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SEPTEMBER/OCTOBER 1999

Michael Dueker is a research officer at the Federal Reserve Bank of St. Louis. Nick H. Meggos and Thomas A. Pollmann provided research assistance.

Measuring
Monetary Policy
Inertia in Target
Fed Funds Rate
Changes
Michael Dueker

I

nflation in the United States has been
relatively low and stable following the
difficult disinflation during the early
1980s. Since then, the Federal Reserve
has been perceived as following policies
designed to preempt rising inflation. At
the same time, empirical studies of Federal
Reserve policy actions find that policy
responses are generally stodgy and that a
great deal of interest rate smoothing takes
place, relative to rule-based policy prescriptions, such as the Taylor rule (Taylor,
1993). Several explanations have arisen as
to why a central bank that is focused primarily on inflation control would exhibit
policy inertia when changes seem indicated. Rudebusch (1999) and Orphanides
(1998) study data uncertainty as a possible
justification for stodgy policy responses,
because revisions take place before estimates of output and price indices are final
and policymakers want to avoid acting on
false signals. This justification falls under
the umbrella of recognition lags in that it
takes time for monetary policymakers to
observe that inflation has moved decisively
upward or that an output gap has developed. Sack (1998) suggests that uncertainty regarding the structure of the
economy may be a reason for the Federal
Reserve to respond cautiously. Goodfriend
(1997) notes that if aggressive Federal
Reserve actions subsequently proved to be
mistimed, the public’s trust in the Fed

would diminish. Hence, policymakers
might tend to act less aggressively, again
due to uncertainty regarding the timeliness
of currently contemplated policy actions.
Woodford (1999) offers a different explanation of policy inertia that is not based
on model or instrument uncertainty. In
Woodford’s view, every policy action also
is a hint of how policy will be conducted
in the future. In this case, part of the central bank's credibility rests on making current policy roughly consistent with the
path to which it had hinted through earlier
policies. In this case, some policy inertia
results as policymakers balance their impetus to respond to current news against
their implicit prior commitment to a particular path for interest rates.
This article presents two distinct measures of inertia in the target fed funds rate,
relative to the prescriptions of Taylor’s
(1993) policy rule, including the inertia
inherent in the discreteness of the target
fed funds rate. Previous empirical estimates of policy inertia have not addressed
the discrete nature of target funds rate
changes; instead, they use quarterly or
monthly averages of the funds rate, which
can mask an important feature of the policymaking process. The Federal Open
Market Committee (FOMC) sets its objective, or target, for the federal funds rate,
the interest rate that banks charge each
other for overnight loans of Federal
Reserve deposits. In practice, the FOMC
usually changes the target fed funds rate in
discrete amounts by multiples of 25 basis
points. Thus, an important facet of policy
inertia takes the form of the following
question: How far does the FOMC let the
prevailing target funds rate get out of line,
relative to a shadow desired level that
changes continuously? Another facet,
which has been the subject of previous
study, is the degree to which the fed funds
rate obeys a partial-adjustment mechanism
and the sluggishness implied by such a
mechanism. A joint view of these two

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

3

SEPTEMBER/OCTOBER 1999

facets of policy inertia ought to provide a
more complete picture, from which subsequent research can investigate whether
policy appears to display either too much
or the right amount of inertia.
In particular, this article presents an
econometric model of discrete changes in
the target fed funds rate in order to estimate thresholds at which the FOMC
decides to change the target and by how
much. The model defines a latent desired
target level, so the threshold coefficients
represent the sizes of gaps between the
desired and actual target funds rates that
are necessary to induce target changes of
various sizes. These estimated thresholds
are compared with the sizes of the actual
changes in the target fed funds rate—usually 25 or 50 basis points—to arrive at a
quantitative measure of the Fed’s readiness
or reticence to initiate changes in the target
funds rate. The complete set of threshold
coefficients also provides estimates of cutoff levels at which the Fed chooses to
make either a small or large change in the
target funds rate. The payoff to estimating
threshold coefficients is that we can then
separate any slugghishness in changes to
the target fed funds rate introduced by its
discrete nature from sluggishness due to
data or model uncertainty. Also, tests for
asymmetry in the thresholds between
increases and decreases in the target funds
rate are possible.

basis points, with some other small
changes of 12.5 basis points. I classified
monthly changes of less than 18 basis
points as “no change” with two
exceptions: In September 1985 and
November 1988 the target funds rate
increased by 12.5 basis points for the
second month in a row; I counted the
combined change as a 25 basis point
increase during the second month.
Table 1 summarizes the five discrete
categories I use for the changes in the
target funds rate, where the target funds
rate is denoted FFT. The last column
shows that, despite a number of odd-sized
changes in the target through 1989, the
means within the five categories correspond very closely to multiples of 25 basis
points: (–.50, –.25, 0, +.25, +.50). The
target funds rate has decreased on net
since 1985, resulting in more 25 basis
point decreases than increases.

TAYLOR’S RULE IGNORING
DISCRETENESS
Following Judd and Rudebusch (1998),
I use Taylor's rule to motivate an empirical
specification for modeling changes in the
federal funds rate. Taylor (1993) suggested
that the FOMC’s behavior from 1987 to
1992, with respect to setting a target for
the federal funds rate, appeared to be wellsummarized by a simple monetary policy
rule. This interest-rate rule, which became
known as Taylor’s rule, is one in which the
Federal Reserve changes its objective for
the federal funds rate in response to the
gap between the actual and desired levels
of inflation, and to the percentage gap
between actual and potential output. In its
original specification, Taylor’s rule takes
the following form under the assumptions
that the FOMC’s long-run desired rate of
inflation is 2 percent and that the equilibrium real short-term interest rate also is
2 percent (Orphanides, 1998):

DISCRETE NATURE OF
TARGET CHANGES
The discrete nature of changes in
the target fed funds rate poses special challenges to empirical analysis. Almost all
changes in the target funds rate are in multiples of 25 basis points. In this article,
I use data on the target funds rate that
start in 1985 (Rudebush, 1995). A plot of
the target funds rate is shown in Figure 1.
To match the frequency of some of the
explanatory variables, I calculate the
change in the target funds rate from the
last business day of the month to the last
business day of the previous month. Prior
to 1990, some changes were as small as six

(1)

(

FFt = 1 + 1.5π t + .5 y − y p

)

t

,

where FF stands for the federal funds rate,
π for the inflation rate, y for the log of

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

4

SEPTEMBER/OCTOBER 1999

actual output and yP for the log of potential output. In long-run equilibrium, the
output gap will be zero and the equilibrium real rate of interest (FF – π) will
equal two by assumption. Thus, equation
1 implies a long-run inflation target of
2 percent.
The most important empirical lesson
from Taylor’s rule has not been to check
whether actual policy is consistent with
2 percent inflation, however. Instead,
Taylor (1998) gives considerable importance to the coefficient on inflation having
an absolute value greater than one,
because if the Fed were to raise the fed
funds rate by more than any increase in
inflation, then the real interest rate would
increase, thereby dampening inflationary
pressures in the economy. Any policy
equation in which the response of the
nominal interest rate instrument to a
change in inflation is greater than one is
said to have the Taylor-rule property,
regardless of the implied long-run inflation
target. In empirical research, Taylor’s original equation often is modified to include a
lagged dependent variable. Rules with
gradual adjustment have the Taylor property if the long-run response of the
interest-rate instrument to a change in
inflation is greater than one:
(2)

Figure 1

Fed Funds Target
Percent
11
10
9
8
7
6
5
4
3
2
1985 86

(

)

t

88

89

90

91

92

93

94

95

96

97

98

Table 1

Observation Categories Based on Size
of Target Rate Change.
Monthly Sample: 1/85 — 12/98
Category

1
2
3
4
5

Criterion

∆FFT , – .25
–.25 # ∆FFT # – .18
–.18 , ∆FFT , 1 .18
1.18 # ∆FFT # 1 .25
∆FFT . 1 .25

Frequency

Mean D FF T within category

11
25
111
10
10

lated from the consumer price index
without the food and energy components.
The funds rate data, FF, are the monthly
averages of the effective funds rate in the
upper panel of Table 2 and are the end-ofmonth values of the target fed funds rate
in the lower panel of Table 2. The log of
real GDP (deflated by the chain-weighted
price index) is y, and yP is the log of
the potential output series from the
Congressional Budget Office. Note that
y and yP only are available at the quarterly
frequency. The output gap tends to evolve
slowly, however, so I used the same value
of the output gap for three months running in order to estimate equation 2 at a
monthly frequency. Figure 2 plots the
output gap since 1985 in logs, so that
100 times the log gap is the output gap
as a percentage.
Table 2 shows that for either

FFt = ρFFt − 1 + λ o + λ1π t
+ λ2 y − y p

87

+ δ∆FFt − 1

λ1 / (1 − ρ ) > 1
For positive values of ρ, equation 2
allows for more gradual adjustment of the
federal funds rate to changes in inflation.
Sack (1998) and Judd and Rudebusch
(1998) have used such a partial
adjustment approach to model FOMC
policy. The caveat is that ordinary least
squares estimation of the partialadjustment mechanism from equation 2
ignores the discreteness in the actual
changes to the target fed funds rate. Estimates of equation 2 with monthly data
starting in 1985 appear in Table 2, where
π is the year-over-year inflation rate calcu-

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

5

–.523
–.248
1.0056
1.244
1.538

SEPTEMBER/OCTOBER 1999

coefficients on the output gap are larger
than originally specified by Taylor in
equation 1.

Table 2

Estimated Taylor Rules from Equation 2
Monthly Data: 1/85 — 12/98
Coef cient

Description

Value

Std. Error

A DISCRETE EMPIRICAL
MODEL WITH THRESHOLDS

Results for Effective Funds Rate

λ1
λ2
ρ

d

λ0

Inflation
Output Gap
Autoregression
Lagged change
Constant

0.086
0.063
0.937
0.379
0.061

0.044
0.022
0.022
0.074
0.072

In this section, I examine a Taylor-rule
specification of the target federal funds
rate in an ordered probit model that has
been enhanced with time-series features.
An ordered probit model, unlike the ordinary least-squares regression from Table 2,
takes into account the discrete nature of
target changes. As mentioned in the introduction, the discrete-variable model
includes threshold coefficients that
provide information on another possible
manifestation of policy inertia: the degree
of interest-rate misalignment required to
induce a discrete change in the target level
of the funds rate.
The five categories defined in Table 1
fit naturally into an ordered probit framework. As in probit models in general, one
assumes that there is a continuous latent
or desired level of the target funds rate,
which is denoted as FFT*. A standard
assumption in probit models is that the
latent variable is a linear function of some
lagged explanatory variables, X, plus a normally distributed, mean-zero error term, ε:

Results for Target Funds Rate

λ1
λ2
ρ

d

λ0

Inflation
Output Gap
Autoregression
Lagged change
Constant

0.080
0.065
0.939
0.342
0.068

0.044
0.023
0.023
0.075
0.072

Figure 2

Real GDP and Real Potenial GDP
(in Logs)
Log
9
8.9
8.8

Real Potential GDP
Real GDP

8.7
8.6
8.5
1985 86

(3)
87 88 89

90

91

92

93

94

95 96

97

98

FFtT ∗ = Xt' −1β + ε t .

In keeping with the Taylor-rule specification
of equation 2, the X variables are inflation,
the output gap, and an intercept. Given
the evidence of a partial-adjustment mechanism from the estimates of equation 2,
I also add a lagged dependent variable
and the lagged change in the dependent
variable to equation 3, following Judd
and Rudebusch (1998):

99

dependent variable the long-run response
of the funds rate to a percentage point
increase in inflation is greater than one
λ1 / (1 – ρ) = 1.37 for the effective fed
funds rate and 1.31 for the target fed funds
rate. In Table 2, the estimated long-run
response of the funds rate to a one
percentage point increase in the output
gap, λ2 / (1 – ρ), is about one, which is
larger than the 0.5 coefficient Taylor wrote
in his original rule. Judd and Rudebusch
(1998) also find that estimated feedback

(4)

FFtT ∗ = ρFFtT−∗1 + λ 0 + λ1π t

(

)

+ λ 2 y − y p + δ∆FFtT−∗1 + ε t .
t

The assumed mapping between the
latent variable and the observable discrete

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

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SEPTEMBER/OCTOBER 1999

changes in the target funds rate is
(5)

is needed to induce a discrete change in
practice. For the threshold coefficients
to have this meaning, the latent variable
must be restricted to economically relevant
values. I do this by constraining the intercept such that the mean of the latent
variable is the same as the mean of the
observed target rate:

∆FFtT is in category j if

(

)

FFtT ∗ − FFtT− 1 is in c j − 1 , c j ,
where the categories are defined in Table 1
and c is a vector of threshold coefficients.
The difference FFtT* – FFtT–1 represents the
latent “desired” change in the target funds
rate, as defined by the econometric model.
The estimated threshold coefficients indicate the degree of underlying pressure that

FF T * = FF T = 5.91.
This restriction implies that the discrete
variable has the same sample-wide mean
as the continuous latent variable.

MODEL ESTIMATION

[

E ε t ∆FFt is in cat. j

The log-likelihood function for
the observed changes in the target fed
funds rate is
(6)

(

)

5

(

j =1

−

{

/ f ∆FFtT

ρEFFtT−∗1

− λ1π t − 1 − λ 2( y − y p ) t − 1

{ ( )}
( )}

)

where λ0 is always restricted to make

− δE∆FFtT−∗1 + c j ) / σ )

FF T * = FF T =

−Φ((FFtT−1 − ρEFFtT−∗1

5.91, c j > c j − 1 ,

(

− λ1 π t −1 − λ2 y − yp

δE∆FFtT−∗1

)

j = 1,..., 4, c 0 = − ∞,

t −1

+ c j −1 ) / σ )]},

and c5 = ∞.
The variance parameter, σ 2, was
assigned a value and was not estimated, since we cannot identify jointly the
threshold constants c and the variance
parameter. The value of σ 2 was set at
0.12, which implies a standard deviation of the disturbance to the desired
fed funds rate of about 35 basis points
per month. If a much larger variance
were chosen, the threshold constants
would increase in absolute value, but
some experimentation showed that
estimates of the threshold coefficients
are fairly stable across a range of
plausible values of the variance.

where F(.) is the cumulative normal
density function and D(cat. j) is a
dummy variable for category j at time
t. For the lagged dependent variable,
FFtT*, we need to take an expected
value, because we do not observe the
realized residual, ε. Therefore, we use
EFFtT ∗ = ρEFFtT−∗1 + λ 0

(
+ E[ε

+ λ1π t − 1 + λ 2 y − y p
−δE∆FFtT−∗1
is in cat. j

]

t

)

=

.5
−σ / (2π ) exp −c 2j / 2σ 2

2
− exp −c j − 1 / 2σ 2 


ln f ∆FFtT = ∑ D (cat. j)
ln{[Φ ((FFtT− 1

]

t −1

∆FFt

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

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SEPTEMBER/OCTOBER 1999

output gap also closely matches the
estimates from the simple regresssions:
λ2 / (1 – ρ) = 1.09.
In addition, the discrete-variable model
provides information on the thresholds at
which the FOMC tends to move the target
funds rate. To induce either an increase or
a decrease in the target of 25 basis points,
the latent target funds rate, FFT*, must
be about 45 basis points above or below
the actual target, according to the point
estimates. In other words, the gap between
the latent desired level of the target fed
funds rate and the actual target level must
be considerably larger than 25 basis points
to induce a 25 basis-point change.
The symmetry of the threshold levels
across increases and decreases suggests
that the FOMC does not require more
pressure to raise the target funds rate than
to lower it. That is, we cannot come close
to rejecting the hypothesis that c2 1 c3 = 0.
Less obvious is the failure to reject symmetry across the thresholds for large target
changes: c1 1 c4 = 0. The standard error
on the sum is 0.36, so we cannot reject
symmetry for large changes either. The
thresholds are significantly greater in
absolute value than the 25 and 50 basispoint levels corresponding with the
category means. We can easily reject the
joint hypothesis that c3 = –c2 = 0.25, and
c4 = –c1 = 0.50, with a Wald test statistic
that has a probability value well below
0.001. Similarly, the probability value of
the Wald test that c3 = –c2 = 0.25
is almost equally low. Thus, the threshold
coefficients reveal significant evidence that
the discrete nature of the target federal
funds rate adds a dimension of sluggishness to monetary policy responses to
inflation and output gaps that goes beyond
the partial adjustment specification of
equations 2 and 4.

Table 3

Autoregressive Ordered Probit Model
of Target Fed Funds Rate
Monthly Sample: 1/85 — 12/98
Coef cient

Value

(by variable)
Lagged EFF T *
Inflation
Output gap
Lagged E∆FFT *
Threshold c1
Threshold c2
Threshold c3
Threshold c4

0.906
0.152
0.102
0.118
–0.799
–0.439
0.459
0.658

Category mean
(from Table 1)

–0.523
–0.248
0.244
0.538

Std. Error

0.032
0.063
0.029
0.067
0.186
0.191
0.191
0.188

Log - Likelihood Value = –150.4

ORDERED PROBIT
ESTIMATION RESULTS
Monthly data also were used in the
ordered probit estimation, with the same
caveat mentioned earlier about the measures
used for the output gap. Quarterly
changes in the target funds rate would not
have fit cleanly into the 25-basis-point categories illustrated for the monthly data in
Table 1. Table 3 presents the parameter
estimates for equation 4. Interestingly, the
discrete-variable model also shows evidence
of Taylor’s (1998) criterion for an inflationfighting monetary policy; that is, the longrun response of the latent target funds rate
(FFT*) to a unit increase in inflation is
greater than one: λ1 / (1 – ρ) = 1.62. In
particular, the estimates suggest that it
takes about nine months for the latent
target funds rate to increase by more than
one percentage point in response to a onepercentage-point increase in the inflation
rate. Thus, from a discrete-variable model
of the target funds rate, we have recovered
parameter estimates that have the Taylorrule property—a greater than one-to-one
response of the interest rate instrument to
a unit increase in inflation. This finding
adds corroborative evidence to the simple
regression results from Table 2. The longrun response of the latent target funds rate
to a percentage point increase in the

SUMMARY AND
CONCLUSIONS
Previous studies have shown that
movements in the federal funds rate can be
described by a Taylor-rule equation with
interest-rate smoothing via a partial adjust-

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

8

SEPTEMBER/OCTOBER 1999

Judd, John P., and Glenn D. Rudebusch. “Taylor’s Rule and the Fed:
1970-1997,” Federal Reserve Bank of San Francisco Economic
Review (1998), pp. 3-16.

ment mechanism. The contribution of
this article is to examine the smoothing
or policy inertia within a model of discrete
target funds rate changes. To do so, I
estimate the thresholds that govern the
relationship between an underlying
partial-adjustment model of the latent or
desired target level and the discrete changes
observed in practice. The estimates show
a substantial degree of sluggishness in the
discrete responses of the target level of the
funds rate to gaps between the underlying
desired target level and the actual target
level. Nevertheless, the estimated
threshold coefficients are less than twice
the size of their corresponding discrete
changes, so that there is a limit to the size
of any misalignment of the target funds
rate brought by its discrete nature.
Furthermore, the estimates of the parameters that govern the latent desired level of
the target funds rate display the long-run
responsiveness property that Taylor (1998)
associates with a sound inflation-fighting
policy rule.
In addition, one area where the estimates of threshold coefficients would be
useful is the federal funds futures market.
Market participants would not want to
forecast the fed funds target rate changes
using ordinary least-squares estimates,
given that discrete target changes face substantial threshold hurdles. With estimates
of the thresholds, participants in the fed
funds futures market can gauge more
accurately the likelihood of a change in
the target level in the near term, and
thereby more accurately forecast the future
monthly average for the federal funds rate.

