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ECONOMIC REVIEW

FEDERAL RESERVE BANK
OF CLEVELAND

1
http://clevelandfed.org/research/review/

ECONOMIC REVIEW
2001 Quarter 4
Vol. 37, No. 4

Estimates of Scale and Cost Efficiency
for Federal Reserve Currency Operations

by James Bohn, Diana Hancock, and Paul Bauer
Meeting the currency demands of depository institutions, businesses,
and consumers costs the Federal Reserve more than half a billion dollars
each year, yet very little research has been devoted to understanding what
factors affect such costs. This paper estimates a cost function in order to
obtain estimates of scale and cost efficiency for this service. Similar to
other paper-based technologies, such as checks, we find that scale
economies are achieved at a relatively low level of output, implying that
currency services are not a natural monopoly. We also provide estimates
of facility-specific marginal costs and returns-to-scale measures that
could potentially be used to improve resource allocations. Lastly, we find
that the average processing facility operates at more than 80 percent of
the efficiency of the “best-practice” facility, comparable to cost-efficiency
estimates that have been reported elsewhere for private-sector financial
institutions.

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ISSN 0013-0281

Estimates of Scale and Cost
Efficiency for Federal Reserve
Currency Operations
by James Bohn, Diana Hancock, and Paul Bauer

Introduction
It is the conventional wisdom that a government monopoly in the provision of currency is
an appropriate public policy. In fact, although
Congress required the Federal Reserve to
establish a system of fees for its payment
services (check clearing and collection, wire
transfers, automated clearinghouse transfers,
and securities safekeeping) to encourage competition and to promote payment system efficiency, it did not require any charges for cash
services of a “governmental nature,” such as
the disbursement and receipt of new or fit coin
and currency.1 Accordingly, provisions in the
Monetary Control Act of 1980 require a schedule
of fees only for cash services such as coin
wrapping and transportation. Congress felt that
it could safely open such services to competition
from the private sector because the provision
of these services is not essential to the Federal
Reserve in its pursuit of its primary responsibility
“to provide the nation with currency and coin
of high quality” nor with the Federal Reserve’s
ability to “expand or contract the amount of
currency and coin in response to the public’s
demand.”2

James Bohn is an associate at the Brattle
Group, in Cambridge, Mass., Diana Hancock
is the chief of monetary and financial studies
at the Board of Governors of the Federal
Reserve System, and Paul Bauer is an
economic advisor at the Federal Reserve Bank
of Cleveland. The authors thank Jon Cameron,
Eric Severin-Lossin, and James Thomson for
their valuable comments and suggestions.
All errors remain those of the authors.

Recently, some researchers have developed
stylized theoretical models to defend this conventional wisdom, while others have begun to
question it. Two themes, which do not necessarily depend upon one another, have emerged
to support the view that a currency monopoly
is economically efficient. One theme is that
currency provision is a natural monopoly.3
This natural monopoly arises in part because
there are increasing returns to scale that result
from the cross-sectional independence of
demands for individual redemptions of currency.4 Increasing returns to scale could also
arise because fixed costs are high—sophisticated technology for soil measurement and

■ 1 During the course of congressional consideration of the
Monetary Control Act of 1980, Senator Proxmire indicated that the
Federal Reserve would not be required to charge for these services.
(Remarks of Senator William Proxmire, Congressional Record (daily
edition), March 27, 1980, p. S 3168.)
■ 2 See U.S. Congress (1980, S3168, March 27).
■ 3 See King (1983, pp. 132–33).
■ 4 Miller and Orr (1966) provide a cash-management model that
possesses this increasing-returns-to-scale property.

counterfeit note detection is needed to process
currency, and transporting currency is expensive. The second theme focuses on the impracticality of interest-bearing currency. It is argued
that the computation, information, and transaction costs of collecting interest on currency
can easily exceed the value of the interest that
might be collected, particularly for low-denomination notes.5 In this environment, it is argued
that competitive currency providers would have
an incentive to take actions that increase the
“quality” of currency (for example, by making
expenditures that would reduce counterfeiting
or improve the fitness of notes). To the extent
that such in-kind benefits are valued by consumers at less than their cost of production,
seigniorage (the difference between the nominal interest rate and the cost of production)
would be wastefully dissipated.6
The view that a competitive currency market
would be more efficient than a monopoly
provider is based on the argument that competitive providers would choose to offer higherquality currency services—at a higher cost—
only when the additional cost is justified by the
additional value of output.7 Implicitly, it is
assumed that competitive firms are not legally
restricted from freely employing whatever technology is most cost efficient.8 That is, the
monopolist and the competitive firm have
identical costs for providing a given quantity
and quality of currency services. Under such
circumstances, nonprice competition improves
social efficiency because a monopolist has no
incentive to provide an appropriate level of
currency services with the valued quality
enhancements.
It is unlikely, however, that a monopolist
and a competitive firm would have identical
costs for providing a given quality and quantity
of currency services. This is because monopolists tend to pursue the objective of cost minimization less effectively than do competitive
firms, being more likely to produce at an
inefficient level of output (scale inefficiency) or
to produce a given level of output with more
resources than are required (cost inefficiency).
Thus, competition among providers of currency
services may be beneficial because such
providers may be induced to be more scale and
cost efficient than a monopoly provider.
Although an empirical understanding of
currency cost considerations would enlighten
the foregoing discussion, there is a dearth of
research on such topics. First, only two studies
have analyzed the scale economies for currency
provision, Zimmerman (1981) and Dotsey
(1991). Neither of those studies is likely to

shed light on potential scale economies today,
however, because they were based on data
from periods (1977 and 1988 –90, respectively)
when the Federal Reserve used relatively
unsophisticated technologies to determine the
fitness level of notes, detect counterfeits, and
destroy unfit notes. New currency processing
technologies may have increased potential
scale economies. Second, because it is a complex task to estimate the costs of improving
currency quality, such studies have been
performed even more sporadically. Currencyquality cost estimates require quality measurements (such as soil-detection standards) and
calculations that measure changes in currency
handling costs that might arise from changes to
these qualities. These calculations are complicated even more because handling costs also
depend on a number of other intertwined
factors. For example, if currency quality is
improved (by improving the quality of existing
notes or adding additional anticounterfeiting
features, for example), handling costs may rise
due to factors such as a higher destruction rate
for unfit currency, additional printing costs for
the new notes, a shorter life span for these
notes, and possibly the need to process additional volume.9 Finally, there are no studies
that estimate the cost efficiency of Federal
Reserve currency operations. For Federal
Reserve payment services that do compete
with private sector providers, cost-efficiency
estimates are available (Bauer and Hancock

■ 5 See Fama (1981, 1983), White (1987), and Sumner (1993).
■ 6 See, for example, Fama (1983) and Sumner (1993, 2000).
■ 7 See White and Boudreaux (2000, p. 152).
■ 8 Lacker (1996) has discussed the case in which competitive
private issuers have an industry cost curve everywhere higher than that of
a monopoly issuer because of legal restrictions on the competitors’
technology choice.
■ 9 Although the following example moves currency quality in the
opposite direction, in 1991 the Federal Reserve System estimated that
it would cost about $1.2 million per year (in 1990 dollars) if it lowered
the minimum quality threshold for recirculated notes by one step on a
16-step measurement scale, but such costs would be offset by lower
annual printing costs of about $7.6 million per year, which would be
absorbed by the Bureau of Engraving and Printing. Over a 10-year period,
the discounted net present value of savings from a one-step decrease in
the minimum quality threshold for U.S. currency was estimated to be
$82.9 million. See Board of Governors of the Federal Reserve System
(1991, pp. 1–14).

[1993], Bauer and Ferrier [1996]). Such estimates
are comparable to those for private-sector
financial institutions reported elsewhere (such
as Bauer, Berger, and Humphrey [1993] and
Berger, Hancock, and Humphrey [1993]).
This paper explores the Federal Reserve’s
cost of providing currency services, using
quarterly data from 1991 to 1996. Whereas
previous studies (Zimmerman [1981] and Dotsey
[1991]) were concerned only with whether a
Federal Reserve currency processing and handling facility was producing an efficient level
of output (scale efficiency), this study also
considers cost inefficiency (deviations from the
cost frontier), which is sometimes interpreted
as X-inefficiency. Cost inefficiency occurs when
actual costs are higher than the minimum
possible for a given level of output, either
because more of each input is employed than
is required by the production process or
because inputs are employed in suboptimal
proportions.
We construct and compare several different
models of currency operations to test the
robustness of our results. A unique aspect of
this study is that we have detailed information
about the equipment that was used at each
facility. This information included the number
of processing machines of each type, an implementation schedule for new equipment installations, and usage statistics that indicated the
amount of “downtime” each piece of equipment experienced at each facility. These data
allow us to account in our cost-function specifications for the unavoidable transition costs
associated with the introduction of a new
technology. Such adjustment costs could significantly affect the scale and cost efficiency
of each facility as it deployed the new technology.10 In addition, because the cost functions
we estimate depend not only on costs associated with keeping fit currency in circulation
but also on the costs associated with destroying
unfit currency, the parameter estimates could
possibly be used to forecast changes in processing costs associated with changing the
quality of currency in circulation.11
The next section describes the currency
operations of the Federal Reserve System.
Section II discusses the cost-function specifications we use and the econometric techniques
we employ to estimate the cost frontier and
facility-level returns to scale and cost efficiencies. Section III describes the data for output
and input quantities as well as input prices.
Section IV presents our estimates of returns
to scale, marginal costs of different outputs,
and facility-level cost efficiencies for

Federal Reserve currency processing and
handling facilities. Section V concludes and
discusses some policy implications of our
empirical findings.

I. Background
The Federal Reserve’s involvement in the
provision of paper currency dates back to its
founding in 1913. The provisions of the Federal
Reserve Act relating to currency were designed
to provide for an “elastic currency” that could
expand and contract as the public’s demand
for cash increased and decreased.12 Prior to
that time, the kinds of currency in circulation
had proved incapable of meeting the needs for
additional amounts that developed from time
to time on a seasonal and cyclical basis as well
as in periods of financial crisis.
The first Federal Reserve notes were issued
in late 1914. By statute, these notes were
obligations of the United States, a first lien on
the assets of the issuing Federal Reserve Bank,
backed 100 percent by discounted commercial
notes and bills and a 40 percent gold reserve.13
These notes were redeemable in gold or
lawful money.
In 1920, the Appropriations Act authorized
the Secretary of the Treasury to transfer to the
Federal Reserve Banks and branches various
functions that were performed in connection
with the issue, exchange, and replacement of
U.S. paper currency and coins and the receipt
for redemption of national bank notes and
Federal Reserve Bank notes.14 This assumption
of duties by the Federal Reserve Banks and
branches led to an improvement in the overall
quality of U.S. currency and an improvement
with respect to the supply of notes of desired
denominations.15

■ 10 See Hancock, Humphrey, and Wilcox (1999).
■ 11 As noted above, such cost estimates would play a role in
estimating the social costs that would be incurred to improve currency
quality.
■ 12 See Booth (1989).
■ 13 In 1934, the Gold Reserve Act stopped redemption of currency
for gold. In 1968, the requirement of gold reserves against Federal
Reserve notes was eliminated. Also in 1968, the redemption of currency
for silver was discontinued.
■ 14 See U.S. Treasury Department, Circular No. 55.
■ 15 These improvements were noted in the 1921 Annual Report of
the Board of Governors of the Federal Reserve System.

In 1980, Congress again expanded the role
of Federal Reserve Banks with respect to the
distribution of currency and coin. The Monetary
Control Act of 1980 (MCA) authorized Federal
Reserve Banks and branches to distribute
available supplies of coin and currency to
depository institutions, including not only
member and nonmember banks, but also savings
banks, savings and loan associations, and credit
unions. This change dramatically increased the
number of end points served by the Reserve
Banks. In addition, the MCA required that
transportation of coin and currency as well as
coin-wrapping services be provided according
to a schedule of fees established by the Board
of Governors of the Federal Reserve System.
The growing number of institutions with
access to Federal Reserve cash services, in
conjunction with the limited facilities of
Reserve Banks, led to the adoption of “uniform
cash service standards” in 1984. These standards
defined normal service to each depository
institution as once per week; indicated that
Reserve Banks would accept deposits of
reusable currency and coin when a depository
institution accumulates a surplus that cannot be
reasonably stored or disposed of by direct
exchange with other depository institutions;
and minimized or eliminated, where practicable, “cross-shipments” (the deposit of excess
fit currency and reorder of the same denomination within five business days).16
Today, Federal Reserve Banks and branches
have significant currency and coin responsibilities. Most Federal Reserve Banks and branches
maintain facilities for currency processing,
handling, and distribution. These facilities are
specially constructed, high-security areas that
receive new notes from the Bureau of Engraving
and Printing and used notes from depository
institutions with excess currency holdings.
Used notes are deposited in the form of straps
(bundles of one hundred notes) and blocks
(bundles of ten straps). Straps and blocks are
manually counted in the receiving area,
catalogued, and stored in a vault for a short
period of time, generally between 10 and 15
days, although deposits of $1 notes often
exceed 30 days.
Used notes are counted and verified as
genuine on high-speed currency sorters. This
equipment is fairly sophisticated and performs
many tasks. First, the packaging material on
each strap is removed. Second, sensors determine which notes are fit for circulation. A note
may be deemed unfit because of its physical
condition: It may be torn or have holes in it,
be too soiled, or no longer have a sufficiently

crisp texture. Unfit notes are destroyed using
on-line shredders that are attached to the highspeed equipment. Fit notes are repackaged by
the sorter into straps and blocks for workers to
return to the vault. Third, counterfeit notes or
those that cannot be read by the high-speed
equipment are sent to workers who manually
examine each note and pass it through a lowspeed machine that, along with the high-speed
machines, reconciles the account of the
depositing depository institution.
Over the last 20 years, the Federal Reserve
has adopted increasingly sophisticated
machines that are better able to determine the
fitness level of notes and detect counterfeits.
The first generation of high-speed currency
sorters, Currency Verification, Counting, and
Sorting (CVCS) machines, were installed during
the 1980s. These machines were gradually
replaced by a second generation of high-speed
currency sorters, Banknote Processing System
(BPS) 3000 machines, which were installed
during the 1990s. This second generation
of machines was subsequently upgraded with
new software and hardware to improve
performance.
Currency, whether fit or new, enters circulation when withdrawn by a depository
institution. Depository institutions cannot
specifically request new currency from the
Federal Reserve. Rather, orders are filled with
the first available currency from the vault.
Federal Reserve offices handle a considerable
amount of currency each year (table 1). In
1999, for example, more than 7 billion notes
were destroyed and more than 9.5 billion new
notes were put into circulation.

II. Estimation
Techniques
A variety of econometric techniques have been
developed for estimating cost frontiers. Such
techniques employ a specific flexible functional
form for the cost function, and each one
imposes some additional assumptions about
the statistical properties of the inefficiency
terms. In this paper, we use two different

■ 16 These standards have since been modified. See the Federal
Register notice dated April 30, 1996, for a detailed discussion of the
uniform cash access policies, which became effective May 1, 1998.

T A B L E

Currency in Circulation, New Notes Issued, and
Notes Destroyed, 1999 (millions of pieces)
Dollar
denomination

Notes in
circulation

New notes
issued a

Notes
destroyed

3,767

7,536

3,865

602

1,799

866

694

1,620

788

616

5,804

2,744

1,736

1,294

426

183

100

3,862

879

257

Total

22,516

9,593

7,257

a. Does not include additions to inventory at Reserve Banks.
SOURCE: Annual Report, Budget Review, Board of Governors of the Federal
Reserve System (2000).

functional forms for the cost function. This
allows us to examine the robustness of our
results to different assumptions with respect
to the functional form of the cost function. In
addition, we use two different frontier estimation techniques to ascertain how robust our
facility-level efficiency rankings are to alternative assumptions about the statistical properties
of the inefficiency terms.
The first functional form for the cost function
we consider is the translog,
J

1
(1) ln Cit = β0 + βj ln yjit + _
2
j=1
L

+ δl ln w lit +
l=1

1
+_
2

lar quarter and zero otherwise and is meant to
allow for seasonal effects. The Tit terms allow
for adjustment costs associated with the installation of second-generation equipment (BPS
3000 machines). Since such costs were not
necessarily linear over time, we define three
adjustment-cost variables, T1it , T2 it , and T3it .
The first two, T1it (T2 it ), are indicator variables
that equal one in the first (second) quarter that
a machine was installed, and zero otherwise.
The third, T3it , is a time-trend variable that
begins three quarters after the new machine
was installed. Finally, u and v represent deviations from the cost frontier due to facility-level
cost efficiency (u ≥ 0) and statistical noise (v).17
The translog cost function is a second-order
approximation to any function about a point of
expansion and has been used extensively in
recent years. Unfortunately, as one moves
away from the point of expansion, the approximation becomes less precise.18
Because we derive our estimates of scale
economies and marginal costs from the relationship between outputs and cost, we must
be careful to specify the relationship with a
sufficient amount of flexibility to ensure that
the true underlying relationship between cost
and output can be revealed. To explore
whether the translog is flexible enough, we
also employ a “hybrid-translog” cost function.
This cost function includes the terms of the
translog model (equation [1]) together with
first-, second- and third-order trigonometric
terms of the Fourier functional form.19 More
formally, the hybrid-translog takes the form

βjk ln yjit ln ykit

j=1 k=1

δjl ln yjit ln wlit

j=1 l=1

L M

lm lnwlit lnwmit + χn ln enit

l=1 m=1

n=1

1996

t=1992

q=1

+ t Dt + ηq Q q
3

+ j Tjit +uit + vit ,
j=1

where i and t indicate that an observation is for
facility i at time t, y is a vector of output
quantities, w is a vector of input prices, and e
is a vector of N environmental variables (these
are described in more detail later). D is a set of
indicator variables that equals one in a particular year and zero otherwise and is meant
to allow for technical change. Q is a set of
indicator variables that equals one in a particu-

■ 17 Estimates of ui , the facility-specific cost-efficiency term, need
to be interpreted with care. These estimates are conditional on assumptions about the functional form for the cost function and its error terms.
■ 18 Generally, the expansion point used is the mean of the data.
■ 19 The hybrid-translog functional form has been used by Gallant
(1982) and Berger, Leusner, and Mingo (1997).

