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Can the Fed be a Payment
System Innovator?
Jeffrey M. Lacker and John A. Weinberg

W

e live in a time of rapid technological change, in which the arrival
of new ways of conducting business has become a commonplace
occurrence. One segment of the economy where these changes are
having a particularly significant effect is the payment system, the web of
banks and other institutions through which payments for goods and services are
cleared and settled. New mechanisms such as smart cards and internet-based
electronic money have captured the imagination of many payment system observers and participants. While earlier predictions of the death of paper money
have proven premature, the unprecedented pace of technological advance in
the last decade has given new hope to the prophets of the electronic age.
The Federal Reserve (the Fed) plays a prominent role in the payment
system, both as a provider of payment services and as a regulator. The public
interest in an economically efficient payment system has been at the core of Fed
payment system policy since the Fed’s founding in 1914. With new electronic
payment mechanisms apparently within grasp, there has been renewed attention
to the role of the Fed in the innovative process. A committee headed by Federal
Reserve Board Vice Chair Alice Rivlin recently completed a study of the Fed’s
role in the payment system, which gave special attention to how active a role
the Fed should play in guiding payment system innovation.1
Within the Federal Reserve System, electronic check presentment (ECP)
is seen as a potentially promising step in the evolution toward electronic payments. With ECP, consumers and businesses continue to make payments with
paper checks, but banks and clearinghouses that clear and settle payments use

Jeffrey M. Lacker is a vice president and economist in the Research Department. John A.
Weinberg is a research officer and economist in the Research Department. This article originally appeared in this Bank’s 1997 Annual Report. The authors wish to thank Ed Green, Tom
Humphrey, Ned Prescott, Marsha Shuler, John Walter, Marvin Goodfriend, Walter Varvel, and
Al Broaddus for helpful comments and discussions. The views expressed do not necessarily
reflect those of the Federal Reserve System. The authors remain solely responsible for the
contents of this article.
1 Federal Reserve System (1998).

Federal Reserve Bank of Richmond Economic Quarterly Volume 84/2 Spring 1998

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Federal Reserve Bank of Richmond Economic Quarterly

electronic information “captured” from the checks shortly after they are first
deposited in the banking system. (See Appendix.) While some ECP services
are now available, many important aspects of full-scale implementation are still
under discussion. The Fed’s role in developing and promoting ECP is clearly
aimed at the public interest objective of enhancing payment system efficiency.
In what follows, we ask whether the Fed can be a payment system innovator
while remaining loyal to its fundamental public interest objective. In particular, how can we ensure that the Fed’s payment system leadership contributes
to economic efficiency?
Our approach to this policy question is founded on the notion that the payment system is a communications industry. Such industries involve substantial
common costs—costs that cannot be uniquely attributed to any one user. This
cost characteristic has important implications for industry behavior. The critical
issue in such industries is how common costs are allocated across users.
Markets for communication services (including payment services) tend to
be heavily regulated and, in some instances, served by government-owned enterprises, such as the U.S. Postal Service. Concerns about “universal access”
often motivate government intervention. Here, universal access is usually interpreted as a concern about the cost of services to a particular class of users:
residential phone customers, rural postal patrons, or small and remote depository institutions. Access has been provided through price regulation, as in
telecommunications, and by direct government provision, as in the U.S. Postal
Service.
We show that government involvement in other communications industries
offers lessons for the role of the Federal Reserve in the payment system. In
both the telecommunications and postal services industries, legal barriers to
competition historically have helped sustain the provision of universal access.
Barriers to competition allow the shifting of common costs to be pushed to the
point where some users are subsidized, in a sense that we will make precise
later. Such subsidization is inconsistent with economic efficiency, and would
be impossible without barriers to competition. We point out that the Federal
Reserve Banks still benefit from some barriers to competition—privileged treatment under current check presentment regulations—that would allow them to
subsidize should they choose to do so. Federal Reserve policy explicitly seeks
to prevent subsidization, and there is no direct evidence that the Fed currently
subsidizes any segment of the check collection market. At the same time, however, it is clear that available analytical methods for determining the absence
of subsidies are imperfect.
Barriers to competition impede technological progress by distorting adoption choices. The contrasting experiences of the telecommunications and postal
services industries illustrate this fundamental conflict. In telecommunications,
the removal of barriers and a retreat from access have been accompanied by
rapid technological innovation. The U.S. Postal Service has retained barriers to

J. M. Lacker and J. A. Weinberg: Payment System Innovator

3

competition and in the view of some observers has been relatively slow to adopt
innovations. Barriers provide the opportunity for cross-subsidies that distort the
innovative process. Against this background, we argue that the Fed should act
to preclude subsidization by removing remaining barriers to competition. As
we emphasize, however, this step may require some retreat from the goal of
providing universal access.

1.

THE PAYMENT SYSTEM AS A
COMMUNICATIONS INDUSTRY

In the U.S. economy, roughly 220 million market transactions are made without cash daily, with a total dollar value of $1.6 trillion.2 These transactions all
involve credit. The seller receives a financial instrument representing a claim
on either the buyer or a third party. For example, a check is the liability of
the check writer and his or her bank. A credit card sale results in a claim—a
“sales slip”—that entitles the merchant to good funds. Similarly, a debit card
transaction gives the merchant a claim to good funds.
The clearing and settling of credit instruments used as means of payment intrinsically requires communication. A vast web of bookkeeping systems records
the assets and liabilities of various economic entities—bank accounts, loan
balances, investment funds, and the like. Noncash payment instruments are
fundamentally bookkeeping instructions to debit an account of the buyer and
credit an account of the seller. Those instructions must be communicated to the
relevant bookkeeping systems in order to carry out the necessary accounting
entries.
The payment system bundles together communication and financial services. Arrangements governing the use of payment instruments specify the
allocation of risks associated with payment failures. For example, the merchant
accepting a check bears the risk that the check writer may fail to cover it, but
the merchant does not bear the risk of a fraudulent credit card purchase. While
these risk-sharing arrangements are an important feature of the evolution of
the payment system, they do not make the fundamental function of payment
arrangements inherently different from other communication services.
Every new development in communication technology brings with it a
new possibility for sending payment instructions. Improvements in freight
transportation increase the speed and reliability with which checks can be
delivered to a buyer’s bank. Improvements in computer and telecommunications technologies facilitate the sending of payment instructions in electronic form directly to and from banks. Optimism about the transition to
electronic payment instruments is based on the assessment that the technologies
2 Bank

for International Settlements (1996).

