
3
1975:IIQforecasts of a given number of steps ahead
1977:IQ
Y
2
7
4
1
3
8
6
5
for each variable in each model specification.
2
r
4
8
5
6
7
3
1
Therefore, we do not have enough forecasts to
4
7
U
6
1
2
3
5
8
utilize their method for comparing predic­
1981:IIIQP
7
4
2
1
5
6
8
3
tion errors. No test is currently available to
1983:IIQ
4
6
8
Y
1
3
7
2
5
examine the Theil U biases of different models
6
r
4
1
2
7
3
5
8
for statistical significance.
MSE = mean squared error of
the forecast.

1983:IQ1984:IIIQ

Total ranking

U

3

5

6

8

4

1

7

2

P
Y
r
U

2

7

8
2
3
8

6
3
2
6

7
7
6
2

5
6
5
5

4
5
4
4

3
8
7
1

4
8
3

66

70

72

88

84

63

68

65

1
1

1

IV. Estimation Results
As the lag length increased, the in-sample
fits improved. This follows directly from the
theory of least squares regression, which states

7. This technique is
being used by the
Federal Reserve
Bank o f M inneapo­
lis to model and
forecast economic
conditions in the
Ninth Federal Re­
serve District. The
forecasts are pre­
sented in District
Econom ic Condi­
tions, available free
o f charge from the
Research Depart­
ment o f the Federal
Reserve Bank o f
Minneapolis, M in ­
neapolis, M N 55480.
8. The Minnesota
prior constrains the
variance o f the coeffi­
cient o f any n-period
lagged variable to be
l/n times the vari­
ance o f the coefficient
o f that variable when
lagged once.
9. This is done by
multiplying each rel­
ative prior variance
o f a cross variable
by sa/sc, where s0 is
the standard error o f
the regression in
which the own vari­
able is the endoge­
nous variable, and
sc is the standard
error o f the equation
in which the cross
variable is the endog­
enous variable.

that as more explanatory variables are added
to a model, the in-sample fit should improve
or stay the same. However, the graphs and the
tables of rankings show that, by the method­
ology described above, the out-of-sample fore­
casts worsened as the lag lengths increased. In
the case of the seven- or eight-quarter-ahead
forecasts, forecast accuracy decreased over
the entire range of lag lengths, with one lag
giving the best forecasts and eight lags the
worst. These results are shown in table 1 and
figure 1. In table 2 and figure 2 we see that,
in the case of the one-step-ahead forecast errors,
the one-period lag gave, by far, the most accu­
rate predictions. The forecasts got uniformly
worse, as longer lags were used, until the
seven-period lags, when there was a slight
improvement. For the Theil U biases, shown
in table 3 and figure 3, the rankings deterio­
rated uniformly from one lag period to four,
improved slightly with five-period lags, then
returned to a level very close to that of the oneperiod lag for lag lengths six through eight.
In sum, these results seem to indicate that,
in a vector autoregressive system estimated
with OLSQ, the best forecasts of recessions
and recoveries are obtained by assuming that
the value of each variable depends only on
the values, in the immediately preceding
period, of itself and all other variables in the
model. A one-lag model, in essence, restricts
the coefficients for all longer lags to zero.
It is possible, however, that a forecaster
may have prior information—information not
reflected in the data—which indicates that
some of the coefficients for variables lagged two
or more periods can be nonzero. To explicitly
accommodate these “ priors” in a statistical
model in the hope of obtaining better forecasts,
we can use Bayesian vector autoregression.

V. The Bayesian VAR Method
By using the Bayesian vector autoregression
(BVAR) techinque, one can include, in the
model, subjective estimates of the model’s
parameters and measures of the forecaster’s
confidence in his estimates.7

Very briefly, the BVAR technique involves
the following steps:
1) Choose the lag structure and variables of
the model. Here, we use the same variables
as before (P, Y, r, and U) and regress each on
the past three values of all four variables
and a constant term.
2) Make an estimate of the coefficient val­
ues and your confidence in the estimates.
Here, we have applied what Todd (1984) calls
the Minnesota prior. The Minnesota prior
assumes that all variables in each equation
of the model behave according to a random
walk; that is, all coefficients are zero except
for the coefficient of the most recent value of
the endogenous variable, which is one.
In other words, it is expected that the value
of a variable at any given time equals the value
of that variable in the preceding period. The
Minnesota prior also assumes that one has
more confidence in his estimates of the coef­
ficients as the lag lengths get longer; the longer
the lag, the more certain the forecaster is that
a lagged variable has no effect on the system.8
3) Divide the variables of each equation into
own and cross variables, where the endoge­
nous variable of any given equation is the own
variable for that equation, and all other vari­
ables in the equation are cross variables. Once
this is done, scale the prior variances of the
cross variables to units equivalent to those of
the own variable.9
4) Multiply all own and cross-variances by
hyperparameters H0 and Hc, respectively,
to convert the weights determined in steps
two and three to estimates of the absolute
prior variances. For this estimation, we set
H0 at 0.1 and Hc at 0.05 for all cross variables.
5) Perform a mixed estimation simula­
tion using the method described, for exam­
ple, in Theil (1970). A further discussion of
points two, three, and four may be found in
Todd (1984).
When we compare the results from the
Bayesian VAR with those of the OLSQ esti­
mations, we find that the BVAR performs at a
level comparable to that of the non-Bayesian
VAR with one lag. The ordinals of the root
mean squared errors for the longer term fore­

10. The ordinal
scores in table 5
fo r the OLSQ VARs
are not strictly com­
parable to those pre­
sented in tables 1
to 3. In table 5,
we are comparing
nine specifications:
eight OLSQ and one
Bayesian. The Bayes­
ian model is not
ranked in tables 1
to 3.

casts show that the BVAR performs slightly
better that the one period VAR estimated
with OLSQ. For the one-step-ahead forecast
errors, the BVAR performs better than all
other specifications except for the one-period
non-Bayesian VAR, which does a shade better.
Finally, the Theil U bias statistics show that
the BVAR forecast consistently over- or under­
estimates the realized values by about the
same degree as the one-, six-, seven-, or eight-

Table 4 Rankings of Bayesian VAR Model
by Variable and Forecast Period
Forecast
period

Variables

1973:IVQ1975:IIIQ

7 - ,8 quarterahead
RMSE

P
Y
r
U

1975:IIQ1977:IQ

P
Y
r
U

1981:IIIQ1983:IIQ

Theil
U bias

1
3

2

2

2

7

2

2

8

8

2

8

5

9

2

2

7
4

1
3

1

2

2

6

2

5

1
9
4

2

2

2
2

5
1

2

2

2

6

2

8

49

46

76

P
Y
r
U

1983:IQ1984:IIIQ

1 -stepahead fore­
cast error

3
3
2

3

P
Y
r
U

3

Total ranking

2

7

Table 5 Total Rankings of Bayesian
and Ordinary Least Squares Models
Error
measure

OLSQ (number of lags)
l

2

3

4

5

6

7

1-stepahead

44

71

79

87

89

95

101

98

46

RMSE

55

57

68

84

89

99

108

111

49

Theil
U bias

75

79

81

98

93

70

76

72

76

8

BVAl

period, lagged non-Bayesian VAR. The break­
down of the rankings for the BVAR is shown
in table 4, while table 5 compares the BVAR
performance to that of the OLSQ autoregres­
sions.10 Figures 1 through 3 chart the BVAR
performance against that of OLSQ.