(2) ln Cit = β0 + βj ln yjit
j=1

1
+_
2

βjk lny jit ln ykit + δl ln wlit

j =1 k=1
J

l=1

δjl ln yjit lnwlit

j=1 l=1

L M

1
+ _ lm lnwlit lnwmit
2 l =1m=1
N

+ χn ln enit
n=1

1996

t=1992

q=1

+ t Dt + ηq Q q
3

+ j Tjit
j=1

+ [j cos zjit +j sinzjit ]
j=1
J

+ [jk cos(zjit +zkit ) +jk sin(zjit +zkit )]
j=1 k=1
J

explore how sensitive our results are to differing assumptions. The generalized least squares
(GLS) estimation technique uses the longitudinal aspect of the data and avoids assuming
a specific distribution for the inefficiency
term.21 Basically, this technique uses repeated
observations over time to identify firm-specific,
time-invariant inefficiencies, that is, uit=ui .
Iterative, seemingly unrelated regression techniques are used to estimate the system of cost
and input share equations using longitudinal
data. The inefficiency terms are calculated by
using the average of the residuals for each
facility i,
ˆi . The most efficient currency handling facility in the sample is assumed to be
fully efficient, and the inefficiency of every
other facility i is measured by the proportionate
increase in predicted costs above the predicted
cost of the most efficient facility, or
ˆi – min
ˆj .

+ [jkl cos(zjit +z kit +z lit )
j=1 k=1 l=1

+ jkl sin(zjit +z kit +z lit )] +u it +vit ,
where the zjit are the output quantities normalized over the range (0, 2 π ). Equations (1) and
(2) are estimated along with corresponding
equations for input shares, with the usual
restrictions on symmetry and linear homogeneity imposed.
Although the currency processing machines
themselves are quite intricate, the production
technology for currency processing, as revealed
by the cost function, may be relatively simple.
If this hypothesis is correct, then the translog
functional form should adequately characterize
currency processing. One risk associated with
using the hybrid-translog functional form is
that the data may be overfitted. That is, statistical noise in the data may be absorbed into
the cost function. By estimating both functional
forms, we can obtain a deeper understanding
of the relationship between output and costs.
We use two different econometric techniques to measure facility-level cost efficiencies
for Federal Reserve currency processing and
handling operations because empirical measurements of cost efficiency in the financial
services industry often vary significantly
depending on the methodology employed.20
By estimating the model two ways, we can

For GLS estimators to be consistent, the density
of the inefficiency disturbances must be
nonzero in the neighborhood of (0, ω) for
some ω> 0. In other words, as the number of
facilities in the sample increases, the probability
that a facility lies near the frontier approaches
one. Our efficiency measure is calculated using
the log difference in average residuals between
the facility on the cost frontier and the actual
average residual of facility i , or exp(– (
ˆi –
min
ˆj ). This measure is bounded between zero
j

and one, with the most efficient facility having
an efficiency value equal to one.
The maximum likelihood technique (MLE)
identifies inefficiency primarily by the skewness in residuals, rather than by persistence
over time.22 Statistical noise, v, is assumed to
be normally distributed, while inefficiency, u,
is assumed to be half-normally distributed. Our
MLE measure of inefficiency is calculated as
the conditional mean, E (u|u+v).23 Because the
MLE technique requires a priori assumptions
concerning the distribution of the inefficiency
terms while the GLS technique does not, we
tend to favor the GLS results. Both cost-

■ 20 See, for example, Ferrier and Lovell (1990), Bauer, Berger,
and Humphrey (1993), and Berger (1993).
■ 21 See Schmidt and Sickels (1984).
■ 22 The maximum likelihood technique we employ is based on
Bauer, Ferrier, and Lovell (1987).
■ 23 This technique was developed by Jondrow, Lovell, Materov,
and Schmidt (1982).

efficiency measures are presented below to
ascertain how robust our facility-level
efficiency rankings are to alternative assumptions about the statistical properties of the
inefficiency terms.
In practice, managers at each facility may
have little ability to vary the amount of equipment and building inputs used over the short
run. Adding vault space, for example, would
require considerable modifications to a facility
because of the high security required for such
space. Also, high-speed currency processing
machines are relatively unique, and when they
were last purchased in 1990, enough were purchased to meet anticipated demand through
2003. If an input, l, is, for all practical purposes,
fixed, then it is appropriate to use the input
quantity, qlit , rather than the input price, wlit , in
the cost function. This substitution would be
appropriate regardless of the functional form
chosen for the cost function or the estimation
technique employed. Returns-to-scale measures,
of course, depend on whether inputs are fixed
or variable. When all inputs are variable, returns
to scale (RTS) can be measured using the cost
elasticity ( l δ lnC/δ lnql ). When K inputs are
fixed over the short run, the fixed-input version
of the RTS measure is:
J

[ δ lnC ( yit , wit , qkit )/δ lnyjit ]

(3) RTS =

j=1
K

1 – [ δ lnC ( yit ,wit ,qkit )/δ ln qkit ]
k =1

If the RTS measure is greater than one, then
costs increase more than proportionately with
output, which implies that the facility is operating
in a region where there are diseconomies of
scale. If, however, the RTS measure is less than
one, then the facility is operating in a region
where there are increasing returns to scale.
Only when the RTS measure equals one, is the
facility operating with constant returns to scale.

III. Data
We collected quarterly data (1991 to 1996,
inclusive) on total costs, output volumes, input
prices, input quantities, and environmental
variables for 37 Federal Reserve currency
processing and handling facilities. We chose
this time period because it was a fairly tranquil
period for currency operations. Before 1991,
some Federal Reserve facilities used an assortment of currency processing machines in
addition to the first generation of high-speed

processors, the CVCSs. After 1996, new note
designs were introduced—the $50 note in
October 1997 and the $20 note in September
1998.24 Also, as the century date change drew
near, the amount of currency outstanding
increased substantially.25 In all, the sample
included 886 observations.26
The primary data source is annual functional
cost accounting records from the Federal
Reserve’s Planning and Control System (PACS),
which are collected to monitor costs and
improve resource allocation within the System.
These data are supplemented by other cost data,
machine counts, and usage statistics; data from
occasional Federal Reserve surveys; and price
index information from the Bureau of Economic
Analysis and the Bureau of Labor Statistics.
Total costs for each currency facility, Cit ,
include the direct costs that arise from highspeed currency processing; off-line currency
verification, destruction, and cancellation; and
currency paying and receiving operations.
Associated with these cost-generating activities
are three distinct and measurable outputs. We
include in the output vector, yit , the number of
fit notes generated by the high-speed currency
processing operations, yfit ; the number of notes
destroyed either on-line by the high-speed
machines or off-line at the reconciliation
stations, ydit 27; and the total number of transactions with depository institutions, that is,
the sum of the number of incoming shipments
of currency received at facility i and the
number of outgoing orders for currency filled
by facility i, ynit .
Inputs used in currency operations are classified into buildings, B, labor, L, equipment, E,
and materials, M. Buildings’ share of total
currency costs averages only about 16 percent

■ 24 The new design for the $100 note was introduced in March
1996. Because the average life of a $100 note is about 8.5 years, however,
the number of $100 notes received by the Federal Reserve in 1996 (about
1 billion notes) was relatively small compared to the number of smallerdenomination notes received (about 22.6 billion notes). Thus, the
introduction of the new design for the $100 note is unlikely to have
materially affected the Federal Reserve's currency operations in 1996.
■ 25 Total currency in circulation increased about 22 percent in
1999, although it had only grown about 7 percent per annum in the
previous four years.
■ 26 Although the Helena, Montana, facility operated during the two
quarters when the new BPS 3000 machines were installed, there are no
reported volumes for this period.
■ 27 Off-line destruction is undoubtedly more labor intensive and
consequently more expensive, but these items make up less than half of
1 percent of notes destroyed.

because the interest expenses associated with
the acquisition of buildings are not included in
the cost-accounting framework. For the price
of building services, wB , we use an annual
square-foot replacement cost, adjusted by the
depreciation rate, for the location of each
building with currency operations.28 The quantity of building services, qB , is proxied by the
actual number of square feet of space occupied by currency operations at each facility.
Over the 1991–96 period, approximately
52 percent of total costs for currency operations
are attributable to labor expenses. The price of
labor, wL , is constructed using data on expenditures for labor, including salaries, retirement
and other benefits, and the number of
employee hours spent in currency operations.
Equipment expenditures consist of depreciation and maintenance expenses. For the price
of equipment, wE , we use the price index for
currency processing equipment reported in the
Producer Price Index Detailed Report. For the
quantities of equipment in operation at each
facility during each quarter, qCVCS and qBPS , we
use actual machine counts for CVCS and BPS
3000 machines, respectively.
Expenditures on materials, including currency straps and packaging, computer support,
printing and duplicating, and other centrally
provided support costs, account for about
11 percent of total costs. The price for material
inputs, wM , is constructed from material expenditure shares and various price indexes for
components of materials from the Survey of
Current Business 29 and the Producer Price
Index Detailed Report, using a Tornquist
approximation to a Divisia index.30
Environmental variables are used to control
for the “quality” of incoming shipments and
the operating environment at each facility. To
measure the quality of incoming shipments we
use several proxies: the number of depositor
errors per 100,000 notes deposited; the proportion of incoming notes that are $1 notes; the
proportion of notes that are rejected by highspeed equipment; and the mean shipment size.
A higher value for any of these proxies is
expected to increase costs at the facility.
Depositor errors occur when a strap has more
or fewer than 100 notes of the same denomination. When such errors occur, the depositor’s
reserve account must be reconciled to reflect
the correct deposit balance.31 Small-denomination notes, such as $1 notes, have a relatively
short life compared to large-denomination
notes. For example, the average life of a
$1 note is 1.5 years, while the average life of a
$50 note is 5 years. Consequently, we can use

the proportion of incoming $1 notes in a
shipment to proxy for the shipment’s overall
quality. The proportion of notes rejected by
high-speed equipment would directly affect
the costs of currency handling and processing
because rejects are handled manually by an
operator on a low-speed machine. Also, a large
average shipment size may create a temporary
backlog for processing work.
The operating environment is controlled for
by variables that capture usage intensity of the
equipment. Usage intensity is proxied by the
proportion of scheduled operating time that
processing equipment is “down”; the proportion of notes processed on BPS 3000 machines;
and the mean throughput of processing equipment (measured in notes per hour). In addition, indicator variables are used to account for
temporary cost increases that resulted from an
unusual event that would affect only one Federal Reserve processing facility. One indicator
variable allows for higher costs during the
period when the New York office was testing
the new BPS 3000 machines (between
1992:IIIQ and 1994:IVQ). Because that office
was the first to use the BPS 3000 machines, it is
reasonable to assume that its transition costs
may have been higher than those who adopted
the machines later. Another indicator variable
is used to accommodate higher costs during
the period when the new Dallas branch was
constructed (1995:IQ through 1996:IVQ).

IV. Empirical
Results
The two forms of the cost function, the
translog and the hybrid-translog, are each
specified with different combinations of fixed
and variable inputs. In one specification, all
inputs are variable, in another, equipment
inputs are fixed, and in another, equipment

■ 28 For these purposes, data on replacement costs for buildings
are taken from the 17th edition of Means Square Foot Costs
(Means, 1996).
■ 29 See U.S. Department of Commerce (1990–97).
■ 30 The Tornquist index is constructed using the rates of growth
in the prices in each category. These rates of growth are weighted by the
average proportionate shares of materials expenses to each category
over adjoining periods. The base year is 1990.
■ 31 Note that the Reserve Banks absorb the differences on $1 note
deposits, so there are no depositor errors reported for $1 notes.

T A B L E

Average Returns to Scale for
Federal Reserve Currency Operations
Functional form/estimation technique
Cost-function specification

GLS/translog

GLS/hybrid-translog

MLE/translog

All inputs variable

0.79

0.78

0.77

Equipment fixed

0.81

0.76

0.80

Equipment and
buildings fixed

0.83

0.78

0.81

Arithmetic mean

Weighted mean
All inputs variable

0.93

0.91

Equipment fixed

0.97

0.86

0.93

Equipment and
buildings fixed

0.98

0.78

0.94

SOURCE: Authors’ calculations. Weighted means use the number of notes
processed as the weighting measure.

and buildings are fixed. In all specifications,
labor and materials inputs are treated as variable. Cost frontiers are estimated using the GLS
technique for both cost-function specifications
and the MLE technique for the tranlog costfunction specification. These frontiers are
denoted as GLS/translog, GLS/hybrid-translog,
and MLE/translog.32

Returns to Scale
For every cost-function specification we
estimate, the average-cost curve implied by the
cost frontier is U-shaped with a fairly flat portion
at the bottom of the U. The implied average
cost curve descends rapidly up to 100 million
notes per quarter and then is fairly flat for most
of the remaining observed output range.33
This shape is fairly typical for the average cost
curve of paper-based payment technologies.34
The minimum efficient scale (MES) for
currency depends on whether equipment and
buildings are treated as fixed inputs. For
example, using the GLS/translog model, the
MES is 260 million notes per quarter when all
inputs are variable, 680 million notes per
quarter when equipment is fixed, and 250 million notes per quarter when equipment and
buildings are fixed.35 While this range for the
MES is quite large, the difference in average
costs for the largest and smallest MES output
levels is not economically meaningful because

the implied average cost function is so flat
through the region of 250 million notes per
quarter to 650 million notes per quarter.
Table 2 presents average RTS measures for
Federal Reserve System currency and handling
operations using several cost-function specifications and the two frontier-estimation techniques. In this table, both the arithmetic mean
and a weighted mean of facility RTS measures
are presented in the top and bottom panels,
respectively. Weights each quarter vary across
Federal Reserve facilities and are equal to the
volume of notes processed at each facility.
Strikingly, neither the cost-function specification nor the frontier-estimation technique
greatly affects the average RTS measures. The
measures are fairly robust to whether equipment and buildings are considered fixed. And,
with one exception—the GLS/hybrid-translog
model specified with fixed buildings and
equipment—such measures are fairly robust to
whether a translog or hybrid-translog functional form is used. Regardless of the costfunction specification or frontier-estimation
technique chosen, the mean of the unweighted
RTS is smaller than the mean of the weighted
RTS measure. This happens because, even
though there are substantial unexploited potential scale economies at many facilities in the
System, the vast majority of notes are processed
and handled at the facilities that have already
achieved constant returns to scale.
Focusing on the first and last quarters of the
estimation period, 1991:IQ and 1996:IVQ,
respectively, we calculate facility-specific
returns-to-scale measures. Table 3 presents
these returns-to-scale measures for each office
that is estimated using the GLS/translog model
with all inputs specified as variable. The

■ 32 We did not estimate an MLE/hybrid-translog model because
the computation time required to achieve convergence would have been
unacceptably long on account of the large number of additional
parameters required for this model.
■ 33 Most facilities with output less than 100 million notes per
quarter have only one high-speed currency processing machine.
■ 34 Zimmerman (1981) and Dotsey (1991) report cost-function
estimates for Federal Reserve currency operations that are consistent
with a U-shaped average cost curve. Humphrey (1981), Bauer and
Hancock (1993), and Bauer and Ferrier (1996) also report cost-function
estimates for Federal Reserve check processing operations that are
consistent with a U-shaped average cost curve.
■ 35 MES estimates from the GLS/translog model are representative of MES estimates from the GLS/hybrid-translog and MLE/
translog models.

T A B L E

Returns-to-Scale Measures for Federal Reserve
Currency Processing and Handling Facilities

Federal Reserve office

1991:IQ estimate

1991:IQ t-test

1996:IVQ estimate

1996:IVQ t-test

FR 1

0.800

3.199

0.837

2.652

FR 2

0.933

1.109

0.937

1.046

FR 3

0.691

4.337

0.826

2.801

FR 4

1.006

–0.080

1.030

0.366

FR 5

0.843

1.760

0.594

4.031

FR 6

1.066

0.822

1.052

0.723

FR 7

0.990

0.133

1.122

1.529

FR 8

0.765

4.087

0.821

3.189

FR 9

0.793

3.105

0.874

2.135

FR 10

0.761

3.777

0.804

3.425

FR 11

0.712

4.621

0.810

3.346

FR 12

0.838

2.804

0.815

2.304

FR 13

0.497

6.692

0.619

5.579

FR 14

0.404

6.648

0.493

6.417

FR 15

0.621

5.255

0.795

3.649

FR 16

0.735

3.351

0.687

3.324

FR 17

0.613

5.903

0.680

5.252

FR 18

0.484

6.708

0.689

5.021

FR 19

1.208

2.404

1.141

1.502

FR 20

0.641

5.240

0.701

4.860

FR 21

0.687

4.866

0.734

4.313

FR 22

0.744

2.621

0.676

2.534

FR 23

0.778

2.953

0.787

2.575

FR 24

0.724

4.671

0.715

4.923

FR 25

0.779

3.863

0.815

2.817

FR 26

1.038

0.393

1.042

0.347

FR 27

0.657

5.399

0.690

4.859

FR 28

0.460

6.682

0.583

5.596

FR 29

0.916

1.145

0.946

0.796

FR 30

0.831

2.997

0.787

3.595

FR 31

0.572

5.441

0.554

6.461

FR 32

0.973

0.359

0.922

1.286

FR 33

0.572

6.323

0.509

6.572

FR 34

0.650

5.361

0.759

3.658

FR 35

1.062

0.848

1.013

0.166

FR 36

0.592

5.504

0.707

3.829

FR 37

0.648

5.152

0.754

4.349

SOURCE: Authors’ calculations. The t-test statistic is for a “two-tail” test of the hypothesis that the estimated coefficient is equal to 1.

t-statistics in the table test the hypothesis that
the RTS estimate differs from one. At the
beginning of the sample, 27 facilities have
statistically significant increasing returns to
scale, 9 facilities exhibit constant returns to
scale, and 1 facility has significant decreasing

returns to scale. At the end of the sample, 28
facilities have statistically significant increasing
returns to scale and 10 exhibit constant returns
to scale. Although the number of notes received
by the Federal Reserve System increased by
about 20 percent over this period (figure 1),

F I G U R E 1
Federal Reserve System Notes Paid and
Received Annually (in thousands of notes)

Notes received
40
$100

$50

$20

$10

Notes paid
40
$100

$50

$20

$10

0
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

SOURCE: Board of Governors of the Federal Reserve System.

the introduction of higher-speed processing
machines enabled each facility to achieve similar returns to scale as before their introduction.
Facilities with insufficient processing volume to
achieve scale efficiency in 1991 continued to
have insufficient processing volume to achieve
scale efficiency in 1996. It remains the case,
however, that scale efficiency for Federal
Reserve currency operations improved on
average because no facility operated with
statistically significant decreasing returns to
scale, and far fewer facilities operated with an
RTS measure less than 0.70 by the end of the
estimation period.
Our RTS findings suggest that there was
considerable excess capacity in Federal Reserve
currency operations. This excess capacity has
been used to accommodate the public’s
growing demand for currency, which increases
demand for currency processing, including the
destruction of unfit currency. However, to the
extent that use of the new Sacagawea dollar
coins substitute for $1 notes, more Federal

Reserve facilities may be operating with
increasing returns to scale in the future unless
some smaller facilities are consolidated. Of
course, the higher unit costs of operating with
increasing returns to scale must be weighed
against the costs of being unable to meet
demand shocks for currency processing and
handling. Also, the cost savings of consolidating
facilities would have to be balanced against the
higher costs of transporting currency deposits
and withdrawals over longer distances.36
Alternatively, the overall level of scale efficiency

■ 36 Bauer et al. (2000) considered whether Federal Reserve
System currency processing costs could be lowered by reallocating
currency volume across facilities or by consolidating facilities. They
found most cost savings could be achieved without closing any existing
currency processing facilities. In addition, they argued that a new facility
located in Phoenix, Arizona, would help to lower System currency
processing costs.