Orphanides, Athanasios. “Monetary Policy Evaluation with Noisy
Information,” Federal Reserve Board of Governors FEDS Working
Paper 98-50 (November 1998).
Rudebusch, Glenn D. “Federal Reserve Interest Rate Targeting, Rational
Expectations and the Term Structure.” Journal of Monetary
Economics, (April 1995) pp. 245-74.
_____. “Is the Fed Too Timid? Monetary Policy in an Uncertain
World,” Federal Reserve Bank of San Francisco Working Paper (March
1999).
Sack, Brian. “Does the Fed Act Gradually? A VAR Analysis,”
Federal Reserve Board of Governors FEDS Working Paper 98-17
(March 1998).
Taylor, John B. “Discretion Versus Policy Rules in Practice,” CarnegieRochester Conference Series on Public Policy 39 (December 1993),
pp. 195-214.
_____. “Monetary Policy and the Long Boom,” this Review
(November/December 1998), pp. 3-11.
Woodford, Michael. “Optimal Monetary Policy Inertia,” 1999 manuscript, Princeton University.

REFERENCES
Goodfriend, Marvin. “Interest Rate Policy and the Inflation Scare
Problem: 1979-1992” Federal Reserve Bank of Richmond Economic
Quarterly (Winter 1993), pp. 1-24.
_____. “Monetary Policy Comes of Age: A 20th Century Odyssey,”
Federal Reserve Bank of Richmond Economic Quarterly (Winter
1997), pp. 1-22.
Huh, Chan G., and Kevin J. Lansing. “Federal Reserve Credibility and
Inflation Scares,” Federal Reserve Bank of San Francisco Economic
Review (1998), pp. 3-16.

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

9

SEPTEMBER/OCTOBER 1999

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

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S E P T E M B E R / O C T O B E R 19 99

Michael R. Pakko is a senior economist at the Federal Reserve Bank of St. Louis. Gilberto Espinoza, Daniel Steiner, and Stephen Majesky
provided research assistance.

The U.S. Trade
De cit and the
“New Economy”

Figure 1

Current Account Balance
Annual Data
$ Billions
50
0

Michael R. Pakko

–50
–100

T

he performance of the U.S. economy
during the 1990s has been universally
hailed as stellar. Economic growth has
been strong, unemployment has reached its
lowest rate in over a generation, and inflation has remained relatively low. Consumer
confidence has been high, helping to maintain strong growth in consumption expenditures, and investment spending has
experienced a sustained growth rate that is
unparalleled during the second half of the
twentieth century. Many have gone so far
as to declare that current conditions and
prospects for the future represent a “new
economy” or “new paradigm” in which
these favorable trends might continue
indefinitely.
One economic indicator that often is
viewed with alarm, however, is the nation’s
growing trade deficit. In 1998, the U.S.
trade deficit reached a record level, and
when final data for 1999 is available,
it is projected to be even higher. Each new
release of trade data prompts the financial
press to trumpet headlines announcing
new record deficits. In both the media and
popular opinion, trade deficits often are
portrayed negatively, being blamed on the
unfair trading practices of our trading partners or on a lack of U.S. competitiveness in
world markets. Trade deficits often are
attributed with reducing economic growth
or resulting in lost jobs, and they almost
always are discussed using terms with negative connotation. (For example, a
widening deficit is frequently described as
a “deterioration.”)
Figure 1 illustrates recent movements
in the most comprehensive measure of the

–150
–200
–250
1960

1965

1970

1975

1980

1985

1990

U.S. international trade position, the current
account. Simple logic suggests that the
downward trend established during the
1990s cannot be maintained indefinitely
—if it were to do so, the United States would
ultimately exceed its ability to pay for the
rising tide of imports.
Nevertheless, few economists consider
such a disastrous scenario likely. Long
before the trade deficit could overwhelm
the economy, interest rates, exchange rates,
and relative national incomes would adjust
to re-establish more balanced trade patterns.
A key question that remains after acknowledging such market forces, however, is
how such an adjustment ultimately will
take place. If it is a smooth, gradual process,
the favorable trends in productivity and
incomes in the United States need not be
interrupted significantly. If the adjustment
were to be sharp and disruptive, however,
the claims of proponents about the new
economy would begin to ring hollow.
Understanding the underlying causes
of the present U.S. trade deficit is an
important part of evaluating their future
impact on the economy. This article discusses the factors to consider in such an
evaluation, focusing on a broad measure of

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

11

1995

2000

S E P T E M B E R / O C T O B E R 19 99

Figure 2

Table 1

Composition of the Current
Account in 1998

Components of the Current Account
Annual Data
$ Billions
100

(Billions of dollars)

Services

Income on Investments

50

Merchandise:

0
–50

Exports
Imports

Net Unilateral Transfers

–100

Balance

–150
Merchandise

–200

Exports
Imports
1965

1970

1975

1980

1985

1990

–246.9

Services:

–250
–300
1960

670.2
–917.2

1995

2000

263.7
–181.0
Balance

82.7

Income on Investment:

Inflows
Outflows
Balance

the U.S. trade position: its current account.
The analysis suggests that recent trade deficits
are driven by the same market forces that
are otherwise manifested in the booming
economy of the new paradigm theories.
If the present trade deficit is a temporary (albeit protracted) outcome of the
adjustment to a new, higher long-run
growth path for the economy, then we
should not consider it to be a pressing
concern. If it is driven by unsustainable,
perhaps speculative imbalances, however,
the deficit might forebode the ultimate
demise of the longest economic expansion
in U.S. history. The conditions under
which the present trade deficit ultimately
will be reversed might therefore be considered an important indicator of whether the
new economy has entered a new, more
mature phase, or whether its promises
were illusory.

Net Unilateral Transfers:
CURRENT ACCOUNT

–44.1
–220.6

The largest component, and the one
that accounts for nearly the entire deficit,
is merchandise. This component also is
the most variable, accounting for most of
the fluctuations in the current account
over time.
In contrast to the deficit in merchandise trade, the United States has a stable
surplus in services trade. This surplus has
been growing consistently for more than
two decades, but trade in services remains
quite a bit smaller than merchandise trade.
A commonly used measure of the trade
deficit—often used loosely as interchangeable with the current account concept—
is the combined merchandise and services
accounts.1
The third category of the current
account is income on investments. As
foreign residents have accumulated U.S.
assets over time, rising debt-service
payments reflected in this category have

Components of the Current Account

tage of being available monthly, while other components of
the current account are calculated only on a quarterly basis.

–12.2

SOURCE: Department of Commerce, Bureau of Economic Analysis.
NOTE: Components may not sum to total due to rounding.

UNDERSTANDING THE
CURRENT ACCOUNT

1 This measure has the advan-

258.3
–270.5

The most comprehensive measure of
the U.S. trade position is the current account,
which is comprised of four categories. A
listing of these categories and their magnitudes in 1998 is shown in Table 1, and the
current account’s recent behavior over
time is illustrated in Figure 2.

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

12

S E P T E M B E R / O C T O B E R 19 99

grown. Before 1998, the income-on-investments component represented a net inflow
of payments. Since then, this component
has reflected a net outflow as interest payments on foreign investment in the United
States have risen above payments of interest
on U.S. investments overseas. Nevertheless,
the magnitude and variability of this component contribute little to the behavior of the
overall current account.
The final category is net unilateral
transfers. Because the United States is a
major donor country in economic aid, this
category is consistently in a deficit position.2
As in the case of the investment-income
component, net unilateral transfers are fairly
small, and contribute little to the magnitude
or variability of the overall current account.

Figure 3

Current Account as a Percent of GNP,
1870-1998
Annual Data
Percent
7
6
5
4
3
2
1
0
–1
–2
–3
–4
1870
1890
1910
1930
1950
1970
1990
1880
1900
1920
1940
1960
1980
2000
Historical series is from International Historical Statistics, The Americas 1750-1993,
4th Edition by B.R. Mitchell.

Putting the Deficit in Perspective
As shown in Figure 1, the current
account appears quite volatile over the past
decade or so, and recently has approached
unprecedented levels. It is more meaningful, however, to gauge the magnitude of the
current account deficit against the size of
the total economy. In a growing economy,
it is perfectly natural for the absolute magnitude of trade flows to be increasing over
time. Hence, when we look at the current
account deficit relative to the total production or income in the U.S. economy, the
recent decline in our net export position
—while still large—is not entirely unprecedented. To illustrate this point, Figure 3
shows the U.S. current account as a fraction
of gross national product (GNP)—a broad
measure of total economic activity.
Although the current account deficit was
a record $221 billion in 1998, this figure
represented only 2.6 percent of GNP.
In relative terms, the peak deficit of the
1980s was larger, reaching 3.5 percent of
GNP in 1987.
Figure 3 also adds a longer historical
perspective to the analysis.3 It shows that
even though the relative magnitude of current account fluctuations in the 1980s and
1990s is greater than during the 1960s and
1970s, swings in the U.S. current account
balance in recent years are not quite as

exceptional in the context of the past century or more.

The Determinants of Deficits
The recent steep decline in the U.S.
trade position is significant, however, and
perhaps not something we should simply
dismiss. Deficits often are cited as either a
cause or a symptom of economic weakness.
The underlying implication of such a position is that selling is good, while buying is
bad. When stated this starkly, the assumption loses much of its intuitive appeal.
In truth, deficits are neither causes nor
symptoms of weakness, but are among the
many macroeconomic quantities that are
determined jointly by the decisions and
interactions of households, firms, and governments in the United States and abroad.
In the short-run, the current account can
be affected by exchange rate fluctuations—
which alter relative prices of imports and
exports—and by differences in income
growth at home and abroad. In fact, one
of the fundamental forces behind the recent
widening of our trade deficit has been the
strength of the recent U.S. expansion relative to the growth rates of our major trading
partners. As U.S. income growth outpaces
growth abroad, our demand for both

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

13

2 A notable exception was in

1991, when payments to the
United States from allies in the
Persian Gulf war resulted in a
net inflow in the unilateral
transfers account.
3 Data for years prior to 1960

are from Mitchell (1998).
GNP (rather than GDP) is used
as the measure of aggregate
economic activity to maintain
consistency with the historical
data.

S E P T E M B E R / O C T O B E R 19 99

THE SIMPLE ALGEBRA OF SAVING, INVESTMENT,
AND THE CURRENT ACCOUNT
where the superscript P designates private saving. The government also saves
(or dissaves) to the extent that tax revenues exceed (or fall short of)
government spending:

To derive the fundamental relationship among saving, investment, and the
current account, one must begin with
the national income accounting identity, which states that the total quantity
of goods produced domestically (Yprod)
and imported (M) are used for consumption (C), investment (I), purchased by
the government (G) or exported (X):
(1)

(3)

Noting that every transaction involves a
matched sale and purchase, aggregate
equilibrium requires that the total value
of goods produced is equal to the total
value of income Yprod = Yinc . Using
this equilibrium condition, and substituting the definitional relationships (2)
and (3) into (1) yields the savings/
investment/current account nexus:

Yprod + M = C + I + G + X,

or, in a more conventional form,
(1')

Yprod = C + I + G + NX,

where NX = X – M represents net
exports.

(4)
Household income (Yinc ) is used to
purchase consumption goods, save for
the future (S ), and pay taxes (T ):
(2)

NX = (SP + SG) – I.

Consequently, a trade surplus is associated with an excess of saving over
investment, while a trade deficit occurs
when saving falls short of investment.

Yinc = C + SP + T,

domestic goods and imports rise, while
foreign demand for our exports languishes.
This is one sense in which a current
account deficit reflects underlying strength
in the U.S. economy.
Even more fundamentally, the current
account or net export balance reflects the
outcome of the collective saving and
investment decisions in an economy. (See
shaded insert.) The relationship can be
summarized as
(1)

SG = T – G.

(2)

National Savings = Private Saving
– Government Deficits.

To understand this relationship more
intuitively, note that a trade deficit reflects
an excess of purchases over sales. Just as
is the case for a household or a business
firm that has current expenses exceeding
current income, the difference must be
financed through borrowing. Whether or
not this borrowing is wise depends on
what is being purchased. For example, a
household that is continually running up
credit card debt to finance current consumption, or a firm that is accumulating debt to
cover operating losses, might well be following an unwise and unsustainable practice. On the other hand, when borrowing
is undertaken to finance investments that
will yield a flow of profits or services over

Net Exports = National Saving –
Investment,

where the relevant measure of national
saving includes both private sector saving
and government saving (which is positive
for government surpluses, negative for
deficits), and

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

14

S E P T E M B E R / O C T O B E R 19 99

Figure 4

Fixed Investment and Net Exports as a Percent of GDP
Quarterly Data
Percent
19

Fixed Private Domestic Investment

17
15
13
11
1960
Percent
1
0
–1
–2
–3
–4
–5
1960

1965

1970

1975

1980

1985

1990

1995

1985

1990

1995

Net Exports

1965

1970

1975

1980

time, it is a perfectly sound policy. The
question of whether our national current
account deficit is good or bad similarly
hinges on the questions of why we are borrowing from the rest of the world, and
what we are doing with the resources we
are borrowing.
The relationship expressed in equation 1
represents a complex interaction of households, firms, and governments both at
home and abroad. As such, it can be misleading to think of a clear, consistent
causal relationship among the various
components of the equation. Rather, it
should be interpreted as summarizing an
accounting identity that must hold in the
context of all the components of the equation being affected simultaneously by overall economic conditions.
Sometimes it is useful to identify possible paths of causality within the overall
relationship, however. For instance, much
was made during the 1980s of the “twin
deficits” of the United States—a combination of government deficits and current
account deficits. Although it is beyond
the scope of this article to discuss the
issues involved in evaluating the claim that
government budget deficits caused or con-

tributed to the trade deficits of the 1980s,
equations 1 and 2 demonstrate the plausibility of such a relationship. The basic
current account/savings/investment relationship in equation 1 also demonstrates
the conditions under which such an hypothesis would hold—namely that private
savings and investment do not adjust to
offset the effect of the government deficit.
Regardless of whether or not the relatively large current account deficits of the
1980s were related to government budget
deficits, that surely cannot be the explanation for the 1990s experience. The U.S.
government budget has been in a surplus
position since 1997.
The low savings rate of U.S. households
often is pointed to as one factor contributing to our negative current account and net
export position. Generally speaking, the
savings rate does not fluctuate markedly
enough to be a key determinant of fluctuations in the current account. The decline
of the personal savings rate throughout the
1990s—falling from over 5 percent at the
beginning of the decade to nearly zero in
1998—has been a factor contributing to
the widening current account deficit. I
will suggest below, however, that this

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

15

S E P T E M B E R / O C T O B E R 19 99

Figure 5

ated with surpluses, or at least smaller
deficits. This is particularly true for the
1990s: As investment spending as a percent
of GDP has surged through most of 199698, the U.S. trade deficit has expanded
in tandem.

Savings and Investment in
a Large Open Economy
r
S*

S

S+S*

The Analytics of Investment,
Savings, and Deficits
r

Figures 5 and 6 illustrate a diagrammatic representation of the savings/
investment/current account relationship.
Figure 5 shows an economy in the situation of balanced trade. Domestic savings,
S, and the supply of potentially available
foreign savings, S*, both are represented as
increasing in response to a higher domestic
interest rate, r (relative to interest rates
abroad). Investment demand, I, declines
when domestic interest rates rise because
the interest rate is the key cost of financing investment spending. When the supply
of domestic savings matches investment
demand, as is the case in Figure 5, no net
inflow or outflow of foreign savings is
necessary (S*= 0) and the current account
is balanced.
In Figure 6, the demand for investment in new capital goods has increased.
Assuming for simplicity that the position
of the supply curves for domestic and foreign savings are unaffected, the quantities
of both domestic and foreign savings rise
(to S′ and S*′) in response to the upward
pressure on the interest rate. Investment
spending rises and the country experiences a current account deficit equal to
the shortfall of domestic savings relative
to investment, I′ – S′.
Note that if the opportunity to draw
on the pool of foreign savings was not
available in this instance, the increase in
investment demand could only be financed
by domestic savings (the intersection
between the S and I curves in Figure 6).
If this were the case, the interest rate
would have to rise further in order to
establish the balance between savings
and investment, limiting the amount of
investment spending that would actually
take place.

I
S, I

S=I

0

Figure 6

Investment Demand and
the Current Account
r
S*

S

S+S*

r′
r
I

{

CA Deficit

S, I

{

S=I S′ I ′

0 S*′

I′

decline reflects the very same underlying
forces driving the deficit, rather than being
a root cause.
Investment has been remarkably strong
during the current expansion. In 1996, fixed
private domestic investment as a percent of
(gross domestic product) GDP matched its
previous peak of 15.0 percent. In 1997 and
1998, investment spending rose to new
record highs of 15.7 percent and 16.8 percent of GDP. Generally speaking, large
swings in investment correspond to
commensurate movements in the trade
deficit, as illustrated in Figure 4.
Although the relationship is not exact,
there is a clear tendency for large upswings
in investment to be associated with widening
trade deficits, and for troughs to be associ-

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

16

S E P T E M B E R / O C T O B E R 19 99

DEFICITS AND THE NEW
ECONOMY

increase the demand for domestic labor
and capital. To the extent that investment
spending rises to meet higher demand for
physical capital, this type of supply shock
also tends to give rise to a current account
deficit—as described in the previous section.
The two types of supply shocks differ
in key respects, however. A decline in the
price of an imported factor of production,
like oil, often is reversed—witness the
increases in oil prices in early 1999. Investment demand will increase only to the extent
that productive capacity can be brought
online and maintained to exploit the favorable cost environment. In and of itself, a
temporary oil price decline is more likely
to increase capital utilization, rather than
capital investment. Moreover, a temporary
increase in economic activity would be
expected to raise aggregate savings, as households set aside some of the windfall income
gains for the future. Hence, domestic savings and investment demand both rise, and
there is little, if any, pressure for widening
trade and current account deficits.
The adaptation of new technologies to
the production process, on the other hand,
is more likely to be associated with a sustained increase in investment as new equipment replaces “vintage” capital.8 To the
extent that capital productivity is expected
to rise permanently (or at least for an
extended period of time), the rise in investment demand will be larger than it would
be for a temporary supply shock. At the
same time, domestic savings might rise
very little—and might even fall, which has
happened during the 1990s. This is because
there is less incentive to set aside a portion
of the increase in income for the future, with
the future looking so bright. Consequently,
longer-lasting supply shocks would be
expected to induce larger current account
movements than more short-term shocks.

With this analysis in mind, what can
we say about the relationship between the
widening trade deficit of the 1990s and the
new economy?

What is the New Economy?
Two, or sometimes three, factors generally are cited as the underlying positive
performance of the economy during the
1990s.4 First is the adoption of new technologies in information processing and
telecommunications. A second factor is
the world-wide commodity glut that has
caused sharp declines in the prices of some
key U.S. imports—particularly oil. An
additional factor often cited is the competitive effects of globalization.
The globalization argument suggests
that competition from abroad has forced
U.S. firms to keep costs down and prompted
workers to scale back expected wage
increases. While it is undoubtedly true
that foreign competition is an important
consideration for many firms, there is little
empirical evidence that foreign competition significantly affects wages or aggregate
income in the United States.5 Even though
trade has taken on increased prominence
in the composition of economic activity in
the United States, it still comprises only a
small share of total GDP. In 1998, exports
and imports represented only 13 percent
and 16 percent of GDP, respectively. For
all practical purposes, trends in the United
States depend on domestic factors, with
influences from abroad taking on a distinctively secondary role.6
It is the main argument of this article
that the U.S. trade position, in relation to
the rest of the world reflects the underlying
determinants of recent economic performance,
rather than being a fundamental cause in
and of itself.
The other two factors underlying the
new economy—low oil prices and technological advances—fall in the general category of supply shocks.7 Both would be
expected to raise economic output and to

Assessing Recent Deficits
The decline in U.S. net exports as a
fraction of national income eventually will
be reversed, either as the investment boom
runs its course or as foreigners become
increasingly unwilling to finance mounting

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

17

4 In his public speeches, Federal

Reserve Board Chairman,
Alan Greenspan (1997, 1999)
has described the factors underlying current strong economic
conditions.
5 Burtless (1995) provides a

survey of economic research
on the effect of trade on U.S.
wages and incomes.
6 Krugman (1996a,b) forcefully

and persuasively argues this
contention about the quantitative irrelevance of globalization,
which he calls “globaloney.”
7 These types of supply shocks

figure prominently in so-called
real business cycle theories.
8 The notion that technological

progress is embedded in
new capital replacing vintage
capital is explored by Jorgenson
(1966) and more recently
by Greenwood, et al (1997).
Greenwood et al find that as
much as 60 percent of postwar productivity growth can
be attributed to this type of
investment-specific technological change.