VI. Conclusions and Caveats
The results indicate that, at least when the
economy moves from an expansionary period
to one of contraction, or vice versa, the fore­
casting ability of a VAR system deteriorates as
longer lags are incorporated into the model. It
also seems that a Bayesian estimation proce­
dure does not produce forecasts that are sub­
stantially better than those of the non-Bayes­
ian VAR with one lag per variable. Since the
Bayesian method is more difficult to imple­
ment than the standard OLSQ technique, a
forecaster using VAR techniques under these
circumstances would probably want to stick
with OLSQ.
Three important considerations must be
noted, however, concerning these results.
First, it may be that the comparative forecast­
ing abilities of VARs with different lag spec­
ifications would change if the forecasts were
made at points other than those considered
here. For example, the one-lag model might
not be superior to the others if the forecasts
were being made in the middle of a cyclical
expansion. Such an investigation might prove
to be a useful topic for future work. If the
one-lag specification is still the best method
at any point of the business cycle, there is no
need to use longer lags at any time. If this is
not so, then we need a measure of when to
change between different VAR specifications
in forecasting.
The second issue is that a forecaster usu­
ally doesn’t know when a recession or recov­
ery has begun until several periods after the
fact. Would the one-lag method still be best
if applied when a forecaster became aware
that the economy had taken a turn, rather
than at the turn itself?

Finally, there is no guarantee that the
Minnesota prior provides the best Bayesian
VAR forecasts at the times we consider. The
data may, in fact, be strongly rejecting the
imposition of a random walk, producing biased
coefficient estimates. A different set of esti­
mates for the values of the coefficients and
variances might yield even better predictions.
It must also be noted that, for many econ­
omists, it is more important to predict when
the economy will turn than to forecast the
magnitude of the turn. How well can VARs
forecast the timing of the beginning and end
of a recession compared to other small models
and large econometric systems? Also, what
VAR lag specification calls the timing of the
turns most accurately? These questions must
be addressed to better evaluate the usefulness
of VAR forecasting methods.
As we have seen, VARs, while freeing one
from the assumptions underlying a structural
economic model, present problems of their own.
However, since even the prototype BVARs,
for instance, outperformed many commercial
forecasters (see, for instance, Doan, Litterman, and Sims [1984]), further research on
the models should prove very fruitful in clear­
ing up our crystal balls.

References
Ashley, R., C.W.J. Granger, and R. Schmalensee. “Advertising and Aggregate Consump­
tion: An Analysis of Causality,” Econometrica, vol. 48, no. 5, pp. 1149-67.
Box, George E.P., and Gwilym M. Jenkins.
Time Series Analysis: Forecasting and Con­
trol. Revised Edition, San Francisco, CA:
Holden-Day Inc., 1976.
Christ, Carl F Econometric Models and
Methods. New York, NY: John Wiley and
Sons, Inc., 1966.

Doan, Thomas, Robert Litterman, and Chris­
topher Sims. “ Forecasting and Conditional
Projection Using Realistic Prior Distribu­
tions,” Econometric Reviews, vol. 3, no. 1,
pp. 1-100.
Intriligator, Michael D. Econometric Models,
Techniques, and Applications. Englewood
Cliffs, NJ: Prentice-Hall Inc., 1978.
Litterman, Robert B. “ Techniques of Forecast­
ing Using Vector Autoregressions,” Work­
ing Paper 115, Federal Reserve Bank of
Minneapolis, Revised November 1979.
Lucas, Robert E. “ Econometric Policy Evalu­
ation: A Critique,” in K. Brunner and
A. Meltzer, eds., The Phillips Curve and
Labor Markets, Vol. 1, Carnegie-Rochester
Conference Series on Public Policy. Amster­
dam: North-Holland, 1976, pp. 19-46.
Lupoletti, William M., and Roy H. Webb.
“ Defining and Improving the Accuracy of
Economic Forecasts: Contributions From a
VAR Model,” Working Paper 84-6, Federal
Reserve Bank of Richmond, October 1984.
McNees, Stephen K. “An Evaluation of Eco­
nomic Forecasts,” New England Economic
Review, Federal Reserve Bank of Boston,
November/December 1975, pp. 3-39.
Sims, Christopher A. “ Macroeconomics and
Reality,” Econometrica, vol. 48, no. 1 (Janu­
ary 1980), pp. 1-48.
Theil, Henri. Economic Forecasts and Policy,
2nd Revised Edition, Amsterdam: NewHolland Publishing Co., 1961.
______ Principles of Econometrics, New York:
John Wiley and Sons, Inc. 1970.
Tiao, G.C., and G.E.P. Box. “ Modeling Mul­
tiple Time Series with Applications,” fournal of the American Statistical Association,
vol. 76, no. 376 (December 1981), pp. 802-16.
Todd, Richard M. “ Improving Economic Fore­
casting With Bayesian Vector Autoregres­
sions,” Quarterly Review, Federal Reserve
Bank of Minneapolis, Fall 1984, pp. 18-29.

Paul Gary Wyckoff
is an economist at
the Federal Reserve
Bank o f Cleveland.
The author would
like to thank John
Beck and Ronald
Fisher fo r helpful
comments on an
earlier draft.

Revenue Sharing
and Local Public
Expenditure:
Old Questions,
New Answers
by Paul Gary Wyckoff

During his first four years in office, Presi­
dent Reagan has been an active reformer of
the structure of American federalism. In the
Omnibus Budget Reconciliation Act of 1981, the
President achieved a sweeping reform of the
nation’s system of categorical grants to state
and local governments, consolidating many of
these programs into block grants and reduc­
ing overall funding levels.
A second major Reagan initiative, a “ swap”
in which the federal government was to take
complete responsibility for Medicaid (which
provides medical care for the poor) in exchange
for the states’ pledge to take over Aid to Fam­
ilies with Dependent Children (AFDC) and food
stamps, failed to win the approval of state
and local leaders and has been shelved.
Now the Reagan administration proposes to
further trim federal assistance to state and
local governments by deleting the general
revenue sharing program from its latest bud­
get. Even if supporters manage to continue
funding for one more year, the program’s future
is highly uncertain, since its authorizing leg­
islation expires on September 30,1986.
The evaluation of such a sweeping reform
calls for detailed knowledge of the workings of
the recipient governments. To answer the
questions of the efficiency, equity, and politi­
cal acceptability of this proposal, a model of
local expenditure decision-making is required.
Fortunately, there is a rich literature in eco­
nomics on the effect of lump-sum, generalpurpose aid on local spending; the question has
become a focal point for the theoretical anal­
ysis of local public choice, shaping investiga­
tors’ viewpoints on larger questions about the
nature and efficiency of the local public sector.
The empirical results in this field, how­
ever, pose a serious challenge to the generally
accepted models of 10 to 20 years ago, and have
broken down rather than built consensus
among economists. Thus, existing literature
offers no unified framework from which to
judge the Reagan proposal.

1. Here, I am
abstracting from
any considerations
as to the relative
permanence o f these
different kinds o f
income. I f a wage
gain is considered
a permanent increase
in income, while a
capital gain is con­
sidered transitory,
this will affect the
consum er’s savingsconsumption decision
and perhaps may
affect the type o f dur­
able goods purchases
that he will make.

In this paper, I provide some theoretical
background to the current public policy dis­
cussion on revenue sharing. In section I, the
nature of the economists’ previous consensus
is explored, along with the empirical irregu­
larities that broke down that consensus and
invited new approaches to local public choice.
Section II reviews the various ways in which
economists have tried to amend or replace their
previous notions in light of these empirical
results. Section III offers a critique of these
efforts. A new model to explain these empiri­
cal facts is summarized in section IV, along
with a description of an empirical test of this
model. The concluding section contains a few
preliminary comments on the public policy
ramifications of this new model.