T A B L E

achieved by Federal Reserve currency operations could potentially be improved over time
by adjusting standards for normal service levels
or by changing fees for nonstandard access or
nonstandard cash services.37

Marginal Costs of Production for Fit Currency,
Destroyed Currency, and Cash Shipments
Functional form/estimation technique
GLS/translog

GLS/hybrid-translog

MLE/translog

Fit currency
(Cents per note)

0.358

0.344

0.398

Destroyed currency
(Cents per note)

0.161

0.145

0.175

Cash shipments
(Dollars per shipment)

22.63

30.43

14.09

Fit currency
(Cents per note)

0.428

0.369

0.521

Destroyed currency
(Cents per note)

0.234

0.200

0.235

Cash shipments
(Dollars per shipment)

38.82

58.15

21.11

Marginal Costs

Arithmetic mean

Weighted mean

SOURCE: Authors’ calculations. Weighted means use the number of notes
processed as the weighting measure.

T A B L E

The Effects of Environmental Variables
on the Cost of Currency Operations
Environmental variable

Sample mean

Estimate

The number of depositor errors per
$100,000 notes deposited

13.152

0.0317**

The proportion of incoming notes that
were of $1 denomination

0.370

–0.024

The proportion of notes rejected by highspeed equipment

0.022

0.156***

The mean shipment size (in notes)

70,757

0.345***

The proportion of scheduled operating time
that processing equipment was “down”

0.041

0.083***

The proportion of notes processed on
BPS 3000 machines

0.223

0.068***

The mean throughput of processing
equipment (in notes per hour)

66,030

0.234*

Quality of incoming shipments

Usage intensity of equipment

Recently, some observers have argued that the
Federal Reserve should explicitly charge for
currency services because outgoing currency
from the Reserve Banks is of higher quality
than the incoming currency from depository
institutions.38 Such observers typically argue
that some currency users would be willing to
pay for a higher-quality, “superfit” currency
because they manage newer technologies that
would perform better with higher-quality
currency (such as ATMs or vending machines).
With the view to improve economic efficiency, potential prices for currency services
would likely depend on the marginal costs of
production for fit currency, for destroying
currency, and for currency shipments. We
estimate such marginal costs at each facility by
using cost frontiers that assume all inputs are
variable in the short run. In table 4, both the
arithmetic mean and a weighted mean of
Federal Reserve facility-level marginal cost
estimates for fit currency, destroyed currency,
and cash shipments are presented.
As with the weighted RTS measures presented in table 2, the weights used in table 4
each quarter vary across Federal Reserve
facilities and are equal to the volume of notes
processed at each facility. The average Federal
Reserve System marginal cost for fit currency,
destroyed currency, and cash shipments is
higher when each facility’s marginal cost is
weighted by its output volume. This happens
because the marginal cost is less than the
average cost when a facility operates with
increasing returns to scale, as did most facilities. The average marginal costs for fit and
destroyed currency, unweighted or weighted,
are higher when the MLE technique is used

SOURCE: Authors’ calculations. Estimates significantly different from zero at
the 10, 5, and 1 percent significance level are indicated with *, **, and ***,
respectively. All significance tests used a two-tailed t-test.
■ 37 Although the uniform cash access policy established normal
access for a depository institution as once per week, Reserve Banks can
charge for more frequent nonstandard access. In addition, Reserve Banks
can and do charge for services such as nonstandard packages and nonstandard packaging of same-day express cash orders.
■ 38 See Supel and Todd (1984) and Lacker (1993).

than when the GLS technique is used, but of
similar magnitude.
The average Federal Reserve marginal cost
for fit currency is typically less than one-half of
a cent per note during the period studied. The
average marginal cost for destroyed currency is
about half that. Marginal cost estimates for cash
shipments, which are reported at the bottom
lines of the top and bottom panels of table 4,
are very sensitive to both the functional form
of the cost function and the econometric
technique used to estimate the cost frontier:
Depending on which forms and techniques are
used, the arithmetic mean marginal cost for
Federal Reserve cash shipments ranges from
$14 to $30, and the weighted mean ranges
from $21 to $58.

F I G U R E 2
Year-Indicator Effects for Various
Estimation Techniques
Index
1.200
GLS/translog
GLS/hybrid-translog
MLE/translog
1.150

1.100

1.050

Environmental
Factors

1.000

0.950
1990

1991

1992

1994

1993

1995

1996

SOURCE: Authors’ calculations.

F I G U R E 3
Year-Indicator Effects for Various
Model Specifications
Index
1.250

1.200

GLS/translog
GLS/translog, with fixed equipment
GLS/translog, with fixed equipment and buildings

1.150

1.100

1.050

In every specification for the cost frontier we
estimated, environmental factors are important
cost determinants. Table 5 presents the effects
of environmental variables on the cost of
production when the cost frontier estimated is
the GLS/translog and all inputs are considered
variable.39
The quality of incoming currency deposits
significantly influences Federal Reserve costs.
The number of depositor errors per 100,000
notes deposited, the proportion of notes that
are rejected by high-speed equipment, and the
mean shipment size each significantly raises
Federal Reserve currency handling and
processing costs at the 5 percent level of significance. A 1 percent increase in the number of
depositor errors increases costs by 0.03
percent, a 1 percent increase in the proportion of notes rejected by high-speed equipment increases costs by 0.16 percent, and
a 1 percent increase in mean shipment size
increases costs by 0.35 percent. Only the
proportion of incoming notes that are of
$1 denomination is not significant among the
variables that measure incoming currency quality.

1.000

0.950
1991

1992

1993

1994

1995

1996

SOURCE: Authors’ calculations.

■ 39 The environmental effects we present in table 5 are representative of the others we derive using alternative cost frontiers.

Operating environment variables also affect
the cost of providing currency services. The
proportion of scheduled operating time that
processing equipment is down and the proportion of notes processed on BPS 3000 machines
each significantly raises costs at the 1 percent
level of significance. In addition, the meanthroughput-of-processing-equipment variable
is significant at the 10 percent level.

F I G U R E 4
Learning-by-Doing Effect for Various
Estimation Techniques
Index
1.300

1.200

Time Adjustment
Factors

1.100

1.000
GLS/translog
GLS/hybrid-translog
MLE/translog
0.900

0.800
0

4
Quarter

SOURCE: Authors’ calculations.

F I G U R E 5
Learning-by-Doing Effect for Various
Model Specifications
Index
1.200

1.100

1.000

0.900
GLS/translog
GLS/translog, with fixed equipment
GLS/translog, with fixed equipment and buildings
0.800
0

SOURCE: Authors’ calculations.

4
Quarter

The last environmental coefficients we
consider are the variables included to control
for technical change in general and the introduction of the new machines in particular.
The estimated coefficients for these variables
are fairly consistent across the various specifications. Figure 2 plots the effects of the yearindicator variable for the GLS/translog,
GLS/hybrid-translog, and MLE/translog models.
Figure 3 plots the GLS/translog model with all
inputs variable, with equipment fixed, and
with equipment and building inputs fixed.
Although it appears that the cost function has
shifted up 10 to 15 percent from 1991 to 1996,
it should be noted that because we include
variables that control for the transition to new
machines, it is not possible to interpret these
coefficients as a technical change index, as is
often done. The reason is that the full effect of
technical change must include the effects of
these other variables.
Recall that we include an indicator variable
for the first quarter during which a processing
site employed the new machines, another
indicator variable for the second quarter of
use, and a time trend to capture the effects in
later quarters. The combined effect of these
three variables, which we call the learning-bydoing effect, is plotted in figure 4 for the GLS/
translog, GLS/hybrid-translog, and MLE /
translog models. As one might suspect, new
machines disrupt the previous work environment, and all the models report higher costs
in the quarter in which the new machines are
introduced. The models do differ as to what
happens after that. Our preferred estimation
technique, GLS, estimates that, after spiking
sharply in the quarter when the new machines
are introduced, costs fairly rapidly decline.
After just two years, the learning-by-doing
effect of the new machines would be more
than enough to offset the year-indicator variables. When the model is estimated using MLE,

T A B L E

Facility-Level Efficiency Estimate Statistics for
Federal Reserve Currency Operations
Functional form/estimation technique
Type of specification

GLS/translog

GLS/hybrid-translog

MLE/translog

Arithmetic mean

0.815

0.844

0.893

Weighted mean

0.810

0.838

0.888

Minimum

0.596

0.633

0.770

Maximum

1.00

0.952

Median

0.822

0.848

0.897

Arithmetic mean

0.825

0.863

0.902

Weighted mean

0.819

0.850

0.896

Minimum

0.623

0.662

0.800

Maximum

1.00

0.946

Median

0.834

0.861

0.903

Arithmetic mean

0.844

0.861

0.917

Weighted mean

0.836

0.866

0.911

Minimum

0.716

0.722

0.871

Maximum

1.00

0.958

Median

0.839

0.855

0.918

All inputs variable

Equipment inputs fixed

Equipment and building
inputs fixed

SOURCE: Authors’ calculations. The weighted mean level of cost efficiency
weights each facility-level cost-efficiency estimate by the mean number
of notes processed per quarter at that facility during the 1991:IQ to
1996:IVQ period.

the learning-by-doing effect is much smaller,
and consequently, the decline in costs is much
slower. As figure 5 reveals, the GLS estimates
of the learning-by-doing effect demonstrate the
same pattern whether capital or buildings are
treated as variable or fixed inputs.

Cost Efficiency
The estimates for cost efficiency using the
alternative functional forms, estimation techniques, and specifications are presented in
table 6. The GLS/translog model yields the
lowest average cost-efficiency estimates for
Federal Reserve System currency operations.
Depending on whether equipment and building inputs are fixed, the arithmetic average of
facility-level cost-efficiency estimates ranges
between 0.81 and 0.84, and the minimum cost-

efficiency estimates range between 0.60 and
0.72. These statistics suggest that during the
period studied, the average facility operated at
more than 80 percent of the efficiency of the
“best-practice” facility, and the worst performer
in the system could have substantially improved
its efficiency.
Estimates of average cost-efficiency levels
are higher when a hybrid-translog functional
form is used for the cost function. This is not
surprising because the hybrid-translog attributes a larger proportion of the variance in cost
to the structural component of the model. This
attribution results in higher average costefficiency estimates. In addition, estimates of
average cost-efficiency levels are higher when the
MLE technique is used to estimate the frontier.
The weighted means of the cost-efficiency
estimates are lower than the corresponding
arithmetic means. The weighted means are
lower because larger facilities in the System
typically have lower cost-efficiency estimates
than do smaller facilities.40
In general, cost-function specifications with
fixed inputs yield higher average levels of cost
efficiency, regardless of the functional form for
the cost function or the technique used to
estimate the cost frontier. This consistency
across the top, middle, and bottom panels of
table 6 suggests that managers view equipment
and building inputs as largely fixed. Because
changes to such inputs require substantial lead
times, this view seems quite plausible.
If facility-specific efficiency measures are
to be useful for managerial or policymaking
purposes, they should rank facilities consistently and be robust to different specifications
of the cost function or to different econometric
techniques. In tables 7, 8, and 9, we present
facility-specific cost-efficiency estimates for all
of our models. Table 7 reports estimates when
all inputs are variable, table 8 when equipment
inputs are fixed, and table 9 when equipment
and buildings are fixed inputs. Each table
shows the results of all combinations of the
functional form of the cost function and the
two estimation techniques we consider. In
addition, for each model, cost-efficiency
estimates are ranked from most efficient (costefficiency estimate equals one) to least efficient

■ 40 Currency processing and handling facilities with the largest
output levels tend to be Reserve Bank head offices. Such facilities have
additional administrative staff for the District. Even after incorporating a
head office indicator variable into the cost-function models, facilities with
the largest output volume tend to have lower levels of cost efficiency than
smaller facilities.

T A B L E

Cost-Efficiency Estimates and Relative
Rankings, Cost Model with All Inputs Variable

Federal
Reserve facility

GLS/translog costefficiency estimate

Rank

GLS/hybrid-translog
cost-efficiency estimate

FR 1

1.000

0.989

0.943

FR 2

0.991

1.000

0.941

FR 3

0.982

0.992

0.952

FR 4

0.958

0.971

0.931

FR 5

0.900

0.967

0.916

FR 6

0.872

0.910

0.899

FR 7

0.871

0.863

0.898

FR 8

0.871

0.849

0.926

FR 9

0.868

0.900

0.924

FR 10

0.859

0.890

0.920

FR 11

0.859

0.874

0.896

FR 12

0.855

0.848

0.916

FR 13

0.854

0.849

0.893

FR 14

0.854

0.874

0.912

FR 15

0.845

0.901

0.899

FR 16

0.837

0.854

0.882

FR 17

0.833

0.838

0.895

FR 18

0.831

0.821

0.893

FR 19

0.822

0.874

0.910

FR 20

0.810

0.853

0.896

FR 21

0.809

0.826

0.881

FR 22

0.808

0.848

0.900

FR 23

0.799

0.821

0.879

FR 24

0.786

0.817

0.897

FR 25

0.770

0.827

0.901

FR 26

0.764

0.802

0.891

FR 27

0.760

0.808

0.872

FR 28

0.756

0.801

0.882

FR 29

0.744

0.835

0.897

FR 30

0.728

0.804

0.906

FR 31

0.726

0.780

0.867

FR 32

0.722

0.712

0.839

FR 33

0.714

0.726

0.866

FR 34

0.706

0.759

0.838

FR 35

0.706

0.784

0.865

FR 36

0.693

0.723

0.852

FR 37

0.596

0.633

0.770

Rank

MLE/translog
cost-efficiency estimate

Rank

SOURCE: Authors’ calculations. Facility with rank 1 in each column is the “best-practice” facility using the specification/econometric technique specified. Cost-efficiency estimates are for the full period from 1991:IQ to 1996:IVQ.

T A B L E

Cost-Efficiency Estimates and Relative
Rankings, Cost Model with Equipment Fixed

Federal
Reserve facility

GLS/translog costefficiency estimate

Rank

GLS/hybrid-translog
cost-efficiency estimate

FR 1

0.921

0.957

0.931

FR 2

0.974

0.975

0.941

FR 3

0.943

0.969

0.946

FR 4

1.000

0.943

FR 5

0.911

0.983

0.927

FR 6

0.890

0.918

0.917

FR 7

0.862

0.891

0.908

FR 8

0.863

0.861

0.925

FR 9

0.861

0.918

0.924

FR 10

0.867

0.904

0.920

FR 11

0.865

0.882

0.902

FR 12

0.840

0.868

0.918

FR 13

0.815

0.851

0.883

FR 14

0.862

0.876

0.915

FR 15

0.846

0.905

0.908

FR 16

0.875

0.868

0.899

FR 17

0.809

0.856

0.903

FR 18

0.814

0.829

0.899

FR 19

0.844

0.885

0.916

FR 20

0.809

0.867

0.899

FR 21

0.828

0.858

0.894

FR 22

0.856

0.897

0.921

FR 23

0.812

0.807

0.896

FR 24

0.834

0.861

0.923

FR 25

0.788

0.842

0.894

FR 26

0.783

0.833

0.897

FR 27

0.732

0.801

0.864

FR 28

0.755

0.823

0.892

FR 29

0.781

0.851

0.903

FR 30

0.870

0.875

0.925

FR 31

0.750

0.810

0.891

FR 32

0.725

0.744

0.853

FR 33

0.712

0.769

0.874

FR 34

0.709

0.788

0.862

FR 35

0.754

0.842

0.905

FR 36

0.734

0.786

0.861

FR 37

0.623

0.662

0.800

Rank

MLE/translog
cost-efficiency estimate

SOURCE: Authors’ calculations. Facility with rank 1 in each column is the “best practice” facility using the specification/econometric
technique specified. Cost-efficiency estimates are for the full period from 1991:IQ to 1996:IVQ.