S E P T E M B E R / O C T O B E R 19 99

is a recipe for disaster, while borrowing to
invest in assets that will pay off in future
flows of goods and services is more likely
to be a prudent course.
Figure 7 considers one dimension of
the question: “What are we doing with the
borrowing?” Looking literally at the composition of imports, we see that the rise in
the capital goods imports as a share of
total imports during the 1990s has been
remarkable, rising from around 25 percent
at the beginning of the decade to more
than 44 percent in 1997 and 1998. Figure
8 illustrates an important feature of the
composition of total investment during the
1990s. The share of investment in information processing equipment and technologies
as a fraction of total investment has been
rising steadily since the mid-1970s, but
has increased dramatically during the
latter half of the 1990s.
Moreover, the United States is taking
the world lead in investing in cutting-edge
technologies. In 1997, for example, spending on information technology accounted
for a full 4.5 percent of U.S. GDP, compared
to only 2.6 percent in Japan and 2.3 percent
in Western Europe (Koretz, 1999).
These measures suggest that unprecedented rates of investment in the latter half
of the 1990s are associated with the widespread and rapid adoption of new technologies. To the extent that these investments
do, in fact, pay off in future higher productivity and output growth, undoubtedly we
will look back on this period as setting the
stage for what truly will be a new economy.
Until very recently, there has been little
indication that the adoption of new technologies has resulted in any significant
gains in productivity. In fact, the early
stages of the 1990s’ economic expansion
were characterized by very slow productivity and employment growth by historical
standards. This is consistent with economic models of technological advancement,
however.9 During the early stages of technological breakthroughs, like those we are
witnessing in information processing and
telecommunications, a period of slow
growth is predicted as new technologies
are integrated and adapted to production

Figure 7

Capital Goods Imports as a Percent
of Total Merchandise Imports
Quarterly Data
Percent
50
45
40
35
30
25
20
1989

1991

1993

1995

1997

1999

Figure 8

Information Processing Equipment as
a Percent of Total Fixed Investment
Quarterly Data
Percent
50
45
40
35
30
25
20
15
10
5
0
1960
1965

9 Theoretical analyses of the

effects of breakthroughs in such
general purpose technologies
are explored in depth in Aghion
and Howitt (1998).

1970

1975

1980

1985

1990

1995

deficits and the debt. The question of
whether the reversal is likely to take place
as an orderly adjustment, or as a “crashand-burn” scenario, is crucial for evaluating the prospects for continued economic
strength suggested by advocates of the new
economy view. Which of these scenarios is
more likely depends, in turn, on the factors
underlying the burgeoning trade deficit.
The key question to ask is: “What are
we doing with the resources that we’re
borrowing from the rest of the world?”
Recalling the analogy to individual
households or businesses, we maintain that
borrowing to finance frivolous consumption

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

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S E P T E M B E R / O C T O B E R 19 99

processes. Only after this transition phase
does productivity rise. The relatively high
and rising rates of productivity for the
United States during the latter part of 1998
and early 1999 might forebode the beginning of long-awaited productivity gains.
Allen (1997) assesses various theories
explaining the lack of obvious productivity
gains over the course of the 1990s. He
cites as an historical precedent the work of
David (1990), who compared the modern
information technology revolution to the
invention of the electric dynamo in the
nineteenth century. David suggested that
fully exploiting the new technology represented by the dynamo took decades. In
the meantime, its effect on productivity
lagged its ultimate potential.
If the analogy holds true, it is not surprising that productivity growth has not
yet accelerated as much as one might think
with the adoption of new technology. The
ultimate benefits of adopting new technologies only will become apparent over
the course of years to come. Once the initial surge in investment demand subsides,
we would expect the deterioration in the
U.S. current account to show signs of
reversal, suggesting that the economic
expansion associated with this transition
has reached a more mature stage.

is strong, but in transition. A turnaround
of the deficit is likely to be an important
indicator of when that transition is complete.
Only after we reach this more mature phase
of the current economic expansion will we
be able to fully evaluate the claims of those
who suggest that we are on the threshold
of a new economy in which rising rates of
productivity and economic growth will last
far into the future.

REFERENCES
Aghion, Philippe, and Peter Howitt. Endogenous Growth Theory, MIT
Press, 1998.
Allen, Donald S. “Where’s the Productivity Growth (from the
Information Technology Revolution)?” this Review (March/April
1997), pp. 15-25.
Burtless, Gary. “International Trade and the Rise in Earnings Inequality,”
Journal of Economic Literature (June 1995), pp. 800-16.
David, Paul. “The Dynamo and the Computer: An Historical Perspective
on the Modern Productivity Paradox,” The American Economic Review
(May 1990), pp. 355-61.
Greenspan, Alan. Remarks at the Annual Convention of the American
Bankers Association, Boston, Massachusetts, October 5, 1997.
________. “The American Economy in a World Context,” Remarks
at the 35th Annual Conference on Bank Structure and Competition of
the Federal Reserve Bank of Chicago, Chicago, Illinois, May 6, 1999.
Greenwood, Jeremy, Zvi Hercowitz, and Per Krussell. “Long-Run
Implications of Investment-Specific Technological Change,” The
American Economic Review (June 1997), pp. 342-62.

CONCLUSION

Jorgenson, Dale W. “The Embodiment Hypothesis,” Journal of Political
Economy (February 1966), pp. 1-17.

This article has described the basic
determinants of the current account, challenging the common, but simple notion
that trade deficits are inherently bad. In
fact, deficits are neither good nor bad:
Rather, they are reflections of the more
fundamental underlying forces affecting
the economy.
In the context of the U.S. economy
during the 1990s, rising trade and current
account deficits are consistent with the
notion that strong investment spending is
associated with the adoption of new technologies, with the anticipation of rapid
economic growth in the future suppressing
domestic saving. The resulting weakness
of the U.S. current account balance is,
therefore, a reflection of an economy that

Koretz, Gene. “Info Tech: Who’s Spending What,” Business Week
(May 3, 1999), p. 27.
Krugman, Paul R. Pop Internationalism, MIT Press, 1996a.
________. “The Adam Smith Address: What Difference Does
Globalization Make?” Business Economics (January 1996b), pp. 7-10.
Mitchell, B.R. International Historical Statistics: The Americas 17501993, Stockton Press, 1998.

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S E P T E M B E R / O C T O B E R 19 99

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

20

S E P T E M B E R / O C T O B E R 19 9 9

Donald S. Allen is an economist for the Federal Reserve Bank of St. Louis. Thomas A. Pollmann provided research assistance.

Seasonal
Production
Smoothing

inventory/production decisions. For example,
Carpenter and Levy (1998) use frequency
domain analysis and find a large and statistically significant average squared coherence
between inventory investment and the change
in output in the manufacturing sector at
both seasonal and business-cycle frequencies.
It seems appropriate, therefore, to focus
some attention on inventory decisions at
seasonal frequencies.
In this paper we look for evidence of
seasonal production smoothing in seasonally
unadjusted monthly data on manufacturing
and retail inventories and sales. Using
detrended, seasonally unadjusted data we
find that the variance of production is less
than the variance of sales for 23 out of 35
industries. The equivalent test using seasonally adjusted data found none with
production varying less than sales. We
interpret this as stronger evidence of production smoothing than found in previous
literature.
The Fourier series of the inventory-tosales (I/S) ratio of the industries with the
lowest variance of production relative to
sales revealed strong seasonal components
(annual, six months, and three months).
A strong seasonal component in the I/S
ratio suggests a possible negative seasonal
correlation between sales and inventory
and is an intuitive indication that
smoothing occurs at higher frequencies.2
The results confirm Ghali’s (1987) finding
of seasonal smoothing using detrended,
seasonally unadjusted data for the cement
industry. The results also suggest that a
model other than production smoothing may
be more appropriate for explaining trend
movements in production relative to sales.

Donald S. Allen

I

nventory investment dynamics appear to
dominate the economy’s historical movement around its long-run path. Blinder
and Maccini (1991) show that the average
movement in inventory investment during
post-war recessions account for 87 percent
of the peak-to-trough movement in Gross
National Product (GNP).1 Because inventory
fluctuations have historically played such a
major role in business cycles (and possibly
seasonal fluctuations), it is important to
understand the theoretical motivation for
inventory holdings and the implied dynamics.
The received view, established by Holt,
Modigliani, Muth and Simon (1960), is that
inventories are used to smooth production
in the presence of increasing marginal cost
(convex costs). An empirical fact of inventory investment, however, is that production
is more volatile than sales. The failure to
confirm production smoothing empirically
has been explained by inadequacies of the
data or exceptions to the abstraction of
convex costs.
Intuition suggests that even with convex
costs, firms may not be likely to smooth
production over periods longer than a
year. Production horizons are likely to be
shorter than a year and inventory holding
costs may make it uneconomical to hold
inventory for as long as a year. Many
industries have well documented seasonal
patterns in demand allowing them to plan
production in concert with available capacity,
required lead times, and labor market flexibility. In addition, evidence has been
uncovered suggesting that seasonal fluctuations in output also can be affected by

Background and Literature Survey
Holt, Modigliani, Muth, and Simon (1960)
established the analytical framework demonstrating that optimizing firms facing convex
production costs and uncertain demand
are motivated to smooth production and

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

21

1

There is some debate whether
more recent practices still
induce this effect. Allen (1995)
suggests that recent improvements in inventory management may be reducing the
"boom/bust" effects of inventory swings, but empirical confirmation is not strong. Filardo
(1995) finds no evidence of a
muted inventory cycle.

2

If inventories are high when
sales are low, and vice versa,
then the I/S ratio will fluctuate
accordingly. Obviously, if inventory remained constant and
sales varied seasonally, the I/S
ratio also would fluctuate seasonally, so this is not an exact
metric of smoothing. The seasonality of the ratio does suggest, however, the frequency
over which smoothing is taking
place.

S E P T E M B E R / O C T O B E R 19 9 9

use inventories to buffer demand shocks.
If the marginal cost of production is increasing, then storing output during periods of
low demand is prudent as long as storage
costs are sufficiently low. (See the shaded
insert on page 5.) Much of the research
in inventory since Holt et al., has focused
on the efficacy of using the productionsmoothing paradigm at the macroeconomic level. If firms use inventories to
smooth production, then production should
vary less than sales. Empirical testing of
this hypothesis has yielded mixed results.
Using a simple test of the ratio of the variance of production to the variance of sales,
a majority of researchers have found a ratio
greater than 1.0, contradicting the theory.
As a rule, data on production are not
available. Production can be readily
estimated, however, by adding current
period sales to the change in inventory
from last period. If production exceeds (is
less than) sales in a given period, then the
difference must go to increasing (decreasing)
inventories. This can be represented by
the following equation:

• Cost shocks are present,
• Firms see demand shocks before
they make their production
decisions,
• Demand shocks build before
they decay,
• Or, technological parameters dictate
a rapid speed of adjustment.
If firms do not face convex production
costs, production smoothing is not optimal.
Ramey (1991) finds indication of nonconvex
costs in some industries. Blinder and Maccini (1991) observe that wholesale and
retail trade, and the materials and supplies
portion of manufacturing inventory, make
up a large portion of total inventories and
are likely to face nontrivial “quasi-fixed”
costs of ordering. This type of cost structure makes an (S,s) inventory rule more
economical. That is, firms will wait until
inventory falls below a trigger point (s)
then order sufficient stocks to raise inventory to an upper bound (S). This way the
quasi-fixed costs are spread over a larger
quantity. This behavior, sometimes called
“bunching” will result in a higher volatility
of production than sales. This leads Blinder
and Maccini to conclude that the (S,s) paradigm is more consistent with the empirical
evidence.
Another source of empirical failure may
be the data. Ghali (1987) demonstrated
that seasonal adjustment and aggregation
will remove evidence of seasonal smoothing,
and Lai (1991) shows that aggregation can
distort the data sufficiently to negate production-smoothing tests. Some researchers,
using disaggregated physical product data,
find some support for production smoothing.
Fair (1989), and Krane and Braun (1991)
use disaggregated physical product data for
the United States and confirm smoothing
in several industries, while Beason (1993)
has similar success with Japanese data.
Dimelis and Ghali (1994) detect statistically
significant evidence of smoothing in disaggregated physical product data for three
out of five industries, using the variance

Pt = S t + ∆I t ,
where P is production, S is sales and ∆I is
the change in inventory. This fundamental
equation implies an important relationship
among the variances and covariance of P, S,
and ∆I:
Var( P ) = Var( S ) + Var( ∆I ) + 2Cov( S, ∆I )
For the variance of production to be less than
the variance of sales, the covariance of sales
and the change in inventories, Cov(S, ∆I)
must be negative and greater in absolute
value than half the variance of inventories.
Testing this covariance relationship,
Miron and Zeldes (1988) find no support
for production smoothing using both seasonally adjusted and unadjusted data after
removing an estimated linear trend from
monthly data. Blinder (1986) also finds
little empirical support for the basic production smoothing model. He identifies,
however, conditions under which the facts
could be compatible with production
smoothing, to wit, if:

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

22

S E P T E M B E R / O C T O B E R 19 9 9

bounds test introduced by West (1986)
and generalized by Kollintzas (1995).
Physical unit information is more
appropriate for testing the implications of
inventory management. It makes more
sense, when discussing the motivation for
holding inventory, to talk about the number
of cars in stock than the value. Unfortunately,
the most readily accessible data, particularly
at an aggregate level, are the nominal values
of inventory. One way of getting closer to
physical quantities is to remove the effects
of price changes. Finding the appropriate
price deflator to convert the nominal values
to real values is a difficult task. And, even
when data are converted to remove price
increases, trend growth in the real level of
sales also can disguise smoothing. If sales
are trending up (down), then production
will also trend up (down). If firms smooth
production annually and adjust the target
level of smoothed production each year, then
the variance induced by the trend growth
also will distort the smoothing measure.
Miron (1996) page 18 finds noticeably
less seasonal variation in price variables
than quantity variables.

Table 1

Industries Analyzed

Years of Data

All Manufacturing Industries

1/58 to 12/98

Stone, Clay and Glass (SIC 32)

1/58 to 12/98

Primary Metals (SIC 33)

1/58 to 12/98

Nonferrous and other Primary Metals

1/58 to 12/98

Fabricated Metal Products (SIC 34)

1/58 to 12/98

Industrial Machinery and Equipment (SIC 35)

1/58 to 12/98

Electrical Machinery (SIC 36)

1/58 to 12/98

Transportation Equipment (SIC 37)

1/58 to 12/98

Instruments/Related Products (SIC 38)

1/58 to 12/98

All Other Durable Goods

1/58 to 12/98

Nondurable Goods Manufacturing Industries

1/58 to 12/98

Tobacco Products (SIC 21)

1/58 to 12/98

Textile Mill Products (SIC 22)

1/58 to 12/98

Paper and Allied Products (SIC 26)

1/58 to 12/98

Chemical and Allied Products (SIC 28)

1/58 to 12/98

Petroleum and Coal Products (SIC 29)

1/58 to 12/98

Automotive Equipment

1/58 to 12/98

Home Goods and Apparel

1/58 to 12/98

Consumer Staples

1/58 to 12/98

Machinery and Equipment *

1/68 to 12/98

Business Supplies

1/58 to 12/98

Construction Materials/Supplies /Intermediate

1/58 to 12/98

Capital Goods Industries

1/58 to 12/98

Producers’ Durable Equipment *

1/68 to 12/98

Household Durable Goods

1/58 to 12/98

All Retail

1/87 to 12/98

Retail: Durable Goods Stores

1/87 to 12/98

Retail: Bldg Matls/Hdwre/Garden Supply/
Mobile Home Dealers (SIC 52)

1/87 to 12/98

Retail: Automotive Dealers (SIC 55)

1/87 to 12/98

Retail: Furniture, Home Furnishings &
Eqpt Stores (SIC 57)

1/87 to 12/98

Retail: Nondurable Goods Stores

1/87 to 12/98

Retail: General Merchandise Group Stores (SIC 53)

1/87 to 12/98

Retail: Department Stores ex Leased
Departments (SIC 531)

1/87 to 12/98

Retail: Food Stores (SIC 54)

1/87 to 12/98

DATA SOURCE AND TRANSFORMATION

Retail: Apparel and Accessory Stores (SIC 56)

1/87 to 12/98

The data used are from the Census
Bureau’s monthly data on manufacturing

* Data available starting in 1968.

Seasonal movements in both real and
nominal price variables are noticeably
smaller than those in quantity variables.
For example, the standard deviation of
the seasonals in the growth rates of prices
is 0.2 percent, and seasonal dummies
explain only 3.1 percent of the total
variation. The same conclusions hold
qualitatively for nominal interest rates,
real interest rates, nominal wages, and
real wages. Miron (1996).
This observation means that if we remove
the trend from seasonally unadjusted data,
the high frequency movements are more
likely to reflect changes in quantities. This
provides justification for the data transformation that we discuss in the next section.

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

23

S E P T E M B E R / O C T O B E R 19 9 9

Figure 1

for the most recent 10 years for the Stone,
Clay and Glass manufacturing industry.
The smooth line shows the trend that is
extracted to get the filtered data.

Stone, Clay and Glass Products
(Monthly Sales, Seasonally Unadjusted, Millions of Current Dollars)
9.2

Frequency Domain

9
8.8

Looking at the data in the frequency
domain highlights the effect of the seasonal
adjustment and the HP filter.3 The Fourier
series representation decomposes the data
into the contribution of individual frequencies to the variance. The vertical axis
indicates the value of the coefficient applied
to that frequency. If there is a trend present,
there will be a large contribution from the
low frequencies. If there is a strong contribution at a particular frequency compared
to others, there will be a noticeable spike at
that frequency. The Fourier series displayed
here are truncated at 1.0 to focus attention
on the higher frequency components.
Figure 2 compares the Fourier series of the
logarithm of sales for Stone, Clay and Glass
Industries for the raw seasonally unadjusted
series, the seasonally adjusted series, and
the series after an HP filtered trend is
removed from the raw (unadjusted) data.
The spikes in the unadjusted data occur at
cycles of 12 months, six months, four months
and 3 months, reflecting harmonics of the
seasonal cycle. The appearance of harmonics
in the data may reflect the aggregation of
individual firms with seasonal cycles that
are offset, (i.e. some may have peak sales
in winter while others peak during the
summer). The seasonally adjusted data
have no spikes. The HP filtered data show
the absence of the low frequency components
(zero near the origin), while the high frequency contributions appear to be intact.
Figure 3 shows the I/S ratio of selected
industries, and Figure 4 shows the Fourier
series of the ratios. In the next section, we
report the results of the variance ratio test,
then compare this to the frequency spectra
of the I/S ratios of the sectors.

Log Levels

8.6
8.4
Trend
8.2
8811 8911 9011 9111 9211 9311 9411 9511 9611 9711
0.2
Detrended Log

0.1
0
–0.1
–0.2
–0.3

8811 8911 9011 9111 9211 9311 9411 9511 9611 9711

and retail inventories and sales, seasonally
unadjusted and adjusted. Production is
computed by adding the change in inventories to sales each period. A total of 35
series, 25 manufacturing and 10 retail,
were analyzed. Table 1 lists the series and
the years of data used. Most manufacturing
data covered the period between 1958 and
1998. Retail data covered the period
between 1987 and 1998.

HP Filtering

3

Harvey (1994), chapter 6, provides an excellent exposition of
frequency domain analysis.