I. Flypaper Effects
Two approaches have dominated the literature
on modeling local public expenditure deci­
sions. The first approach, exemplified in the
work of Henderson (1968), Inman (1971), Ehrenberg(1973), Gramlich and Galper (1973), and
Deacon (1978), applies standard consumer
theory to this sector. Without specifying either
the actors in the local decision-making pro­
cess or their preferences, local governments
are assumed to behave as if they are maxi­
mizing a well-behaved utility function over
public and private goods, subject to a budget
constraint that the total income of the com­
munity (intergovernmental grants as well as
private income) must not exceed the total
amount spent on private spending and local
public goods.
Although it is seldom made clear in these
studies, this approach implicitly assumes that
the city’s budget is under the control of some
individual or party within the city, since a
well-behaved utility function for the commu­
nity will not exist unless this is the case
(Arrow 1950). Subject to certain legal limits
on the type of taxes collected, this controlling
party determines the type and quantity of local
public goods produced and the total amounts

spent in the public and private sectors of
the economy.
Remarkably, even this very unrestrictive
approach, in which the identity of the control­
ling party is left unspecified, carries implica­
tions for local expenditure behavior that are
inconsistent with the empirical work in this
field. Since the controlling party can tax local
private income at will, this model acts as if all
intergovernmental aid, as well as all private
income, were under the control of this anon­
ymous decisionmaker. Just as the choice for a
consumer between new furniture or a new
car is independent of the composition of income
between wages, capital gains, dividends, and
interest, so the controlling party’s division of
resources between private consumption and
public goods should be independent of whether
the community’s money comes from private
income or from intergovernmental aid.1 If all
that concerns the city is to maximize some
utility function over private consumption
and public services, the source of the money
used to pay for the city’s budget is irrelevant.
Therefore, the expenditure effect of a onedollar increase in revenue sharing ought to
be the same as that resulting from a one-dollar
increase in aggregate private income in the
community.
In his review of the early econometric work
on this question, Gramlich (1977) noted that
this equivalence was consistently rejected by
the data. “ Whether half or all the revenuesharing money goes into higher expenditures,
however, at this point all empirical studies
indicate long-run responses appreciably greater
than would be implied by the response of expen­
ditures to changes in income . . (Gramlich
[1977], p. 230). This pattern of behavior has
come to be known as the flypaper effect: money
originally from the public sector (intergov­
ernmental grants) sticks in the public sector
and is spent on public goods, while money
originally from the private sector (local taxes
on private income) sticks in that sector and
is spent on private consumption.
The second major approach to modeling
local public expenditure decisions retains the

framework of consumer theory but also spec­
ifies the identity and preferences of the con­
trolling party. Early writers in the theory of
voting (see Hotelling [1929], Bowen [1943], and
Black [1948]), showed that whenever binary
choice is involved (two political parties, two
candidates, or two sides of an issue), a position
at the median of the community’s preferred
spending levels will generate the greatest elec­
toral support. This result ensures that com­
petitive political processes will always produce
median outcomes. Drawing on this theoretical
foundation, numerous empirical studies have
utilized the assumption that local governments
behave as if they were maximizing the utility
of the median voter in each community (see
Bergstrom and Goodman [1973], Borcherding
and Deacon [1972], Ladd [1975], Lovell [1977],
Perkins [1977], Inman [1978], and Pack and
Pack [1978]). Under further assumptions
about the demand function for local public
goods and the distribution of income and wealth
in the community, the income and the tax

Fig. 1

Aid in the Median Voter Model

Equivalence of a Lump-Sum Grant of Amount A
to an Income Increase of Amount TA

price facing the median voter can be calculated,
and the response of individuals to changes in
their public and private good budget constraint
can be estimated.
Even before this approach was well devel­
oped, however, Bradford and Oates (1971)
showed that it did not explain flypaper effects.
They made their argument with the help of
a simple graph, reproduced here as figure 1.
The median voter’s budget constraint between
private goods and public expenditures is dis­
played, with a slope equal to the negative of
the median voter’s tax share (here labeled T).
A lump-sum, general-purpose grant of amount A
(which I will refer to later as simply a lump­
sum grant) shifts out the budget constraint in
parallel fashion. Since the budget constraint
is a straight line, an income increase of amount
TA ought to generate the same final budget
constraint as under the aid increase, and hence
the same equilibrium amounts of private goods
and public expenditures. Thus, under the
median voter model, an income increase of
amount TA is equivalent to an aid increase
of amount A.
Another way to think about this result is
to note that the median voter controls a share
of the lump-sum aid equal to TA. Since the
median voter is the dominant actor in local
politics, he or she can move this bundle of
resources in and out of the public sector as
desired. If, for example, the median voter
decides to use none of the lump-sum aid for
public expenditures, the money would be used
to lower taxes and the median voter would
receive a rebate in the amount TA. Under the
median voter model then, the voter’s “ public
income” (TA) can simply be added to his or
her private income (Y) to derive the total
income (Z):
Z = Y + TA.

Public
expenditures

It follows that under the median voter model
an increase in the median voter’s share of
lump-sum aid ( TA) ought to have the same
expenditure effect as an increase in his or her
private income (F).

Table 1 (reproduced with permission from
Fisher [1982]) shows the results of a recent
survey of tests of the flypaper effect in both
the median voter model and in the older

Table 1

expenditure-as-utility-maximization litera­
ture. For each study, the first column shows
the expenditure effect that would be predicted
for lump-sum aid if flypaper effects were

Estimates of the Flypaper Effect

Study

Predicted by theory

Estimated

Error8

Total local government
expenditures
Gramlich-Galper (1973)

0.03 < dE/dA < 0.05
0.06 < dE/dA < 0.10

dE/dA = 0.25
dE/dA = 0.43

$0.20 - $0.22
0.33 - 0.37

Inman (1971)b

0.02 < dE/dA < 0.04

dE/dA = 1.00

0.96 - 0.98

eE,A = 0.22

0.14 - 0.22

Ehrenberg (1973)b

0

Study

< eE,A < 0.08
Predicted by theory

Estimated

Error8

Education

o

< € e,a < 0.05
< eEiA < 0.05

£ e ,a = 0.21
^ e ,a = 0.06

0.16 - 0.21
0.01 - 0.06

Inman (1971)b

o

< eE,A

0.06

€ e ,a = 0.71

0.65 - 0.71

Ladd (1975)

o

< eE,A < 0.05

eE,A = 0.03

—

Inman (1978)

o

< eEjA < 0.06
and
< CE A < 0.08

€ e ,a = 0.23

0.15 - 0.34

Feldstein (1975)b

0

0

s

Olsen (1972)b

0.02 < dE/dA < 0.04

Weicher (1972)b

0

Gramlich-Galper (1973)

0.01 < dE/dA < 0.02

Johnson (1979)b

< dE/dA < 0.001

0.004 < dE/dA < 0.006

and
^ e .a = 0.40
dE/dA = 0.27

$0.23 - $0.25

0.41 < dE/dA < 0.58

$0.41 - 0.58

dE/dA = 0.10

$0.08 - 0.09

0.38 < dE/dA < 1.61

$0.37 - 1.60

a. Reported in cents per dollar of grant for studies measuring marginal effects and in points for studies measuring elasticities.
b. These works do not appear in this article’s reference list. They can be found in Inman (1979) and Fisher (1982).
SOURCE: Used with permission from Fisher (1982). For references, see Inman (1979) and Fisher (1982).

absent, based on that study’s estimate of the
expenditure effects of income. The second
column displays the actual effect of aid on
expenditures, while the last column shows
the discrepancy between the actual and pre­
dicted effects.
In the case of studies reporting marginal
effects, the expenditure effect of lump-sum aid
ranged from $0.20 to $1.60 larger than pre­
dicted by the theory. For those studies report­
ing elasticities, the expenditure effects were
from zero to 71 percent larger than expected.
As table 1 makes clear, although these effects
are not ubiquitous (see, for example, Gram­
lich [1982]), the vast majority of studies sup­
port the idea that flypaper effects are signif­
icant and in need of explanation. Moreover,
flypaper effects results occurred across a wide
variety of data sets and empirical methodolo­
gies, as discussed below.