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Federal Reserve Bank of Richmond Economic Quarterly

underlying electronic communications systems are improving rapidly, while
physical transportation technologies are improving only slowly at the present
time.3

2.

SOME NOTEWORTHY CHARACTERISTICS OF
COMMUNICATIONS INDUSTRIES

Economists have long noted that communications industries share certain distinct characteristics that have, in turn, heavily influenced industry behavior. The
most salient of these is the prevalence of common costs. The allocation of these
costs among diverse users is fundamental to the operation of communications
industries. Governments tend to intervene in such industries to allocate these
common costs in such a way as to promote access.
In what follows we employ a few technical terms that are necessary for
a clear understanding of the economics of communications industries. While
these terms are defined as they are introduced, they also appear in a glossary
at the end of the article.
Common Costs
Every communication benefits two parties, the sender and the receiver. How
should the costs of a message (a phone call, a letter, an e-mail) be divided
between the two beneficiaries? The answer is not entirely obvious. While
providers of communication services often collect fees from the sender, services
are provided jointly to both parties. The costs of providing these services cannot
be uniquely attributed to either of the beneficiaries. We call such costs common
costs. Common costs also extend beyond the level of the individual message.
A large part of the infrastructure costs of a communication system, such as
phone lines and information processing resources, are common to all users of
the system.
The significance of common costs distinguishes communications from
many other industries. For most other goods and services, a large part of the
costs of an individual’s consumption can be uniquely attributed to that individual. The time that a dentist, a barber, or a mechanic spends serving a customer
is a cost of serving that customer exclusively. Costs that can be unambiguously
associated with the provision of goods or services to a particular individual are
attributable costs.
For some costs, specifying whether they are common or attributable is not
so simple. Costs that arise from a single message from a sender to a receiver
(a single phone call, for instance) are attributable to that pair of users but are
common between them. Similarly, the transportation costs of a single shipment
3 Federal

Reserve System (1998).

J. M. Lacker and J. A. Weinberg: Payment System Innovator

5

of mail between two points are attributable to the group of people sending
or receiving letters on that shipment but are common among the members of
that group. In communications industries, there are very few costs that are
attributable to individual users, but there are many costs that are attributable to
specific groups of individuals. There are also substantial costs that are common
to entire communication systems.
Common costs are often fixed costs; they do not vary with the amount of
goods or services produced. An industry that has large fixed costs and relatively
small variable costs will exhibit economies of scale (declining average costs)
over some range of output levels. When there are costs that are common to
the production of multiple goods, then production is said to exhibit economies
of scope. Economies of scale and scope are important characteristics of many
communications markets because many costs are common among all users of
the network.
Another notable feature of communications markets is in the nature of
demand for such services. The economic value to an individual of having access to a communication system depends on the individual’s own demands for
connection to others and on the extent of the network of individuals connected
by the system. A consumer will be willing to pay more for a communication
service that allows communication with a larger set of correspondents. This
relationship between an individual’s valuation of a communication service and
the extent of the network is referred to by economists as a network effect. Note,
however, that a network effect is a consequence of both the interdependence of
demand for communication and the existence of common costs. The idea that
an individual “belongs to a network” is only meaningful if there are common
costs associated with linking people together.
The presence of common costs and network effects makes it difficult to
unambiguously specify the cost of serving a particular individual or group. On
the one hand, one can ask, “Given that services are already being provided
to others, what would it cost to extend service to this particular group?” The
answer to this question yields the incremental cost of serving a group of users.4
This definition excludes costs that are common to the delivery of service to
this group and to others. On the other hand, one might ask, “What would it
cost to provide services to this group if no one else were being served?” The
answer to this question yields the group’s stand-alone cost, which includes all
common costs. Clearly, when common costs are substantial, incremental cost
is much smaller than stand-alone cost.

4 It is important to distinguish between incremental and marginal costs. Marginal cost is the
added cost of the last unit of a good produced. Incremental cost is all of the additional costs that
arise from extending a particular set of services to a particular set of users. This may include costs
that are fixed with regard to the quantity of services provided, such as the costs of connecting a
group of users to an existing network.