Rank

T A B L E

Cost-Efficiency Estimates and Relative Rankings,
Cost Model with Fixed Equipment and Buildings

Federal
Reserve facility

GLS/translog costefficiency estimate

Rank

GLS/hybrid-translog
cost-efficiency estimate

FR 1

0.963

0.961

0.943

FR 2

0.982

0.958

FR 3

0.994

0.977

0.944

FR 4

1.000

0.946

FR 5

0.858

0.911

0.931

FR 6

0.875

0.902

0.932

FR 7

0.844

0.854

0.919

FR 8

0.897

0.878

0.931

FR 9

0.844

0.864

0.927

FR 10

0.847

0.864

0.925

FR 11

0.823

0.845

0.919

FR 12

0.890

0.886

0.930

FR 13

0.817

0.845

0.905

FR 14

0.820

0.849

0.918

FR 15

0.801

0.831

0.918

FR 16

0.927

0.891

0.933

FR 17

0.863

0.861

0.918

FR 18

0.902

0.890

0.938

FR 19

0.837

0.853

0.914

FR 20

0.807

0.825

0.913

FR 21

0.800

0.814

0.910

FR 22

0.909

0.922

0.927

FR 23

0.803

0.902

FR 24

0.851

0.849

0.932

FR 25

0.839

0.875

0.910

FR 26

0.821

0.855

0.911

FR 27

0.796

0.846

0.896

FR 28

0.747

0.807

0.886

FR 29

0.811

0.874

0.912

FR 30

0.881

0.874

0.932

FR 31

0.753

0.819

0.903

FR 32

0.716

0.722

0.877

FR 33

0.796

0.816

0.916

FR 34

0.766

0.815

0.884

FR 35

0.860

0.888

0.924

FR 36

0.744

0.770

0.871

FR 37

0.747

0.760

0.882

Rank

MLE/translog
cost-efficiency estimate

Rank

F I G U R E 6
Cost-Efficiency Rankings,
GLS/Translog
Rank
40
All inputs variable
Equipment fixed
Equipment and buildings fixed

35
30
25
20
15
10
5
0
0

20
25
Efficiency rank

SOURCE: Authors’ calculations.

F I G U R E 7
Cost-Efficiency Rankings,
GLS/Hybrid-translog
Rank
40
All inputs variable
Equipment fixed
Equipment and buildings fixed

35
30
25
20
15
10
5
0
0

Efficiency rank

SOURCE: Authors’ calculations.

(cost-efficiency equals the minimum costefficiency estimate). Facilities are identified
using their cost-efficiency estimate rank for the
GLS/translog model that considered all inputs
variable (table 7, second column).
Although the relative ranks of cost-efficiency
estimates for individual facilities vary considerably across our different models, a number of
facilities are consistently ranked among the
most and least efficient in the Federal Reserve
System. Facilities denoted by FR1 through FR4
are consistently ranked among the five most
efficient facilities. FR1 through FR6 are consistently among the top 10 efficient facilities. Consistently ranked among the least efficient facilities are facilities denoted by FR32, FR34, FR36,
and FR37. Interestingly, both the most efficient
and least efficient groups contain head offices
and branches. Rankings in the middle range of
efficiency rankings are more volatile because,
for facilities in that range, a small change in
efficiency leads to a large change in ranking,
and efficiency estimates for facilities in the
middle range are very close. The consistency
of the relative rankings of the most and least
efficient offices and the considerable disagreement about the rankings of facilities in
the middle of the range of rankings is illustrated
in figures 6 through 8.
We calculate Spearman and Kendall Tau-b
rank-order correlations, reported in tables 7, 8,
and 9, to determine the association between
cost-efficiency estimates. The Spearman rankorder correlation measure is concerned with
differences in absolute rankings, putting the
highest weight on facilities at the extremes,
whereas the Kendall Tau-b rank-order correlation measure captures the differences in
relative rankings. These rank-order correlations
are presented in tables 10 and 11 along with
rank-order correlations between cost-efficiency estimates and two accounting-based
performance measures—the number of notes
processed on high-speed equipment per
man-hour (a labor productivity measure) and
the number of notes processed per dollar of
cost (a unit cost measure). These accountingbased measures of performance do not take
into account differences in environmental
variables, nor do they account for the effect of
differences in the scale of operations between
facilities, but they are commonly used as
performance measures.

F I G U R E 8
Cost-Efficiency Rankings,
MLE/Translog
Rank
40
All inputs variable
Equipment fixed
Equipment and buildings fixed

35
30
25
20
15
10
5
0
0

20
Efficiency rank

SOURCE: Authors’ calculations.

The Spearman correlation coefficients
presented in table 10 are generally greater than
0.70, and each is statistically significant at the
5 percent level. Overall, such correlation
coefficients are larger when the models’
assumptions are more similar or when the
same econometric technique is used to estimate
the cost frontier. Not surprisingly, the weakest
relationships are between cost-frontier-based
and accounting-based measures of facility-level
efficiency.
The Kendall Tau-b correlation coefficients
presented in table 11 are smaller than the corresponding Spearman correlation coefficients
presented in table 10. This implies that the
efficiency rankings do not perform as well for
facilities in the middle cost-efficiency range.
As with the Spearman correlation coefficients,
every Kendall Tau-b correlation coefficient is
statistically significant at the 5 percent level,
which suggests an extremely high degree of
concordance between our cost-efficiency
measures. Again, consistency is greatest
between cost-efficiency measures when the
models’ assumptions are most similar or where
the same econometric technique is used to
estimate the cost frontier. Consistency is weakest
between cost-frontier-based and accounting-

based measures of facility-level efficiency.
Indeed, the Kendall correlation coefficients
between cost-frontier-based and accountingbased measures of facility-level efficiency are
all less than 0.50. This suggests that econometric measures of site-level efficiency may
provide useful insights for the identification
of “best-practice” currency processing and
handling facilities within the Federal Reserve
System, which accounting measures of performance may overlook.
Some Federal Reserve districts may focus on
cost efficiency to a greater degree than others.
Because five of the six consistently most efficient facilities are located in just two of the
twelve Federal Reserve districts, we test for
differences in the estimates of the mean level
of cost efficiency of facilities in those two
Federal Reserve districts against the remaining
ten districts. We find that the average efficiency
of the facilities in the two districts exceeds that
of the remainder of the Federal Reserve System
at the 1 percent significance level using a onesided t-test.
We were curious to see whether costefficiency estimates show any pattern across
services. To do so, we compare our baseline
estimates of currency cost efficiency with those
for check as reported by Bauer and Ferrier
(1996). The Spearman correlation coefficient is
0.309 and is statistically significant only at the
10 percent confidence level. The Kendall
Tau-b correlation coefficient is lower, 0.232,
but is statistically significant at the 5 percent
confidence level. These results suggest that
senior officers who oversee currency operations
well also tend to oversee check operations
well. These correlations also suggest that high
cost efficiency in one area is not achieved by
shifting costs to other operations.

T A B L E

Spearman Correlation Coefficients Between
Site-Level Measures of Efficiency

Cost-frontier-based cost-efficiency measures
All inputs variable
GLS/
translog

All
inputs
variable

GLS/translog

1.0

GLS/hybridtranslog
MLE/translog

Equipment
fixed

GLS/translog
GLS/hybridtranslog
MLE/translog

Equipment
and
buildings
fixed

GLS/translog
GLS/hybridtranslog
MLE/translog

Other

Labor
productivity
Unit cost

SOURCE: Authors’ calculations.

GLS/
MLE/
hybrid- translog
translog

Equipment fixed
GLS/
GLS/
MLE/
translog hybrid- translog
translog

Equipment and buildings fixed

Accounting-based
performance measures

GLS/
translog

GLS/
hybridtranslog

MLE/
translog

Labor
Productivity

Unit Cost

0.938

0.825

0.881

0.865

0.743

0.690

0.645

0.712

0.598

0.639

1.0

0.848

0.881

0.934

0.772

0.649

0.653

0.684

0.612

0.667

1.0

0.845

0.881

0.910

0.737

0.743

0.750

0.630

0.645

1.0

0.925

0.864

0.794

0.730

0.836

0.578

0.554

1.0

0.892

0.717

0.716

0.766

0.574

0.598

1.0

0.825

0.798

0.867

0.595

0.564

1.0

0.936

0.575

0.463

1.0

0.871

0.561

0.483

1.0

0.535

0.465

1.0

0.810
1.0

T A B L E

Kendall tau-b Correlation Coefficients Between
Site-Level Measures of Efficiency

Cost-frontier-based cost-efficiency measures
All inputs variable
GLS/
translog

All
inputs
variable

GLS/translog

1.0

GLS/hybridtranslog
MLE/translog

Equipment
fixed

GLS/translog
GLS/hybridtranslog
MLE/translog

Equipment
and
buildings
fixed

GLS/translog
GLS/hybridtranslog
MLE/translog

Other

Labor
productivity
Unit cost

SOURCE: Authors’ calculations.

GLS/
MLE/
hybrid- translog
translog

Equipment fixed
GLS/
GLS/
MLE/
translog hybrid- translog
translog

Equipment and buildings fixed

Accounting-based
performance measures

GLS/
translog

GLS/
hybridtranslog

MLE/
translog

Labor
Productivity

Unit Cost

0.804

0.670

0.742

0.691

0.592

0.526

0.496

0.565

0.411

0.456

1.0

0.697

0.727

0.802

0.625

0.486

0.480

0.544

0.426

0.471

1.0

0.670

0.703

0.778

0.562

0.574

0.571

0.465

0.486

1.0

0.781

0.689

0.616

0.568

0.661

0.429

0.414

1.0

0.727

0.541

0.534

0.598

0.396

0.423

1.0

0.664

0.662

0.715

0.429

1.0

0.790

0.787

0.399

0.324

1.0

0.697

0.399

0.354

1.0

0.396

0.345

1.0

0.637
1.0

V. Conclusion
I t costs more than half a billion dollars each
year to meet the demands for currency by
depository institutions, businesses, and consumers.41 Yet very little research has been
devoted to understanding the factors that affect
such costs. This paper has attempted to fill a
portion of this gap by considering the scale
and cost efficiency of Federal Reserve currency
operations.
Our finding that there are limited scale
economies for Federal Reserve currency operations suggests that currency services are not a
natural monopoly. As with other paper-based
payments technologies, the average cost curve
implied by the cost frontier for currency
operations is U-shaped with a fairly wide, flat
portion at the bottom of the U. Indeed, the
Federal Reserve System processes the vast
majority of notes at facilities that have nearconstant returns to scale. By the end of
1996, 10 Federal Reserve facilities were already
operating at constant returns to scale, and the
volume of notes processed (figure 1) has continued to increase since that time. Going forward, information on facility-specific marginal
costs and returns-to-scale measures could
potentially be used to improve resource allocations. For example, such information could
be used to set fees for some currency services
or to tailor cash service standards that define
normal service levels to each depository institution. From a policymaking perspective, the
technology for currency handling and processing does not appear to have the declining unit
costs that would give rise to a market failure
that is sufficient to justify or to sustain a
monopoly currency provider. Of course, there
may be other reasons for preserving the current arrangement given the Federal Reserve’s
critical role in supplying and maintaining the
integrity of currency in the United States.
Our finding that the average facility operates
at more than 80 percent of the efficiency of
the “best-practice” facility is comparable to
cost-efficiency estimates reported elsewhere
for private-sector financial institutions.42 Just
like its for-profit services,43 the Federal Reserve
could potentially reduce costs by having
the worst-performing facilities adopt the
procedures and operations of the bestperforming facilities.

Our finding of significant concordance
between cost-efficiency estimates for currency
processing and handling services, which are
not required by the MCA to recover economic
costs in the marketplace, and check processing
services, which are, suggests that the Federal
Reserve may have realized some of the benefits that a more competitive currency market
might have delivered. By encouraging the
formation of a competitive market for check
services, the MCA also gave Reserve Banks a
greater incentive to control costs and improve
resource allocation. Thus, the MCA appears to
have generated spillover benefits by creating a
management culture that increased operational
efficiency even for currency services in which
the Federal Reserve maintained its monopoly.
This spillover benefit from the Federal Reserve’s
participation in competitive payments markets
to services of a more purely governmental
nature has previously been ignored in studies
that have examined the Federal Reserve’s role
in the payments system.44

■ 41 In 2000, for example, the Federal Reserve spent about
$133 million on high-speed currency operations; $4.6 million on currency
cancellation, verification, and destruction; $65 million on paying and
receiving activities; and $456 million for printing of new Federal Reserve
notes, shipment of new notes by the Bureau of Printing and Engraving
(BPE), intra-System shipments of fit notes, counterfeit deterrence research,
the return of currency pallets to the BPE, and reimbursement to the U.S.
Treasury Office of Currency Standards. Federal Reserve outlays do not
include the costs of currency operations borne by depository institutions.
■ 42 See, for example, Bauer, Berger, and Humphrey (1993) and
Berger, Hancock, and Humphrey (1993).
■ 43 See Bauer and Hancock (1993) and Bauer and Ferrier (1996).
■ 44 See, for example, Green and Todd (2001).

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The Employment of
Nations—A Primer
by Richard Rogerson
Richard Rogerson is the Rondthaler
Professor of Economics at Arizona State
University and a research associate at the
Federal Reserve Bank of Cleveland. He
thanks Nathan Porter and Yasuo Terajima
for research assistance and the National
Science Foundation for financial support.

Introduction
One of the striking macroeconomic developments of the last 30 years has been the marked
rise in European unemployment in comparison
to that in the United States. As of 2000, U.S.
unemployment was basically unchanged from
1970 at around 4 percent, whereas over the
same period, the unemployment rate in the
European Union almost tripled, increasing
from around 3 percent to almost 9 percent.
Not surprisingly, a relatively large literature has
emerged that both documents various aspects
of this differential evolution of unemployment
rates and tries to account for it.1
The premise of this paper is that our understanding of this and other related phenomena
will likely be facilitated by placing them in a
broader context. In particular, since economics
is often defined as the study of how scarce
resources are allocated, I follow the standard
economic approach of approaching the labor
market from the perspective of documenting
differences in resource allocations. Because
labor is a key input in the market production
of goods and services, it follows that how
much time is allocated to the market production of goods and services is likely to be an

important feature of the resource allocation
achieved by an economy. While economists
have long recognized variation in labor input
as a (if not the) central element in business
cycle fluctuations, in contexts other than
business cycles, variation in labor input has
received much less attention. The objective of
this paper, then, is to document the empirical
properties of the low-frequency component of
labor input in a cross section of industrialized
countries over the period 1960–95. This is
done using both aggregate data as well as data
that are disaggregated by age and sex.
While the larger issue of interest is that of
the allocation of time, this study will concern
itself almost exclusively with employment
patterns. As such, it abstracts from differences
in such things as workweeks and vacation
days. Obviously, it would be of interest to

■ 1 The literature is too large to reference exhaustively. See,
however, Bertola and Ichino (1995), Millard and Mortensen (1997),
Ljungqvist and Sargent (1998), Blanchard and Wolfers (2000), and
Blanchard (2000).

supplement the analysis provided here with
information on these additional aspects of time
allocation, but due to data limitations, I do not
undertake it in any great detail here. I also
restrict attention to a study of industrialized
countries, since there are reasons to believe
that countries at very different stages of development face considerations which make their
time-allocation problems less comparable.
Specifically, countries with large rural or agricultural populations may behave quite differently.
The paper presents its findings in the form
of nine stylized facts. I will not present them
all in this introduction, but a few are worth
emphasizing. First, large and persistent differences in employment-to-population ratios are
common throughout the period. While differences have become larger since 1970, persistent differences exist throughout the entire
sample and are in no way a novel feature of
the post-1970 world. Second, countries move
about considerably in the distribution of
employment-to-population ratios. Some countries move up, and some countries move
down. Third, and perhaps most important, a
comparison of aggregate and disaggregate data
shows that there is substantial variation in disaggregated labor input that is obscured when
examining aggregate data. When employmentto-population ratios change in a persistent
fashion, the changes are distributed across
groups disaggregated by sex and age in a very
disproportionate fashion. Because changes
across demographic groups display so much
variation, it seems natural to think that they
contain a great deal of information that will be
helpful in sorting out the causes of the aggregate changes.
The paper is unapologetically atheoretical.
There is no attempt to discuss what the facts
uncovered have to say about various models
of the labor market or various explanations for
differences in labor market outcomes. Rather,
the objective here is to simply lay out the facts
that a general theory of low-frequency movements in employment should be able to
account for.
An outline of the paper follows. The next
section gives a brief description of data
sources. Section II examines the aggregate
data and presents the main stylized facts that
follow from them, while section III does the
same for the data disaggregated by age and
sex. Section IV discusses some additional measures of labor input, and section V concludes.

I. Data
The measure of labor input that I use in this
study is employment to population. For the
aggregate analysis, I use the ratio of total
employment to the population of individuals
between the ages of 15 and 64.2
All of the data used in this analysis come
from Organisation for Economic Co-operation
and Development (OECD) sources, which in
turn are based on surveys carried out by individual member countries. Aggregate data on
employment relative to the population of individuals aged 15–64 are taken from various
issues of the OECD publication Historical
Statistics. Data on employment rates disaggregated by sex and age are taken from various
issues of the OECD publication Labor Force
Statistics. This publication actually provides
information on participation rates and unemployment rates, from which I have computed
the employment-to-population ratios. The
disaggregated data are not available for as
many countries or for as long a time, so the
time period and countries analyzed differ for
the two exercises. Section IV of the paper,
which considers some additional measures of
labor input, relies on data that appear in
various issues of the OECD publication
Employment Outlook.
As is true for any study that relies on crosscountry data from country-level sources, an
important caveat that must be mentioned is the
possibility that the data are not strictly comparable. Survey procedures may differ from
country to country, as may classification procedures. Additionally, there are occasional
changes in the accounting methods for some
countries.3 For examining cross-country differences in employment, these accounting issues
do not appear to be very significant. The
OECD publications listed above provide documentation of the various country surveys and
definitions used to determine employment,

■ 2 Note that this measure includes employed individuals above 65
in the numerator but not in the denominator. It is obviously debatable
whether this measure is preferable to the employment-to-population ratio
for all individuals or the employment-to-population ratio for all individuals
above the age of 15. Since much of the analysis is also carried out with
data that are disaggregated by age and the basic findings there are similar,
this is probably not an important issue for the purposes of this paper.
■ 3 For the most part, these did not appear to be too serious.

and there is a high degree of uniformity of the
criteria. Basically, in order to be counted as
employed, an individual has to have either
worked at least one hour for pay during the
reference period, had a job from which he or
she was absent (due to sickness, vacation,
strike, weather, and so on), been self-employed,
or been an unpaid employee in a family
business.4 Having said this, I will take the
employment data at face value, and no additional space will be devoted to this potentially
important measurement issue. However, in
section IV, when data are presented on hours
of work and part-time versus full-time employment, measurement issues are likely to be
substantial, and the appropriate caveats will
again be raised.