II. Previous Explanations
of the Flypaper Effect
In examining the theoretical literature on
flypaper effects, I begin with six conservative
approaches. These six explanations, while
modifying the theory briefly outlined above,
retain the assumption that local expenditure
decisions can be modeled as the choice of a
single, rational decisionmaker such as the
median voter. These studies blame flypaper
effects on misinformation, arguing 1) that pre­
vious investigators have missed salient fea­
tures of the problem in modeling the response
of communities to grants-in-aid, or 2) that
the median voter himself is mistaken about
the effects of grants on his budget constraint.
Chernick (1979) and Fisher (1979) assert
that previous analysts have classified much
government aid as lump-sum although it
does not properly belong in that category.
Chernick notes that, if lump-sum aid is con­

strued to include project grants, this money
may represent the outcome of utility-maxi­
mizing decisions by the bureaucratic agency
that administers the program. This creates
two problems in estimating the effect of
aid on expenditures.
First, the process of awarding grants appears
to be influenced by the number and dollar
amount of previous grant applications, so
that actions of the community influence the
amount of grants it receives. If these grant
applications are correlated with community
expenditures, a simultaneous equations bias
exists in which expenditures affect aid and
aid affects expenditures.
Second, in a more fundamental argument,
Chernick says that grant determination is
a complex process that involves the bureau­
crat’s utility benefit from additional expen­
ditures in that community and the commu­
nity’s willingness to share in the costs of the
new project. Therefore, both grant amounts
and local expenditures are endogenous vari­
ables in the model; they are not related by any
consistent function that can be compared to
the effect of income on expenditure. Depending
upon the level and rates of change of the truly
exogenous variables in the model, any com­
bination of grant and local expenditure levels
can occur.
Fisher argues that, when lump-sum aid in­
cludes revenue sharing, the frequent inclusion
of tax-effort factors into the distribution for­
mula for this money creates what amounts to
a price effect as well as an income effect on
local government spending. A community’s
tax effort is usually defined as the compound
fraction formed by taking the ratio of the
community’s tax revenue, divided by its tax
base, to the tax revenue of the entire nation or
state, divided by the tax base of this larger
political unit.
When such a factor is included in a revenuesharing formula, it creates an incentive for
local governments to raise taxes and expendi­
tures in order to raise their tax effort and re­

ceive more aid from higher levels of govern­
ment. In other words, the price of another unit
of expenditure by the community is reduced
by the effect of this spending on its tax effort
and revenue-sharing collections. Because of
this price effect, Fisher argues, we ought not
to expect revenue sharing to have the same
effect as an equivalent amount of private
income.
In a related but more complex argument,
Moffitt (1984) examines the role of closed-end
matching grants on the budget constraint of
the median voter. In many cases, these grants
have been considered lump-sum aid on the
grounds that, once the program’s upper limit
has been achieved, the cost of each additional
unit of the good is unaffected by the grant.
This effect is shown in figure 2, which
depicts the median voter’s budget constraint
with and without the program. When the
community’s expenditures are supplemented
by the program, the slope of the voter’s bud­
get constraint is -T (l-m ), where m is the fed­
eral government’s matching rate, up to some

Fig. 2 The Case of Closed-End
Matching Grants

expenditures

limit E*. Above that level of expenditures,
the grant amount remains unchanged, and
the slope reverts to -T (as in figure 1). For any
community locating between B and C, the
budget constraint is shifted by the program,
but its slope remains the same.
Moffitt argues that when the budget con­
straint becomes nonlinear, estimation becomes
much more complicated and previous tech­
niques yield biased results. For example, sup­
pose that the functional form used in esti­
mation implies a preference function that
includes indifference curve Iq, but that com­
munities have diverse preferences so that
median voters in some cities have indifference
curve I\. Then the variation in preferences will
be picked up by the error term. Notice, how­
ever, that the change in preferences implies a
change in the equilibrium price faced by the
voter so that the error term and the price
variable are correlated. This contemporane­
ous correlation will lead to bias in the esti­
mated coefficients. Moffitt also presents sug­
gestive evidence (using a more sophisticated
estimating technique, but employing an ad hoc
demand equation to test for flypaper effects)
that, in the case of AFDC grants, flypaper
effects disappear when these nonlinearities
are accounted for.
Hamilton (1983) believes that previous ana­
lysts were fooled because they failed to realize
that, in many cases, private income represents
both a pool of resources for consumption and
a surrogate for certain unobserved factors
in the production of local public goods. His case
is strongest with respect to local education:
not only does increased income in a community
make possible increased spending on schools,
but educational studies show that children
from families with higher income and educa­
tional levels tend to learn more rapidly than
other children. Thus, as income increases,
expenditure increases may be held down by
the fact that children from higher-income
homes require fewer educational resources to
achieve a given level of educational achieve­
ment. This effect will again cause lump-sum

2. It should be
noted that Oates’
model includes a
budget-maximizing
bureaucrat, and in
that sense his model
replaces rather than
reforms the stan­
dard median voter
model. However, the
bureaucrat in this
model derives his
power solely from the
voter’s mispercep­
tion o f the marginal
cost o f local public
goods. For that rea­
son, I have included
it in this section.

aid to have a greater expenditure effect than
income increases.
Courant, Gramlich, and Rubinfeld (1979)
and Oates (1979) argue that it is the voter, and
not the analyst, who is being fooled by the
effect of intergovernmental grants.2 Specific­
ally, since the typical voter has little informa­
tion about the extent of grants to his com­
munity, the voter estimates the unknown mar­
ginal cost of public goods using other known
variables. By taking the ratio of his tax pay­
ments to total expenditures in the community,
the voter can determine the average cost of
public goods and use this as an approximation
for their marginal cost. When lump-sum aid
is present, however, the use of this proxy will
cause the voter to err in his estimate of mar­
ginal cost. If the lump-sum aid is used to
finance additional expenditures, total expen­
diture will increase while the median voter’s
tax payments will remain unchanged, thus
driving down the average price of public goods
and leading the voter to mistakenly demand
more public goods. Because of this “ fiscal illu­

sion,” these writers argue, lump-sum aid has
a price as well as an income effect and we
should not expect the aid to have an expen­
diture impact that is equivalent to the effect
of an income increase.
In contrast to these six arguments, Romer
and Rosenthal (1980) and Filimon, Romer, and
Rosenthal (1982) insist that a more radical
revision of the model is needed to explain fly­
paper effects. In these papers, the authors
remove the median voter from his preeminent
position in local decision-making and replace
him with a bilateral monopoly model in which
both the voter and a budget-maximizing
bureaucracy are important actors. Flypaper
effects occur, they say, because of the influ­
ence of this bureaucracy. This influence springs
from the agencies’ superior knowledge as com­
pared to that of the median voter and/or the
bureaucrats’ ability to control the agenda
of the decision-making process.
The “ asymmetric information” model pre­
sented in Filimon, Romer, and Rosenthal is
straightforward: the median voter is simply