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Federal Reserve Bank of Richmond Economic Quarterly

When there are no network effects, a group’s incremental cost is simply
the attributable cost of extending service to that group. When there are network
effects, the addition of the new group also has the effect of creating benefits
for other users. These benefits work to reduce the net cost of adding a new
group of users. Hence, we need a more general definition of incremental cost:
The incremental cost of extending service to a new group of users is
the cost of adding that group to the network, minus the benefits for
others created by that group’s participation.
Some commentators have interpreted governmental concern for universal
access in communications industries as a necessary response to network effects.
Many believe reducing prices to some users may enhance efficiency by compensating them for the network benefits they bring to other participants. If the
total benefits of an added participant, both to himself and to others, however,
are greater than the costs of adding that participant, then a privately operated
network will have an incentive to compensate the added participant. This would
be the case even in the absence of government intervention. Network effects
do not, by themselves, induce market failures.5
Allocating Common Costs
In pricing a communication service, a provider must decide who should bear the
common costs. There are many possibilities. One could recover all such costs
from one small group of buyers, or try to spread the burden evenly among all
buyers. We can evaluate alternative cost allocations according to two criteria.
First, are they consistent with efficient use of the service? Second, could they
arise under competitive market conditions?
While there are many dimensions to the efficiency of a communication
services market, one essential consideration is that the allocation of costs must
provide customers with the right incentives to participate in the network. An
individual’s participation is economically efficient if the resulting benefits exceed the additional costs incurred. If the prospective customer is charged less
than incremental cost, his or her participation could be inefficient, creating
benefits smaller than the costs incurred. Hence, a minimal requirement for a
cost allocation to be consistent with efficient use of the service is that no
individual or group of users should pay less than its incremental cost.
Like prices that are too low, prices that are too high can also interfere with
efficient use of the service. In particular, suppose some prices were greater than
stand-alone cost. There might then be users willing to pay this cost, but not
willing to pay the higher cost imposed by the seller’s prices. Such users would
5 For

alternative discussions of network effects as a source of market failure, see Economides
(1996) and Weinberg (1997).

J. M. Lacker and J. A. Weinberg: Payment System Innovator

7

be inefficiently excluded by prices that exceed stand-alone cost. Efficiency also
requires prices below stand-alone costs.
There is a natural tendency for market forces to produce prices that respect
the bounds of incremental and stand-alone costs. If there are no barriers to the
entry of new competitors, then the threat of such entry will serve to discipline
the pricing and cost allocation practices of incumbent suppliers. Suppose, for
example, that a group of customers is collectively paying more than its standalone costs. This market segment would be particularly vulnerable to entry by
an alternative provider. The threat of such entry will limit the ability of the
incumbent to charge more than stand-alone cost.
The threat of competition, which prevents any individual or group from
bearing too large a share of common costs, also prevents anyone from bearing
too small a share. If a provider is to at least break even on the sale of services
and tries to charge some group less than their full incremental cost, then the
provider must recover from other users all of the common costs plus the deficit
created by undercharging the favored group. Consequently, some set of buyers
must pay more than their stand-alone cost. With potential competition, however, this allocation of costs is not sustainable. Potential competition therefore
places both an upper and a lower bound on how much a customer or group of
customers can bear. The lower bound is the incremental cost of serving those
users, while the upper bound is stand-alone cost or the incremental cost of
adding those users to a competing network. Note that these bounds are the same
as those that guard against inefficient use of a service. In short, competitive
pressures prevent inefficiency.
The evaluation of cost allocations on efficiency grounds is complicated by
the fact that incremental cost can be difficult to measure. The categorization
of costs as attributable and common is not always straightforward. Even more
difficult, however, is the identification and measurement of the benefits that
one individual’s or group’s participation brings to others. On the other hand, it
is relatively easy to determine whether there are significant barriers to competition. If one can guard against such barriers, then market forces will tend to
produce cost allocations that respect the bounds of incremental and stand-alone
cost.
Government Intervention
In the United States and other countries, communications industries have typically been the object of substantial government intervention. Government
agencies or government-owned firms have typically provided postal services
and, in many countries, telecommunication services. In other cases, such as
telecommunications in the United States, provision of services by private enterprises has been subject to substantial price and product regulation.
The structural characteristics of communications industries drive government intervention. There are, however, two distinct views about how these

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Federal Reserve Bank of Richmond Economic Quarterly

characteristics motivate intervention. These industries are conducive to relatively concentrated markets, which could give sellers the ability to exercise
monopoly (or near monopoly) power over prices. One common view is that
government intervention in communications industries is motivated by a desire to limit anticompetitive behavior in markets that have natural monopoly
characteristics.
An alternative view states that government intervention is motivated by a
desire to place the cost allocation problem inherent in the pricing of communication services under political control. In communications industries, government
intervention has tended to tilt the allocation of common costs away from those
buyers with high attributable costs. This group of buyers often represents individuals in remote, rural locations. For instance, postal rates are independent
of the location to which mail is sent, although delivery costs are clearly higher
in rural areas. Also, when there are scale economies associated with service to
individual buyers, the per-unit attributable costs of serving large commercial
and industrial users will be less than those of serving small residential users.
When government intervenes to allocate service costs away from some
users and toward others, it might appear that the latter are subsidizing the
former. Intuitively, we might say that an individual buyer or a market segment
is subsidized if it is paying less than its share of production costs. As emphasized earlier, however, common costs make it difficult to unambiguously define
the share of total costs borne by an individual or group. Subsidization is less
ambiguously defined with reference to incremental costs. That is, an individual
or group is subsidized if it pays less than its incremental cost. If the provider
must cover all costs while subsidizing a set of buyers, payments received from
other buyers must be covering more than 100 percent of the common costs.
In this case (and only in this case) we say that some buyers cross-subsidize
others. As previously noted, competition or potential competition will limit a
seller’s ability to engage in pricing that results in such subsidies.
Government intervention that respects the bounds of incremental and standalone costs can be consistent with the efficient provision of services. The history
of public sector intervention in communications markets suggests that sometimes the beneficial treatment of groups has gone further, resulting in prices
that are below incremental cost. First-class mail service to many hard-to-reach
endpoints, for instance, is widely believed to be subsidized. This sort of crosssubsidization, however, is only possible if there are limits on competition. Prices
in a market segment in which the seller enjoys a legally protected monopoly
are not constrained to be below stand-alone cost. The seller might then be able
to raise enough revenues in the protected segment to cover any losses incurred
in selling to a subsidized segment.
When cost allocations are subject to political control, through either the
regulation of private providers or the public provision of services, allocation
choices are often justified in terms of access. Governments have tended to view

J. M. Lacker and J. A. Weinberg: Payment System Innovator

9

themselves as guarantors of widespread access to communication systems. This
interest in access has sometimes been motivated by the view that the universality of a communication network is an inherently worthy goal. In other instances,
the motivation arises from the concern for the consequences of market outcomes
for certain high-cost segments of users—rural postal customers, for example.
In either case, interest in access may result in cost allocations in which some
users subsidize others.