II. Facts about
Employment Rates I:
The Aggregate Data
This section focuses on patterns found in the
aggregate data. I examine 18 countries over
the period 1960–95.5 Because we are interested in low-frequency rather than highfrequency movements, I present five-year
averages at five-year intervals.6 In each case,
the indicated year is the center of the five-year
period used to construct the average; that is,
data for 1985 represent the average for the
period 1983–87.7 Table 1 presents the data on
aggregate employment relative to the total
population for individuals between the ages of
15 and 64 for 18 countries plus some summary
statistics: the mean, standard deviation, and the
85:15 ratio for the cross-sectional distribution
in each year. The 85:15 ratio is the ratio of the
highest to the lowest value for the employment ratio after having excluded the top two
and bottom two values.8 I report this rather
than the ratio of maximum to minimum values
in order to downplay the possible role of
extreme values. Note also that the mean value
reported is the simple mean of the cross-country
observations and does not weight countries by
their size.
Some of the important features of these data
are described next.

Fact 1. The average employment rate
remained roughly constant over this
period.
As table 1 indicates, there is no evidence of
a secular trend in the average employment rate
across countries. The average values from 1980
onward are slightly lower than the average
values before 1975, but by less than one-half
of a percentage point. The average value does
fluctuate somewhat over time, and the fluctuations seem larger in the post-1975 period.
Fact 2. Differences in employment rates
across countries are large.
No matter which of the cross sections we
look at, the variation in employment rates is
strikingly large. For the sample as a whole, the
maximum values exceed 80 percent, whereas
the lowest values are less than 50 percent. The
standard deviations are also large, though it
can be difficult to gauge what constitutes large
in this context. The 85:15 ratio is perhaps more
informative in this regard. Note that this ratio
exceeds 1.20 for each cross section. To understand the significance of this value, note that
in the largest postwar recession in the United
States (1982), the ratio of employment to population at the peak was only about 1.03 times
larger than it was at the trough. It is particularly significant that the large difference in
employment rates across countries is not a
phenomenon that emerged after the early
1970s. Cross-country differences were large
even in the 1960–70 period.

■ 4 We note that cross-country studies of unemployment are
potentially more problematic because of differences in criteria across
countries, particularly in what constitutes searching for employment.
However, the OECD does publish a series of “standardized” unemployment
rates that attempts to correct for cross-country differences in measurement.
■ 5 See Blanchard and Wolfers (2000) for a presentation of the
low-frequency movements in unemployment rates over this period.
■ 6 An alternative procedure to isolate the low-frequency component
would be to use the trend component generated by applying the Hodrick–
Prescott filter to the data. The results of using this alternative procedure are
very similar and hence are not reported.
■ 7 The exception to this is 1960. Due to data limitations, 1960
simply refers to the average for 1960–62.
■ 8 More accurately, this is really the 83:17 ratio.

T A B L E

Aggregate Employment/Total
Population, Ages 15–64

1960

1965

1970

1975

1980

1985

1990

1995

Canada
United States
Japan
Australia
New Zealand
Belgium
Denmark
France
Germany
Ireland
Italy
Netherlands
Norway
Portugal
Spain
Sweden
Switzerland
United Kingdom

58.9
62.2
74.3
64.6
62.9
59.5
70.0
68.6
70.1
64.4
62.6
61.1
63.6
59.2
59.9
73.0
78.2
70.8

60.9
62.9
71.5
66.6
63.7
60.5
72.2
66.4
69.6
64.3
58.8
59.9
63.0
59.8
59.8
71.9
78.7
71.4

61.3
64.5
71.1
68.8
64.1
61.3
74.3
65.8
68.6
62.0
56.3
57.3
64.1
62.2
60.1
72.7
77.5
70.4

63.4
64.4
69.7
67.5
64.8
61.1
73.3
65.4
65.7
58.0
55.6
54.5
68.9
64.5
58.1
76.3
75.3
70.8

65.5
66.8
70.3
65.5
64.2
58.4
73.1
63.5
63.6
57.0
55.7
53.6
73.8
63.8
50.2
78.7
73.7
68.7

66.1
68.5
70.6
64.7
62.3
54.5
75.3
59.4
62.5
51.7
54.0
53.3
76.0
64.6
45.4
79.3
74.6
65.7

68.9
72.4
72.5
67.6
66.8
56.6
76.8
60.1
65.8
52.7
55.0
61.5
74.3
68.9
48.9
79.8
81.7
70.7

67.3
73.4
74.4
67.4
69.2
56.3
74.1
58.9
65.2
55.2
52.5
65.3
74.2
67.3
46.4
70.4
79.9
68.6

Mean
Standard
deviation
85:15 ratio

65.7

65.4

64.8

63.8

66.7

65.9

5.81
1.23

5.71
1.20

5.91
1.21

6.38
1.26

7.67
1.32

9.45
1.41

9.30
1.40

8.82
1.34

SOURCES: Organisation for Economic Co-operation and Development, Historical Statistics, various issues; and
author’s calculations.

Fact 3. The spread of employment rates
across countries changes substantially
across time.
Whether one looks at the standard deviation
or the 85:15 ratio, the spread of employment
rates across countries has exhibited substantial change over time. The distribution
became significantly more spread out during
the first part of the sample period, and though

it subsequently became more compressed,
there has still been a significant spreading out
over the period as a whole.
Fact 4. Differences in employment rates
across countries are persistent.
To see this, I report the correlation matrix
for the country-level observations across time
in table 2.

T A B L E

Correlation Matrix for County-Level
Observations across Time

1960
1960
1965
1970
1975
1980
1985
1990
1995

1965

1970

1975

1980

1985

1990

1995

1
.95

1
.95
.88
.76
.66
.59
.60
.53

1
.96
.84
.72
.65
.68
.62

1
.93
.81
.75
.77
.69

1
.94
.89
.87
.76

1
.98
.93
.84

1
.97
.89

SOURCES: Organisation for Economic Co-operation and Development, Historical Statistics, various issues;
and author’s calculations.

Note that at one lag (five years), the average
correlation coefficient exceeds 0.95. Obviously,
this indicates a great deal of persistence.9 Note
also, however, that the average persistence
decreases as the number of lags increases. At
four periods (20 years) the average correlation
drops to 0.70. It is also interesting to note that
these correlations are not driven by changes
that occurred before and after the oil shock of
the mid-1970s. For example, the correlation
between 1980 and subsequent years looks
very similar to the pattern of correlations
between 1960 and subsequent years. The fact
that at longer horizons the correlations
decrease considerably suggests our next fact.
Fact 5. There is considerable mobility
within the distribution.
There are several ways to motivate this fact.
One is to simply look at the changes in individual countries over the entire sample. Table 3
reports changes over three horizons—1960 to
1995, 1960 to 1970, and 1985 to 1995. This
split is of interest because the latter two lie on
either side of the 1970s’ oil shocks.

From the perspective of mobility, the key
is dispersion in changes. The dispersion of
changes over each period in table 3 is large.
Over the 1960–95 period, some countries see
their employment rates climb by more than
10 percentage points, while others see their
employment rates fall by more than the same
amount. Moreover, there is very little correlation between a country’s starting value in
1960 and the subsequent change; the
correlation is only –0.18. It is important to
emphasize that the situation is not characterized as one in which countries simply differ in
the extent to which their employment rates
decrease—almost half of the countries experience an increase in their employment rates
over this period, and as we know from above,
there is virtually no secular trend in the average employment rate across these countries.

■ 9 Keep in mind that our observations are themselves five-year
averages, which obviously induce some persistence relative to what
would be found using annual data.

T A B L E

Changes in Employment Rates

∆ (1960 –95)
Canada
United States
Japan
Australia
New Zealand
Belgium
Denmark
France
Germany
Ireland
Italy
Netherlands
Norway
Portugal
Spain
Sweden
Switzerland
United Kingdom

+8.4
+11.2
+0.1
+2.8
+6.3
–3.2
+4.1
–9.7
–4.9
–9.2
–10.1
+4.2
+10.6
+8.1
–13.5
–2.6
+1.7
–2.2

∆ (1960 –70) ∆ (1985–95)
+2.4
+2.3
–3.2
+4.2
+1.2
+1.8
+4.3
–2.8
–1.5
–2.4
–6.3
–3.8
+0.5
+3.0
+0.2
–0.3
–0.7
–0.4

+1.2
+4.9
+3.8
+2.7
+6.9
+1.8
–1.2
–0.5
+2.7
+3.5
–1.5
+12.0
–1.8
+2.7
+1.0
–8.9
+5.3
+2.9

SOURCES: Organisation for Economic Co-operation and Development, Historical Statistics, various issues;
and author’s calculations.

As suggested earlier, it is significant that
there is substantial mobility even abstracting
from the 1970–85 period. In the period
1960–70, the range of changes exceeds
10 percentage points, and the same holds true
for the period 1985–95 as well. It is also of
interest to note the heterogeneity of experiences
for countries that experience similar changes
over the full sample. Specifically, France, Italy,
and Spain all experience drops in their employment rates of around 10 percent. However,
Italy experiences over half of this drop in the
first 10 years, while France experiences
roughly a third in the first decade, and Spain
experiences virtually no decline in this period.
It should also be noted that there is virtually
zero correlation between changes in the first
decade and changes in the final decade.

Lastly, to highlight the range of mobility
experiences found in the data, consider the
evolutions of the Netherlands and Sweden.
Consider first the Netherlands. Beginning in
1965, the employment rate in the Netherlands
begins a steady decline, losing almost 8 percentage points and bottoming out in 1985.
Subsequently, however, the rate increases
by more than 10 percentage points, and the
Netherlands climbs significantly in the distribution. Next consider Sweden. Between 1960 and
1970, Sweden’s employment rate is relatively
constant, after which it increases substantially,
raising Sweden to the top of the distribution
between 1980 and 1990. Subsequently, however, the employment rate falls back to a value
very near its level in the 1960–70 period.

T A B L E

Correlation between Employment
and Unemployment Rates

Trend components

Cyclical components

.96
.53
–.30
–.42
–.97
–.89
.73
–.99
–.87
–.98
–.88
–.32
.79
.86
–.98
.10
–.36
–.94

–.92
–.92
–.60
–.90
–.90
–.76
–.88
–.77
–.77
–.85
–.72
–.52
–.81
–.77
–.89
–.93
–.57
–.97

Canada
United States
Japan
Australia
New Zealand
Belgium
Denmark
France
Germany
Ireland
Italy
Netherlands
Norway
Portugal
Spain
Sweden
Switzerland
United Kingdom

SOURCES: Organisation for Economic Co-operation and Development, Historical Statistics, various issues;
and author’s calculations.

A Digression on
Unemployment
versus Employment
The previous analysis has focused on employment-to-population ratios as the measure of
labor input. As noted earlier, many studies
focus instead on unemployment rates. I have
argued that from the perspective of understanding differences in resource allocations, it
is differences in labor input that are of primary
interest. But is the choice really substantive, or
is it the case that movements in employment
and unemployment are close to mirror images
of each other, in which case the issue is largely
irrelevant? In this section I present some
evidence on the matter. It turns out that while
movements in employment and unemployment
are highly negatively correlated at cyclical
frequencies, this is not necessarily true at lower

frequencies. To investigate this I examined the
series for employment-to-population ratios
used earlier and the standardized unemployment rate series produced by the OECD for the
period 1960–95. For each country I apply the
Hodrick–Prescott filter to each series and compute the trend and cyclical components. For
each country I compare the behavior of the
two trend series and the two cyclical series,
in each case computing the correlation
between the two series. Table 4 displays the
correlations.
The two columns of table 4 tell quite a
different story. The first column shows that
there is really no tendency for trend increases
in the employment rate to be associated with
either trend increases or decreases in the
unemployment rate; while there are many
values that are close to negative one, there are
also several that are close to positive one, as

well as several that are not close to either of the
extreme values. Reflecting this, the average of
the values in the first column is –0.27. On the
other hand, the values in the second column
are all negative, are all greater than 0.5 in
absolute value, and all have an average value
of –0.80.
The message from this is that when studying
low-frequency movements in the labor market,
one may get a very different picture depending
upon the measure one uses. Having said this, it
would appear that in at least one context—that
of the “European unemployment problem”
mentioned in the introduction—the differences
are likely to be quantitative rather than qualitative in nature, at least in terms of changes over
this period. The main reason for this is that
many of the European countries that experienced large decreases in employment over the
sample period, including Belgium, France,
Germany, Italy, Ireland, and Spain, are countries
for which the correlation between employment
and unemployment is close to negative one.

highest to lowest values after removing the
two highest and lowest values for each category.
Several features of the data in table 5 are
worth remarking on. First, the basic shape of
the life-cycle employment rate profile is the
same across all countries for both men and
women. The basic shape is that of an inverted
U. The peak in most cases occurs for the
35–44 age group, though in some cases it
occurs for the 45–54 age group. However,
although the basic shape is the same across
countries, there are important quantitative
differences in the profiles across countries. In
particular, the disaggregated data show that the
large differences in aggregate data do not
reflect an aggregation phenomenon; that is, it
is not the case that aggregate differences are
accounted for by different age distributions
across countries that have very similar lifecycle profiles. Examination of tables 5(a) and
5(b) lead to the following conclusions.

III. Facts about
Employment Rates II:
The Disaggregated
Data

Fact 6.2. Differences in employment rates
are much larger for young and old individuals than for prime-aged individuals.
These are pretty much self-evident from
table 5. For example, the 80:20 ratios are
U-shaped for both men and women, and the
values are much higher for women than for
men with the lone exception of the over-65
group. It follows that many of the differences
in aggregate data are driven by differences
among women and men who are not of prime
age. Specifically, the tables show that the
highest correlation between disaggregate and
aggregate values occurs for prime-aged
women—the correlation of employment rates
for women in the two age groups 35–44 and
45–54 is 0.86. In contrast, the correlation coefficient between aggregate employment rates and
those for men aged 35–44 is only 0.33 and
0.41 for those aged 45–54. In fact, excluding
workers over the age of 65, the lowest value
of this correlation occurs for males aged
35–44. However, even though differences are
smallest for prime-aged males, it is worth noting that the data still support the following
conclusion.

This section examines employment rates from
the perspective of data that are disaggregated
by age and sex. As mentioned earlier, data
availability limits the scope of the analysis in
terms of time period and the set of countries
that can be examined. I note first that using the
available data, one can establish the equivalent
to facts 2, 4, and 5 for the disaggregated data
as well: there are large differences in the rates
across countries, and they are persistent, but
there is also substantial mobility. Hence, in this
section I focus on additional findings that the
disaggregated data present us with. A basic
issue to explore here is the extent to which
the aggregate data capture the differences that
exist across countries at a point in time and
the changes that take place across countries
over time.
We begin by examining the cross sections
for 1995 for a set of 15 countries. For the timeseries analysis we are restricted to a much
smaller set of countries, but it is of interest to
examine one cross section for a much larger
set. In this case, the data represent a three-year
average, taken over the period 1994 –96.
Table 5 presents the data and several summary
statistics. The 80:20 ratio represents the ratio of

Fact 6.1. Differences in employment rates
are much larger for women than for men.

T A B L E

Employment Rates over the
Life Cycle, 1995

A. Men
15–24

25–34

35–44

45–54

55–64

65+

Canada
United States
Japan
Korea
New Zealand
Belgium
Denmark
France
Germany
Ireland
Italy
Portugal
Spain
Sweden
United Kingdom

52.2
58.0
44.9
27.6
61.3
29.3
68.5
22.0
51.4
37.7
26.4
42.7
26.6
41.3
61.2

81.7
88.0
94.3
90.5
86.2
86.9
87.0
83.7
83.6
81.1
71.1
86.4
72.2
79.0
84.2

84.6
88.6
96.1
95.2
87.7
89.0
88.5
88.7
90.4
81.7
88.6
91.9
83.2
85.0
86.0

82.8
85.7
95.7
92.3
87.1
82.5
86.1
86.3
87.4
77.2
90.2
86.6
80.3
86.4
85.8

54.4
63.7
80.9
78.8
62.9
34.8
60.5
38.7
47.4
59.0
55.5
58.9
48.8
65.0
56.6

10.1
16.2
36.4
41.6
9.9
2.3
4.3
2.6
4.2
15.0
6.0
21.8
2.8
13.2
7.5

Mean
Standard deviation
Coefficient of variation
80:20 ratio
Correlation with
aggregate aged 15–64
Correlation with
men aged 35–44

43.4
15.0
.35
2.30

83.7
6.2
.07
1.11

88.3
4.0
.05
1.09

86.2
4.5
.05
1.09

57.7
12.5
.22
1.37

12.9
12.1
.93
7.79

.66

.59

.33

.41

.45

.30

–.06

.68

.86

.44

.65

B. Women
15–24

25–34

35–44

45–54

55–64

65+

Canada
United States
Japan
Korea
New Zealand
Belgium
Denmark
France
Germany
Ireland
Italy
Portugal
Spain
Sweden
United Kingdom

51.6
55.2
44.5
39.3
55.4
24.0
60.7
18.3
48.6
34.0
21.6
33.5
21.4
41.9
57.5

69.4
70.4
57.6
47.6
62.0
69.9
72.6
65.2
65.8
62.1
46.9
73.0
44.9
73.9
66.2

71.8
73.8
63.9
61.6
70.0
63.1
80.9
69.3
67.7
45.7
51.8
74.5
43.1
83.0
71.9

66.4
72.2
68.1
59.6
73.6
45.5
73.7
67.3
62.2
36.2
47.4
61.0
32.0
85.3
71.7

33.9
47.5
47.5
49.9
38.3
12.5
37.8
28.6
24.5
20.3
20.2
34.1
17.6
59.9
38.9

3.3
8.5
15.5
20.5
3.1
0.9
1.2
1.3
1.5
2.7
1.7
9.7
1.3
4.6
3.1

Mean
Standard deviation
Coefficient of variation
80:20 ratio
Correlation with
aggregate aged 15–64
Correlation with
females aged 35–44

40.5
14.4
.36
2.56

63.2
9.8
.15
1.53

66.1
11.7
.18
1.44

61.5
15.0
.24
1.62

34.1
13.6
.40
2.35

5.3
5.9
1.11
7.46

.75

.63

.86

.78

.32

.60

.79

.92

.64

.06

SOURCES: Organisation for Economic Co-operation and Development, Labor Force Statistics, various issues; and
author’s calculations.