A Primer on Aid Types
Intergovernmental aid can be classified according to
two criteria. The first involves restrictions placed on
the recipient government about how the money is to be
used. The second way of classifying aid is by determin­
ing how closely the amount of aid is tied to the recipi­
ent’s expenditures. Grants are usually identified ac­
cording to their positions along these two dimensions.
At one end of the spectrum of restrictions placed on
recipient governments are categorical grants, which can
be used only for a single, well-defined purpose. Federal
grants for highways are of this type. Many categorical
grants are of the project grants type, in which money is
awarded for a specific undertaking (usually a capital
project) at the discretion of the federal agency admin­
istering the program. Urban development action grants
fit under this category. Somewhat less restrictive are
block grants, which allow state and local governments
to use aid for a broad class of activities. Examples in­
clude the federal government’s community develop­
ment block grant, social service block grant, and ele­
mentary and secondary education block grant. At the
other end of this spectrum lies general purpose aid,
which can be used for whatever the recipient govern­

ment wants, including lowering taxes. Revenue shar­
ing is an example of general purpose aid.
Along the second dimension, matching aid requires
that the recipient government spend its own money as
well as funds from grants on the aided goods. Typi­
cally, as in the aid to families with dependent children
(AFDC) program, this takes the form of a cost-sharing
arrangement; the federal government pays a percen­
tage of program costs. Matching aid can be closed- or
open-ended, depending upon whether the grantor gov­
ernment sets a ceiling upon the amount each recipient
can receive (closed-ended), or if aid is available at the
matching rate for whatever level of expenditures the
recipient chooses (open-ended). At the opposite end of
this dimension of grants is lump-sum aid, which is
entirely independent of the expenditures of the recipi­
ent government. Revenue sharing is typically catego­
rized as lump-sum aid, although strictly speaking it
has some features of a matching grant if tax effort con­
siderations are used in distributing these funds (see
text). In this paper, the term lump-sum aid has also
been used as shorthand for the more cumbersome term

lump-sum, general purpose aid.

unaware of the presence of lump-sum grants in
his community (even its impact on the aver­
age price of public goods) and the well-informed
bureaucrat simply uses all the lump-sum aid
for additional expenditures.
The “ agenda control” model presented in
both Romer and Rosenthal and in Filimon,
Romer, and Rosenthal is more complex and
more specialized. This model deals only with
the case in which voters approve or disapprove
local expenditures through a referendum, a
situation which is not uncommon in local
education. If the school board’s request is not
approved (and subsequent proposals are also
turned down by the voters) the school district’s
expenditure will be set to a “ reversion” level
of spending, which is usually mandated by
the state. The bureaucrat’s power in this sit­
uation springs from his ability to determine
what proposal, if any, is brought before the
voters, who must choose between the board’s
request and the reversion level. For high rever­
sion levels, the bureaucrat will bring forth no
budget at all and will allow the state’s rever­
sion level to take effect. For very low (and
hence unattractive to voters) reversion levels,
the bureaucrat will propose the largest bud­
get which will give the voter the same utility
as the reversion level.
The comparative statics of this model are
quite complex and depend critically upon the
relationship of the reversion level of spending to
the median voter’s preferred level of spending.
Under certain circumstances, however, the
model will generate flypaper effects. Suppose
for example that the reversion level is very
large so that the bureaucrat simply accepts the
reversion level. Then increases in income will
have no effect on expenditures since it is the
exogenous reversion level, not voter prefer­
ences, that determines spending. On the other
hand, since most states require that aid be
included in the reversion level, an increase
in lump-sum aid increases spending by the full
amount of the grant.

Thus, in this stylized example, a flypaper
effect equal to the amount of the grant will
occur (based upon the expenditure effect
of income, the grant should have no effect on
expenditure, but expenditure increases equal
to the grant are observed). In other situations,
in which the reversion is less than, or in the
neighborhood of, the median voter’s preferred
level, flypaper and even anti-flypaper effects
(income generating larger expenditure effects
than grants) can occur, depending upon the
nature of the voter’s preference map.

III. A Critique of Previous
Explanations
The explanations outlined above offer only lim­
ited descriptions of the flypaper effect that
are confined to particular institutional situa­
tions, to particular kinds of grants, or to partic­
ular government services.
For example, Hamilton develops his argu­
ment that income is a proxy for inputs into the
production of local public goods in a general
way, but is able to offer examples only for local
education and police protection. Romer and
Rosenthal’s “ agenda control” model applies
only to the case of local direct (not represen­
tative) democracy. Chernick’s work applies only
to project grants, not revenue sharing. Fish­
er’s arguments apply only to revenue sharing
that is distributed according to a tax effort
formula. Moffitt’s model is relevant only for
closed-end grants, particularly those with
more than one matching rate (such as AFDC)
where the applicable rate depends upon the
community’s expenditures.
In a more subtle way, the fiscal illusion model
and the “ asymmetric information” model of
Filimon, Romer, and Rosenthal are also lim­
ited; without further modification, they are con­
fined to the institution of direct democracy.
In these models, voters are misinformed about
the fiscal situation facing their community
and so make incorrect choices. But voters are
typically represented by elected officials who
know the extent of aid to their communities

3. Fisher’s point
might continue to
have some relevance
because most states
do have a program
o f revenue sharing or
grants fo r general
relief, although these
programs are usu­
ally small in dollar
value. Some o f these
programs include
effort considerations.

(it is a prominent part of each annual budget)
and who therefore know that marginal costs
are unchanged by lump-sum aid. Moreover,
since the decisions made by the voter in the fis­
cal illusion and asymmetric information mod­
els will be suboptimal, elected officials will
have a political incentive (in order to maxi­
mize their chances of reelection) to both act
on this information about the true cost of pub­
lic goods and to release it to the general public.
For example, if voters would be happier
with a smaller public sector and a reduction
in local taxes, ambitious politicans have an
incentive to give it to them. Thus, in a rep­
resentative democracy, these models require
one of two unpalatable modifications: either
elected officials ignore even the most basic
elements of their city’s financial situation or
political competition in the city has completely
broken down.
The limited scope of these explanations
contrasts sharply with the comprehensive na­
ture of flypaper effects, which appear across
a wide range of data sets, local public goods,
and empirical methodologies. This means that,
for every explanation given above, a study
can be found that is beyond the scope of that
argument but that still finds evidence of
flypaper effects.
For example, Hamilton’s hypothesis about
income as an input leads to the conclusion
that flypaper effects should occur primarily
in education and public safety, but Gramlich
and Galper (1973) report flypaper effects for
social services (health and hospitals, and hous­
ing) and urban support (sewers, sanitation,
highways, and parks and recreation) as well,
while Inman (1971) reports additional flypaper
effects for sanitation, sewers, parks and rec­
reation, transportation, libraries, and welfare.
These two studies also carefully separate
project grants from their lump-sum aid variable
to obviate Chernick’s arguments about the
exogenous nature of project grants. In a simi­
lar way, Wyckoff (1984) removes all categori­
cal grants of any kind from his lump-sum aid

variable, thus ensuring that the arguments
of Moffitt do not apply.
Since the subject of all the studies in table 1
was representative democracy, none of the
arguments that rest on direct democracy
(Romer and Rosenthal’s agenda control model;
Filimon, Romer, and Rosenthal’s asymmetric
information model; and the fiscal illusion
model) are applicable. In addition, Fisher’s
tax effort considerations are probably not rel­
evant to these results, since those studies took
place before the onset of federal general reve­
nue sharing and/or involved independent
school districts that do not receive federal
revenue sharing money.3
It is perfectly possible that flypaper effects
are due to a combination of the theories just
discussed, with each explanation being more
important in a particular place and time. If
this were the case, however, we might expect
more variation as to the presence or absence
of flypaper effects across empirical studies
than illustrated in table 1. Without a unifying
theory, we are forced to conclude that 10 out
of the 11 studies in table 1 happened by chance
to choose data sets and empirical techniques
that led, through many distinct mechanisms,
to flypaper effects.
While this multiple-cause explanation cer­
tainly cannot be ruled out, table 1 at least
suggests that a more general explanation of
flypaper effects might be useful, one which is
not tied to a particular public service, insti­
tutional situation, or empirical specification.
If such a theory existed, it would be easy to
explain the consistencies noted in that table.
For this reason, the next section summarizes a
new attempt to explain flypaper effects, based
on institutional features of government that,
it is hoped, are more universal than the factors
that underlie the explanations given above.