3.

A LOOK AT OTHER COMMUNICATIONS INDUSTRIES

Communications industries, we have argued, are characterized by common
costs—costs that cannot be uniquely attributed to any particular user or set of
users. Government intervention in such industries is often aimed at altering the
allocation of common costs across users. In the name of universal access, such
intervention often reduces the portion of common costs borne by some users.
Legal barriers to competition aid in cost shifting, but distort the decisions of
potential competitors.
The twentieth-century experience of two prominent communications
industries—telecommunications and postal services—offers valuable insights.
In both there are significant common costs and a tendency toward few competitors. Both were subject to significant government intervention that shifted
the incidence of common costs and raised barriers to competition, although
in recent decades these barriers have come under pressure. Public policy has
responded very differently in each industry with divergent results, particularly
with regard to technological innovation. The history of these two industries
offers revealing lessons for the Federal Reserve’s role as a payment system
innovator.
Telecommunications
For many decades, the telecommunications industry adhered to the model of
protected, regulated monopoly.6 The prevailing industry structure had its beginnings in the 1920s, when AT&T was allowed to amass a virtual monopoly
in phone services and operate free from the threat of competition. In exchange,
AT&T made large sunk investments in infrastructure to extend the national
network and subjected itself to rate-of-return regulation that sought to keep
charges to any buyers from being “too high.” This deal was supported by
AT&T’s argument that telephone service was a natural monopoly and that it
(AT&T) could provide universal access at lower cost than could a fragmented
industry.
6 For

further resources on the history of the U.S. telecommunications industry, see Brock
(1986) or Bornholz and Evans (1983).

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Federal Reserve Bank of Richmond Economic Quarterly

For basic local telephone services, buyer-specific fixed costs are significant
and variable costs are low. Hence, attributable costs per call tend to fall with
the number of calls over a wide range. Large industrial and commercial users’
average attributable costs are likely to be lower than those for small business
and residential users. The public interest in widespread access has typically
promoted price structures that mute these cost differences by shifting common
costs away from small users and toward large business users. In addition, cost
allocations tended to favor local service at the expense of long distance.
Through a series of moves by market participants and regulators, the structure of the telecommunications industry has evolved from one of an integrated,
regulated monopolist to one of more open competition. The Consent Decree of
1982, which settled a Justice Department antitrust case against AT&T, brought
competition to long distance markets, while the regional Bell companies retained monopoly positions in local telephony.
Regulated pricing of local service continued to attempt to shift common
costs away from high-cost residential and rural users in particular. Such an allocation required higher recovery from large commercial users and contributed
to commercial customers’ interest in alternatives to the regional Bells’ local
service, particularly with the proliferation of fax and data services. The longstanding status of local service providers as protected, regulated monopolies
was increasingly unsustainable in the changing technological environment. The
1996 Telecommunications Act opened all markets to competition, and explicitly
recognized that doing so would put pressure on the industry’s ability to provide
inexpensive access to such high-cost users as rural hospitals.
The dismantling of barriers to competition in telecommunications has been
accompanied by rapid adoption of new technologies. While the by-pass services
that hastened the arrival of competition were made possible by technological
progress, competition itself has accelerated technological change by encouraging innovation. In the process, the telecommunications industry and its regulators have retreated from the goal of providing access through subsidized cost
allocations.
Postal Services
The U.S. government has been involved in postal services since the founding
of the nation and has long made universal access the central goal of federal
postal policy. In the nineteenth century, the flow of information arising from a
universally accessible and affordable postal service was seen as an important
factor in the growth of a nation. The U.S. Postal Service’s legal monopoly
status has been seen as essential to the goal of universal access. With its protected position, the Postal Service can deliver first-class mail to all locations in
the United States at a single price. Without this protection, competitors would
“skim the cream” by taking low-cost local business, thereby raising the costs

J. M. Lacker and J. A. Weinberg: Payment System Innovator

11

of serving the remaining markets. This view suggests cross-subsidized pricing,
since prices that are free of subsidies would be immune to cream-skimming.
The Postal Service’s legal monopoly on first-class mail appears to have
affected other markets in which the monopoly does not apply. In parcel post
and package delivery, for instance, private firms are allowed to compete directly with the U.S. Postal Service, although they are significantly constrained
in their ability to do so.7 Critics have claimed that the Postal Service uses funds
earned in the protected first-class market to offer new services priced below
incremental cost in the more competitive package delivery business. A private,
profit-seeking provider might not have an incentive to engage in such pricing
of new products; unprofitable entry into a new market is not a compelling goal
by itself. As a public entity, however, the Postal Service’s motivations are less
well defined. While a public entity is charged with serving the public interest
and may generally seek to do so, it is hard to prevent at least some decisions
from being motivated by other goals. Entry into a new market, for instance,
may enhance the overall size and influence of the organization.
Without the discipline of potential competition, the U.S. Postal Service’s
incentives to maintain and enhance the cost efficiency of its operations are
muted. Some observers have noted the difficulties the Postal Service has experienced in the automation of mail processing.8 At the same time, potential
competitors incentives to develop innovative products and processes may well
be blunted by the Postal Service’s ability to subsidize its prices in competitive
market segments.
In short, the postal services and telecommunications industries in the United
States have followed divergent paths. While the telecommunications industry
has placed increasing reliance on markets to provide pricing discipline and
incentives to innovate, the U.S. Postal Service has retained a protected monopoly structure that may distort competition and can stifle technological progress.
And while in telecommunications the pace of technological innovation has been
quite brisk, with the U.S. Postal Service the pace has been relatively slow.