After taking logs of the data, a nonlinear
trend was removed using a Hodrick-Prescott
(HP) filter with a penalty set to 14,400, the
default value for monthly data in Eviews.
This method removes the “low frequency”
components from the data, whether due to
price increase or trend growth. Figure 1
illustrates the transformation of the data

Results
The typical measure of production
smoothing is the ratio of the variance of

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

24

S E P T E M B E R / O C T O B E R 19 9 9

THE PRODUCTION SMOOTHING WITH TREND
Figure A

Figure B

Periodic Production Smoothing
7

$

Production

6

P3

5
C2

P2

4

(C 1+C 2)/2

A

Cbar

3
2

B

C1

P1

Addition to Inventory
Reduction to Inventory

1
Q1

Qbar

Q2

Sales

Period 1

Period 2

Period 3

Quantity

Figure A illustrates the production smoothing motivation when increasing marginal
costs exist. If Q 1 and Q 2 represent the demand in periods 1 and 2 respectively, then
the point A represents the average cost, (C1 + C2)/2 , if Q 1 is produced during period 1
and Q 2 is produced during period 2. Point B represents the average cost, Cbar, if
(Q 1+Q 2)/2 is produced during both periods, with the excess produced in period 1 carried over to period 2. The trade off is between the cost of storage for one period
versus the saving from smoothing. The difference between A and B must be greater
than the cost of holding inventory to justify smoothing. Note also that if mean
demand is expected to decrease below current production for an extended period (i.e.,
Q 2 is current demand and Q 1 is next period's expected demand), then it becomes
optimal to reduce production and serve part of the current demand from inventory.
Thus production-smoothing motivation can lead to level changes if forecast sales
change direction.
Figure B illustrates how periodic adjustments to production to match trend
growth can result in lumpy movements in production even with production
smoothing. The blue line indicates trend growth in sales with a seasonal component.
If sales are forecast and production planned at the beginning of each period, then P1
represents the production level for the first period, P2 the second period, and P3 the
third period. During the first half of each period, production exceeds sales and the
difference goes into inventory. During the second half of the period, production is
less than sales and the difference is made up out of inventory. Each period,
production is smoothed. Because of the trend growth in sales, however, production
jumps at the start of each new period. If data over all three periods are used, the variance of production may exceed the variance of sales.

4

production to the variance of sales.4 A
ratio more than 1.0 implies that production
is more volatile than sales and, therefore,
contradicts the smoothing hypothesis. A

negative correlation between sales and the
change in inventory may be insufficient to
produce a lower variance in production
than in sales. Tables 2, 3, and 4 summarize

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

25

A more appropriate test of production smoothing would be a
comparison of the variance of
production to the variance of
forecasted sales.

S E P T E M B E R / O C T O B E R 19 9 9

Table 2

Manufacturing
Variance

Variance

Covariance

Variance

Sales

Inventory
Investment

Sales and
Inven. Invest.

Production

Variance Ratio

All Manufacturing Industries

NSA
SA

0.00272
0.00061

0.00029
0.00014

–0.00015
0.00009

0.00270
0.00092

0.99554
1.50964

Stone, Clay and Glass (SIC 32)

NSA
SA

0.00883
0.00117

0.00076
0.00023

–0.00176
0.00000

0.00606
0.00141

0.68635
1.20013

Primary Metals (SIC 33)

NSA
SA

0.01106
0.00731

0.00072
0.00054

–0.00015
0.00035

0.01148
0.00855

1.03841
1.16922

Nonferrous and other Primary Metals

NSA
SA

0.00729
0.00462

0.00059
0.00037

0.00010
0.00021

0.00808
0.00541

1.10774
1.17196

Fabricated Metal Products
(SIC 34)

NSA
SA

0.00399
0.00104

0.00112
0.00065

–0.00027
0.00011

0.00456
0.00190

1.14233
1.83141

Industrial Machinery and Equipment (SIC 35)

NSA
SA

0.00721
0.00133

0.00123
0.00050

–0.00089
0.00029

0.00667
0.00240

0.92451
1.80271

Electrical Machinery (SIC 36)

NSA
SA

0.00496
0.00104

0.00086
0.00034

–0.00020
0.00022

0.00542
0.00182

1.09311
1.75383

Transportation Equipment
(SIC 37)

NSA
SA

0.01422
0.00388

0.00118
0.00039

–0.00148
–0.00014

0.01244
0.00399

0.87488
1.02722

Instruments/Related Products
(SIC 38)

NSA
SA

0.00418
0.00072

0.00121
0.00058

–0.00074
0.00003

0.00391
0.00137

0.93591
1.89900

All Other Durable Goods

NSA
SA

0.00634
0.00155

0.00048
0.00024

–0.00046
0.00012

0.00590
0.00204

0.92985
1.31248

Nondurable Goods
Manufacturing Industries

NSA
SA

0.00164
0.00038

0.00019
0.00011

–0.00006
0.00005

0.00171
0.00058

1.03902
1.52003

Tobacco Products (SIC 21)

NSA
SA

0.01631
0.00396

0.02009
0.00469

–0.00220
–0.00005

0.03199
0.00855

1.96182
2.15891

Textile Mill Products (SIC 22)

NSA
SA

0.00668
0.00139

0.00099
0.00025

–0.00073
0.00012

0.00620
0.00188

0.92822
1.35705

Paper and Allied Products
(SIC 26)

NSA
SA

0.00227
0.00109

0.00023
0.00011

0.00008
0.00014

0.00265
0.00148

1.16834
1.35517

Chemical and Allied Products
(SIC 28)

NSA
SA

0.00338
0.00096

0.00038
0.00019

–0.00036
0.00010

0.00304
0.00134

0.89854
1.40595

Petroleum and Coal Products
(SIC 29)

NSA
SA

0.00534
0.00423

0.00080
0.00058

0.00032
0.00036

0.00678
0.00552

1.27019
1.30557

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

26

S E P T E M B E R / O C T O B E R 19 9 9

Table 3

"Other" Manufacturing
Variance

Variance

Covariance

Variance

Sales

Inventory
Investment

Sales and
Inven. Invest.

Production

Variance Ratio

Automotive Equipment

NSA
SA

0.02848
0.00898

0.00097
0.00027

–0.00213
–0.00012

0.02518
0.00901

0.88435
1.00339

Home Goods and Apparel

NSA
SA

0.00898
0.00088

0.00138
0.00024

–0.00195
0.00014

0.00647
0.00140

0.72049
1.58834

Consumer Staples

NSA
SA

0.00133
0.00032

0.00035
0.00014

0.00004
0.00002

0.00177
0.00049

1.32663
1.52705

Machinery and Equipment

NSA
SA

0.00722
0.00096

0.00130
0.00041

–0.00142
0.00012

0.00567
0.00161

0.78549
1.68163

Business Supplies

NSA
SA

0.00183
0.00051

0.00033
0.00019

–0.00015
0.00004

0.00186
0.00078

1.01557
1.54868

Construction Materials/Supplies /Intermediate

NSA
SA

0.00563
0.00124

0.00041
0.00020

–0.00052
0.00012

0.00499
0.00167

0.88617
1.35123

Capital Goods Industries

NSA
SA

0.00694
0.00080

0.00144
0.00048

–0.00163
0.00010

0.00513
0.00148

0.73934
1.85593

Producers’ Durable Equipment

NSA
SA

0.00667
0.00120

0.00083
0.00033

–0.00066
0.00010

0.00619
0.00173

0.92711
1.43817

Household Durable Goods

NSA
SA

0.00840
0.00114

0.00149
0.00047

–0.00133
0.00018

0.00723
0.00196

0.86042
1.72187

Manufacturing

the results, showing the variance of sales,
inventories and the covariance of sales and
the change in inventories. Of the 35 seasonally unadjusted series, there are only three
manufacturing industries with positive
covariances between sales and the change
in inventories: Nonferrous and Other Primary Metals (a sub-category of Primary
Metals); Paper and Allied Products; and, the
Petroleum and Coal Products. By contrast,
the covariances of all but three manufacturing
series with seasonally adjusted data are
positive. The seasonally adjusted retail data
indicate some with negative covariance of
inventory investment and sales, but none
sufficiently negative to result in a variance
ratio less than 1.0.

The variance ratio of the detrended
seasonally unadjusted data for all manufacturing is less than 1.0, but only barely;
leaving unanswered the question of whether
the production-smoothing model is adequate
at this level of aggregation. At the twodigit SIC level of aggregation, SIC codes
33, 34, and 36 have variance ratios greater
than 1.0 for the detrended log data, while
SIC codes 32, 35, 37, and 38, as well as the
“all other durable goods” category have
variance ratios less than 1.0. The implication is that most durable goods industries
smooth production over high frequency
periods.5 The seasonally adjusted data do
not show smoothing, indicating that

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

27

5

This implication holds at least if
we interpret production smoothing as meaning that the growth
rate of production varies less
than the growth rate of sales.

S E P T E M B E R / O C T O B E R 19 9 9

Table 4

Retail
Variance

Variance

Sales

Inventory
Investment

Covariance

Variance

Sales and
Inven. Invest.

Production

Variance Ratio

All Retail

NSA
SA

0.00630
0.00011

0.00222
0.00009

–0.00206
–0.00001

0.00439
0.00018

0.69691
1.68785

Retail: Durable Goods Stores

NSA
SA

0.00618
0.00046

0.00264
0.00038

–0.00116
–0.00004

0.00650
0.00077

1.05145
1.67262

Retail: Bldg Matls/Hdwre/Garden Supply/
Mobile Home Dealers (SIC 52)

NSA
SA

0.02100
0.00065

0.00199
0.00034

–0.00361
0.00003

0.01576
0.00104

0.75081
1.60598

Retail: Automotive Dealers (SIC 55)

NSA
SA

0.00805
0.00075

0.00402
0.00087

–0.00241
–0.00016

0.00727
0.00130

0.90217
1.72889

Retail: Furniture, Home Furnishings
& Eqpt Stores (SIC 57)

NSA
SA

0.01237
0.00041

0.00749
0.00058

–0.00483
0.00004

0.01021
0.00107

0.82485
2.63839

Retail: Nondurable Goods Stores

NSA
SA

0.00809
0.00006

0.00270
0.00004

–0.00325
0.00000

0.00430
0.00009

0.53181
1.45016

Retail: General Merchandise
Group Stores (SIC 53)

NSA
SA

0.04588
0.00011

0.01966
0.00037

–0.02139
–0.00004

0.02276
0.00041

0.49608
3.60050

Retail: Department Stores
ex Leased Departments (SIC 31)

NSA
SA

0.04906
0.00013

0.02083
0.00043

–0.02225
–0.00005

0.02539
0.00046

0.51750
3.70666

Retail: Food Stores (SIC 54)

NSA
SA

0.00190
0.00008

0.00019
0.00002

–0.00006
0.00000

0.00198
0.00010

1.04026
1.28350

Retail: Apparel and Accessory Stores (SIC 56)

NSA
SA

0.03814
0.00030

0.01931
0.00048

–0.01861
0.00002

0.02023
0.00082

0.53035
2.73757

removing the higher frequencies from the
data masks evidence of smoothing.
In the nondurable goods category in
Table 2, only Textile Mill Products (SIC
22) and Chemical and Allied Products
(SIC 28) have variance ratios less than 1.0
for the detrended log seasonally unadjusted
data. The aggregate nondurable goods
industries has a variance ratio greater than
1.0. Intuitively, we would expect production of some nondurables to be less amenable
to storage. For instance, Tobacco Products
may be largely influenced by crop size
rather than by demand, while demand may

be less elastic seasonally. Of the nine other
manufacturing sectors, which reflect a
lower level of aggregation, evidence of
smoothing is revealed in seven when seasonally unadjusted data are used. (See
Table 3). This suggests that aggregation
may be playing a role as well.

Retail Sector
The seasonally unadjusted data for the
retail sector reveal smoothing by most
industries, suggesting that some retail

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

28

S E P T E M B E R / O C T O B E R 19 9 9

firms may accumulate inventory in anticipation of
seasonal increases in sales. Retail Food Stores (SIC
54) and aggregate of Retail Durable Goods stores
are the only two of the 10 series that have a variance ratio higher than 1.0. Given that fixed costs
associated with transportation are likely to induce
(S,s) behavior at the retail level, detecting smoothing may appear to be contradictory. Here again,
however, the frequency of observation influences
the detection of the underlying decision rule.
It is likely that adjustments to inventory based on
the (S,s) rule takes place at frequencies less than
one month. So, on average, inventory moves
between upper and lower bounds within a month.
Consequently, monthly data reveals seasonal movements in the bandwidth, while obscuring higher frequency (S,s) movements. Seasonal smoothing at the
retail level does not preclude (S,s) behavior at
higher frequency. In addition, aggregation over a
large number of establishments is likely to dampen
high frequency movements.

Figure 2

Fourier Spectrum of Stone, Clay
and Glass Industries Sales
(Seasonally Adjusted and Unadjusted)
Seasonally Adjusted
1
0.8
0.6
0.4
0.2
π
—
6

ππ
—
2

2π
—–
3

5π
—–
6

π

5π
—–
6

π

Seasonally Unadjusted
1

CONCLUSIONS

0.8

Empirical evidence of production smoothing
has been relatively elusive. Part of the problem
appears to be the tendency to use seasonally
adjusted data. This paper finds that smoothing
takes place in a large proportion of manufacturing
industries at seasonal frequencies or higher.
Seasonal adjustment of the data removes this
evidence. Removing the trend from the data allows
us to exclude changes in production associated
with trend growth in sales. This confirms empirical results of Allen (1997B), which suggest that
inventory management at the firm level reflects
planned and unplanned changes. The trend component of production reflects planned additions to
inventory levels based on trend movement in sales,
while the higher frequency component of production reflects smoothing over shorter horizons.
Evidence of seasonal smoothing in the retail
sectors suggests that retail firms also manage
inventory to smooth seasonal fluctuations in sales.
Although smoothing is not generally associated
with retail inventory management, it is not inconsistent with (S,s) behavior at frequencies higher
than the observed data.
In summary, we find evidence of
production smoothing at relatively high
frequencies when the trend is removed from
seasonally unadjusted data. We interpret this to

0.6
0.4
0.2
π
—
6

π
—
3

ππ
—
2

2π
—–
3

π
—
6

π
—
3

ππ
—
2

2π
—–
3

HP Filtered
1
0.8
0.6
0.4
0.2

mean that using data that has been
seasonally adjusted and includes trend
growth, limits the ability to extract the

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

29

π
—
3

5π
—–
6

π

S E P T E M B E R / O C T O B E R 19 9 9

Figure 3

Inventory-to-Sales Ratios Selected Industries
Machinery and Equipment

Home Goods and Apparel
2.2

2.8
2.6

2.0
20

40

60

80

100

120

1.8

2.4
2.2
2.0

1.6

20

1.8

40

60

80

100

120

80

100

120

1.6
Capital Goods Industries

Stone, Clay and Glass Products

4.0
1.8
3.5
1.6
3.0
1.4
2.5
1.2
2.0

20
20

40

60

80

100

40

60

120

Blinder, Alan S. "Retail Inventory Behavior and Business Fluctuations,"
Brookings Papers on Economic Activity, 2 (1981), pp. 443-505.

underlying motivation for holding inventories. To the extent that seasonal cycles
mimic business cycles, analysis of production/inventory behavior at seasonal
frequencies may provide insights into business cycle dynamics.

_______. "Can the Production Smoothing Model of Inventory
Behavior be Saved?" Quarterly Journal of Economics, (August,
1986), pp. 431-53.
_______., and Louis J. Maccini. "The Resurgence of Inventory
Research: What Have We Learned?" Journal of Economic Surveys
(1991), pp. 291-328.

REFERENCES
Allen, Donald S. “A Multi-Sector Inventory Model," Journal of Economic
Behavior and Organization, (January 1997A), pp. 55-87.

Carpenter, Robert E., and Daniel Levy. "Seasonal Cycles, Business Cycles,
and the Comovement of Inventory Investment and Output," Journal of
Money, Credit, and Banking, (August 1998), pp. 331-46.

_______. "Do Inventories Moderate Fluctuations in Output?" this
Review, (July/August 1997B), pp. 39-50.
_______. "Changes in Inventory Management and the Business
Cycle," this Review, (July/August 1995), pp. 17-26.

Dimelis, Sophia P., and Moheb A. Ghali. "Classical and Variance Bounds
Tests of the Production Smoothing Hypothesis," International Journal
of Production Economics, (June 1994), pp. 15-22.

Beason, Richard. "Tests of Production Smoothing in Selected Japanese
Industries," Journal of Monetary Economics, (June 1993), pp. 381-94.

Fair, Ray C. "The Production-Smoothing Model is Alive and Well," Journal
of Monetary Economics, (November 1989), pp. 353-70.

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

30

S E P T E M B E R / O C T O B E R 19 9 9

Figure 4

Fourier Spectrum of Inventory-to-Sales Ratios, Selected Industries
Home Goods and Apparel

Machinery and Equipmentl

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

π
—
6

π
—
3

ππ
—
2

2π
—–
3

5π
—–
6

π
—
6

π

Capital Goods Industries

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2
π
—
3

ππ
—
2

2π
—–
3

5π
—–
6

π

2π
—–
3

5π
—–
6

π

Stone, Clay and Glass Products

1

π
—
6

π
—
3

ππ
—
2

2π
—–
3

5π
—–
6

π

π
—
6

π
—
3

ππ
—
2

Filardo, Andrew J. "Recent Evidence on the Muted Inventory Cycle,"
Federal Reserve Bank of Kansas City Economic Review, (second quarter
1995), pp. 27-43.

Krane, Spencer D., and Stephen N. Braun. "Production Smoothing
Evidence from Physical-Product Data," Journal of Political Economy,
(June 1991), pp. 558-81.

Ghali, Moheb A. "Seasonality, Aggregation and the Testing of the
Production Smoothing Hypothesis," The American Economic Review
(June 1987), pp. 464-69.

Lai, Kon S. "Aggregation and Testing of the Production Smoothing
Hypothesis," International Economic Review, (May 1991), pp. 391-403.
Miron, Jeffrey A., and Stephen P. Zeldes. "Seasonality, Cost Shocks, and
the Production Smoothing Model of Inventories," Econometrica, (July
1988), pp. 877-908.

Harvey, Andrew C. Time Series Models, Second Edition, (1994), The
MIT Press, Cambridge, Massachusetts.

Miron, Jeffrey A. The Economics of Seasonal Cycles, (1996),
Massachusetts Institute of Technology, Cambridge, Massachussets.

Holt, Charles C., Franco Modigliani, John F. Muth, and Herbert A. Simon.
Planning Production, Inventories, and Work Force (1960), PrenticeHall Inc., Englewood Cliffs, NJ.

Ramey, Valerie A. "Nonconvex Costs and the Behavior of Inventories,"
Journal of Political Economy, (April 1991), pp. 306-34.

Kollintzas, Tryphon. "A Generalized Variance Bounds Test with an
Application to the Holt et al. Inventory Model," Journal of Economic
Dynamics and Control, (Jan/Feb 1995), pp. 59-89.

West, Kenneth D. "A Variance Bounds Test of the Linear Quadratic
Inventory Model," Journal of Political Economy, (April 1986),
pp. 374-401.

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

31

S E P T E M B E R / O C T O B E R 19 9 9

Appendix

FOURIER SERIES

this sector while inventory shows more of
an annual cycle. Whereas the seasonally
unadjusted variance ratio of Stone, Clay
and Glass Products was 0.6864, the variance
ratio for Instruments and Related Products
was 0.9359.
For the three industries with positive
covariance between sales and the change
in inventory, Nonferrous and Other Metals
(Figure 1A) and Paper and Allied Products
(Figure 2A) show seasonal spikes in the I/S
spectra, while no significant seasonality is
depicted for Petroleum and Coal Products
(Figure 2A). The positive co-movement
between sales and inventory for all three is
observable in Figures 1B and 2B. For the
Petroleum and Coal industry the positive
co-movement between sales and inventory
eliminates all seasonal components from
the I/S ratio while the other two industries
show higher swings in sales than inventory,
leaving some seasonality in the ratio.