IV. A New Theory of
Flypaper Effects
Wyckoff (1985) details a new model of fly­
paper effects, based upon two basic ideas.
First, local public goods are produced by pub-

lie employees (bureaucrats) whose interests
do not always match those of the community.
Second, this bureaucracy has influence over
city council because it knows more about the
true cost of producing public goods than the
council does. Because of his or her profes­
sional training and day-to-day contact with
these matters, the head of each department is
assumed to have an advantage over council
members in knowing both the production func­
tion for public goods (what inputs are needed
for a particular level of output) and the min­
imum cost for these inputs.
To highlight the influence of these two no­
tions, the model uses three simplifying assump­
tions. Local decision-making is assumed to be
a simple two-way struggle between city coun­
cil and a single, well-informed bureaucrat.
Due to political competition, the preferences
of city council are taken to accurately reflect
those of the median voter in each community.
Following Niskanen (1971), the bureaucrat
is assumed to be solely interested in increasing
the size of his budget, because this budget is
systematically related to variables of direct
interest to him: salary, fringe benefits, profes­
sional prestige, and power over others. Use of
this third assumption means that the result­
ing model is an application and extension of
Niskanen’s model.
According to the public choice literature on
bureaucracy, the bureaucrat’s information
advantage has an effect on public expendi­
ture, allowing him to expand the city’s bud­
get beyond what the median voter would pre­
fer. To increase his budget, the bureaucrat
submits the largest request he thinks council
will approve. In reviewing this request, city
council is hampered by its lack of knowledge of
the effects of marginal changes in the budget;
since it doesn’t know the true cost of public
goods, it doesn’t know what budget changes
will mean in terms of changes in output. A
risk-averse city council will therefore tend
to avoid making changes in the bureau’s bud­
get request.

Moreover, an expansion-oriented bureaucrat
will compound the council’s timidity in mak­
ing budget changes by acting strategically. Not
only does the bureaucrat have no incentive
to reveal correct information about the true
cost of public goods, he will try to release dis­
torted information and respond to budget cuts
by cutting the most popular programs first
(“ cutting the meat instead of the fat” ). Another
budget-increasing tactic is to respond to coun­
cil’s tendency to cut all budget requests by a
certain proportion by inflating requests so as to
maintain desired spending levels even after
allowance is made for token budget-cutting.
By using his information advantage this way,
the bureaucrat in this simplified model will
push the city council to the point where the
median voter is indifferent between the bud­
get that is finally approved and doing without
the local public services (and the taxes that
go to pay for them) entirely. This is a standard
proposition of the Niskanen model. However,
the local government case differs fundamen­
tally from the central government case (the
subject of Niskanen’s study) because city res­
idents have a stronger “ exit” option (to use
Hirschman’s [1970] term) than do citizens of a
nation. If he becomes dissatisfied with his
community, the voter can always move.
Two standard comparative static results from
the Niskanen model carry over to the model
in Wyckoff (1985). First, the community’s
demand function for public goods, as filtered
by negotiation with bureaucrats, will always
be cost-elastic. Second, a dollar of lump-sum
aid to this community will always generate
more than a dollar of additional expenditures
(for proofs of these two propositions, see
Wyckoff [1984]).
Since it is set in the local context, however,
the model has additional consequences that
explain flypaper effects. The intuition behind
these results is that the median voter’s bar­
gaining position with respect to the bureau­
crat is not the same when he gets lump-sum
aid as when he receives an increase in his
private income.
When the voter receives an increase in pri­
vate income, he can use this extra income

both in his present circumstances and in any
alternative city he moves to. The increase in
the income (and hence the utility) of the voter’s
next best alternative is of prime importance
for the model: this effect leads to greater credi­
bility in the voter’s threat to leave if the bureau­
crat goes too far. An increase in the value of
the voter’s alternative helps constrain the
bureaucrat’s demands and reduces the equi­
librium size of the community’s budget.
An increase in lump-sum aid, by contrast,
improves the voter’s current circumstances but
cannot be moved to a new location with the
voter—it is tied to his current city. Hence there
is no corresponding increase in the value of
the voter’s threat to move in the case of an
increase in intergovernmental aid. It is this
asymmetry in bargaining position that creates
flypaper effects.
The situation facing city council and the
bureaucrat is similar to that facing the man­
agement of a company and its labor union.
During labor negotiations, the wages and work­
ing conditions that are eventually agreed upon
depend not only on current circumstances,
but on each side’s alternative situation if an
agreement is not reached. For example, if man­
agement can creditably assert that it does
not really need the plant due to, say, the pos­
sibility of filling orders from overseas pro­
duction, then the perceived value of its next
best alternative will be high, and it will be
able to more effectively restrain the wage
demands of the union.
To continue this analogy, consider man­
agement’s bargaining position with respect to
the union in two situations: 1) an increase
in profitability in this one plant due to a reduc­
tion in the local price of materials; and 2) an
increase in the profitability in the entire com­
pany due to a worldwide increase in demand
for the product.
The former situation, which parallels the
effect of lump-sum aid in the case of local
governments, improves management’s profit
picture in the current situation (with this plant
open) but not in any other situation (overseas

supply). The latter situation, which is anal­
ogous to the effect of private income on local
decision-making, increases management’s
profits in current as well as in alternative
production schemes. Because management’s
threat to move production overseas is more
credible in the latter situation than the for­
mer, workers will demand higher wage in­
creases when the profit increase is localized
to their own plant.
This new model of flypaper effects was tested
using 1977 expenditure data from 115 small
cities in Michigan. Using a single-equation,
double-logarithmic functional form, expendi­
ture was regressed on to population, the median
voter’s tax share, total income (Z = Y + TA),
the share of total income from lump-sum aid
( TA/Z), non-revenue-sharing aid, and several
additional demographic variables.
In testing this bureaucratic model against the
standard median voter model, a joint hypoth­
esis test involving two coefficients was em­
ployed. First, the coefficient on population
was included because of population’s role in
influencing the cost to the median voter of local
public goods. Since the model retains the pri­
macy of the median voter vis-a-vis other citi­
zens in the local decision-making process (so
that the preferences of other voters don’t mat­
ter), if the median voter’s tax share is held
constant, the only effect of increasing popula­
tion in a community is crowding of public
facilities. If public goods are defined in terms
of the resources available to each individual
resident (for example, park space per capita),
then, ceteris paribus, this crowding raises
the cost of providing a uniform level of these
goods to the median voter.
Second, the coefficient on the share of income
from lump-sum aid was also utilized to test
for the presence or absence of flypaper effects.
If flypaper effects are absent, the composi­
tion of the median voter’s income between
private income and aid should have no effect
on expenditures; the coefficient should be