Fact 7. Differences in employment rates
across countries, even for prime-aged
males, are large.
To see this, simply recall the comment made
earlier to put the 80:20 ratios in perspective.
In postwar time series data for the United States,
a value of 1.03 is big. Hence, values of 1.1
must also be viewed as large.
Fact 8. Differences in disaggregated
employment rates are not proportional
to differences in aggregate data.
Another way to phrase this is to say that
when two countries have very different
aggregate employment rates, the corresponding
life-cycle profiles of employment rates are not
simply shifted up or down in a parallel fashion,
even controlling for sex. The relatively low
correlations between prime-aged employment
rates and the rates for other age groups
(controlling for sex) indicate this. A few examples serve to illustrate the significance of this

point. The three largest economies of continental Europe, Germany, Italy, and France, all
have employment rates at the aggregate level
(or even for males) that are substantially lower
than that of the United States in 1995. However, each of these countries has prime-aged
employment rates for men that actually exceed
the corresponding value for the United States!
Yet, in sharp contrast, for the 55–64 age group
the employment rate in the United States is
roughly double that in these other countries.
Spain has the lowest employment rates in the
aggregate level, and this continues to hold
when the data are disaggregated by sex.
Canada, on the other hand, has a relatively
high aggregate employment rate. Yet the
employment rates for prime-aged males are
roughly similar in these two countries. On the
other hand, male youths in Canada are almost
twice as likely to be employed as their Spanish
counterparts, as is roughly true for females of
all age groups in the two countries.

T A B L E

Changes in Employment Rates:
1972 to 1995

A. Men
Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

15–24

25–34

35–44

45–54

55–64

65+

–4.7
–8.6
–10.3
–33.7
–18.5
–16.0
–43.2
–22.8

–9.9
–3.1
–2.4
–12.4
–10.8
–23.6
–21.1
–12.5

–8.2
–4.5
–0.9
–9.6
–7.1
—
–13.0
–8.6

–7.7
–3.6
–0.1
–7.7
–6.8
–5.0
–14.0
–6.6

–23.3
–12.1
–4.1
–32.4
–26.6
–13.2
–32.3
–16.3

15–24

25–34

35–44

45–54

55–64

65+

6.2
7.5
–4.8
–25.0
–13.3
–7.6
–29.4
–14.9

27.2
24.4
13.4
10.0
15.0
15.6
16.9
11.3

30.4
23.8
5.6
19.6
17.9
—
18.5
12.9

25.7
18.7
7.9
16.6
13.3
17.5
5.5
16.5

4.4
7.3
3.6
–8.1
–1.3
11.3
–5.7
15.4

1.0
0.2
–0.6
–5.6
–4.3
0.3
–6.5
–2.9

–7.4
–5.5
–9.7
–16.3
–10.2
–1.4
–22.5
–10.8

A. Women
Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

SOURCES: Organisation for Economic Co-operation and Development, Labor Force Statistics, various issues; and
author’s calculations.

Having examined the differences in lifecycle employment rates from a single cross
section, I next turn to a look at the evolution
of life-cycle profiles over time and across
countries. For this exercise, data availability
limits us to a set of eight countries—Canada,
the United States, Japan, France, Germany,
Italy, Spain, and Sweden, and the period
1972–95. The appendix contains a complete
set of tables for the evolution of these life
cycles over time. For the sake of illustration I
focus on changes between 1972 and 1995.
The data for 1995 are a three-year average
centered on 1995, whereas the data for 1972
are simply an average of 1972 and 1973.10
Table 6 presents changes in life-cycle employment profiles, disaggregated by age and sex
for eight countries.11

A look at table 6 indicates a striking pattern
for this period—in all countries there was a
huge reallocation of employment away from
males and toward females. In the table for
males, every entry is negative. In the table for
women, the entries are all positive for ages
25–54. A closer look reveals the following fact.

■ 10 Data for 1971 are not available for all countries, so the two-year
average is used rather than further reducing the number of countries in the
sample. It also seemed preferable to not use 1974 since this marks the
beginning of the oil price shocks.
■ 11 Note that there are two missing values for Italy.

T A B L E

Changes in Normalized Life-Cycle
Profiles, 1972–1973 to 1994–1996

A. Men
Canada
United States
Japan
France
Germany
Italy
Spain
Sweden
Standard deviation

15–24

25–34

45–54

55–64

Scale

1.00
.91
.82
.43
.79
.69
.44
.71
.21

.97
1.01
.98
.95
.96
.83
.89
.95
.06

1.00
1.01
1.01
1.01
1.00
1.05
.98
1.02
.02

.77
.88
.96
.60
.69
.82
.69
.88
.12

.91
.95
.99
.91
.93
.91
.86
.91
.04

15–24

25–34

45–54

55–64

Scale

.95
1.04
1.19
.85
.95
.90
.92
1.00
.11

.94
.95
1.03
.95
.94
.95
.69
1.05
.11

.66
.80
.99
.56
.70
1.36
.43
1.14
.31

1.73
1.48
1.10
1.39
1.36
1.67
1.75
1.18
.24

B. Women
Canada
United States
Japan
France
Germany
Italy
Spain
Sweden
Standard deviation

.66
.78
.82
.30
.58
.44
.24
.62
.21

Absolute
deviations
.26
.23
.26
1.03
.56
.71
1.00
.48

Absolute
deviations
.79
.51
.41
1.34
.83
1.07
1.72
.57

SOURCES: Organisation for Economic Co-operation and Development, Labor Force Statistics, various issues; and author’s
calculations.

Fact 9. Changes in aggregate employment
rates are associated with large changes in
the shape of life-cycle employment-rate
profiles.
This fact is really a time-series equivalent to
fact 8. There we saw that if two countries have
very different aggregate employment rates, the
life-cycle profiles of employment rates are not
simply parallel transformations of each other.
What table 6 shows is that when the employment rate changes in a country, the life-cycle
employment-rate profiles do not shift in a parallel fashion. Consider a few examples. Aggregate employment and male employment rates
fall significantly over this period in France,
Germany, Italy, and Spain. Yet the change is
disproportionately accounted for by changes
in the employment rates of young and old

workers. The changes would look even more
skewed if we considered them relative to the
starting values—in some countries, youth
employment rates are falling by more than
half. Similarly, female employment rates are
actually increasing over this period in France,
Germany, and Spain, yet despite this, there are
massive decreases in the employment rates for
female youths.
I next present this same information in a
manner that can better highlight the relative
contribution of parallel movements of the lifecycle profile against changes in the shape of
the profile. I adopt the following procedure to
normalize the shape of the life-cycle profile.
Normalize the employment rate for the 35–44
age group to one, and then express all other
values relative to this value. This profile of

relative values plus the actual employment rate
for the 35–44 group completely describes the
whole profile. This procedure is carried out for
both the 1972 and 1995 data. Then, to summarize the changes in life-cycle profiles over time,
I compute the ratio of the relative values and
the ratio of the actual values for the 35–44 age
group. I do this for both sexes for each of the
countries in our sample, and table 7 presents
the results. The column labeled scale indicates
the ratio of the employment rate for the 35–44
group in 1995 relative to its value in 1972–73.
The columns with age ranges show the ratios
of the relative life-cycle employment profiles.
The column labeled absolute deviations gives
the sum of the absolute deviations of the four
life-cycle points from one. Note that if the
shape of the profile stayed the same but was
shifted up or down proportionately, each of
the first four columns would have a value of
one, and the sum of absolute deviations would
be zero. Hence, the last column is a measure
of how much the shape of the profile is
changing. Table 7 does not report data for the
over-65 age group since its relatively low
employment rates make it relatively unimportant from our perspective.
Consider the results for men first. It is
striking that the values in the third column
(ages 45–54) are so close to one. This implies
that the shape of the life-cycle employment
profile changes very little for prime-aged
males. For the other age groups, the changes
are much larger. Note that the scale factor is
less than one for each country. Note also that
the vast majority of the values in the table are
less than one as well. Comparing the standard
deviations of the various columns gives us a
way to ascertain the extent to which the
changes in scale dominate the changes in
shape. For three of the four age groups, the
standard deviation of the shape ratios exceeds
the standard deviation of the scale factors.
Now consider the case of women. First note
the magnitude of the scale factors—they are
all much larger than one, indicating that in all
countries the employment rate for women
aged 35–44 increased. However, the rest of the
entries are typically less than one, indicating
that although the employment rates were
increasing for most age groups in most countries, the increase was less than proportionate
to the increase for prime-aged women. Once
again, however, with the exception of Spain,
the entries for the 45–54 age group are fairly
close to one. Interestingly, however, for
women the standard deviation in scale factors
exceeds that of three of the four changes in

shape. This is the opposite of what was found
for men.
Note the asymmetry of the changes for men
and women. For men, the changes for primeaged workers are much smaller proportionately
than are the changes for other age groups.
For women, the opposite is true. Changes are
proportionately largest for prime-aged women.
An important development is that in 1994–96,
women’s life-cycle profiles increasingly resemble those of their male counterparts, whereas
in the 1972–73 period, women’s profiles
tended to be relatively flat.

A Closer Look at
Sweden and the
Netherlands
To illustrate the range of experiences that
exists across countries, we now take a closer
look at Sweden and the Netherlands for the
period 1972–96. Recall from the analysis of
aggregate data that these two countries follow
quite different paths over this period. Sweden
experiences a significant increase in its
employment rate over the first part of the
period and then witnesses a decline at the end
that brings it back roughly to where it began.
In contrast, the Netherlands experiences a
large decrease in its employment rate over the
first part but subsequently experiences a large
increase and ultimately ends the period with a
higher employment rate. What happened to
the life-cycle employment profiles for these
countries over this period? That is the issue I
turn to next. I examine the profiles at the dates
1972, 1980, 1985, 1990, and 1995. In each case,
the data represent a three-year average with
the given year as the midpoint of the period,
except for the initial point, which is a two-year
average based on 1972–73. Data limitations
require that we focus on three age groups:
15–24, 25–54, and 55–64. For each year, I
present normalized profiles that give the
relative employment rates for the two extreme
age groups relative to the 25–54 age group.
I also report a scale factor that gives the employment rate of the 25–54 group relative to its
value in 1972. Table 8 gives the results. These
data are aggregated for men and women.

T A B L E

Changing Profiles in Sweden
and the Netherlands

A. Sweden

1972
1980
1985
1990
1995

ER15–24
ER25–54

ER55–64
ER25–54

Scale

.76
.75
.68
.71
.50

.79
.75
.72
.76
.76

1.00
1.10
1.13
1.14
1.03

ER15–24
ER25–54

ER55–64
ER25–54

Scale

.93
.71
.64
.76
.75

.77
.56
.44
.41
.40

1.00
1.06
1.04
1.21
1.28

B. Netherlands

1972
1980
1985
1990
1995

SOURCES: Organisation for Economic Co-operation and Development, Labor Force Statistics, various issues;
and author’s calculations.

The differences across the two countries are
rather striking. First consider the case of Sweden.
As the scale column indicates, the employment
rate for prime-aged workers mimics the behavior
of the aggregate employment rate: a substantial
increase between 1972 and 1980, relative
constancy over the 1980s, and then a decline
back to its earlier value. Moreover, until the
final year, the relative life-cycle profile of
employment rates changes little. However,
when the aggregate employment rate falls in
1995, the shape of the profile changes a good
deal, as the employment rate for young workers
falls disproportionately. Next, consider the case
of the Netherlands. What is most striking in the
Netherlands is that the behavior of the primeaged employment rate does not really mimic at
all the behavior of the aggregate employment
rate. Whereas the aggregate employment rate
drops continuously between 1970 and 1985,
the prime-aged-employment rate experiences
a mild increase between 1972 and 1985. Subsequently, it does mirror the large increase
between 1985 and 1995 found in the aggregate
rate. In contrast to the case of Sweden, however, the shape of the life-cycle employment

profile changes substantially. Over the period
1972–85, there are massive relative downward
shifts for both young and old workers. Employment rates for these groups fall relative to those
for prime-aged individuals by roughly a third.
Moreover, over the period 1985–95, although
the employment rate for young individuals
partially recovers, the relative rate for older
individuals falls slightly.

A Closer Look at
Prime-Aged Males
Prime-aged males are a group that attracts
considerable attention in cross-country comparisons of labor market outcomes. One reason
for this interest is that they correspond to a
group whose main activity is presumed to be
market work. They are too old to be in school,
too young to be retired, and, even though
social norms are changing, they typically do
not have primary responsibility for child care
or other family situations. Although fact 7
explicitly deals with differences among primeaged males in the 1995 cross section (noting

T A B L E

Changes in Employment Rates:
1972 to 1995

Males 35–44
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

93.0
93.1
97.0
97.3
97.5
—
96.2
93.6

91.9
91.8
96.5
95.2
95.9
97.1
90.6
95.6

88.2
90.3
95.7
92.9
92.6
95.0
85.0
95.1

88.0
90.2
96.6
92.1
91.4
93.1
88.9
94.7

84.6
88.6
96.1
88.7
90.4
88.6
83.2
85.0

Mean
90:10 ratio

95.4
1.05

94.3
1.05

91.9
1.08

91.9
1.07

88.2
1.07

SOURCES: Organisation for Economic Co-operation and Development, Labor Force Statistics, various issues; and
author’s calculations.

that differences across countries are large), it
is of interest to look at the evolution of this
group in our panel of eight countries. Table 9,
which also appears in the appendix, shows the
employment-to-population ratios for males
aged 35–44 over the period 1972–95.
Three points are worth making about the
data in table 9. First, as already mentioned,
one of the striking facts for this age group is
the negative secular trend in all countries, even
for those in which aggregate employment rose
during the period. Second, while it is true that
cross-country differences among other demographic groups tend to be much larger, the
differences for this group are still substantial.
Third, the patterns found for this demographic
group do not reflect the patterns in aggregate
data. For example, in table 9, Germany appears
to be a high-employment country and Canada
appears to be a country with low employment,
but aggregate data suggest just the opposite.

IV. Other Measures
of Labor Input
This paper began by arguing that it is of interest
to understand differences in labor input, both
across time within a given economy and at a
given point in time across different economies.
Until now, however, all of the data analysis
has pertained to employment ratios. In fact,
employment is but one, albeit important,
component of labor input. Other components
include hours of actual work per employed
person and work effort. Differences in actual
hours of work per employed person can be
further subdivided by differences in normal
weekly hours of work, overtime hours, the
extent of multiple job holding, or paid vacation
and sick days. While there seem to be no
attempts to officially document work effort by
national statistical agencies, most countries do
attempt to measure hours of work.
Unfortunately, strictly comparable crosscountry time-series data on hours of work per
employed person do not exist. Differences in
procedures across countries with regard to
such matters as whether the category “hours of
work” refers to hours paid versus hours actually
worked limit the appropriateness of crosscountry comparisons. Having made this qualification, I present in table 10 data reported by

T A B L E

Annual Hours of Work per
Employed Worker

h1970
1970

1975

1979

1983

1990

1996

h1996

Canada
United States
Japan
France
Germany
Italy
Norway
Spain
Sweden

1890
1889
2201
1962
1949
1969
1766
—
1641

1837
1832
2112
1865
1801
1841
1653
—
1516

1832
1845
2126
1806
1696
1722
1514
2022
1516

1780
1808
2095
1712
1657
1699
1485
1912
1518

1788
1819
2031
1657
1598
1674
1432
1824
1546

1784
1839
1892
1608
1511
1636
1407
1810
1623

1.06
1.03
1.16
1.22
1.29
1.20
1.25
—
1.01

Mean
Standard deviation
90:10 ratio

1908
163.1
1.11

1807
172.2
1.13

1757
197.8
1.22

1719
189.9
1.19

1693
185.0
1.18

1663
165.6
1.22

1.15
.108
1.22

SOURCES: Organisation for Co-operation and Economic Development; Employment Outlook, various issues; and
author’s calculations.

the OECD for annual hours of work for a set of
nine countries over the period 1970–96.12
All of the summary statistics are for the set of
eight countries not including Spain, since
values for Spain are not available before 1979.
I chose to include the available data for Spain
because in our earlier comparisons Spain was
typically the country with the lowest labor
input as measured by employment. However,
in table 10 we see that as of 1996, annual
hours per employed worker in Spain were
some 10–15 percent higher than their corresponding values in France, Germany, and Italy.
Assuming that this comparison is appropriate,
it indicates the care that one must take in
extrapolating from cross-country differences in
employment (and hence unemployment) to
differences in labor input.
There are several patterns worth noting in
table 10. First, in all countries the tendency
since 1970 has been for annual hours of work
per employed person to decrease, though the
range of decreases is very large. Second, as
already discussed, comparisons at a point in
time across countries may be misleading due
to differences in how the data are collected.
However, assuming that the effects of these
differences are roughly constant over time, the

data suggest very large relative movements in
labor input across countries. As the last column
in the table indicates, annual hours per worker
fell in Germany by more than 25 percent relative to the United States.13 One issue to keep in
mind when interpreting these differences is the
fact that in all countries there is a tendency for
the workweek in manufacturing to decrease as
a country becomes richer. While this decrease
for the United States occurred prior to the 1970s,
in many other countries it occurred after 1970.

■ 12 These data are taken from various issues of the OECD
Employment Outlook. The OECD reports these measures with a strong
warning that they should not be used for cross-country comparisons at a
point in time. The value for Sweden in 1996 is not directly comparable to
the earlier values because of survey changes. It seems that the effect of the
change is to increase the value of hours worked in 1996 by around 3 percent.
■ 13 Although cross-country, point-in-time comparisons are not
recommended with these data, there are some indications that such
comparisons may be meaningful in some cases. In their study of the
auto industry, Fuss and Waverman (1992) document differences in
annual hours of work per auto-industry employee in Canada, the
United States, Japan, and Germany between 1961 and 1981. In 1961,
the values were Canada 1970, United States 2042, Japan 2495, and
Germany 2007. In 1981 the values were Canada 1857, United States
1923, Japan 2200, and Germany 1602.

T A B L E

Full- and Part-Time Employment
Ratios (1970 and 1995)

1970

Full-time
1995

Canada
United States
Japan
Australia
New Zealand
Belgium
France
Germany
Italy
United Kingdom

55.4
54.4
61.2
60.6
56.9
59.0
61.9
61.7
52.7
59.1

54.4
59.4
53.3
49.0
45.3
47.2
50.1
54.4
45.1
53.5

Mean
90:10 ratio

58.3
1.13

51.2
1.20

Part-time
1970
1995
6.0
10.1
9.9
8.2
7.2
2.3
3.9
6.9
3.6
11.3
6.9
2.81

12.9
13.0
16.2
17.2
13.1
9.1
8.8
10.2
5.8
15.9
12.2
1.84

SOURCES: Organisation for Co-operation and Economic Development; Employment Outlook, various issues; and
author’s calculations.