Figures 1A-3A in the appendix show
plots of the Fourier spectra of the I/S ratios,
and Figures 1B-3B show detrended sales
and inventory movements of all 35 series.
The horizontal axes of the plot of the spectra
are labeled in multiples of π. Annual
cycles are at π/6, cycles of 6 months are at
π/3, and so on. The magnitude of the spike
at each frequency gives an indication of
the dominant cycles. In Figure 1A, the
Fourier spectrum of the I/S ratio of the
Stone, Clay and Glass Products sector has
a high annual component (compared to 6month). Figure 1B shows for that industry
a negative correlation between detrended
inventory and sales. By comparison, the
Instruments and Related sector shows a
high 3-month (quarterly) component
(compared to annual) in Figure 1A. The
corresponding chart in Figure 1B shows
the high frequency composition of sales in

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

32

S E P T E M B E R / O C T O B E R 19 9 9

The charts for this appendix follow on pages 34-39.

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

33

Figure 1A

Fourier Series of Inventory-Sales Ratio
Stone Clay and Glass Products

All Manufacturing Industries

Primary Metals

1

1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

π
6

π
3

π
2

2π
3

5π
6

π

0

π
6

π
3

π
2

2π
3

5π
6

π

0

Fabricated Metal Products

Nonferrous and Other Primary Metals
1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

π
3

π
2

2π
3

5π
6

π

0

π
6

π
3

π
2

2π
3

5π
6

π

0

1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

π
6

π
3

π
2

2π
3

5π
6

π

0

π
6

π
3

π
2

2π
3

5π
6

π

0

1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

π
6

π
3

π
2

2π
3

5π
6

π

0

π
6

π
3

π
2

2π
3

π

π
2

5π
6

π

2π
3

5π
6

π

2π
3

5π
6

π

2π
3

π
6

π
3

5π
6

π
2

Tobacco Products

1

0

π
3

Nondurable Goods Industries

All Other Durable Goods

5π
6

2π
3

Instruments/Related Products

1

0

π
6

Transportation Equipment

Electrical Machinery

π
2

π

0

π
6

π
3

π
2

The Fourier Series shown in these charts are made up of complex numbers. Ther vertical scale measures the absolute values of the Fourier Series. The horizontal scale shows the frequency measured
on a scale from zero to π.

S E P T E M B E R / O C T O B E R 19 9 9

34

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

π
6

π
3

Industrial Machinery & Equipment

1

0

π
6

Figure 1B

Detrended Log of Inventory (black) and Sales (blue)
All Manufacturing Industries

Stone Clay and Glass Products

Primary Metals

0.15
0.10

0.10

0.05

0.05
0.00

0.05

0.00

0.00

–0.05
–0.05
–0.10

–0.10

–0.05

–0.15

–0.10

–0.20
8901.

9101.

9301.

9501.

–0.15
8901.

9701.

9101.

Nonferrous and Other Primary Metals

9501.

8901.

9701.

9101.

Fabricated Metal Products

0.15

0.10

0.10

0.05

0.05

9301.

9301.

9501.

9701.

Industrial Machinery & Eqpt
0.20

0.10

0.00
0.00

0.00
–0.05
–0.05

S E P T E M B E R / O C T O B E R 19 9 9

9101.

9301.

9501.

9701.

–0.20
8901.

9101.

Electrical Machinery

9301.

9501.

9701.

8901.

9101.

Transportation Equipment

9301.

9501.

9701.

Instruments/Related Products

0.15
0.15

0.10

0.10

0.10

0.05

0.05

0.05

0.00

0.00

0.00

–0.05

–0.05

–0.05

–0.10
–0.15

–0.10

–0.20

–0.15
8901.

9101.

9301.

9501.

9701.

–0.10
–0.15
8901.

9101.

All Other Durable Goods

9301.

9501.

8901.

9701.

9101.

Nondurable Goods Industries

9301.

9501.

9701.

Tobacco Products
0.30

0.10

0.20

0.05

0.05

0.10

0.00

0.00

0.00

–0.05

–0.10

–0.05

–0.10

–0.20
–0.15

–0.10
8901.

9101.

9301.

9501.

9701.

–0.30
8901.

9101.

9301.

9501.

9701.

8901.

9101.

9301.

9501.

9701.

The vertical scale depicts log deviations from trend of sales (shown in blue) and of inventories (shown in black). The horizontal scale is time. The data are monthly from January 1989 to
December 1998.

35

–0.15
8901.

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

–0.10

–0.10

–0.10

Figure 2A

Fourier Series of Inventory-to-Sales Ratio
Chemicals and Allied Products

Paper and Allied Products

Textile Mill Products
1

1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

π
6

π
3

π
2

2π
3

5π
6

π

0

π
6

Petroleum and Coal Products

π
3

π
2

2π
3

5π
6

π

0

1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

π
3

π
2

2π
3

5π
6

π

0

π
6

Consumer Staples

π
3

π
2

2π
3

5π
6

π

0

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

π
3

π
2

2π
3

5π
6

π

0

π
6

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

π
6

π
3

π
2

2π
3

5π
6

π

π
2

2π
3

5π
6

5π
6

π

π
3

π
2

2π
3

5π
6

π

π

0

π
6

π
3

π
2

2π
3

5π
6

π

Capital Goods Industries

Construction Matls/Suppl/Intermediate Products
1

0

π
3

2π
3

Business Supplies

1

π
6

π
6

Machinery and Equipment

1

0

π
2

0

π
6

π
3

π
2

2π
3

5π
6

S E P T E M B E R / O C T O B E R 19 9 9

36

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

π
6

π
3

Home Goods and Apparel

Automotive Equipment

1

0

π
6

π

The Fourier Series shown in these charts are made up of complex numbers. The vertical scale measures the absolute values of the Fourier Series. The horizontal scale shows
the frequency measured on a scale from zero to π.

Figure 2B

Detrended Log of Inventory (black) and Sales (blue)
Textile Mill Products

Chemicals and Allied Products

Paper and Allied Products
0.100

0.10

0.15

0.05

0.10

0.00

0.075
0.050
0.025

0.05

–0.05

0.000
0.00

–0.10

–0.025

–0.15

–0.05

–0.050

–0.20

–0.10

–0.075

8901.

9101.

9301.

9501.

9701.

8901.

9101.

Petroleum and Cool Products

9301.

9501.

9101.

9301.

9501.

9701.

Home Goods and Apparel

0.20

0.20

8901.

9701.

Automotive Equipment
0.15
0.10
0.10

0.10
0.00

0

–0.05

–0.10

–0.10

–0.20

–0.20

–0.10

8901.

9101.

9301.

9501.

9701.

8901.

9101.

Consumer Staples

9301.

9501.

8901.

9701.

9101.

Machinery and Equipment
0.15

0.10

9301.

9501.

9701.

Business Supplies
0.10

0.10

0.05

0.05
0.05

0.00

0.00

0.00

–0.05

–0.05

–0.05

–0.10

–0.10

–0.10
8901.

9101.

9301.

9501.

9701.

8901.

9101.

Construction Matls/Suppl/Intermediate Prdcts

9301.

9501.

9701.

8901.

9101.

9301.

9501.

9701.

Capital Goods Industries
0.20

0.10
0.05

0.10

0.00
0.00
–0.05
–0.10

–0.10

–0.15

–0.20
8901.

9101.

9301.

9501.

9701.

8901.

9101.

9301.

9501.

9701.

The vertical scale depicts log deviations from trend of sales (shown in blue) and of inventories (shown in black). The horizontal scale is time. The data are monthly from January 1989 to
December 1998.

37

–0.15
–0.20

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

S E P T E M B E R / O C T O B E R 19 9 9

0.05
0.00

0.00

Figure 3A

Fourier Series of Inventory-to-Sales Ratio
Household Durable Goods Industries
Producers Durable Equipment

Retail

1

1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

π
6

π
3

π
2

2π
3

5π
6

π

0

Retail Durable Goods Stores

π
6

π
3

π
2

2π
3

5π
6

π

0

Retail Bldg Matls\Hdw\Garden Supp\Mobile Homes
1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

π
3

π
2

2π
3

5π
6

π

0

π
6

Retail Furniture Group Stores

π
3

π
2

2π
3

5π
6

π

0

1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

π
6

π
3

π
2

2π
3

5π
6

π

0

π
6

π
3

π
2

2π
3

5π
6

π

0

1

1

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

π
6

π
3

π
2

2π
3

5π
6

π

0

π
6

π
3

π
2

2π
3

5π
6

π

π
3

π
2

2π
3

5π
6

π

π
6

π
3

π
2

2π
3

5π
6

π

Retail Apparel and Accessory Stores

1

0

π
6

Retail Food Stores

Retail Department Stores ex Leased Departments

2π
3

Retail General Merchandise Group Stores

Retail Nondurable Goods Stores

1

0

π
2

5π
6

π

0

π
6

π
3

π
2

2π
3

5π
6

The Fourier Series shown in these charts are made up of complex numbers. Ther vertical scale measures the absolute values of the Fourier Series. The horizontal scale shows the
frequency measured on a scale from zero to π.

π

S E P T E M B E R / O C T O B E R 19 9 9

38

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

π
6

π
3

Retail Automotive Dealers

1

0

π
6

Figure 3B

Detrended Log of Inventory (black) and Sales (blue)
Retail

Household Durable Goods Industries
Producers Durable Equipment
0.20
0.10

0.15

0.10

0.10
0.05
0.00

0.05

–0.10

–0.05

0.00

0.00
–0.05

–0.10
–0.20

–0.10
8901.

9101.

9301.

9501.

9701.

–0.15
8901.

Retail Durable Goods Stores

9101.

9301.

9501.

8901.

9701.

9101.

Retail Bldg Matls\Hdw\Garden Supp\Mobile Homes
0.20

0.05
0.00

0.00

9501.

9701.

0.15

0.10
0.10

9301.

Retail Automotive Dealers

0.10
0.05

–0.05

0.00
–0.05

–0.10

–0.10

–0.15

–0.30
8901.

9101.

9301.

9501.

–0.20
8901.

9701.

9101.

Retail Furniture Group Stores
0.20

9301.

9501.

Retail Nondurable Goods Stores

0.00

0.00

–0.05

–0.10

–0.10

–0.10

–0.20

–0.15

–0.15

–0.05

8901.

9101.

9301.

9501.

9701.

9701.

–0.30
8901.

9101.

Retail Department Stores ex Leased Departments
0.30

9501.

0.10

0.05

0.00

9301.

Retail General Merchandise Group Stores

0.20

0.10

0.10
0.05

9101.

0.30

0.15

0.15

8901.

9701.

9301.

9501.

8901.

9701.

Retail Food Stores

9101.

9301.

9501.

9701.

Retail Apparel and Accessory Stores

0.10

0.30

0.20
0.20

0.05

0.10

0.10

0.00

0.00

0.00

–0.10

–0.10

–0.05

–0.20

–0.20

–0.30

–0.10
8901.

9101.

9301.

9501.

9701.

–0.30
8901.

9101.

9301.

9501.

9701.

8901.

9101.

9301.

9501.

9701.

The vertical scale depicts log deviations from trend of sales (shown in blue) and of inventories (shown in black). The horizontal scale is time. The data are monthly from January 1989 to
December 1998.

39

S E P T E M B E R / O C T O B E R 19 9 9

–0.20

F E D E R A L R E S E R V E B A N K O F S T. L O U I S

–0.10
–0.20

–0.15

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S E P T E M B E R / O C T O B E R 19 9 9

William R. Emmons is a research economist and Frank A. Schmid is a senior research economist at the Federal Reserve Bank of St. Louis.
Robert Webb and Marcela Williams provided research assistance.

Credit Unions
and the
Common Bond

of credit unions, these institutions have
long been a source of controversy in the
United States. Public awareness of this
long-simmering debate was piqued recently
by a Supreme Court case pitting commercial banks against credit unions and their
federal regulator (Supreme Court, 1998).
The Court found in favor of banks in this
case, ruling that the federal credit-union
regulator, the National Credit Union
Administration, must cease granting federally chartered credit unions the right to
combine multiple common bonds (fields
of membership) within a single institution.
Less than six months later, however,
President Clinton signed into law new
legislation that essentially reversed the
Supreme Court’s ruling.
This paper provides background on
credit unions and the debate they have
spurred in the United States. In addition,
we present new evidence relevant to the
credit-union debate concerning fields of
membership (common bonds). Our
analysis is based on a theoretical model
of credit-union formation and consolidation.
Using an extensive dataset and a nonlinear
empirical approach, we find that creditunion participation rates generally decline
as the group of potential members becomes
larger, holding all else equal. That is,
the larger the pool from which a singlegroup credit union can draw, the less
effective it is in attracting members.
We also provide new evidence on two
more general banking policy issues. First,
we find evidence to support the structureconduct-performance paradigm of local
banking competition. This is the prediction,
derived from theoretical considerations,
that more concentrated markets ultimately
lead to higher prices and lower quantities.
Policymakers have used this paradigm
extensively when justifying intervention
in the market for corporate control in
financial services. Using the Herfindahl
index calculated for local bank deposit
market shares as a measure of local

William R. Emmons and
Frank A. Schmid

C

ooperative financial institutions have
their roots in 19th century Europe,
appearing first in the United States
during the early 20th century. Cooperative
financial institutions are ubiquitous in
both developed and developing countries
today, posing something of a puzzle in the
former group of countries where one
might have expected corporate financial
institutions with professional management
and sophisticated capital-market oversight
to have displaced them. This has not
occurred, however, as some groups of
cooperative financial institutions in developed countries are holding steady or even
increasing their market shares. In the
United States, the most prominent types of
cooperative financial institutions today are
mutual savings and loans, mutual savings
banks, mutual insurance companies, and
credit unions.
Credit unions are regulated and insured
financial institutions dedicated to the saving,
credit, and other basic financial needs of
selected groups of consumers. By law,
credit unions are cooperative enterprises
controlled by their members—under the
principle of “one-person one-vote.” In
addition, credit union members must be
united by a “common bond of occupation
or association, or (belong) to groups within
a well-defined neighborhood, community,
or rural district” (Supreme Court, 1998,
p. 2, quoting from the Federal Credit
Union Act of 1934).
Despite the rather low profile and
mundane operations of the vast majority

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market structure, we find that higher levels
of market concentration are associated with
higher participation rates at credit unions.
This is consistent with the notion that
banking competition is weaker in more
concentrated markets, which increases
the attractiveness of credit unions.
The second banking policy issue we
address is that of possible scale economies
among financial institutions. Our empirical results indicate that credit unions
generally encounter significant scale
economies, whether scale is measured by
the log of total assets or by the log of the
number of credit-union members. The latter
finding, however, applies only to relatively
large credit unions.
It is important to point out several
limitations of this study. As in all
empirical investigations, we can describe
relationships in the existing data but we
cannot predict exactly how these relationships would appear under a different set of
operating conditions. For example, an
extended period of growth by many credit
unions could alter the extent of scale
economies that exist. Similarly, significant
changes in credit-union regulation might
result in different empirical regularities
than those identified here. It also is
important to keep in mind that we abstract
from managerial agency problems in credit
unions in this article (see Emmons and
Schmid, 1999, for an extensive discussion
of this issue). Finally, it is hazardous to
draw conclusions about public policy
toward credit unions on the basis of this
rather narrowly focused investigation. We
hope to provide insights into the effects of
common-bond requirements, not to
provide a comprehensive framework for
evaluating competition in the financial-services sector as a whole.
The paper is organized as follows:
The first section provides some institutional
and historical background on credit
unions, while the second section outlines
the current credit-union debate in the
United States. The third section develops
a theoretical model of credit-union formation and consolidation. The model
stresses the countervailing influences

on participation rates of (1) scale economies
in production, and (2) decreasing withingroup membership affinity as a credit
union grows. The model provides intuition
for why the number of common bonds
within a credit union might be important
for their formation and growth. The third
section also describes a simulation of the
theoretical model that can be used to generate some comparative-static results. The
fourth section briefly describes the dataset
and the econometric methods we employ
in analyzing federally chartered occupational
credit unions. The fifth section presents
our empirical results, and the sixth section
draws conclusions. An appendix describes
the data we use.

BACKGROUND ON
CREDIT UNIONS
This section provides some institutional
background to help motivate the theoretical
and empirical analyses later in the article.
The key points this section seeks to illuminate are the restrictions on credit-union
expansion and the arguments that have been
made to support or oppose these restrictions.
The sections that follow investigate the
extent to which the common-bond requirement acts as a binding constraint on
credit-union operations.

Overview of Credit Unions in the
United States
Credit unions numbered 11,392 at
year-end 1996, serving some 70 million
individual members (U.S. Treasury, 1997,
p. 15). At the same time, there were
11,452 commercial banks and thrift institutions (savings and loan associations and
mutual savings banks). Credit-union assets
were only $327 billion, compared to
$5,606 billion held by commercial banks
and thrifts (U.S. Treasury, 1997, p. 21). A
more direct standard of comparison might
be community banks and thrifts, however.
At year-end 1996, there were 7,049
community banks and thrifts (defined as
all federally insured banks and thrifts with
less than $100 million in assets) holding

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combined assets of $324 billion (U.S. Treasury, 1997, p. 21). A comparison of credit
unions and community banks and thrifts is
particularly meaningful because
institutions of both types are relatively
focused institutions, and hence, are unable
to grow beyond certain limits. For
example, a single-employer occupational
credit union is authorized to serve only the
employees of the sponsoring firm and their
immediate relatives, who may total no
more than a few hundred people. A community bank or thrift may operate in only
one geographical area. In addition, credit
unions are restricted in the types of financial services they may provide, with
traditional consumer financial services at
the core of virtually all credit unions’ activities. Community banks and thrifts may
offer a similar array of services.
Both federal and state agencies grant
credit-union charters. Regardless of the
type of charter they hold, the deposits (or
technically, “shares”) of virtually all credit
unions are now federally insured by the
National Credit Union Administration
(NCUA). Federal credit unions are regulated
by the NCUA while state-chartered credit
unions are regulated by an agency of the
chartering state.
Of the 7,068 federally chartered institutions at year-end 1996, about three quarters
were occupational credit unions (U.S. Treasury, 1997, p. 19).1 In an occupational
credit union, one or more firms sponsor a
credit union, sometimes providing office
space, paid time off for volunteer workers,
and perhaps other forms of support. The
remaining federal credit unions were either
single-group associational or community
credit unions, or multiple-group credit
unions with predominantly associational,
community, or more than one type of membership (i.e., several groups that span the
usual classifications).
By size, most credit unions (65 percent
of federally insured institutions) had less
than $10 million in assets (U.S. Treasury,
1997, p. 19). Large credit unions exist,
however, and they are an important part of
the sector. For example, the 11 percent of
credit unions with more than $50 million

in assets (1,284 institutions) accounted for
74 percent of total credit-union assets.
Credit unions play a limited role in the
U.S. financial system, catering to the basic
saving, credit, and other financial needs of
well-defined consumer groups. More than
95 percent of all federal credit unions offer
automobile and unsecured personal loans,
while a similar proportion of large credit
unions (more than $50 million in assets)
also offer mortgages; credit cards; loans to
purchase planes, boats, or recreational
vehicles; ATM access; certificates of
deposit; and personal checking accounts
(U.S. Treasury, 1997, p. 23). Very small
credit unions typically offer a limited
range of services, are staffed by membervolunteers, and are likely to receive free or
subsidized office space. Larger credit
unions offer a broader array of services.
They may employ some full-time workers,
including the manager, and are more likely
to pay a market-based rent for office space.
Historically, members of credit unions
were drawn from groups that were underserved by traditional private financial
institutions; these consumers tended to
have below-average incomes or were otherwise not sought out by banks. While
credit-union members today still must
share a common bond to be eligible for
membership, the demographic characteristics of credit-union members have become
more like the median American. While
only 1 percent of the U.S. adult population
aged 18 or over belonged to a credit union
in 1935, some 33 percent of the adult population had joined by 1989 (American
Bankers Association, 1989, p. 29). Subsequent strong growth of new credit-union
charters has increased that proportion.2
According to a credit-union survey in
1987, 79 percent of all Americans who
were eligible to join a credit union had
done so (American Bankers Association,
1989, p. 29). Given the prominent role of
occupational credit unions, a majority of
members are in the prime working ages of
25-44 (American Bankers Association,
1989, p. 30). Perhaps surprisingly, given
the origins of credit unions, current members are overrepresented in upper-middle

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1

We concentrate on federally
chartered credit unions because
the NCUA does not vouch for
the accuracy of data provided
by state-chartered credit unions,
which report directly to their
state's regulatory authorities.