4. With regard to
the restriction under
the Niskanen model
that a one dollar
increase in lump­
sum aid generates
more than a one dol­
lar increase in expen­
ditures, this hypoth­
esis applies only to
total (current plus
capital) expenditures.
It may be worth not­
ing, however, that
the data appeared to
fulfill this restric­
tion o f the model.
Evaluated at sample
medians, a one dol­
lar increase in un­
restricted aid gener­
ated an extra 5 6 cents
o f current expendi­
tures and an increase
o f 75 cents in capi­
tal spending, fo r a
total increase o f
$1.31.
5. The observa­
tions o f Nathan,
Manvel, and Cal­
kins, however, do
not by themselves
constitute an expla­
nation o f flypaper
effects. Although they
explain why revenuesharing money might
be used fo r capital
rather than operat­
ing expenditures,
their arguments fa il
to show why the
money is not used to
reduce local taxes—
why does the money
stick in the public
sector? I f city coun­
cils are in charge o f
the budget and are
responsive to the
voters, this should
not happen.

zero. If flypaper effects are present, expendi­
tures should increase with the share of total
income coming from lump-sum aid.
Thus, under the bureaucratic model, de­
mand must be cost-elastic and the coefficient
of population on total expenditures must be
negative. In addition, the coefficient on the
share of income from lump-sum grants must
be positive, reflecting flypaper effects. By con­
trast, under the median voter model, there is
no restriction at all on the population coeffi­
cient, but the coefficient on TA/Z must be zero.
The regressions contained in Wyckoff (1985)
show that, when operating expenditures only
are the dependent variable, the bureaucratic
model is rejected by the data, while the median
voter model is not rejected. When capital expen­
ditures are employed, the opposite is true:
the median voter model is rejected by the data,
but the bureaucratic model is not rejected.4
The results suggest that a dichotomy exists
with respect to local governments’ operating
and capital expenditures: the bureaucrat has a
great deal of influence on the latter and not
much on the former. This is not an implau­
sible result, since in the real world city coun­
cils may not be as helpless as portrayed in the
simplified model above. Council members can
often employ monitoring devices that, although
costly in terms of time or money, yield infor­
mation about bureau performance and the true
costs of producing public goods. For example,
strict budgeting and expense reporting tech­
niques may be used, cost and output data can
be compared with those of other communi­
ties, and feedback from citizens and the news
media can be cultivated. It is entirely possible
that these monitoring devices work well in
one context but not in another. The complex­
ity of capital expenditures, along with their
ability to be financed by debt, may make it
easier for the bureaucrat to press his demands
there rather than in operating expenditures.
In addition, as pointed out by Nathan,
Manvel, and Caulkins (1975), city councils
may be more willing to accede to the bureau­

crat’s demands in the capital expense area
because of a fear that revenue-sharing money
might eventually be cut off by the federal
government. Rather than using revenue shar­
ing to fund new operating expenditures, which
would have to be funded by increased taxes
if revenue sharing was discontinued, local gov­
ernments often chose to channel the revenue
sharing money into one-time capital projects
such as highway and sewer repairs.5
Moreover, the dichotomy of spending pat­
terns between capital and operating expendi­
tures observed in these cities suggests that
the bureaucratic model may prove superior to
the other explanations of flypaper effects dis­
cussed above, although no empirical tests of
this hypothesis were undertaken. None of
these previously mentioned theories suggest
such a dichotomy. In fact, differences between
current and capital expenditures are wholly
inconsistent with many of these models. For
example, if flypaper effects are caused by fiscal
illusion, the voter ought to be fooled for both
kinds of expenditures. If, on the other hand,
fiscal effort provisions in revenue sharing are
causing flypaper effects, these effects ought
to show up in both capital and operating expen­
ditures. And, finally, if bureaucrats are able
to hide grants from voters, this should be regis­
tered in both types of spending.

V. Conclusions
The previous discussion ought to establish one
important point: any evaluation of proposals
to change the current system will be strongly
influenced by our model of how the local pub­
lic sector works. For example, proponents
of the Reagan cutbacks have argued that reduc­
tions in aid to state and local government will
be offset by the increases in state-and-localgovernment-taxable private income that results
when tax and deficit burdens on the economy
are reduced. Suppose for the sake of argu­
ment that private income does increase just
enough so that, in the absence of flypaper
effects, local expenditure in each community
would be unchanged. If we accept the argu­

ments of Moffitt and Chernick that observed
flypaper effects are due to the peculiarities
of project grants and closed-end matching
grants, the proposed cuts in revenue sharing
(which does not share these unique features)
will indeed be balanced by an appropriate
increase in private income. According to the
arguments of Filimon, Romer, and Rosenthal, of
Romer and Rosenthal, and of Wyckoff, how­
ever, flypaper effects are endemic to the local
decision-making process, and it would take
very large increases in private income to off­
set the spending cuts caused by the loss of the
revenue-sharing program.
The model of Hamilton, on the other hand,
implies a subtle and interesting position on
this question. Flypaper effects do occur, he
acknowledges, and we ought to expect that the
substitution of private income for intergov­
ernmental aid will reduce total state and local
government expenditure, but we ought not to
conclude from this that the total output of
the local public sector has declined. If income
enters the local production function for pub­
lic goods, then, even if purchased inputs
(which is what is measured by the local bud­
get) have declined, the increase in income may
increase the (unmeasured) output of local
public goods in the community.
Perhaps surprisingly, the model in Wyckoff
does not have unambiguous public policy impli­
cations with regard to economic efficiency.
Despite the bureaucrat’s expansion of the
local budget, the model does not show that
the local public sector is either productively
or allocatively inefficient in a welfare sense.
Because the effective demand function for
local public goods is always cost-elastic, the
bureaucrat can only maximize his budget by
operating at minimum cost, and hence there is
no productive inefficiency (see Wyckoff [1984]).
And although the budget is larger than the
median voter would like, there is no reason to
presume that what the median voter desires
is allocatively efficient. In fact, two studies
have argued that, if the median voter model

is operating in the local public sector, the
output of that sector is probably suboptimal
(see Barlow [1970] and Bergstrom and Good­
man [1973]).
The model does have predictions about the
likely effects of a repeal of the revenue-sharing
program and the political dimensions of such
a move. First, as noted above, we ought to
expect large cutbacks in state and local expen­
ditures because of this change. Second, the
chief opponents of such a cutback would not
necessarily be the citizens of each state and
local government, since the satisfaction of the
median voter in each community is determined
not by the amount of aid received by his or
her state or local government, but by the util­
ity of the voter’s next best alternative com­
munity. The aid raises local expenditure levels
without increasing his satisfaction with his
current community. This result may help ex­
plain both the widespread discontent of citi­
zens with state and local governments and
the fact that the chief proponents of aid pro­
grams are often the employees and managers
of these governments.

References
Arrow, Kenneth J. “A Difficulty in the Con­
cept of Social Welfare,” Journal of Political
Economy, vol. 59, no. 4 (August 1950),
pp. 328-46.
Barlow, Robin. “ Efficiency Aspects of Local
School Finance,” Journal of Political Econ­
omy, vol. 78, no. 5 (September/October 1970),
pp. 1028-40.
Bergstrom, Theodore C., and Robert P. Good­
man. “ Private Demands for Public Goods,”
American Economic Review, vol. 63, no. 3
(June 1973), pp. 280-96.