How do these changes in hours correlate
with the changes in employment ratios documented earlier? The correlation between the
change in hours between 1970 and 1996 and
the change in aggregate employment-topopulation ratios between 1970 and 1995 for
this set of eight countries is 0.36. Norway is
somewhat of an outlier in this regard, and if
Norway is excluded, the correlation increases
to 0.77. This suggests that the relative changes
in aggregate labor input are probably substantially larger than are the relative changes in
employment-to-population ratios.
A closely related issue that often comes up
in this context is cross-country differences in
the extent of part-time employment.14 The
measures of hours presented above do include
part-time employment, and hence do control
for these differences. However, it may also be
of interest to directly examine data on fullversus part-time employment. Here again,
however, a major caveat is necessary since
cross-country measures are not directly comparable due to differences in definitions of
part-time employment.

As a crude attempt to decompose the
previously examined employment-to-population ratios into full-time and part-time components so that I can compare relative changes
in the proportion of the population employed
full- and part-time, I compute full- and parttime employment-to-population ratios for 1970
and 1995. I use the data on the fraction of
employment that is part-time in 1973 and 1997
in conjunction with the earlier data on employment-to-population ratios for individuals aged
15–64 for the years 1970 and 1995. Although
the years do not match exactly, to the extent
that changes in part-time versus full-time
employment patterns have been occurring
gradually through time, this comparison should
give a good idea of the changes over the
1970–1995 period.
The values are in table 11.15

■ 14 In particular, some researchers have argued that the dramatic
improvement in employment in the Netherlands is entirely due to increases
in part-time employment. See, for example, Nickel and van Ours (2000) and
its discussion.
■ 15 The 90:10 ratio in this table refers to the ratio of the secondhighest value to the second-lowest value.

A few patterns emerge. First, note that in
all countries the employment-to-population
ratio has increased for part-time workers, and
in every country except the United States the
employment-to-population ratio for full-time
employment has decreased. Second, it is in no
way true that differences across countries in
aggregate employment-to-population ratios are
dominated by differences in the extent of
part-time work. The 90:10 ratio for full-time
employment exceeds 1.10 for both years.
Moreover, the value increases over time, suggesting that differences in full-time-employment
ratios have become larger. In contrast, differences in part-time-employment ratios have
actually narrowed slightly, though based on
the 90:10 measure, differences in part-timeemployment ratios still exceed those for
full-time-employment ratios. Third, from the
perspective of the “European unemployment
problem,” the full-time-employment ratios
suggest even larger relative changes than do
the aggregate numbers, since in 1970, part-time
work was much less prevalent in Europe but
has since become increasingly common there
relative to the United States.

V. Conclusion
This paper has studied the empirical properties
of aggregate and disaggregate employment in
a cross section of developed countries over the
period 1960–95. It has documented several
facts that a successful theory of employment
should be able to account for. Though much
information is presented here, there is much
additional information that would give a richer
picture of differences in time allocations across
countries. First, we need better cross-country
measures of hours of actual work, especially
at a disaggregated level. Second, additional
disaggregations would be useful, especially by
family structure. Third, it is important to understand how people spend their time when not
working in the market—are they taking care of
other family members, in school, or what?
Three conclusions seem to bear repeating.
First, large and persistent differences in
employment ratios across countries seem to be
pervasive. In particular, although the relative
changes in unemployment between the
United States and Europe over the last 30 years
have been dramatic, one should not be misled
into thinking that in this regard the world is
dramatically different after 1970 than before.

From the perspective of employment-topopulation ratios, there are large cross-country
differences before 1970 as well as after, and
there were substantial changes in cross-country
relative employment ratios in the period before
1970 as well as after. Second, the changes
found in data disaggregated by sex and age
do not at all mirror the changes found in
aggregate data. Changes tend to be concentrated among the young and the old and
among women. Any successful theory of crosscountry changes in employment must successfully account for this concentration. Third, the
patterns found in aggregate data for a cross
section of countries do not carry over to all
demographic groups within those countries.

Appendix—
Disaggregated
Changes in
Employment Rates
This appendix presents the complete set of
tables for disaggregated changes in employment rates between 1972 and 1995 for a set of

T A B L E

eight countries. The data for 1972 represent an
average for 1972 and 1973, whereas for each
other year, the data represent a three-year
average centered on the given year; for example,
for 1980 the data are an average of 1979– 81.
The 90:10 ratio is the ratio of the secondhighest to the second-lowest value.

Disaggregated Changes in
Employment Rates

A. Males 15–24
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

56.9
66.8
55.2
55.7
69.9
42.2
69.8
64.1

62.5
64.0
41.6
46.3
59.4
38.7
54.0
66.8

58.3
62.7
40.7
38.0
57.0
34.3
40.4
61.4

60.7
62.8
41.6
33.6
59.5
33.8
42.5
64.4

52.9
60.9
45.3
25.5
54.0
31.3
31.4
40.8

Mean
90:10 ratio

60.1
1.26

54.2
1.54

49.1
1.62

49.9
1.86

42.8
1.73

B. Males 25 –34
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

91.6
91.6
96.7
96.1
94.4
94.7
94.3
91.5

89.7
89.5
95.2
93.2
88.8
87.6
85.8
92.8

83.9
88.1
94.4
88.6
82.0
82.5
76.3
91.1

84.8
88.6
95.4
88.4
85.0
79.2
81.4
90.5

81.6
88.0
94.3
83.7
83.6
71.1
72.2
79.0

Mean
90:10 ratio

93.9
1.05

90.3
1.06

85.7
1.11

86.7
1.11

81.7
1.22

C. Males 35–44
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

93.0
93.1
97.0
97.3
97.5
—
96.2
93.6

91.9
91.8
96.5
95.2
95.9
97.1
90.6
95.6

88.2
90.3
95.7
92.9
92.6
95.0
85.0
95.1

88.0
90.2
96.6
92.1
91.4
93.1
88.9
94.7

84.6
88.6
96.1
88.7
90.4
88.6
83.2
85.0

Mean
90:10 ratio

95.4
1.05

94.3
1.05

91.9
1.08

91.9
1.07

88.2
1.07

D. Males 45–54
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

90.5
89.3
95.9
94.0
94.2
95.2
94.3
93.0

88.8
88.2
95.0
91.6
92.4
96.3
87.3
93.5

85.2
86.9
94.5
88.7
90.7
94.9
80.6
93.4

85.8
87.2
95.7
88.2
88.7
94.2
84.9
93.3

82.8
85.7
95.7
86.3
87.4
90.2
80.3
86.4

Mean
90:10 ratio

93.3
1.05

91.6
1.07

89.4
1.11

89.8
1.10

86.9
1.09

E. Males 54–64
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

77.7
75.8
85.0
71.1
74.0
—
82.1
81.3

72.5
69.5
81.7
64.5
63.4
72.0
71.6
77.2

64.5
64.9
79.0
46.5
54.4
65.6
59.2
73.2

60.0
64.7
80.5
42.9
51.3
63.1
56.7
73.8

54.4
63.7
80.9
38.7
47.4
55.5
48.8
65.0

Mean
90:10 ratio

78.2
1.11

71.6
1.20

63.4
1.35

61.6
1.44

56.8
1.37

F. Males 65+
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

17.5
21.7
46.1
16.3
14.4
7.4
25.3
24.0

14.5
18.5
40.1
8.2
6.8
7.9
12.3
13.7

12.1
15.5
36.2
5.3
5.0
5.3
6.1
11.6

11.0
15.7
36.3
3.8
4.4
5.2
3.9
13.5

10.1
16.2
36.4
2.6
4.2
6.0
2.8
13.2

Mean
90:10 ratio

21.6
1.76

15.3
2.32

12.1
2.92

11.7
4.03

11.4
5.79

G. Females 15–24
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

45.4
47.7
49.3
43.3
61.9
29.3
50.8
56.8

55.2
54.0
42.5
33.9
53.2
28.1
34.2
65.2

55.9
55.3
41.6
28.0
50.6
24.1
22.4
61.8

59.1
56.0
43.0
25.1
54.2
25.1
28.3
64.8

51.2
55.2
44.5
18.3
48.6
21.6
21.4
41.9

Mean
90:10 ratio

48.1
1.31

45.8
1.63

42.5
2.32

44.5
2.35

37.8
2.39

H. Females 25–34
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

42.2
46.0
44.2
55.2
50.8
31.3
28.0
62.3

58.8
60.7
47.2
63.5
57.5
47.1
32.2
79.4

64.1
65.6
50.2
64.4
56.3
47.3
36.3
85.4

70.2
69.0
54.8
65.7
62.5
50.0
44.3
86.3

69.4
70.4
57.6
65.2
65.8
46.9
44.9
73.9

Mean
90:10 ratio

45.0
1.76

55.8
1.34

58.7
1.39

62.9
1.40

61.8
1.50

I. Females 35–44
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

41.4
50.0
58.3
49.7
49.8
—
24.6
70.1

58.1
61.9
60.1
60.4
55.3
43.1
27.5
83.5

64.5
67.8
62.5
64.7
57.6
48.8
28.3
88.9

72.2
73.0
65.1
67.4
64.3
52.8
37.1
91.4

71.8
73.8
63.9
69.3
67.7
51.8
43.1
83.0

Mean
90:10 ratio

49.1
1.41

56.2
1.44

60.4
1.39

65.4
1.38

65.6
1.42

J. Females 45–54
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

40.7
51.5
60.2
50.7
48.9
29.9
26.5
68.8

50.7
57.2
61.0
54.5
49.6
36.8
26.5
82.2

55.6
61.3
63.4
58.0
50.3
40.5
24.4
87.0

64.1
68.6
67.6
60.9
57.6
45.6
28.1
89.4

66.4
72.2
68.1
67.3
62.2
47.4
32.0
85.3

Mean
90:10 ratio

47.2
2.01

52.3
1.66

55.1
1.57

60.2
1.50

62.6
1.52

K. Females 55–64
1972

1980

1985

1990

1995

Canada
United States
Japan
France
Germany
Italy
Spain
Sweden

29.5
40.2
43.9
36.7
25.8
8.9
23.3
44.5

32.2
40.0
44.6
36.8
26.9
22.0
20.9
54.7

31.1
40.3
43.5
28.6
21.7
20.7
18.5
57.6

32.9
43.8
46.5
28.5
22.2
21.3
18.1
64.3

33.9
47.5
47.5
28.6
24.5
20.2
17.6
60.0

Mean
90:10 ratio

34.8
1.70

34.8
2.03

32.8
2.10

34.7
2.18

35.0
2.35

L. Females 65+
Canada
United States
Japan
France
Germany
Italy
Spain
Sweden
Mean
90:10 ratio

1972

1980

1985

1990

1995

4.3
8.3
16.1
6.9
5.8
1.5
7.7
7.5

4.3
7.9
15.5
3.6
3.2
2.7
4.1
3.9

4.0
7.2
15.4
2.2
2.3
2.2
2.4
3.3

3.7
8.2
16.2
1.6
1.9
2.1
1.6
5.3

3.3
8.5
15.5
1.3
1.5
1.7
1.3
4.6

7.3
1.93

5.7
2.47

4.9
3.27

5.1
5.12

SOURCES: Organisation for Economic Co-operation and Development, Labor Force Statistics, various issues; and
author’s calculations.

4.7
6.53

References
Bertola, Giuseppe, and Andrea Ichino.
“Wage Inequality and Unemployment:
The United States versus Europe,” NBER
Macroeconomics Annual, Cambridge:
MIT Press, 1995, pp. 13–54.
Blanchard, Olivier. The Lionel Robbins
Lectures. Presented at the London School
of Economics, 2000.
Blanchard, Olivier, and Justin Wolfers.
“The Role of Shocks and Institutions in
the Rise of European Unemployment,”
Economic Journal, vol. 110, no. 462
(March 2000), pp. 1–33.
Ljungqvist, Lars, and Thomas J. Sargent.
“The European Unemployment Dilemma,”
Journal of Political Economy, vol.106, no. 3
(June 1998), pp. 514–550.
Millard, Stephen P., and Dale T. Mortensen.
“The Unemployment and Welfare Effects of
Labour Market Policy: A Comparison of the
USA and the UK,” in Unemployment Policy:
How Should Governments Respond to
Unemployment, edited by Dennis Snower
and Guillermo de la Dehesa, Oxford:
Oxford University Press, 1997.

Mortensen, Dale T., and Chris A. Pissarides.
“Unemployment Responses to ‘Skill Biased’
Technology Shocks: The Role of Labour
Market Policy,” Economic Journal, vol. 109,
no. 455 (April 1999), pp. 242–65.
Nickell, Steve, and Jan van Ours. “The
Netherlands and the United Kingdom:
a European Unemployment Miracle?”
Economic Policy, vol. 0, no. 30 (April 2000),
pp. 135–80.
OECD Employment Outlook, various issues,
Organisation for Economic Co-operation
and Development.
OECD Historical Statistics, various issues,
Organisation for Economic Co-operation
and Development.
OECD Labor Force Statistics, various issues,
Organisation for Economic Co-operation
and Development.

Monetary Policy and Asset Prices
with Imperfect Credit Markets
by Charles T. Carlstrom and Timothy S. Fuerst
Charles T. Carlstrom is an economic
advisor at the Federal Reserve Bank
of Cleveland. Timothy S. Fuerst is
the Owens-Illinois Professor in the
Department of Economics at Bowling
Green State University and a
research associate at the Federal
Reserve Bank of Cleveland.

Introduction
In a world with perfect capital markets (the
world of the Modigliani–Miller theorem), a
firm’s financial position—that is, its debt versus
its equity level—is irrelevant to its decisions on
production and investment. The reason is that
perfect capital markets let information flow
freely. If an entrepreneur has a good idea for
a new product, she will be able to produce it
regardless of her personal financial position
because outside investors, well informed and
readily perceiving an attractive profit opportunity,
will provide whatever financing is needed.
The supposition that an entrepreneur’s
financial position is irrelevant has important
implications for monetary policy. A worthy
production activity will be funded whatever
the entrepreneur’s finances may be. Therefore,
monetary policy need not respond to asset
prices.1 The Modigliani–Miller theorem, however, is not necessarily meant to be a description of reality. On the contrary, a voluminous
empirical literature supplies evidence that a
firm’s financial position does affect its ability
to operate. But does this departure from the
Modigliani–Miller theorem provide a rationale
for basing monetary policy partly on equity

prices? As it stands, the theorem provides an
important benchmark and enforces careful
thinking about financial markets’ workings and
the imperfections that would create a world
where a firm’s financial position (hence equity
prices) affects its ability to engage in production.
Many possible imperfections could generate
such a world. This article focuses on failures of
information. Suppose that only the entrepreneur
knows every detail of the proposed project,
while outside investors financing the project
have no way of knowing exactly what the
entrepreneur would do with their funds. Suppose further that outside investors have limited
ability to punish an entrepreneur who runs
off with their money or squanders it on a misguided production activity. In this scenario,
external investors are likely to provide financing only if they know they will be able to

■ 1 A response might be warranted if equity prices help forecast
macro variables of interest such as output and inflation.

recoup their investment if the project turns
sour. One way to ensure this is to restrict the
amount of funds they provide to the size of
the entrepreneur’s financial position. That is,
external financing will be no greater than the
collateral that investors can seize after the fact.
We have just summarized a story in which a
firm’s financial position, which we will henceforth call “collateral” or “net worth,” has a
powerful effect on a its ability to produce.
Increases in its equity price will increase this
collateral—and with it a firm’s ability to produce. Clearly, this is no Modigliani–Miller
world, but what role does monetary policy
have in it? Can policy help the economy
respond to the fundamental shocks that buffet
it? Should policy respond to asset prices in
such a world?
This article uses a theoretical model to
address these questions. The model is highly
stylized to keep the analysis tractable, but its
essential point will survive more complicated
modeling environments.2 A key conclusion is
that there is a role for activist monetary policy.
Imperfect information imposes a collateral
constraint on this economy, and monetary
policy can be useful in alleviating this constraint by responding to productivity shocks
or exogenous changes in equity prices.

I. The Model
The theoretical model consists of households
and entrepreneurs. We will discuss the decision problems of each in turn.

(2)

Notice that labor supply responds positively to
the real wage with elasticity τ. R t denotes the
gross nominal interest rate. Labor supply is
negatively related to the nominal rate because
we assume that households must use cash to
facilitate their consumption purchases (a “cashin-advance constraint”).3 Because the opportunity cost of holding cash is given by the gross
nominal rate, higher nominal rates make it
more difficult to turn labor income into consumption, thus discouraging labor supply. To
put it another way, the gross nominal interest
rate acts like a wage tax where 1 = (1 – tw ). The
Rt
celebrated “Friedman rule”—that the net nominal interest rate should be zero (or R =1)—is
based directly on the observation that a zero
interest rate eliminates this implicit wage tax.4
A household must also make a decision
about consumption versus saving. Households
can save only by acquiring shares to a real
asset that pays out (real) dividends of Dt consumption goods at the end of time t. It is helpful to think of this as an apple tree that produces Dt apples in time t. The tree trades at
share price q t at the beginning of the period
(before the time-t dividend is paid). Under our
assumption on household preferences, the
equilibrium real share price is given by dividends’ present discounted value (the assumption of linear utility implies that the discount
rate on dividends is the constant β )
(3)

Households

Lt =

q–t =E t β j Dt+j .
j =0

Households are infinitely lived, discounting the
future at rate β. Their period-by-period utility
function is given by
1+

(1)

U (ct , L t ) ct –

1
τ

1
1+ τ

where ct denotes consumption and Lt denotes
work effort. We choose this form for convenience. Each period, the household decides
how much to work at a real wage of wt . The
resulting labor supply relationship is given by

■ 2 For example, empirical evidence suggests that collateral
constraints have a stronger effect on small firms than on large ones
(see Gertler and Gilchrist [1999]). We abstract from this heterogeneity
and posit a single representative firm. Future efforts to quantify collateral
effects should model heterogeneity more explicitly.
■ 3 See the appendix for a precise statement of the household’s
problem and the resulting first-order conditions.
■ 4 In our model, the first-best policy will be the Friedman rule.
Our policy section includes analysis of a second-best problem where, for
some unspecified reason, the monetary authority desires to keep the
long-run average interest rate above zero, R >1.