2

The estimated 70 million
current credit-union members
represent a bit more than
34 percent of the 1996 U.S.
population over 16 years
of age numbering 204 million
(U.S. Census Bureau,
<http://www.census.gov>).

S E P T E M B E R / O C T O B E R 19 9 9

income strata, defined as household
incomes between $30,000 and $80,000
in 1987. Overall, it appears that credit
unions, banks, and thrifts are more direct
competitors today than when credit
unions first appeared.

The likelihood that federal credit
unions would serve consumers not served
by banks was an additional element in
Congressional deliberations:
Credit unions were believed to enable
the general public, which had been
largely ignored by banks, to obtain
credit at reasonable rates. (Supreme
Court, 1998, p. 17.)

A Brief Legislative History of Credit
Unions in the United States
The predecessors of American credit
unions were cooperative banking institutions
of various sorts in Canada and Europe
during the 19th century. The first credit
union in the United States was formed in
Manchester, New Hampshire, in 1909 (U.S.
Treasury, 1997, p. 15). Soon thereafter,
Massachusetts created a charter for credit
unions. The credit-union movement swept
across the United States from there,
meeting with particular success in the New
England and upper Midwestern states.
These early cooperative financial institutions often had a social, political, or
religious character in addition to their
explicit economic function. While the
social and political aspects of the cooperative movement were acknowledged and
accepted by the United States Congress,
the Federal Credit Union Act (FCUA) of
1934 was focused more narrowly on the
economic potential of credit unions.
The legislation itself was modeled
closely on state credit-union statutes that
had appeared during the early decades of
the 20th century in the Northeast and
upper Midwestern states. The FCUA
clearly reflected Congressional intent to
create a class of federally chartered financial institutions that would operate in a
safe and sound manner:

Partly because credit unions are
mutual associations, they were not
subjected to federal taxation as were shareholder-owned commercial banks and thrift
institutions. Mutuality cannot be the only
reason why credit unions are not taxed,
however. Other mutually owned enterprises
are subject to taxation. As for the benefits
of tax exemption, credit unions (or any
other firm) could avoid paying taxes by
paying out all “profits” to members in the
form of lower borrowing rates or higher
deposit rates. The real importance of the
tax exemption is that credit unions can
retain earnings tax free. Advocates argue
that this is justified because credit unions
cannot raise equity in a public offering, so
they must be able to build capital internally.
It is clear from the legislative history
surrounding the passage of the FCUA in
1934 that Congress saw the common-bond
requirement as critical to the success of
credit unions:
The common bond requirement “was
seen as the cement that united credit
union members in a cooperative venture,
and was, therefore, thought important
to credit unions’ continued success. ...”
“Congress assumed implicitly that a
common bond amongst members
would ensure both that those making
lending decisions would know more
about applicants and that borrowers
would be more reluctant to default.”
(Supreme Court, 1998, pp. 17-18,
citing 988 F.2d, at 1276.)

… the ability of credit unions to
“come through the depression without
failures, when banks have failed so
notably, is a tribute to the worth of
cooperative credit and indicates clearly
the great potential value of rapid
national credit union extension.”
(Supreme Court, 1998, p. 17, citing
the FCUA, S.Rep. No. 555.)

The subsequent history of credit
unions in the United States largely has
fulfilled the promise envisioned by

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Congress in 1934. Credit unions have
grown and spread across the country.
Although hundreds of individual credit
unions failed during the 1980s and early
1990s, the National Credit Union
Insurance Fund (NCUSIF, formed in 1970)
avoided accounting insolvency—in
marked contrast to the Federal Savings
and Loan Insurance Corporation and the
Bank Insurance Fund of the Federal
Deposit Insurance Corporation (Kane and
Hendershott, 1996). Credit unions control
a small but growing share of household
deposits, and some of our empirical results
indicate that they may play a role in maintaining a high level of retail banking
competition in some local markets.

arguments used in the recent Supreme
Court decision concerning the role of the
common-bond requirement in credit
unions reflect the unsettled nature of the
debate. We focus on two strands of the
credit-union debate here, namely the arguments stressing inefficient governance
structures on the one hand and unfair
competition on the other.
Some have argued that credit unions
are inherently inefficient due to their onemember one-vote governance structure.
One might expect decision-making in
a credit union to be of poor quality due
to a lack of professionalism (i.e., volunteer
managers and workers), free-riding of
members in monitoring the management,
and weak incentives for members to
intervene when action is needed to
correct specific problems or deficiencies.3
According to this argument, credit unions
may waste scarce resources and they may
eventually impose significant costs on
individual sponsoring firms or the
economy as a whole.
The second prominent line of
argument aimed at credit unions takes
a nearly opposite view of their organizational
effectiveness. This view presumes that
credit unions operate efficiently enough to
offer consistently better terms on savings
and credit services than those offered by
commercial banks and thrifts. Bank and
thrift managers and owners often present
this point of view in public discourse.
To be sure, those arguing that credit
unions represent unfair competition
ascribe some or all of their competitive
advantages to subsidies such as their taxexempt status or sponsor subsidies rather
than inherent efficiency.
Proponents of the first view—that
credit unions are inherently inefficient—
have a difficult time explaining why the
number of credit unions and credit-union
members continues to grow, and why
members express high levels of satisfaction
with the services they receive. If most
credit unions were very inefficient, one
might expect their members to become
disaffected and their role in the financial
system to diminish over time.

THE CURRENT CREDITUNION DEBATE
The special status and comparative
success of credit unions in recent decades,
coinciding as it has with a period of stress
on thrift and commercial-banking institutions, has led to political conflicts between
advocates of credit unions and banks.
This conflict reached its high point in a
series of court decisions culminating at the
U.S. Supreme Court in October 1997. The
particular case at issue involved the AT&T
Family Credit Union and the NCUA’s
interpretation of the 1934 FCUA allowing
multiple common bonds of membership.
Brought by several banks and the
American Bankers Association, the case
was ultimately decided in February 1998
(on a 5-4 decision) in favor of the banks
who sued to stop the NCUA from granting
more multiple-group credit-union charters.
The bankers’ victory was short-lived,
however, as Congress almost immediately
drafted new legislation that enables credit
unions to continue growing much as
before—including multiple common
bonds within a single credit union.
The shaded insert summarizes
the key provisions of the Act.
Attacks on credit unions have come
from a wide range of viewpoints, the proponents of which have wielded sometimes
contradictory arguments. Some of the

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3

Free-riding is when members
choose not to exert monitoring
effort because they assume
someone else will do it for them.

S E P T E M B E R / O C T O B E R 19 9 9

THE CREDIT UNION MEMBERSHIP ACCESS ACT
President Clinton signed the Credit Union Membership Access Act on August 7,
1998, following approval in the Senate on July 28 and in the House of Representatives
on August 4. The act substantially reverses a Supreme Court ruling handed down on
February 25, 1998, that would have barred federally chartered credit unions from
accepting multiple membership groups, each with its own common bond.
This landmark credit-union legislation represents a major defeat for the top
lobbying group representing commercial banks, which had argued successfully at
the Supreme Court that credit unions with multiple common bonds violated both
the letter and the spirit of federal legislation dating from 1934. The subsequent
legislative response in support of multiple common bonds at credit unions was
swift and overwhelming, passing both chambers with large majorities.
The act contains three provisions upholding the rights of federal credit unions to
serve membership groups encompassing multiple common bonds. First, all federal
credit unions that already included multiple common bonds before February 25, 1998,
were allowed to continue operating without interruption. Second, all federal credit
unions were given the right to accept additional membership groups with multiple
common bonds so long as the relevant groups have fewer than 3,000 members. Third,
the act gives the National Credit Union Administration the right to grant exemptions
to the 3,000-member limit under certain circumstances, such as when the group in
question could not reasonably support its own credit union.
The act also:
• Requires annual independent audits for insured credit unions with total assets of
$500 million or more.
• Authorizes and clarifies a federally insured credit union’s right to convert to a
mutual savings bank or savings association without prior NCUA approval.
• Limits business loans to members to 12.25 percent of total assets.
• Establishes new capital standards for insured credit unions similar to those
enacted for banks and thrifts in 1991.
• Gives the NCUA authority to base deposit-insurance premiums on the reserve
ratio of the insurance fund.
• Directs the Treasury to report to Congress on differences between credit unions and
other federally insured financial institutions, including the potential effects of
applying federal laws—including tax laws—to credit unions.
Hailing the new legislation, President Clinton said, “This bill ensures that consumers continue to have a broad array of choices in financial services….and [makes] it
easier for credit unions to expand where appropriate.” Meanwhile, a spokeswoman for
the American Bankers Association termed it “ironic” that the bill was presented as a
measure to protect credit unions because in the long run, she said, it will dilute them,
turning them into larger and larger institutions.
Source: BNA Banking Report, “House Passes Credit Union Bill; Clinton Wastes No
Time Signing It,” August 10, 1998, Vol. 71, No. 6.
On the other hand, proponents of the
second view—that credit unions are unfair
competitors due in part to subsidies—
cannot explain easily why credit-union

sponsors and governments are such strong
supporters of credit unions. It is hard to
understand how large net subsidies could
be delivered to credit-union members over

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time without more opposition arising
from constituencies that might be paying
the subsidies, such as shareholders or
employees who do not belong to their
firm’s occupational credit union, or
taxpayers who belong to no credit union.
In fact, the most vocal complaints about
alleged subsidies for credit unions are
heard from banks and thrifts, whose
resentment of credit-union competition
could be expected even if there were no
subsidies flowing to credit unions.
Ironically, the juxtaposition of these
two lines of attack against credit unions
appeared in the argumentation of the
Supreme Court majority that decided
the AT&T Family Credit Union case in
favor of commercial banks. At one point
in its opinion, the majority cited the
legislative history surrounding the 1934
Federal Credit Union Act as support
for the view that credit unions are a
fragile—even flawed—type of institution,
reasoning that:

The irony is, of course, that the
argumentation based on the reductio ad
absurdum of a hypothetical “conglomerate
credit union” did not mention the legislative history of the 1934 Act, which had
essentially predicted that such a huge
credit union would not have been a safe
and sound financial institution, nor consequently a viable one in the long run.

THE MODEL AND
SIMULATION
How should policymakers think about
credit unions? Are they relics of a bygone
era, propped up by subsidies and
distorting financial-sector competition?
Or, are they efficient and focused financial
institutions that could, if unleashed, eventually dominate some or all of the retail
financial landscape? We do not seek to
answer these emotionally charged questions
directly. Instead, we focus on the more
limited question of what effect the
common-bond restriction exerts on creditunion formation and consolidation. In a
sense, we are merely attempting to answer
the question, “Does the common-bond
requirement constrain the existence or
growth of credit unions?” We hope that
our insights may contribute to a better
understanding of the larger policy
questions mentioned above.
In this section we present a model of
credit-union formation and consolidation.
We then describe the results of a simulation
of the model. Subsequent sections of
the paper discuss testable hypotheses
emerging from the model, the data we
examine, and empirical results.

Because, by its very nature, a cooperative institution must serve a limited
market, the legislative history of
Section 109 demonstrates that one of
the interests “arguably…to be
protected” by Section 109 is an interest
in limiting the markets that federal
credit unions can serve. (Supreme
Court, 1998, footnote 6, pp. 8-9.)
Thus, a credit union would become inefficient if it grew beyond its “limited market,”
as defined by its common bond.
At a different point in its opinion,
however, the majority accepted the
argument that credit unions with multiple
groups of members would be more formidable competitors to banks and thrifts
than single-group institutions. The
majority argued that an expansive
interpretation of the 1934 Act “would
allow the chartering of a conglomerate
credit union whose members included the
employees of every company in the United
States (1998, p. 4).” In other words, credit
unions would overwhelm banks and thrifts
unless otherwise constrained.

The Model
We take for granted that credit unions
typically are small; that they encounter
operating economies of scale as they expand
from a very small base of members and
assets; and that they face direct competition
from banks. The key trade-off we model
is between decreasing affinity among
members as the potential membership
grows (i.e., as a given common bond is

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Figure 1

union is located, while commercial-bank
services are available at a fixed price at any
point on the line. This assumption makes
household preferences critical for the existence of and participation in credit unions
while maintaining the realistic assumption
that commercial banks provide an alternative to credit unions (and vice versa).
We assume that the entire city (i.e.,
every point on the line) is covered by at least
one household and at most two households.
Without loss of generality, we assume that
all points covered by two households are
arrayed continuously from zero upward
towards, but potentially short of, one on the
unit interval. For expositional purposes, we
will refer to the households that inhabit the
completely covered zero-to-one interval as
being above the line and all others as below
the line. Thus, two households that possess
identical locations (preferences) are said to
be “back-to-back” households.
Households are further grouped by
affinity, or common bonds. For tractability,
we discuss occupational common bonds
and limit the number of employers in the
economy to three. Each household located
above the line contains an employee of
either firm A or firm B (but not both).
Because all households in employee group
A share a common bond, they are located in
a contiguous segment of the line that does
not overlap the domain of employee group
B. All households below the line contain
employees of firm C. Each employer may
sponsor a credit union, although, as we
will see, not all will do so.
We examine two periods (or regimes),
differentiated according to the permissibility
of forming credit unions with multiple
common bonds. All households are born
at the start of period 1 and live through the
end of period 2. Each household needs to
consume one unit of banking services in
each period. These services can be provided
by an occupational credit union or by a
bank in either period.
At the beginning of the first period,
households find themselves arrayed along
the city’s unit interval. The lengths of
the firm-A and firm-C segments are
distributed as uniform random variables

Linear City with Three Common
Bonds of Occupation

Households employed by firm A

Households employed by firm B

AAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBB
Preferences for Banking Services
0
1
CCCCCCCCCCCCCCCCCCCCCCCC
Households employed by firm C

extended to more people)—making a
credit union less effective—versus the
increasing scale economies that come with
a larger base of members and assets—
making a credit union more effective. We
show that the ability of credit unions to
expand by adding multiple common bonds
to their membership affects this trade-off
in an important way.
We examine a Hotelling (1929)
economy consisting of a “city” that lies on
a straight line of unit length. The city’s
length is covered by a continuum of
households. The location of each
household corresponds to its preferences
for banking services. In particular, each
household demands exactly one unit of
banking services but the nature of desired
services differs among households. Preferences in the real world are, of course,
multidimensional, encompassing tastes for
different menus of financial services,
different levels of service, or different locational preferences. We assume for the sake
of simplicity, however, that a household’s
preferences for banking services can be
represented in terms of a single index running from zero to one. Figure 1 depicts
the linear-city model.
Because we are interested only in the
formation and consolidation of credit
unions, we assume that credit unions are
scarce (or differentiated) while commercial
banks are ubiquitous (or uniform). In other
words, consumption of credit-unionprovided financial services takes place at
the point on the unit interval where a credit

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on the [0, 1] interval. The length of the
firm-B segment is one minus the length of
the firm-A segment.
Suppose, first, that each of the three
employers sponsors a credit union (in the
simulation below, not all firms necessarily
sponsor a credit union). All credit unions
are restricted to a single employee group
during the first period. Each credit union
has a life span of one period. The credit
unions have idiosyncratic technologies for
producing banking services. In particular,
each credit union i operates with fixed
costs fi = fa + fb e i , where fa and fb are common
to all credit unions and e i is an i.i.d. uniform
random variable. In addition, each credit
union faces constant marginal costs of v per
unit of banking services provided. Thus,
the cost function of credit union i is
C(mi) = fa + fb e i + vm i , where m i is the
number of actual members in the credit
union, and i = A, B, or C. An important
feature of this cost function is that average
costs, C(mi)/m i , are declining in the
number of members the credit union is
able to attract.
At the beginning of period 1, households
vote on the credit-union management team
for that period. Voting is costless, the onehousehold one-vote principle applies, and
side payments among households are permitted (to allow those with strongly held
preferences to “buy” the votes of those with
weaker preferences). This implies, by virtue
of the “value maximization principle,” that
the competitive outcome maximizes social
welfare (Milgrom and Roberts, 1992, pp.
36-37). The potential members choose a
management team that locates the credit
union to minimize the sum of member
“travel costs” (which are described in the
following paragraph). It is clear that the
credit union will locate in the center of
the preference spectrum of all potential
members because we assume that travel
costs are quadratically increasing in the
distance between member households
and the credit union.
Credit-union services are offered at the
price p i to all potential members of a credit
union (i.e., employees of the relevant
firm). The price equals the credit union’s

Figure 2

Travel Costs Facing Households
Employed by Firms A and B
Travel
costs
c-p
Marginal HHs

a

O

Credit
Union B

Credit
Union A

r*
Households employed by firm A

Households employed by firm B

average costs ( ACi ) because credit unions
are not-for-profit institutions. Households
face marginal costs of t 3 r per unit of distance r when travelling to a credit union with
t being a travel-cost parameter. This is
because the credit union’s banking services are
(in general) not identical to a given household’s preferences (i.e., location on the
line). The cost of using credit union i at a
distance rj from household j ’s location is
(t/2)r j2. Each household also can access
banking services from a commercial bank
at a constant price c. Together, these
assumptions imply that the membership of
credit union i will comprise all households j
within the potential membership for which
the following inequality holds (see Figure 2):
t 2
r j ≤ c − pi .
2
In particular, the marginal—i.e., most
distant—households will be the ones (on
either side of the credit union) for which
the expression holds at equality:
t 2
r * = c − pi .
2
As Figure 2 illustrates, not every
potential member joins the credit union.
A household relatively far from the credit
union (at a distance greater than r*) buys
banking services from a commercial bank
instead. The number of members credit

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49

1

S E P T E M B E R / O C T O B E R 19 9 9

Figure 3

cubic expression that determines the
optimal number of credit-union members,
m*, expressed in terms of the demand-side
parameters c and t (price of commercialbanking services and the travel-cost
parameter, respectively), as well as the
supply-side parameters f and v (fixed and
marginal costs of credit-union production
of financial services, respectively):

Demand and Supply Curves
for Credit-Union Services
AC
c – t/2 X (m/2) 2

Supply
Demand

2

(2)

m 1pot

m * m 2 pot

The economic interpretation of
Equation 2, the optimality condition,
is straightforward. The left-hand side represents the demand curve for credit-union
services, while the right-hand side represents
the average-cost curve of a credit union.
Credit unions are not-for-profit institutions,
so their average-cost curves also are their
supply curves. A downward-sloping supply
curve indicates that scale economies exist
in the range we consider (see Figure 3). For
mpot > m*, where mpot is the potential membership of the credit union, we obtain an
interior solution. In other words, the participation rate—the fraction of the potential
membership that chooses to join the credit
union—is lower than one. For mpot ≤ m*,
on the other hand, the participation rate is
equal to one because all potential members
choose to join.
Notice that, if the domain of potential
members of a credit union is too small,
the supply and the demand curves may
not intersect. In this case, the credit union
cannot operate because there is no positive
number for m* that satisfies equation 2
(see Figure 4).
The second period of the model corresponds to a regime in which the law allows
credit unions to serve groups of households
united by different common bonds (e.g.,
employees of both firms A and B). A new
management team must be selected at the
beginning of period 2 to operate each credit
union. New credit unions may be formed
in which multiple occupational groups are
included. In addition to single-employer
credit unions, we now might see four
other combinations of common bonds—

m

Figure 4

A Case in Which No Credit Union Exists

AC
c – t/2 X (m/2) 2

Supply
Demand

m

union i attracts is therefore 2r*, which
we denote m*.
Because the average cost as a function
of the number of credit-union members,
m, is (f + vm)/m, and price must be equal
to average cost, we now obtain an expression relating the distance between the
marginal member and the credit union, r*,
and the optimal number of members in the
credit union, m*:
(1)

t  m* 
f + vm *
c− 
.
 =
2 2 
m*

t
f + vm *
c − r *2 =
.
2
m*

But we know that r* = m*/2, so we can
substitute in equation 1 for r* to obtain a

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S E P T E M B E R / O C T O B E R 19 9 9

a multiple-group credit union
encompassing employees of firms:
• A and B (what we term an “A&B”
credit union) plus a single-group credit
union serving employees of firm C;
• A and C (an “A&C” credit union) plus
a single-group credit union serving
employees of firm B;
• B and C (a “B&C” credit union) plus
a single-group credit union serving
employees of firm A; and
• A, B, and C (an “A&B&C”
credit union).
As in period 1, none of these credit
unions necessarily exists; the particular
configuration of parameters will determine
the outcome.
We allow for side payments so there is
no path dependence as we go from period
1 to period 2 (i.e., period-2 results do not
depend on period-1 outcomes). As in
period 1, the socially optimal combination
of occupational groups is chosen. Also,
the new credit unions will again be located
in the center of the preference spectrums
of their potential members. Before voting,
all potential members of the various credit
unions observe the (random) technology
the new credit unions possess. These are
drawn anew at the beginning of period 2.
We allow the fixed costs of a multiplegroup credit union to deviate
systematically from the fixed costs of a
single-group credit union. The fixed costs
of a multiple-group credit union i amount
to fi = fa(1+a) + fbei , with a > –1– fbei /fa.
After the new credit unions have been
established, each household either purchases
one unit of banking services from the credit
union or it buys them from a commercial
bank. The economy ends after period 2.
Finally, we point out several comparative-static features of the model that follow
standard intuition despite the existence of
a downward-sloping supply curve. The two
important demand-side parameters are t,
the households’ travel-cost parameter,
and c, the cost of alternative banking
services as provided by a commercial
bank. Recalling Figure 3, which shows
the supply curve of the credit union and
the demand curve for its services, it is clear

that as a household’s travel costs rise, the
demand for credit-union services declines.
We interpret rising travel costs as an
increase in the strength of a household’s
preferences for its ideal bundle of banking
services. Such an increase causes the
demand curve to shift downward,
decreasing m*. That is, the optimal size
of the credit union declines. On the other
hand, an increase in the price of commercial-bank provided financial services, c,
shifts the demand curve up. This has the
opposite effect on the optimal size of the
credit union, increasing m*.
The important supply-side parameters
of the model are f, the credit union’s fixed
cost, and v, the credit union’s marginal cost
of providing banking services. An increase
in f pushes up the supply curve of creditunion services, with the sharpest increase at
low levels of membership. An increase in
the marginal cost of credit-union production
also translates into an upward shift of the
supply curve. In both cases, the size of the
potential membership required to achieve
full participation increases.