Black, Duncan. “ On the Rationale of Group
Decision Making,” Journal of Political
Economy, in Kenneth J. Arrow and Tibor
Skitovsky, eds., Readings in Welfare Eco­
nomics. Homewood, IL: Richard D. Irwin,
Inc., 1969, pp. 133-46.
Borcherding, Thomas E., and Robert T. Dea­
con. “ The Demand for the Services of NonFederal Governments,” American Economic
Review, vol. 62, no. 5 (December 1972),
pp. 891-901.
Bowen, Howard R. “ The Interpretation of
Voting in the Allocation of Economic
Resources,” Quarterly Journal of Econom­
ics, vol. 58 (November 1943), pp. 27-48, in
Kenneth J. Arrow and Tibor Skitovsky,
eds., Readings in Welfare Economics. Home­
wood, IL: Richard D. Irwin, Inc., 1969,
pp. 115-32.
Bradford, David F., and Wallace E. Oates. “ The
Analysis of Revenue Sharing in a New
Approach to Collective Fiscal Decisions,”
Quarterly Journal of Economics, vol. 85, no. 3
(August 1971), pp. 416-39.
Chernick, Howard A. “An Economic Model of
the Distribution of Project Grants,” in Peter
Mieszkowski and William H. Oakland, eds.,
Fiscal Federalism and Grants-in-Aid. Wash­
ington, DC: The Urban Institute, 1979,
pp. 81-103.
Courant, Paul N., Edward M. Gramlich, and
Daniel L. Rubinfeld. “ The Stimulative
Effects of Intergovernmental Grants: or
Why Money Sticks Where It Hits,” in Peter
Mieszkowski and William H. Oakland, eds.,
Fiscal Federalism and Grants-in-Aid. Wash­
ington, DC: The Urban Institute, 1979,
pp. 5-21.

Deacon, Robert T. “A Demand Model for the
Local Public Sector,” Review of Economics
and Statistics, vol. 60, no. 2 (May 1978),
pp. 184-92.
Ehrenberg, Ronald G. “ The Demand for State
and Local Government Employees,” Amer­
ican Economic Review, vol. 63, no. 3 June
1973), pp. 366-79.
Filimon, Radu, Thomas Romer, and Howard
Rosenthal. “Asymmetric Information and
Agenda Control: The Bases of Monopoly
Power in Public Spending,” Journal of Pub­
lic Economics, vol. 17, no. 1 (February 1982),
pp. 51-70.
Fisher, Ronald C. “ Income and Grant Effects
on Local Expenditure: The Flypaper Effect
and Other Difficulties,” Journal o f Urban
Economics, vol. 12, no. 3 (November 1982),
pp. 324-45.
______ “A Theoretical View of Revenue Shar­
ing Grants,” National Tax Journal, vol. 32,
no. 2 (June 1979), pp. 173-84.
Gramlich, Edward M. “An Econometric Exam­
ination of the New Federalism,” Brookings
Papers on Economic Activity, 2:1982,
pp. 327-60.
______ “ Intergovernmental Grants: A Review
of the Empirical Literature,” in Wallace E.
Oates, ed., The Political Economy of Fiscal
Federalism. Lexington, MA: Lexington Press,
1977, pp. 219-39.
______ , and Harvey Galper. “ State and Local
Fiscal Behavior and Federal Grant Policy,”
Brookings Papers on Economic Activity,
1:1973, pp. 15-58.
Hamilton, Bruce W. “ The Flypaper Effect and
Other Anomalies,” Journal of Public Eco­
nomics, vol. 22, no. 3 (December 1983),
pp. 347-61.

Henderson, James M. “ Local Government
Expenditures: A Social Welfare Analysis,”
Review of Economics and Statistics, vol. 50,
no. 2 (May 1968), pp. 156-63.

Moffitt, Robert A. “ The Effects of Grants-inAid on State and Local Expenditures: The
Case of AFDC,” Journal of Public Econom­
ics, vol. 23, no. 3 (April 1984), pp. 279-305.

Hirschman, Albert O. Exit, Voice, and Loyalty:
Responses to Decline in Firms, Organiza­
tions, and States. Cambridge, MA: Harvard
University Press, 1970.

Nathan, Richard P., Allen D. Manvel, and
Susannah E. Calkins. Monitoring Revenue
Sharing. Washington, DC: Brookings Insti­
tution, 1975.

Hotelling, Harold. “ Stability in Competition,”
Economic Journal, vol. 39 (March 1929),
pp. 41-7.

Niskanen, William A. Bureaucracy and Repre­
sentative Government. Chicago: AldineAtherton, Inc., 1971.

Inman, Robert P. “ The Fiscal Performance of
Local Governments: An Interpretative Re­
view,” in Peter Mieszkowski and Mahlon
Straszheim, eds., Current Issues in Urban
Economics. Baltimore, MD: Johns Hopkins
University Press, 1979, pp. 270-321.

Oates, Wallace E. “ Lump-Sum Intergovern­
mental Grants Have Price Effects,” in Peter
Mieszkowski and William H. Oakland, eds.,
Fiscal Federalism and Grants-in-Aid.
Washington, DC: The Urban Institute,
1979, pp. 23-30.

______ “ Testing Political Economy’s ‘As If’
Proposition: Is the Median Voter Really
Decisive?” Public Choice, vol. 33, no. 4
(1978), pp. 45-65.

Pack, Howard, and Janet Rothenberg Pack.
“ Metropolitan Fragmentation and Local Pub­
lic Expenditures,” National Tax Journal,
vol. 31, no. 4 (December 1978), pp. 349-62.

______ “ Towards an Econometric Model of
Local Budgeting,” in National Tax Associ­
ation, Proceedings of the 64th Annual Con­
ference on Taxation (1971), Columbus, OH:
National Tax Association, 1972, pp. 699-719.

Perkins, George M. “ The Demand for Local
Public Goods: Elasticities of Demand for
Own Price, Cross Prices, and Income,”
National Tax Journal, vol. 30, no. 1 (Decem­
ber 1977), pp. 411-22.

Ladd, Helen F. “ Local Education Expenditures,
Fiscal Capacity, and the Composition of the
Property Tax Base,” National Tax Journal,
vol. 28, no. 2 (June 1975), pp. 145-58.

Romer, Thomas, and Howard Rosenthal. “An
Institutional Theory of the Effect of Inter­
governmental Grants,” National Tax Journal,
vol. 33, no. 4 (December 1980), pp. 451-58.

Lovell, Michael C. “ Spending for Education:
The Exercise of Public Choice,” Review
o f Economics and Statistics, vol. 60, no. 4
(November 1978), pp. 487-95.

Wyckoff, Paul Gary. “ Bureaucracy, Efficiency,
and Local Public Choice: An Empirical Test
of Some New Implications of Bureaucratic
Public Service Provision,” unpublished Ph.D.
dissertation, University of Michigan, 1984.
______ “A Bureaucratic Theory of Flypaper
Effects,” Working Paper 8501, Federal Re­
serve Bank of Cleveland, 1985.

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Economic
Commentary

Ohio’s Electricity Prices
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1/1/85
Will Adjustable Rate Mortgages Survive?
Thomas M. Buynak

1/15/85
Recent Changes in the Consumer
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K.J. Kowalewski

2/1/85
Deposit Rates and Local Markets
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2/15/85
The 1985 Humphrey-Hawkins Testimony
Michael R. Pakko

3/1/85
Will Taxing Imports Help?
Michael F. Bryan and
Owen F. Humpage

3/15/85
Federal Reserve’s Response to the
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4/1/85
Imports and Domestic Steel
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The Debt Burden: What You Don’t See
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CRR and Monetary Control
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5/15/85
The Financial Distress
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6/1/85