4.

FEDERAL RESERVE CHECK CLEARING

Check collection and other payment services share many features with network
communications industries like telecommunications and postal services. From
the earliest years Reserve Banks have enjoyed legal privileges that have aided
the Fed’s entry into check collection and have made the shifting of common
costs in the pursuit of universal access at least possible. Some competitive
advantages remain today, most notably the “six-hour monopoly,” which we
7 Sidak
8 Sidak

and Spulber (1996) give a detailed account on the restrictions facing private carriers.
and Spulber (1996).

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Federal Reserve Bank of Richmond Economic Quarterly

discuss below. These privileges make it theoretically possible for the Fed to
subsidize some check-clearing services, in the specific sense that term was
defined above. If the Fed were engaged in subsidization, by our definition, the
Fed’s presence could detract from economic efficiency. Moreover, as demonstrated by the contrasting cases of telecommunications and postal services, the
capacity to subsidize would not bode well for the Fed’s ability to innovate in
the public interest. The critical question regarding Fed participation in check
collection, then, is whether under barriers to competition some check collection
services are in fact subsidized. If so, then the Fed’s participation would not only
detract from economic efficiency but could also distort the innovative process.
The Six-Hour Monopoly
The Federal Reserve Banks enjoy certain legal privileges in the check collection
business. The most important is the Reserve Banks’ right to present checks to a
paying bank until 2:00 p.m. and receive payment the same day; private-sector
banks must present by 8:00 a.m. in order to insist on same-day funds. In practice, private-sector banks can and often do present after 8:00 a.m., but only after
negotiating a voluntary agreement with the paying bank, presumably offering
the paying bank compensation in the form of reciprocity or presentment fees.
The Reserve Banks need not obtain prior permission. Thus, the Reserve Banks
enjoy a six-hour monopoly on free par presentment for same-day funds. Other
advantages also exist but they appear to be of minor significance.9
The six-hour monopoly originated shortly after the founding of the Federal Reserve System. The Federal Reserve Act of 1913 authorized the Reserve
Banks to offer check collection services to their member banks. An amendment
enacted on June 21, 1917, extended this authorization to allow the Reserve
Banks to clear checks for all banks. The amendment also prohibited charging
presentment fees against Reserve Banks, but this provision only applied to
banks that voluntarily joined the Fed’s collection system.10 The prohibition
9 The Reserve Banks voluntarily refrain from presenting between noon and 2:00 p.m. in
most markets. The six-hour monopoly is not the only legal presentment privilege enjoyed by the
Reserve Banks. For example, private-sector banks do not have as much flexibility as Reserve
Banks in choosing where to present checks to paying banks. In addition, the paying bank controls
the intraday timing of payment to a private-sector presenting bank, while the Reserve Banks have
the right to debit the paying bank’s account within a specified time period. Because the other
legal privileges appear to be of minor significance relative to the six-hour presentment monopoly,
we will focus on the latter, although what we have to say will apply equally well to these other
privileges. See Board of Governors (1998) and General Accounting Office (1989) for more details.
10 The amendment provided that any bank could make “reasonable charges, to be determined
by the Federal Reserve Board, but in no case to exceed 10 cents per $100,” but that “no such
charges shall be made against the Federal Reserve Banks.” An opinion of the U.S. Attorney
General established that this latter provision applied only to banks that voluntarily joined the
Fed’s clearing system. Note that a state-chartered bank did not have to become a member of the
Federal Reserve System in order to participate in the Fed’s check collection plan.

J. M. Lacker and J. A. Weinberg: Payment System Innovator

13

codified and expanded a stipulation the Federal Reserve Board had imposed
earlier by regulatory fiat on member banks.11 Banks retained the right to charge
presentment fees to any other banks presenting by mail, however. Only the Reserve Banks could mail checks to participating banks and demand immediate
par settlement.
The Fed’s par presentment privilege was by all accounts essential in the
subsequent growth of the Reserve Bank check collection system. The ability to
present at par to member banks gave the Reserve Banks a cost advantage over
competitors. This advantage gave nonmember banks an incentive to join the
Fed’s collection system to obtain access to low-cost presentment at member
banks. The Reserve Banks required that banks joining the system also agree to
accept presentment at par. The upshot was that the more banks that joined the
Fed collection system, the greater the value of joining.12
From its founding in 1913, the Federal Reserve was eager to increase participation in the Reserve Banks’ check collection system. For members of the
Federal Reserve System, access to the system was a benefit that offset, in part,
the cost of stricter Fed reserve requirements, while nonmembers gained the
ability to present to participating banks at par. Despite these benefits, the Fed
never completely monopolized interbank check collection. For some nonmember banks the income from presentment fees was apparently worth more than
the net value of lower-cost clearing services available from the Reserve Banks,
so these “nonpar banks” continued to charge presentment fees, a practice that
persisted for decades.13
The Monetary Control Act (MCA) of 1980 dramatically changed the nature of the Fed’s check collection service. The MCA required Reserve Banks
to charge fees for their payment services which must, over the long run, cover
the direct and indirect costs of providing the services, including imputed costs