Simulation of the Model
We simulate the model by drawing
repeatedly (10,000 times) a set of five uniformly distributed random numbers from
the [0, 1] interval. The first draw determines
the length of the segment containing
households with an employee of firm A.
Recall that the length of the segment
containing firm-B households equals one
minus the length of the firm-A segment.
The second draw determines the length of
the segment containing households with
an employee of firm C. This determines
the length of the line segment that is covered by two households. The last three
random numbers enter the three (potential)
credit unions’ cost functions as stochastic
elements of their fixed costs (denoted ei in
the model description above, i = A, B, C).
These random elements in the credit unions’
cost functions ensure that a “conglomerate”
credit union consisting of the employees of
all three firms is not degenerate—i.e., existing
with probabilities of either zero or one.

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S E P T E M B E R / O C T O B E R 19 9 9

Recall that in the first period, all credit
unions must consist of a single common
bond. The first step in the formation of
a credit union is a vote by the potential
membership on the management team.
Since side payments are allowed, the team
that minimizes the sum of the travel costs
of all potential members—i.e., which picks
the most central location—will win. In a
second step, all households decide whether
to become members or to purchase financial
services from a commercial bank.
We calculate the preferred outcome
for each group of households in turn
(A, B, and C). The equilibrium solution
for each employee group must be one of
three possibilities: the credit union exists
at a corner solution, in which all households
participate; the credit union achieves an
interior solution with a participation rate
less than one; or the credit union does not
exist. To compare the various outcomes,
we calculate a welfare index for each group
of households that is simply the sum of the
production costs of the credit union (if it
exists), the travel costs incurred by households that use credit unions, and the
expenditures of households that obtain
financial services from a bank, all
multiplied by negative one (to maintain
the convention that a higher index value
signifies higher social welfare):

that a stand-alone credit union that could
not exist on its own becomes part of a
multiple-group credit union. The reason
is that the post-merger credit union is able
to spread its fixed costs over a larger membership. It also is possible that a credit
union that could not exist on its own also
is not viable as part of a multiple-group
credit union. On the other hand, any
employee group that is served by a credit
union in period 1 also will be served by a
credit union in period 2 because all
mergers must be welfare-enhancing. That
is, all options for operating credit unions
with single common bonds available in
period 1 still are possible after permitting
multiple common bonds in period 2.
Table 1 displays a summary of the
simulation results. The table presents
two measures of credit-union activity:
the fraction of all employee groups served
by a credit union and the fraction of
households served by a credit union.
When only single-employer credit unions
are allowed (period 1), only 6 percent of
the 30,000 simulated employers (A, B, and
C in each of 10,000 simulations) actually
sponsor a credit union and only 4 percent
of households actually belong to credit
unions. Among households that are
eligible to join a credit union, some 50
percent do so. All other households use
commercial banks to obtain financial services. We have chosen parameter values to
reflect the fact that single-group credit
unions are relatively small and may not be
viable for many employee groups.
The bottom part of Table 1 presents
results when multiple-group credit unions
are allowed (period 2). It is clear that the
permissibility of multiple common bonds
dramatically increases the viability of
credit unions. This is a general result in
the sense that restricting credit union
membership to one employee group is a
binding constraint, the relaxation of which
may increase the beneficial role of credit
unions for employees. When two employee
groups may be combined in a single credit
union (A and B, A and C, or B and C), the
fraction of employee groups in the economy
served by a credit union rises to between

r* r*

pot
(3) −( f + mv ) − ∫ ∫ tr dr dr − ( m − m ) c .
0 0

In the second period, multiple-group
credit unions are allowed. We iterate
through the possible combinations by first
allowing mergers between two given credit
unions and forcing the third to operate
independently (if it exists). Then we allow
all three credit unions to merge. In each
regime, households vote on the management
team (i.e., choose the credit union’s
location). In particular, households
choose between a team that would operate
the credit unions independently and a
team that would merge them. Because
bribing is allowed, the team that
maximizes the welfare index over all
potential members will win. It is possible

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S E P T E M B E R / O C T O B E R 19 9 9

Table 1

Simulation Results (1)
Fraction of employee groups
served by…

Participation rates as
a fraction of… 1

(1)
Any Credit
Union

(4)
All
Households

Credit
Unions in
the Economy

Period 1

Welfare index

Only singlegroup credit
unions

–23,951.89

Period 2

(2)
(3)
A SingleA MultipleGroup Credit Group Credit
Union
Union

(7)
(6)
(5)
Those
Those
Those
Households Households Households
Eligible to
Eligible to
Eligible to
Join a Credit
Join a
Join a SingleUnion
Group Credit MultipleGroup Credit (weighted
Union
average of
Union
5 and 6)

0.06

0.06

----

0.04

0.50

----

0.50

Increase in
welfare index

A&B, C

53.09

0.14

0.04

0.10

0.04

0.50

0.31

0.40

A&C, B

1,048.20

0.50

0.03

0.47

0.37

0.48

0.77

0.74

B&C, A

523.49

0.34

0.04

0.30

0.16

0.45

0.60

0.46

A&B&C

1,123.34

0.49

0.01

0.48

0.30

0.58

0.41

0.42

Optimal
Combination

1,590.32

0.94

0.02

0.93

0.43

0.54

0.56

0.56

Parameter values: fa = 0.1; a = 0; fb = 0.1; t = 22; c = 1.6; v = 1.
Participation rate is the fraction of eligible households that belongs to a credit union. Rates are weighted by segment lengths.

1

14 and 50 percent, while the fraction of
households served by a credit union rises
to between 4 and 37 percent, depending
on the combination. When all three
employee groups are allowed to combine
in a single credit union (A and B and C),
the fraction of employee groups served
by a credit union jumps to 49 percent,
although only 30 percent of households
are still served.4
Examination of column 6 indicates
that multiple-group credit unions
comprising groups A and B or A, B, and C
are characterized by relatively low participation rates. This reflects the fact that
many members of employee groups A and
B are located far from any multiple-group
credit union, reducing their incentive to
join. The credit union formed by employee

groups A and C alone, on the other hand
—which are located back-to-back—is
characterized by a very high participation
rate (77 percent of those eligible actually
join). This is because the preferences of
these two groups overlap.
In general, how likely households are
to join credit unions does not depend primarily on whether multiple-group credit
unions are allowed (see column 7, where
the exception is the credit union comprising groups A and C, the back-to-back
case). In other words, participation rates
in multiple-group credit unions are not
necessarily higher. Rather, it is the fact
that more credit unions are viable when
multiple common bonds are allowed that
is responsible for the expanded role of
credit unions in the economy. A comparison

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53

4

Household segments not
involved in a merger during the
second-period simulations face
the same economic situation as
in the first period. Consequently,
they come to the same decision
during the second period of
whether to operate a credit
union as they did during the
first period.

S E P T E M B E R / O C T O B E R 19 9 9

Figure 5

declining participation rates of singlegroup (the gray points in the lower curve,
ending at 1.0) and multiple-group credit
unions (the blue points), respectively. If
we were to show each type of credit union
plotted in Figure 5 in a separate chart, two
important features would be obvious from
the average participation rates shown
in Table 1.
The first feature is that participation
rates of multiple-group credit unions tend
to lie above those of single-group credit
unions for a given number of potential
members. This points to the fact that multiple-group credit unions can be closer to
the average member’s preferences due to
the existence of back-to-back households
(i.e., households with different employers
but identical preferences for banking
services). This effect is due entirely to the
households in employee group C in our
model, whose preferences overlap those
of some households in other employee
groups, most importantly group A.
Figure 5 also shows the second important feature of the model that is not
revealed in the table—the downward slope
of both main sets of points. Greater potential membership tends to generate lower
participation rates. This always holds
for single-group credit unions and for
multiple-group credit unions that comprise
“horizontally neighboring” membership
groups only (i.e., groups A and B). Given
the travel costs that represent preference
heterogeneity among the potential membership, it is not surprising that credit
unions that span a more heterogeneous set
of households are able to attract proportionately fewer of them. For credit unions
that comprise segments B and C, participation rates initially fall with an increase in
the membership base, then rise and later
fall again. Credit unions that unite all
three employee groups (A&B&C credit
unions) exhibit a similar pattern in terms
of participation rates. For A&B&C credit
unions, a rise in the potential membership
is due solely to an increase in the interval
spanned by group C, which means an
increase in the fraction of households
located back-to-back. For back-to-back

Participation Rates as a Function
of Potential Membership
Participation Rate
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.1

0.3

0.5

0.7

0.9
1.1
1.3
1.5
1.7
1.9
Length of Household Continuum

2.1

of columns 1 and 3 shows that newly
viable multiple-group credit unions are
indeed the key to greater credit-union
access by households, as the lion’s share
of all credit unions in every possible configuration in period 2 include multiple
common bonds.
The final row of Table 1 presents
the social optimum, which is the
welfare-maximizing combination of singleand multiple-group credit unions that is
feasible in the economy. Multiple-group
credit unions serve 93 percent of all
employee groups in the social optimum,
while single-group credit unions serve
only 2 percent. Average household participation rates are similar across the two
types of credit unions, with the multiplegroup average slightly higher.
The averages presented in Table 1
conceal two important features of credit
unions in our model, however. Figure 5
is a scatterplot showing the participation
rates of all the (optimally formed) credit
unions from our 10,000 runs as a function
of potential membership. The horizontal
scale runs from about 0.1 (the minimum
segment length needed to support a credit
union under our baseline parameterization)
to 2.0 (the sum of two unit-length segments,
corresponding to the maximum potential
membership of any multiple-group credit
union). The two distinct downwardcurving sets of points represent the

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S E P T E M B E R / O C T O B E R 19 9 9

Table 2

Simulation Results (2)
Column Parameter
Values

(1)
(2)
(3)
(4)
1
2

Participation rates as a fraction of… 2

Number of times this configuration of
credit unions was optimal:1

a

t

c

(1)
A, B, C

(2)
A&B, C

(3)
A&C, B

(4)
B&C, A

(5)
A&B&C

0
0
0
0.05

22
22
24
22

1.6
1.7
1.6
1.6

746
302
926
895

168
394
99
111

4,452
4,580
4,436
4,489

1,168
1,223
1,169
1,148

3,466
3,501
3,370
3,357

(10)
(9)
(7)
(8)
(6)
Those
Those
Number of All House- All HouseHouseholds Households
holds
holds
employee
Eligible to Eligible to Eligible to
groups not
Join a
Join a Credit Join a
served by a
MultipleSingleUnion
credit union
Group
Group
Credit Union Credit Union
7,959
4,782
8,793
8,436

0.43
0.54
0.40
0.43

0.56
0.61
0.55
0.57

Based on 10,000 runs.
Weighted by segment lengths.

credit unions of the type A&C, the
participation rate increases with a growing
membership base if (and only if) the overlap
of the intervals spanned by the two segments
increases. If (and only if) the overlap
shrinks with an increase in the potential
membership, the participation rates shrink,
too. To sum up, the overall effect of the
size of potential membership on the participation rates depends on the relative
importance of the various types of
multiple-group credit unions.
Table 2 presents comparative-static
results for changes in the parameters t, c,
and a (the travel cost parameter, the price
of banking services of commercial banks,
and the parameter in the multiple-group
credit unions’ fixed costs, respectively).
The first row restates the results of the
benchmark simulation summarized in the
last row of Table 1. Columns 1-5 show
the number of times in the 10,000 runs of
the simulation that each configuration of
credit unions was optimal. The most frequently preferred configuration was a
two-group credit union comprising
employee groups A and C (column 3),
the back-to-back solution. In this
configuration, employees of firm B were
sometimes served by a credit union and
sometimes not; the feasibility of a credit

union for employee group B depends on
the size of the membership base and the
random technology of the potential credit
union. The next most frequently preferred
configuration involved a three-group credit
union. Across all simulations, almost 27
percent of employee groups were left
unserved by credit unions even though
all mergers were chosen optimally (this
figure is calculated from column 6, which
is divided by the total number of employee
groups in the simulation, 30,000). It is
apparent that participation rates of multiplegroup credit unions (column 10) are
dragged down primarily by the relatively
low participation rates in the credit unions
with horizontally neighboring groups (i.e.,
credit unions A&B and A&B&C; recall the
result from column 6 of Table 1).
The first comparative-static exercise
we performed is summarized in the second
row of Table 2. When the price of financial
services offered by commercial banks rises,
the fraction of employee groups as well as
the fraction of households served by credit
unions increases, as expected. From
column 6 we know that only 16 percent
of employee groups have no credit union
after the higher cost of bank-provided
services is imposed, while only 46 percent
of households use a commercial bank

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55

0.54
0.64
0.50
0.54

0.56
0.61
0.55
0.57

S E P T E M B E R / O C T O B E R 19 9 9

(down from 57 percent in the benchmark
case; see column 7). Interestingly, all of the
multiple-group credit unions increasingly
are preferred when banking services
become more costly, while only the singlegroup credit unions become less likely
to be optimal. A higher price for bankprovided services is predicted by higher
banking concentration in the structureconduct-performance paradigm, and our
comparative-static result demonstrates that
credit unions are indeed likely to benefit
from more concentrated banking markets.
The second comparative-static result
we computed is summarized in the third
row of Table 2. When the cost of travelling
to a credit union is increased—intuitively,
when preferences for banking services
become more idiosyncratic or strongly
held—both the fraction of employee
groups served by credit unions and the
participation rate of households decline
(columns 6 and 7-10, respectively). Compared to the benchmark case, the number
of single-group credit unions in optimal
configurations increases (column 1).
On the other hand, multiple-group credit
unions appear somewhat less attractive
(columns 2-5).
The last row of Table 2 displays our
third comparative-static result. When the
fixed costs of production are systematically
higher for multiple-group credit unions
than for single-group credit unions, the
formation of multiple-group credit unions
is less advantageous. Relative to the
benchmark case displayed in row 1, fewer
groups of employees are served by credit
unions (column 6). When they exist,
credit unions with multiple-group charters
have higher participation rates than in the
benchmark case (column 10), which is
due mainly to the higher representation of
pure back-to-back credit unions (column
3). This leaves the overall household participation rate unchanged at the reported
two-digit level of precision (column 7).
Taken together, the comparative-static
results in Table 2 indicate that the optimal
configuration of credit unions in the
economy is sensitive to model parameters
such as the market price of bank-provided

financial services, the intensity of
preferences for specific bundles of banking
services, and the potential extra costs associated with multiple-group charters.

Hypotheses
We are now able to state several
testable hypotheses that involve the
determinants of the participation rate and
the average operating costs (i.e., the cost
ratio). First, we focus on participation
rates at credit unions. Our maintained
hypothesis is that a credit union is more
successful in providing services to its
constituency the less heterogeneous is
its membership. This leads to our first
testable hypothesis:
• HYPOTHESIS 1. A credit union’s
participation rate falls with the
number of its potential members,
all else held constant.
Another hypothesis concerns the
effects of local banking-market conditions
on credit-union participation rates:
• HYPOTHESIS 2. A credit union’s
participation rate rises with the level
of concentration in the local banking
market, all else held constant.
Next we investigate the validity of our
maintained assumption that credit unions
face scale economies in production:
• HYPOTHESIS 3a. A credit union’s
cost ratio falls with the number of its
potential members, all else held
constant.
• HYPOTHESIS 3b. A credit union’s
cost ratio falls with its level of total
assets, all else held constant.
Related questions include the effect
of multiple-group charters on the cost
ratio and the participation rate. Neither
the model nor the simulation address the
relationship between multiple common
bonds and the cost ratio. As for the impact

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of multiple common bonds on the participation rate, the model and simulation results
are ambiguous. Consequently, it is purely
an empirical question how multiple-group
credit unions affect operating costs and participation rates, holding all else constant.