If the share price were below this level (qt < q–t ),
then household demand for shares would be
infinite; if the share price were above this level
(qt >q–t ), then household demand for shares
would be negative infinity, that is, a desire to
sell short. Thus, households will hold a finite
and positive level of tree shares only if q–t is
the equilibrium price. The dividend process
is given by
Dt +1 = (1 – ρD ) Dss + ρD Dt + ε Dt+1 .
The symbol Et denotes the rational forecast of
future dividends; recall also that β is the rate of
household time preference, which is also the
real interest rate in this environment. Notice
that the asset price depends only on the
exogenous dividend process and that the
share price is increasing in the current and
future dividend levels. The exogenous discount process is an AR1, which means that
next period’s dividend is a weighted average
of today’s dividend (Dt ) and the long-run
average of dividends (Dss ) plus a random i.i.d.
shock (ε Dt+1 ).

Entrepreneurs
Entrepreneurs too are infinitely lived and have
linear preferences over consumption. They are
distinct from households in that they use a
constant-returns-to-scale production technology
in which labor produces consumption goods
(4)

yt = At Ht ,

where At is the current level of productivity,
and Ht denotes the number of workers
employed at real wage wt . Like dividends
productivity, At is an exogenous AR1 random
process given by
At +1 = (1 – ρA ) Ass + ρA At + ε At+1 .
The entrepreneur is constrained by a
borrowing limit. In particular, she must be able
to cover her entire wage bill with collateral
accumulated in advance. We will denote this
collateral as nt (net worth). The loan constraint
is thus
(5)

first supply their labor input but that output is
subsequently produced if and only if the entrepreneur contributes her unique human capital
to the process. This production sequence
implies that the entrepreneur could force
workers to accept lower wages ex post; otherwise, nothing would be produced. Workers,
anticipating this hold-up possibility, will take
steps to prevent it. This is harder than it
sounds. For example, an equity-type arrangement in which worker and entrepreneur agree
ex ante to split the production ex post will not
work. After the worker has supplied his labor,
the entrepreneur can refuse to provide her
unique human capital unless the worker’s
share is made arbitrarily small. In that case, the
worker’s only choices are to accept this small
share or to take nothing. The worker could
seize the entrepreneur’s existing assets, but
then we are back to our collateral constraint.
In fact, as Hart and Moore (1994) and Kiyotaki
and Moore (1997) demonstrate, these hold-up
problems can only be avoided completely if
the entire wage bill is covered by existing
collateral that workers could seize in case
of default.5
We can easily enrich this story by assuming
the existence of financial institutions that intermediate between workers and entrepreneurs.
For example, suppose that such intermediaries
provide within-period financing to entrepreneurs, who use it to pay workers. An intermediary, however, is concerned about the hold-up
problem, so it limits its lending to the firm’s
net worth. This returns us to the collateral
constraint described in equation (5).6
We assume in what follows that the loan
constraint is binding, so that labor demand is
given by
(6)

Ht =

Notice that labor demand varies inversely
(with a unit elasticity) to the real wage but is
positively affected by the level of net worth.
Firms that have more collateral can employ

wt Ht ≤ nt .

Notice that all variables are in real terms.
Why is the firm so constrained? Many
possible information stories would motivate
such a constraint. We will assume the classic
hold-up problem: Suppose that hired workers

■ 5 This implicitly assumes a one-period problem so that an
entrepreneur who withholds her labor cannot be punished by being
deprived of future income.
■ 6 Kiyotaki and Moore (1997) use a similar constraint. See Hart
and Moore (1994) for more discussion of the hold-up problem.

more workers because hold-up problems are
less severe. The binding collateral constraint
implies that At >wt , that is, the firm would like
to hire more workers but is collateralconstrained.
An entrepreneur’s only source of net worth
is previously acquired ownership of apple
trees. If we let et –1 denote the number of tree
shares acquired at the beginning of time t –1,
then net worth at time t is given by
(7)

nt = et –1 qt ,

so that the loan constraint is given by
(8)

wt Ht ≤ et –1 qt .

As noted above, the assumption of a binding
loan constraint implies that the firm’s marginal
profits per worker employed are (At – wt ).
These profits motivate the entrepreneur to
acquire more net worth. We will need to limit
this accumulation tendency so that collateral
remains relevant. The entrepreneur’s budget
constraint is given by
(9)

c et + et qt = et –1 qt +et Dt + Ht (At – wt ).

The right side of the budget constraint
equation is the entrepreneur’s income in
period t, which consists of her revenue from
the sale of existing trees (et –1 qt ), dividends
from new tree purchases (et Dt ), and profits
(Ht [At – wt ] ). The left side represents her
potential purchases in period t. With her revenue, she purchases either consumption (c et )
or new tree shares (et qt ). Using the binding
loan constraint, we can rewrite this as
At
(10) c te + et (qt – Dt ) = et –1 qt w ,
t

Because of the profit opportunities from net
worth (At >wt ), the entrepreneur would like to
accumulate trees until the constraint no longer
binds (trees are more valuable to collateralconstrained entrepreneurs than they are to
households). To prevent this, we will assume
that entrepreneurs must consume a fraction of
their net income each period
A
(11) cte =(1– )et –1 qt wt ,
t

so that entrepreneurial tree holdings evolve as
A
(12) et (qt – Dt ) = et –1 qt w t .
t

Below we will choose <1 to offset the
high return to internal funds, thus keeping the
entrepreneur’s collateral constrained in equilibrium. This forced-consumption-savings decision
implies that households will price trees so that
in equilibrium qt = q–t .

Equilibrium
In this theoretical model, there are two active
markets, the market for apple trees and the
labor market (the money market and bond
market are discussed in the appendix). We
normalize the supply of tree shares to unity so
that the asset market clears with et +st =1. The
equilibrium tree price is given by (3). As for
the labor market, equating labor supply with
labor demand (Lt =Ht ) and solving for the real
wage yields
τ

(13) wt =nt 1+τ Rtτ +1 .
The equilibrium real wage is increasing in
net worth because higher net worth increases
labor demand. The wage is also increasing in
the nominal interest rate because a higher
nominal rate decreases labor supply. Equilibrium employment is given by

(14) Lt =

τ
1+τ

For the reasons already noted, employment
responds positively to net worth and negatively to the nominal rate.

Log-Linearizing the
Model
Because the model is relatively simple, it is
convenient to express the equilibrium in terms
of log deviations. In what follows, the ~
represents a percent deviation from the
steady state.

τ ~ ~
(15) L~t =
(n –R )
1+ τ t t
~ =q~ +e~
(16) n
t
t
t –1
(17) Et n~t +1 =

τ ~ ~
(n –R ) +A~t ,
1+ τ t t

where (17) comes from (12) and the asset
price (3). Using (16) to eliminate nt , we can
rewrite (15) and (17) in terms of et as

τ ~ ~
~
(18) L~t =
(q +e –R t
1+ τ t t –1

)

τ ~
τ
(19) ~
et =
(e –R~ ) +A~t +
– ρ q~ .
1+ τ t –1 t
1+ τ D t
To calculate (19), we have also used the ability
to express the share price (3) as
~
(20) q~t =Dt

1–β
,
1– βρD

where ρD is the autocorrelation in the dividend
process. To sum up, the model consists of equations (18)–(20). There is one predetermined
variable, et –1, and there are three exogenous
shocks: At , Dt , and Rt .

with current collateral. Thus, the collateral
constraint limits the firm’s ability to respond
to shocks.
There is, however, a delayed response.
A positive shock to At has no effect on current
employment, but it increases et and, through
it, tomorrow’s net worth (see [22]). Hence,
employment responds with a lag to productivity shocks.
This lagged response generates persistence
to a temporary shock. That is, even if the
shock to At lasts only one period, the effect
on employment, Lt , and thus on output, lasts
much longer and only dies out at the rate
given by τ /(1+τ). If the shock to productivity is
serially correlated, this effect remains, so that
the collateral constraint prolongs the effect of
the productivity shock.

Second Experiment:
A Shock to
Dividends

II. The Experiments

Proceeding as before, we have:

Before turning to the question of monetary

1–β D
~
(24) L~t = τ e~t –1 + τ
1+τ
1+τ 1– βρD t

policy, it is useful to sharpen one’s economic
intuition about the model by considering
several experiments.

First Experiment:
A Shock to
Productivity (At )
Suppose that we hold all other variables constant and consider only shocks to productivity.
Then we have

τ ~
(21) L~t =
e
1+ τ t –1
τ ~
(22) e~t =
e +A~
1+ τ t –1 t .
By combining, we obtain

τ ~ ~
(23) L~t +1 =
(L +A ) .
1+ τ t t
Notice that contemporaneous employment
does not respond to shocks to productivity, At
(see [21]). This is a manifestation of the collateral constraint. When productivity is high, the
firm would like to expand employment but it
cannot because it must finance current activity

~.
(25) e~t = τ e~t –1 + τ –ρ 1 – β D
1+τ
1+τ
1– βρD t
By combining, we obtain

τ ~
L~t =
(L +ε~D ).
1+ τ t –1 t
Recall that εDt is the innovation in the dividend
process. The most remarkable observation is
that employment responds positively to dividend
shocks, even though these shocks have no
effect on either worker productivity or labor
supply. Instead, dividends affect employment
solely through the collateral constraint. Because
trees are used as collateral, and a dividend
shock drives up their price, the collateral
constraint is relaxed and the firm can expand
employment. Once again, these effects are
highly persistent.

Maximizing Vt with respect to Lt yields the
optimality condition

Third Experiment:
A Monetary
Policy Shock

(30) Lt = Atτ .

We will assume that monetary policy is given
by directives for the gross nominal interest
rate, Rt . The implied path for the money supply
can be backed out of the money demand
relationship (see the appendix).
Proceeding as before, we have

τ ~
(26) L~t =
(e – R~ )
1+ τ t –1 t
τ ~
(27) e~t =
(e – R~ ).
1+ τ t –1 t
By combining, we obtain

τ ~
~
(28) Lt =
(L – R~ ).
1+ τ t –1 t
There are two differences between the interest
rate shock and the productivity shock. First,
the interest rate shock has an immediate effect
on employment because it alters labor supply
contemporaneously. Second, its effect is negative because the higher interest rate lowers the
households’ desire to work. As in the previous
cases, the shock has a persistent effect through
the collateral constraint.

III. Monetary Policy
Optimal Monetary
Policy
What is the nominal interest rate’s optimal
response to productivity and dividend shocks?
To answer such a question, we need a welfare
criterion. The most natural choice in the present context is the sum of household and
entrepreneurial utility, which is given by
(29) Vt ct + cte –

1
1+–
Lt τ

1
1+ τ

= At Lt +Dt –

1
1+–
Lt τ

1
1+ τ

where the equality follows from the fact that
total time-t consumption must equal the total
supply of time-t consumption goods, which
comes from the goods produced using the
entrepreneur’s production technology, and
dividends produced by the apple tree. The
only choice variable in Vt is employment.

We will call this solution the “first-best” outcome because the welfare criterion can go no
higher. The first-best has two natural features.
First, employment responds positively to productivity shocks. When productivity is high, it
is efficient for employment to respond positively. Second, the first-best employment does
not respond to dividend or share prices. The
welfare criterion Vt is increasing in Dt , but
these shocks have no effect on labor productivity; thus, it is efficient for employment not to
respond to these shocks.
Is the first-best achievable? If there were no
collateral constraint, we would have wt = At ,
and the first-best could be achieved by setting
Rt =1, that is, by setting the net nominal rate to
zero. This is the celebrated Friedman rule. It
is optimal in this model because the cash-inadvance constraint on consumption distorts the
labor margin.
But in a world with agency costs, the firstbest is impossible because employment is
given by (14), which, as noted above, is
rendered too low (At >wt ) by the collateral
constraint, Furthermore, according to (14),
employment fluctuates with net worth and not
with the level of productivity. Compared to the
first-best outcome, these employment responses
are dreadful. Contemporaneous employment
does not respond to productivity, even though
it is efficient to do so; employment, however,
does respond to share prices which, in an
efficient world, should not affect it. In short, the
collateral constraint causes the economy to
under-respond to productivity shocks and to
over-respond to dividend shocks.
The advantage of the Friedman rule is that
it minimizes the distortion on labor from the
cash-in-advance-constraint.7 The disadvantage
is that a pegged zero nominal interest rate precludes the monetary authority’s responding to
shocks to make employment respond efficiently. It turns out that the benefit of a lower
nominal interest rate always wins out in this

■ 7 Recall that because cash must be held to facilitate transactions,
higher nominal rates discourage labor supply in (2).

environment—the first-best policy is simply to
set the nominal interest rate to zero (that is,
R =1) and leave it there. But what happens if
the monetary authority does not set the long-run
interest rate to zero but keeps it positive for
some unspecified reason? 8 Can monetary
policy improve on this economy’s ability to
respond to shocks in this world? Yes. To illustrate, let us consider a second-best exercise.

Optimal Policy in
Log-Deviations
We take the steady state of the economy as
given and use monetary policy so that the
economy responds to shocks efficiently.
Optimal employment (in log deviations) is
given by
(35) L~t = τ A~t .
To find the optimal (second-best) interest rate
policy, we can impose equation (35) in the
system (18) –(19), and back out the implied
interest rate. This exercise yields
(36) R~t =q~t + e~t –1 – (1+ τ )A~t
(37) e~t = (1+ τ )A~t – ρD q~t .
By combining, we obtain
R~t = εtD – (1+ τ) [ εtA + ( ρA –1)A~t –1 ] .
What are the properties of this (secondbest) optimal monetary policy? 9 When there is
a positive shock to productivity At , the central
bank should lower the nominal interest rate
so that employment can expand efficiently.
A constant-interest-rate policy does not allow
this because of the collateral constraint, but a
procyclical interest rate policy overcomes the
collateral constraint and allows the economy to
respond appropriately.
Suppose that productivity shocks are
autocorrelated with coefficient ρA . A positive
technology shock of 1 percent calls for an
immediate interest rate decline of (1+ τ ) percent,
but then an increase to (1+ τ )(1 – ρA ). The
increase is needed to prevent over-expansion
of employment, because net worth rises with
the initial interest rate decline.

In contrast, if there is a shock to share
prices that drives up net worth, nt , the central
bank should increase the interest rate enough
to keep employment constant. It is inefficient
for employment to respond to these dividend
shocks, and the central bank can ensure no
response by raising the nominal rate in response.
Notice, however, that even if a shock to share
prices (dividends) is autocorrelated ( ρD > 0),
the optimal interest rate response is iid.

IV. Conclusion
This article addresses the question of how
monetary policy should be conducted in a
world where asset prices affect real activity
directly because of binding collateral
constraints, that is, a world in which the
Modigliani –Miller theorem does not hold.
How should monetary policy be conducted
in such a world? Should it respond to asset
prices? How should it respond to productivity
movements? In this environment, there is a
welfare-improving role for a monetary policy
that responds actively to asset price and
productivity shocks. This activist interest rate
policy allows the economy to respond to
shocks in a Pareto efficient manner. By
assumption, monetary policy cannot eliminate
the long-run impact of the information constraint, but it can improve welfare by smoothing
the fluctuations in this constraint.
Our results are stark because all firms in the
economy are subject to this hold-up problem.
One can imagine an environment in which
small firms are the ones most subject to agency
costs. This will change the quantitative—but
not the qualitative—predictions of the model.
This article uses a monetary model with
flexible nominal prices. In contrast, Bernanke
and Gertler (1999) analyze a similar question
in a model with sticky prices. They conclude
that as long as monetary policy responds
aggressively to inflation, there is no rationale

■ 8 For example, a positive nominal interest rate may be set to give
the government inflation-tax revenues.
■ 9 Optimal monetary policy refers to how the central bank should
change the interest rate in response to technology shocks and share
prices. Money growth is endogenous and, as discussed in the appendix,
can be backed out of the money demand relationship, that is, the cash-inadvance constraint.

for a direct response to asset prices. They
reach this conclusion because, in their model,
asset price shocks directly increase aggregate
demand and thus the price level. Hence, a
policy that responds aggressively to inflation
is automatically responding to asset prices. The
model described in this article creates no direct
link between inflation and asset prices, so
the central bank must respond directly to the
latter. It suggests that, to the extent that asset
prices do not immediately lead to price
inflation, there may be a role for a monetary
policy response to asset price movements.

Appendix 1

s.t.

E β t ct –
t =0

1
1+ τ

Mt –1+Xt
+st –1 qt +st Dt
Pt
+

Rt –1 Bt –1 –Bt
– st qt –ct ≥ 0
Pt

Mt –1 +Xt
+ st –1 qt +st Dt +wt Lt
Pt
+

st =

Rt –1 Bt –1 –Bt
M
–st qt – ct – t ≥ 0 ,
Pt
Pt

where Bt denotes bond holdings (in zero net
supply), and households are assumed to receive
s
lump-sum monetary injections, Xt = Mt –1, at
s
Mt –1
the beginning of the period (Mts denotes the
per capita money supply at time t). Notice that
the bond and tree markets open either simultaneous to or before the consumption market.
The first constraint is the cash-in-advance constraint: The cash remaining after leaving the
bond and tree markets is the cash that can be
used to purchase consumption. The second is
the intertemporal budget constraint.
After minor simplification, household
optimization is defined by the binding cash
constraint and the following Euler equations:
(A1) 1 = β Rt Et (Pt /Pt +1)

if qt < q–t

st indeterminate if qt = q–t
st = 0 if qt > q–t , where
q–t =Dt +Et β q–t +1 .
Substituting (A1) into (A2), we have
Lt =

The household’s maximization problem is
given by
Max

P
(A2) L 1 = wt β Et ( t )
τ
Pt +1

wt τ
,
Rt

which is equation (2) in the text. Along with
the equilibrium conditions given in the text,
we also have Bt = 0 and Mts = Mt . Since we
are following an interest rate policy, the
implied inflation behavior is given by (A1).
The supporting money growth process can
then be backed out of the binding cashin-advance constraint.

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