11 The

first Reserve Bank check-clearing arrangement, the so-called “voluntary plan” adopted
in 1915, required that member banks joining the plan accept checks at par from the Reserve
Banks. The “compulsory plan” adopted in May 1916 also included the same requirement but
had the Reserve Banks covering the expense of shipping notes or lawful money from the bank
to the Reserve Bank in payment. Such expenses were obviously not the only paying bank costs
attributable to check collection. Note that because nonmembers had to agree voluntarily to join
the Fed clearing plan, the amendment gave the Reserve Banks no real advantage over private
banks, since both needed to offer inducements to obtain par presentment rights. The amendment’s
effect was to codify the Reserve Bank’s right to present to member banks at par, by mail, without
prior permission. For discussions of the Fed’s entry into check clearing see the classic account
of Warren Spahr (1926), or more recently, Ed Stevens (1996, 1998) and Alton Gilbert (1998).
12 Note that the effect of the size of the Fed check collection system on the value of joining
did not necessarily reflect a network effect. Federal Reserve policy deliberately tied the service of
collecting a bank’s outgoing checks to that bank’s willingness to pay par on its incoming checks.
There was no technological link between the number of banks sending checks to the Fed and the
number of banks to which the Fed could send checks.
13 See Jessup (1967) and Stevens (1998).

14

Federal Reserve Bank of Richmond Economic Quarterly

that would be incurred if the services were provided by a private firm.14 The
MCA also imposed uniform reserve requirements on all depository institutions
and granted nonmembers access to Reserve Bank payment services. Prior to
the MCA, free check clearing was one of the benefits of membership. Access
to Fed services was now divorced from membership and was explicitly priced.
By forcing the Reserve Banks to charge prices that cover actual and imputed costs, the MCA went a long way toward leveling the competitive playing
field. The Fed retained presentment privileges nonetheless. Private collecting
banks had no practical means of obtaining same-day funds.15 In response to
public concerns about the remaining asymmetry, the Board sought public comment in 1988 on a proposal to extend Reserve Bank presentment rights to
private-sector banks, allowing them to present until 2:00 p.m. for settlement
the same day. Corporations objected to the proposal, however, because it would
hamper their ability to manage their accounts within the day.16 The compromise
that was finally adopted, effective January 1994, established the current regime
in which all banks have the right to same-day settlement for checks presented
by 8:00 a.m. The Reserve Banks retained the privilege of presenting until 2:00
p.m. for same-day funds.17
The six-hour monopoly could give the Reserve Banks an advantage over
competitors in some market segments. It means that the Reserve Banks can
collect a given set of checks on better terms than a private provider: for example, by offering a later deposit deadline or better availability (less check
float). A private-sector competitor would have to incur additional costs to
clear the same checks with the same availability. In some markets, particularly
for small and remote depository institutions where transportation time can be
14 The Federal Reserve’s cost recovery requirement includes a “private sector adjustment
factor” that consists of the taxes, fees, and return on capital applicable to a comparable privatesector provider.
15 The rights of private collecting banks were governed by provisions of the Uniform Commercial Code. For a description, see General Accounting Office (1989), p. 28.
16 In arrangements called “controlled disbursements,” banks notify their corporate customers
early in the day of the value of the corporation’s checks presented that day, allowing the customers
to fund their accounts by selling money market securities. Later presentment makes such arrangements more difficult because money markets become progressively less liquid in the afternoon.
These costly efforts effectively skirt the prohibition on interest on corporate demand deposits and
are wasteful from society’s point of view. Note that corporate objections to extending private
presentment time to 2:00 p.m. are not directly relevant to the question of whether private and
Reserve Bank presentment times should be equalized; presumably they would also object if asked
whether the Reserve Banks should be able to present at 2:00 p.m. The objections might suggest
that, without interest on corporate checking accounts, equalization should take place at a time
earlier in the day rather than later. See Board of Governors (1991), p. 4747, for discussion of
public comments on the 1988 proposal.
17 The Board of Governors has recently requested public comment on the effect of the January 1994 same-day settlement rule. In addition, the Board is considering reducing or eliminating
legal disparities between Reserve Banks and private-sector collecting banks in the check collection
process, including the six-hour monopoly (Board of Governors 1998).

J. M. Lacker and J. A. Weinberg: Payment System Innovator

15

significant, this advantage has given the Reserve Banks a dominant market
share. Indeed, in some locations only the Fed presents checks. In more geographically concentrated markets—large cities, for example—the six-hour monopoly provides little or no competitive advantage and the market share of the
Reserve Banks is correspondingly low.
The Allocation of Common Costs
How do the Fed’s check collection activities affect the allocation of the common costs? Since implementation of the MCA in the early 1980s, the Reserve
Banks price structure has determined the allocation of common costs. Early on,
Reserve Bank pricing under the MCA was relatively uniform, although prices
varied according to the destination of the check. At first, prices at various Fed
offices depended only on whether the item was bound for a city or a remote
location. More recently, the price structure has become increasingly complex
with finer geographical differentiation.
The increasing complexity of the Reserve Banks’ pricing has been a response to competitive pressures. Initially, alternatives to Fed check clearing
were not well established. As private-sector clearing has grown over time, increased price differentiation has lowered margins in market segments in which
alternative providers can compete effectively with the Fed. Maintaining full
cost recovery then requires higher margins in market segments where customers have relatively few viable alternatives. Such markets are generally those
in which the Fed’s six-hour monopoly supports a dominant market share—
presentment to remote banks. Accordingly, common costs have shifted away
from market segments in which the six-hour monopoly yields no significant
competitive advantage for the Fed—presentment to city endpoints.
The six-hour monopoly could allow the Fed to set prices below incremental
costs so that subsidization results. We previously noted that in industries which
have substantial common costs (like communications), competitive pressures
constrain the way those costs can be allocated across market segments; market
discipline generally prevents subsidization. Governmental barriers to competition can loosen the constraints of competitive pressure, however, because
they allow over-recovery of costs in protected market segments in order to
fund prices below incremental costs in other market segments. The six-hour
monopoly is exactly this type of barrier to competition. By raising the costs
of competitors, this advantage could allow the Reserve Banks to charge more
than stand-alone cost in the protected market segment (checks drawn on remote
banks) in order to price below incremental cost in contested market segments
(checks drawn on city banks). While these prices could further the goal of
universal access, they would be detrimental to economic efficiency, since some
users would face prices below incremental social cost.
Reserve Bank price setting is constrained by a specific methodology
designed to prevent cross-subsidies. Per-item fees must be above “floor cost,”