Table 3

Distribution of Credit Unions by
Type Of Membership (TOM)
Number of
TOM
Credit Unions Codes 1
299
37
392
744
508
469
124
621
821
718

DATA AND EMPIRICAL
METHODS
We examine a subset of all federally
chartered and federally insured occupational
credit unions in 1996 (see the appendix
for details on construction of the dataset
and the variables we use). Table 3 provides
a breakdown of our sample according to
the type of membership group characterizing
each credit union. The table distinguishes
between credit unions with a single common
bond and those with multiple common
bonds. Credit unions sponsored by a
single educational institution, for example,
numbered 299 in our sample. Credit
unions with a membership comprising
multiple common bonds, most of which
were educationally oriented, numbered
469, and so on for the other membership
types. Overall, 1,980 credit unions in our
sample had a single common bond (41.8
percent of the sample) while 2,753 credit
unions had multiple common bonds
among the membership (58.2 percent).
In addition to data on individual credit
unions, we collected three types of
environmental variables. To control for
differences in local economic conditions,
we gathered levels and computed growth
rates of real gross state product for each
state. Measures of economic activity may
capture systematic differences in demand
for credit union services that we have not
modeled explicitly. We also calculated the
Herfindahl index of concentration of bank
deposit shares in each credit union’s local
banking market, since concentration
measures often are used to control for
differences in the competitiveness of local
markets. The index is calculated as the
sum of the squared market shares of all
participants in each local market. Third,
we collected data on population density
by county, which might be another factor

4
5
6
10-15
20-23
34
35
36
40-49
50-53

Type of Membership
Educational
Military
Federal, state, local government
Manufacturing
Services
Multiple group – primarily educational
Multiple group – primarily military
Multiple group – primarily federal, state, local government
Multiple group – primarily manufacturing
Multiple group – primarily services

Total: 4,733
1

National Credit Union Association (NCUA), Instruction No. 6010.2, July 28, 1995.

in credit unions’ competition with
commercial banks.
We use a semiparametric model to allow
the influence of the number of members
and total assets on the dependent variable
to be nonlinear. The parametric part of
the model contains independent variables
whose effects may be approximately linear,
such as the Herfindahl index. In particular,
we use a semiparametric model of a credit
union’s participation rate of the form:
(4)

yi = x pi × β p + f ( x i ) + ε i , i = 1,K , n,

where yi is the i-th observation of the
dependent variable; xpi is a row vector
consisting of the i-th observation of the
explanatory variables of the linear
(parametric) part of the model; bp is a
column vector of the parameters of the
linear part of the model; xi is a vector
consisting of the i-th observation of the
explanatory variables in the nonparametric
part of the model; and (εi is the i-th realization of the error term. For details on this
econometric approach, see the appendix
in Emmons and Schmid (1999).
Our hypotheses are framed in terms of
two different dependent variables, namely:
1) PARTICIPATION, the participation rate
of those eligible to join the credit union,

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Table 4

Descriptive Statistics1
Minimum
Participation Rate
(PARTICIPATION)

Median
–2

3.050 3 10

–1

6.246 3 10

–3

3.897 3 10

4

6.231 3 10

1

1.865 3 10

1

3.193 3 10

–2

1.966 3 10

Cost Ratio (COST)

6.268 3 10

Total Assets

4.300 3 10

Number of Members

4.500 3 10

Number of Potential Members

7.500 3 10

Herfindahl Index

5.346 3 10

1

Mean
–1

6.142 3 10

Maximum

Standard
Deviation

1

2.139 3 10

–1

–2

–1

4.169 3 10

1.739 3 10

7

8.922 3 109

1.652 3 10

3

1.601 3 10

6

2.860 3 10

4

2.032 3 10

6

5.540 3 10

–1

1

9.469 3 10

–2

4.088 3 10

6

3.300 3 10

3

6.833 3 10

3

1.432 3 10

–1

2.080 3 10

–2
8
4
4

–2

4,733 observations.

defined as the number of actual members
divided by the number of potential members as specified in the credit union’s
charter; and 2) COST, the credit union’s
total operating expenses divided by total
assets. There are four independent
variables of interest: the number of members (or the number of potential members
when we examine participation rates);
total assets (for the COST regression); the
Herfindahl index of local bank-deposit
concentration (HERF); and the indicator
variable MULTGROUP, which is equal to
one if the credit union has a multiplegroup charter and zero otherwise.
Membership (or potential membership)
and total assets are included in the
nonparametric part of both regression
approaches. They are in logarithmic form
and—to avoid simultaneity problems—are
lagged by one period. The parametric part
of the model includes the other two variables
of interest, HERF and MULTGROUP. The
parametric part also contains the following
control variables: the credit union’s home
state’s real gross state product per capita
(REALGSPPC) in the PARTICIPATION
regression; the log growth rate of real
gross state product (GRREALGSP) in the
COST regression; and indicator variables
corresponding to the credit union’s primary
field of membership (in both regression
approaches). Fields of membership include
educational, military, government,

manufacturing, and services. Because there
is a constant included in the nonparametric
part of the regression equation, we must
drop one of the membership indicator
variables; we chose the educational
indicator variable for exclusion.
The variable REALGSPPC in the
PARTICIPATION regression controls for
preferences for banking services as they
may vary with real income. In the COST
regression, GRREALGSP serves as a measure
for real growth, which is a main factor in
the capacity utilization of credit unions.
In the PARTICIPATION regression, the
Herfindahl index is lagged to avoid simultaneity problems that may arise from the
interaction between credit-union participation rates and concentration in the local
banking market.
Table 4 presents descriptive sample
statistics for the dependent and some of
the independent variables. The participation
rate among sample credit unions ranged
from 3 percent to 100 percent, with the
median at 62 percent. The median cost
ratio was 3.90 percent, with a range of
0.63 to 41.70 percent of assets. Although
this range may contain some extreme
values, we retain all observations because
all of them contain information. In
addition, our locally weighted regression
approach is somewhat robust to outliers.
Total assets ranged from $43,000 to
$8.92 billion, with the median credit

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Figure 6

union holding $6.23 million in assets.
The number of actual and potential members ranged from 45 to 1.6 million and 75
to 2.03 million, respectively, while median
actual and potential membership counts
were 1,865 and 3,198, respectively.
Finally, Herfindahl indexes in relevant
banking markets ranged from 0.0535
to 1.00 with a median value of 0.1966
(recall that the index is defined on the
interval ((0,1]).

Participation Rate – Number
of Potential Members
Partial Impact
8
6
4
2
0
–2
–4

EMPIRICAL RESULTS

–6
–8

Our results are presented in two
sections corresponding to the dependent
variable used. The first section discusses
results from regressions using credit
unions’ participation rate while the second
section reports results from regressions
using credit unions’ cost ratio.

4

6

8

10

12

14

16

Log of Number of Potential Members
Figure 7

Cost Ratio – Number of Members
Partial Impact
–2

Participation Rates

–4

Hypothesis 1 relates the size of a
credit union’s potential membership to its
participation rate. Regressions including
PARTICIPATION use (the lagged value of
the log of) potential members instead of
actual members. Potential members are
relevant for evaluating participation rates
because all individuals eligible to join constitute the predetermined economic potential
that each credit union seeks to exploit.
The series of plots presented in
Figures 6-8 are “conditioning plots.”
The solid lines in Figures 6-8 are point
estimates and the dashed lines indicate
90-percent confidence bounds. In each
plot, one variable is held at its median
value while the other variable (identified
on the horizontal axis) is allowed to vary.
The graph displays the impact of this
independent variable on the level of
the dependent variable. In other words,
the slope of the graph at a particular point
reflects the marginal impact of the independent variable at that point. The intercept
is not identified in regressions of this
type, so only vertical distances are
meaningful (not the level itself). In sum,
the key to interpreting these graphs is

–6
–8
–10
–12
–14
–16
–18
2

4

6

8

10

12

14

16

22

24

Log of Number of Members

Figure 8

Cost Ratio – Total Assets
Partial Impact
0
–2
–4
–6
–8
–10
–12
–14
–16
10

12

14

16

18

20

Log of Total Assets

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Table 5

result of a reduction in average operating
costs and hence in the credit union’s price
of banking services. On the other hand,
for a given credit-union charter, a higher
number of potential members typically
means more heterogeneity and thus a lower
participation rate as the travel distance of
the members located in the tails of the
preference distribution increases.
Table 5 presents results from the
parametric part of the model. The results
provide evidence on the question of
whether credit-union participation rates
differ when comparing credit unions
with a single common bond to those with
multiple common bonds, holding all else
equal. Recall from Tables 1 and 2 that
credit unions with multiple-group charters
will (on average) have higher participation
rates than single-group credit unions if
back-to-back membership combinations
dominate (i.e., if there is a significant
overlap of banking preferences among
employees of different firms). Table 5
indicates that multiple-group credit unions
in our sample indeed have higher participation rates, perhaps reflecting the ability
of multiple-group credit unions to capitalize
on similar preferences among employees
of different firms.
Another interesting result in Table 5
is the positive and significant coefficient
on the lagged Herfindahl index of bank
deposit concentration in credit unions’
local markets (Hypothesis 2). This
indicates that, the more concentrated its
local banking market is, the higher a credit
union’s participation rate will be. In other
words, credit unions may provide an
attractive alternative for consumers who
face a relatively uncompetitive local
banking market.

Participation Rate
t-statistic

Independent Variable

Coefficient

MULTGROUP

8.684 3 10

HERF (lagged)

3.628 3 10

–2

2.834 ***

–1

2.535 **

REALGSPPC

–1.820

POPDENS

–3.743 3 10

–1.090
–6

3.004 ***

–2

1.496

–2

–0.560

TOM: Military

2.266 3 10

TOM: Government

6.205 3 10
–2.123 3 10

TOM: Manufacturing

1.304 3 10

TOM: Services
Number of Observations

–1.002

–1

–1

3.284 ***

4,691

**/*** Significant at the 5/1 percent level (two-tailed tests).

5

See Cleveland and Devlin
(1988).

to focus on the slope of the curve and
on the vertical differences moving along
the horizontal axis.5
Figure 6 provides evidence supporting
Hypothesis 1 (a negative relationship
between participation rates and potential
membership). The plot supports Hypothesis 1 because the lower confidence bound
at small credit unions (small number of
potential members) lies above the upper
confidence bound for large credit unions,
except for the very smallest and very largest
credit unions, where the small number
of observations widens the confidence
intervals. This confirms our findings
when we simulated the theoretical model
(recall Figure 5) and is consistent with the
idea that larger membership pools contain
greater heterogeneity of preferences for
banking services. This leads to greater
differences in the most preferred bundle
of banking services between the median
member and members in the tails of the
preference distribution.
An existing single-group credit union
that adds one or more membership groups
to its common bond encounters both benefits and costs of expansion. On the one
hand, adding membership groups whose
preferences are close to those in the existing
field of membership (the back-to-back
case) may increase the participation rate.
This outcome would be predicted as a

Cost Ratio
Hypotheses 3a and 3b refer to tests
of an important maintained assumption
of our model, namely, that a credit union’s
operating expenses should decline with an
increase in its scale of operation. We also
would like to know whether serving multiple-group memberships is costly.

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Table 6

Figure 7 plots COST against the
number of members, while holding the
level of total assets constant at its median
value in the sample. The plot shows that
COST decreases sharply beyond a certain
threshold level of membership. For small
credit unions, average costs seem to increase
slightly with the number of members.
While wide confidence intervals indicate
that in this range the relationship between
average costs and number of members is
estimated imprecisely, an initial increase in
the average operating costs actually might
be supported by the data. For small credit
unions, subsidies (such as rent-free office
space, volunteer workers, etc.) tend to be
relatively more important than for large
units. As these subsidies become less
important for credit unions with higher
numbers of members, measured operating
costs might approach shadow operating
costs. Overall, the findings support our
maintained assumption of declining
average costs as the scale of operations
increases. Similar evidence is provided in
Figure 8, which is generated by the same
regression that produced Figure 7. Figure
8 plots the influence of another measure
of the size of operations, total assets, on
the credit union’s average operating costs
(Hypothesis 3b) while holding the number
of members constant at its median value
in the sample.
Table 6 presents results from the
parametric part of the model. The results
indicate that there is a positive relationship
between the existence of multiple membership groups in a credit union and COST.
One might think that multiple-group credit
unions would have high cost ratios due
to agency costs. According to this line of
reasoning, as membership groups try to
free-ride on each other’s monitoring, supervision of management might be inefficiently
low. As Emmons and Schmid (1999) show,
however, there is no evidence of multiplegroup charters causing agency costs.
Finally, the significantly negative coefficient on the Herfindahl index in Table 6
implies that higher levels of bank concentration in a local market lead to lower levels of
the cost ratio reported by credit unions.

Cost Ratio
t-statistic

Independent Variable

Coefficient

MULTGROUP

7.509 310–2

6.847 ***

HERF

–1.813 310–1

–3.427 ***

GRREALGSP

–8.448 3 10–1

–2.377 **

TOM: Military

–1

1.038 3 10

4.533 ***

TOM: Government

1.149 3 10–1

8.043 ***

TOM: Manufacturing

–1

1.036 3 10

7.444 ***

TOM: Services

8.915 3 10–2

6.019 ***

Number of Observations

4,733

**/*** Significant at the 5/1 percent level (two-tailed tests).

One possible explanation is that less
intense competition from banks allows
credit-union managers to enjoy a “quiet
life.” For example, credit unions may
be able to attract or retain members with
lower marketing efforts or lower quality
services than would be the case in a more
competitive market. On the other hand,
the quiet life that comes with less competitive markets might allow greater scope
for managerial agency costs. If the latter
were the case, however, it would generate
predictions opposite to our empirical findings of lower average operating expenses.

CONCLUSIONS
Continued expansion of credit unions
has been accompanied by public debate
and courtroom confrontations. Advocates
argue that credit unions provide needed
competition to banks and thrifts in local
markets for retail financial services. Opponents, including most notably the banks
and thrifts themselves, point to various
subsidies to credit unions that create an
unlevel playing field. Previous research
findings do not provide unambiguous
conclusions favorable to either camp, while
recent federal legislation favorable to creditunion expansion merely has intensified the
debate. More research into the fundamental
operation of credit unions is needed.

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In this article, we investigate the
relationships between several features
of credit unions, namely the number of
members in a credit union, the amount of
total assets on its balance sheet, and the
existence of single and multiple common
bonds among its membership, on the one
hand, and two measures of credit-union
effectiveness, on the other. We also examine
the effect of several environmental variables,
including economic conditions and banking
concentration in the local market, on
credit-union operations.
We find that a larger potential creditunion membership translates into lower
credit-union participation rates. Credit
unions with multiple common bonds,
holding all else constant, have higher participation rates. We also find evidence that
credit unions in more concentrated
banking markets exhibit higher participation rates.
While greater asset size appears to be
associated with lower average operating
costs, holding all else equal, we find that
a larger number of members is associated
with a lower cost ratio only for larger credit
unions. Thus, asset size and the size of the
membership are distinct aspects of creditunion operations. Multiple-group credit
unions have higher costs on average, all
else equal. We also find that credit-union
cost ratios are lower in more concentrated
banking markets, perhaps indicating that
credit unions can economize on marketing
or service provision when competition
from banks is less intense.
Our findings are particularly interesting
in light of the recent AT&T Family Credit
Union case decided by the Supreme Court
in February 1998, and its sequel in the
U.S. Congress that culminated in the
Credit Union Membership Access Act of
August 1998. This new federal legislation
upholds the right of federally chartered
credit unions to grow under an expansive
definition of the common-bond requirement.
The new law allows multiple groups of
members to belong to a single credit union
as long as the members of each group are
united by a common bond. This statute
therefore upholds regulatory actions taken

in recent years and overturns the Supreme
Court’s narrow reading of the 1934 Federal
Credit Union Act restricting a federal
credit union to a single common bond.

REFERENCES
American Bankers Association. The Credit Union Industry: Trends,
Structure, and Competitiveness (Washington, D.C., 1989).
BNA Banking Report. “House Passes Credit Union Bill; Clinton Wastes
No Time Signing It,” August 10, 1998, Vol. 71, No. 6.
Cleveland, William S., and Susan J. Devlin. “Locally Weighted
Regression: An Approach to Regression Analysis by Local Fitting,”
Journal of the American Statistical Association (September 1988),
pp. 596-610.
Emmons, William R., and Frank A. Schmid. “Wages and Risk-Taking in
Occupational Credit Unions: Theory and Evidence,” this Review
(March/April 1999), pp.13-31.
Hotelling, Harold. “Stability in Competition,” Economic Journal,
(March 1929), pp. 41-57.
Kane, Edward J., and Robert Hendershott. “The Federal Deposit
Insurance Fund that Didn’t Put a Bite on U.S. Taxpayers,” Journal
of Banking and Finance (September 1996), pp. 1305-27.
Milgrom, Paul, and John Roberts. Economics, Organization and
Management, Prentice Hall, 1992.
Supreme Court. “National Credit Union Administration, Petitioner, v. First
National Bank & Trust Co., et al.; AT&T Family Federal Credit Union,
et al., Petitioners, v. First National Bank and Trust Co., et al.” Decided
Feb. 25, 1998. Nos. 96-843, 96-847. 118 S. Ct. 927.
U. S. Treasury Department. Credit Unions, U.S. Government
Printing Office, 1997.

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Appendix

DATASET AND VARIABLES

deposits (as of June 30) within a county
based on FDIC Summary of Deposits data.
These data are available online at
<http://www2.fdic.gov/sod/>.
We used either the log level of Real Gross
State Product (REALGSP) or its log growth
rate to control for cross-sectional differences
in macroeconomic conditions facing credit
unions. The REALGSP data are in millions
of chained 1992 dollars. We obtained the
data from the U.S. Department of
Commerce, Bureau of Economic Analysis,
Regional Economic Analysis Division. The
data are available online at <http://www.bea.
doc.gov/bea/regional/data.htm>.
Population density at the county level
was calculated by dividing the total county
population by the total land area of the
county (in square miles). Both the county
population and land area data were
obtained from the U.S. Census Bureau
<http://www.census.gov>. The population
data are Census Bureau estimates as of
July 1, 1996. The land area measurements
are from the 1990 census.

The Dataset
We analyze a dataset comprising all
federally chartered and federally insured
credit unions during the year 1996. The
dataset was obtained from the Report of
Condition and Income for Credit Unions
(NCUA 5300, 5300S), produced by the
National Credit Union Administration
(NCUA). These reports are issued semiannually in June and December. We used
the December data. The flows in the
December income statements include
the entire year of 1996.
We concentrate on the following Types
Of Membership (TOM) groups among
occupationally based credit unions: educational; military; federal, state, and local
government; manufacturing; and services.
This means that we do not include
community credit unions, associational
credit unions, or corporate credit unions.
Lists of TOM classification codes are from
the NCUA (Instruction No. 6010.2, July
28, 1995).
We excluded observations for any of
the following reasons:
• Missing TOM codes.
• Activity codes other than “active.”
• Number of members or of potential
members not greater than one; applies
to actual and to lagged values.
• Nonpositive values for total assets
or lagged total assets.
• Zero number of employees.
• Zero value for “employee
compensation and benefits.”
Total assets, number of members,
potential number of members, and the
Herfindahl index were all lagged one year
(i.e., 1995 values). All other observations
are from year-end 1996.
We calculated county-specific
Herfindahl indexes as measures of concentration of the local banking market. A
Herfindahl index is defined as the sum of
squared market shares. We measured
market shares by the fraction of total bank

Definition of Variables
We transformed the dependent
variables in some cases to ensure that they
are not bounded. These transformations
are necessitated by the assumption of
normally distributed error terms. For
variables that are restricted to the positive
orthant of real numbers, we substitute their
natural logarithms. For variables expressed
as fractions (i.e., restricted to the interval
[0,1]), we applied the logit transformation
log(y/(1–y)), with log being the natural logarithm. In this case, observations equal to
one were eliminated from the set of observations; there were no cases in which the
transformed variable equaled zero.
Definitions of variables and underlying
data sources are listed below. For data
taken from the Report of Condition and
Income for Credit Unions, produced by
the National Credit Union Administration,
the relevant item numbers are in brackets.

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Dependent Variables. We employed two
dependent variables in the regressions:
1) Participation Rate (PARTICIPATION):
Number of actual credit-union
members [CUSA6091] divided by
the number of potential members
[CUSA6092]. In the regressions,
we use the logit transformation
log(y/(1–y)). No zero values for the
number of members occurred. Fortytwo cases of full participation (y = 1)
were eliminated from the dataset for
these regressions only.
2) Cost Ratio (COST): Total operating
expenses [CUSA4130] divided by total
assets [CUSA2170]. In the regression,
we use log values.
Independent Variables. When total assets
(measured in units of one dollar), the
number of members, or the number
of potential members served as regressors,
they were lagged by one period and transformed into natural logarithms.
1. MULTGROUP: equal to one if the
credit union has multiple groups;
zero otherwise.
2. HERF: Sum of squared market shares
of commercial banks within a county
based on total bank deposits. By definition, the Herfindahl index is greater
than zero; its maximum value is one.
3. REALGSPPC: Real gross state product
per capita (chained 1992 dollars).
4. GRREALGSP: Logarithmic changes in
the real gross state product (chained
1992 dollars).
5. POPDENS: Population Density,
people per square mile in each
local banking market.
6. TOM code variables: equal to one if
the credit union is of a specific type
(educational, military, government,
manufacturing, or services). Because
we use an intercept in (the nonparametric part of) the regression, the
TOM code variable for the educational
credit union was dropped.

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64