16

Federal Reserve Bank of Richmond Economic Quarterly

which is defined essentially as average (attributable) variable cost. The individual check is not the only relevant increment, however. There are often
significant costs that are attributable to a group of checks but not specifically
attributable to individual checks. For example, local transportation costs are
attributable to the collection of checks drawn on a particular group of banks,
though not to an individual customer or item. The total floor cost for a group
of checks is an underestimate of incremental cost if it excludes costs that are
attributable to that group of checks but not to any individual item.18 It is also
possible that floor costs overstate incremental costs, since network effects, if
they exist, reduce the true incremental cost of serving a market segment.
We need to entertain two alternative hypotheses, therefore, about the Fed’s
allocation of common costs. One hypothesis is that the Reserve Banks generally do not set fees below incremental costs or above the stand-alone costs.
The other is that in some market segments the Reserve Banks set some fees
below incremental costs and thus set fees above stand-alone costs elsewhere.19
These two hypotheses have different implications, as we will see, for how we
approach questions about the Fed’s role in payment system innovation.
Access
As noted earlier, the Federal Reserve lists payment system accessibility as an
important policy goal.20 The usual articulation of this goal speaks of the Fed
providing payment services to all depository institutions, particularly “smaller
institutions in remote locations that other providers might choose not to
serve.”21 Since there is undoubtedly some price at which alternative providers
would choose to serve a given location, access to the payment system must be
interpreted in terms of the cost of payment system services to small and remote
banks. Enhancing access to the payment system must mean lowering the cost
to small and remote banks.
Does the Fed lower the costs of check clearing for small and remote banks?
We have argued that the Fed’s presence tends to shift common costs toward
checks drawn on remote banks. Hence, cost allocation among banks is determined by whether checks drawn on remote banks make up a smaller portion
of the checks collected by remote banks than they do of checks collected by
18 Critics who have charged the Fed with unfairly subsidizing check collection have focused
on whether the Fed’s cost accounting methodology understates the overall cost of Fed check
collection. This question is separate from the question we discuss: cross-subsidization within Fed
check processing. The Board of Governors requires that the Reserve Banks annually recover the
full cost of check collection services from check collection fees.
19 Our reasonable hypothesis is that the Reserve Banks recover the full costs of check
collection in the aggregate.
20 The Monetary Control Act states that prices for Federal Reserve services “shall give due
regard to competitive factors and the provision of an adequate level of such services nationwide.”
21 Board of Governors (1990), p. 295.

J. M. Lacker and J. A. Weinberg: Payment System Innovator

17

city banks. If so, the Fed’s presence tends to favor small and remote banks.
Although to our knowledge no formal data is available, anecdotal evidence
suggests that the difference, if there is one, is not large. The shift of common
costs toward checks drawn on remote banks does not appear to alter appreciably
the relative burden imposed on small and remote banks. There are, however,
other dimensions of pricing along which the Federal Reserve may still be able
to pursue a goal of moderating costs for small and remote banks, although
direct quantitative evidence is unavailable.22
While we lack direct evidence on the extent to which the Fed shifts common
costs away from small and remote banks, some indirect evidence is available.
Last year Federal Reserve Board Vice Chair Alice Rivlin headed a committee
that examined the role of the Federal Reserve in the payment system.23 As part
of its work, the committee held a series of public forums. Many participants at
these forums expressed the widely shared belief that the Fed’s exit from check
clearing would raise the cost of check collection to small and remote banks.
Thus according to many people intimately involved in the check collection
industry, the Fed’s cost allocation does have the effect of enhancing universal
access. A reasonable working hypothesis is that the Fed’s presence does shift
at least some common costs away from small and remote banks.24

5.

THE FED AS A PAYMENT SYSTEM INNOVATOR:
ELECTRONIC CHECK PRESENTMENT

We have argued that the Federal Reserve’s involvement in the check collection
industry closely parallels government involvement in the telecommunications
and postal services industries. Under this view, the Fed promotes universal
access by shifting common costs in the presence of legal barriers to competition. Rapid technological change is currently creating new opportunities for
innovation in payment services. As a major provider of payment services, the
Federal Reserve must determine its appropriate role in pursuing and promoting
innovations.
Our reading of the history of communications industries strongly suggests
that barriers to competition are fundamentally incompatible with the efficient
22 For instance, Reserve Banks’ prices depend on the amount of sorting done by depositing
banks prior to depositing checks with the Fed. Small, remote banks are more likely to make
unsorted deposits than are large, city banks. The Fed could pursue its interest in access by setting
lower price-cost margins for unsorted than for sorted deposits, thereby lowering the cost of check
collection for small, remote banks.
23 Federal Reserve System (1998).
24 The shift of common costs away from small and remote banks might be independent
of the six-hour monopoly. Some participants in the Rivlin Committee Forums believe that the
Federal Reserve accepts a lower rate of return than would be required by commercial providers
or that the Fed does not account for the full costs of providing service.

18

Federal Reserve Bank of Richmond Economic Quarterly

adoption of new technologies. Barriers weaken the effectiveness of an organization’s innovative efforts, and they create opportunities for subsidies that can
distort the choices users make with respect to new technologies. For both reasons, truly good innovations may fail to reach the market, while unworthy ones
may actually take hold. Without barriers to competition, cross-subsidization
would not be sustainable, and so we can have confidence that the innovative
process is genuinely beneficial.
How does one resolve the conflict between cross-subsidization and innovation? One approach is to measure incremental costs rigorously in order
to prevent subsidization. This approach, in essence, is the Federal Reserve’s
current practice. Earlier, however, we pointed out that the need to gauge incremental costs and network effects across a wide assortment of user subgroups is
likely to make comprehensive measures of incremental costs difficult to obtain.
Accounting data alone are not likely to convince a skeptic of the absence of
cross-subsidies.
An alternative approach to the conflict between cross-subsidization and
innovation as it pertains to Reserve Banks is to remove the conditions that
might lead to cross-subsidization. In the absence of special legal privileges,
competitive pressures will preclude cross-subsidization, as we defined it earlier.
Removing the remaining barriers to competition would clearly demonstrate the
Fed’s commitment to efficient innovation.
These principles apply to the Fed’s current efforts to implement ECP. As
with any innovation, the near-term prospects of ECP are uncertain. A recent
study by Joanna Stavins (1997), an economist at the Federal Reserve Bank
of Boston, attempts to quantify the overall costs and benefits to society of a
transition to ECP. One advantage would come from replacing the resource cost
of transporting and processing paper checks with the lower cost of sending
electronic messages. On the other hand, some people prefer to get their checks
back. Further, under a variety of state laws, certain check writers are either
entitled or required to receive their canceled checks. While the estimates reported by Stavins favor ECP, the results are sensitive to reasonable alternative
assumptions, particularly with regard to the intrinsic value of canceled checks
to consumers. As with other recently proposed payment innovations, such as
stored-value (“smart”) cards, it is probably too early to tell whether ECP will
make society better off or not.
Ideally, innovations would succeed in the marketplace if and only if they
were truly beneficial to society. Accordingly, the Fed should introduce ECP in
such a way that we can be assured it will succeed if and only if it improves
payment system efficiency. In the absence of impediments to competition, a
new product or service generally will be profitable if its value to customers, as
measured by willingness to pay, exceeds the cost at which providers are willing

J. M. Lacker and J. A. Weinberg: Payment System Innovator

19

to supply it.25 The usual presumption is that innovation in competitive settings
yields outcomes that are beneficial to society as a whole. A necessary condition
is that prices are not inefficient, that is, they do not embody cross-subsidies.
Barriers to competition allow inefficient pricing. One way to ensure that the
Fed’s implementation of payment system innovations contributes to payment
system efficiency, therefore, is to remove artificial barriers to competition like
the six-hour monopoly.
Removing barriers to competition would help avoid some of the potential pitfalls that face a public entity participating in a commercial enterprise.
The Reserve Banks’ special legal status as public institutions, as opposed to
private, profit-seeking businesses, could inhibit their pursuit of improvements
in products and processes. The structure of Federal Reserve decisionmaking
could result in unnecessarily high costs of research and development. It is
often difficult for large organizations, particularly public institutions, to respond nimbly to new technological opportunities. The difficulties experienced
by the U.S. Postal Service in implementing automation illustrate the challenge
of innovating at large, public-sector institutions.
An even more worrisome possibility is that an organization that is not
fully subject to market discipline could make wasteful investments designed
to hold on to market share. Many observers expect electronic payment instruments, such as debit cards, credit cards, or smart cards, increasingly to
displace checks. In this context, ECP could be viewed as an attempt to stem
the expected decline in check use. By reducing the cost of paper checks, ECP
could slow the transition to fully electronic payment instruments that are even
more beneficial. As long as barriers shield the Fed from competitive pressures,
there is the potential for the Fed’s pursuit of payment system innovations to
conflict with payment system efficiency.
Yet there are good reasons for the Fed to pursue ECP research and development. The Fed, the largest processor of paper checks in the economy, maintains
a substantial capital stock dedicated to that activity. The Fed would need to
integrate ECP investments into its current check collection infrastructure. As
a result, the Fed is likely to have a comparative advantage in evaluating the
technical characteristics of ECP investments. In addition, the Reserve Banks
have strong incentives to pursue innovations that, if successful, would enhance
the value of their existing check infrastructure. To the extent that the Fed’s decisionmaking mimics that of a private business, the interdependence of paper
and electronic check collection gives the Fed appropriate incentives regarding
ECP research and development.
25 We

mean profitability in the sense that the expected present discounted value of net cash
flows from the introduction of an innovation are positive. The Board of Governors imposes a
tighter constraint on Reserve Banks; net cash flows must be positive each year in each priced
service line (check collection, automated clearing house, and so on).

20

Federal Reserve Bank of Richmond Economic Quarterly

Implementing ECP
What does all this mean for the implementation of ECP? Because it is uncertain
whether ECP will actually contribute to economic efficiency, the Fed should do
everything possible to ensure that ECP flourishes only if genuinely warranted.
If ECP truly is to enhance economic efficiency, it ought to be possible to offer
it in a competitive market at prices that cover costs and attract users voluntarily. Any implicit cross-subsidy could distort outcomes by driving some prices
below costs, so that users find ECP attractive even if social costs exceeded
benefits. Similarly, a legal privilege that dampens competitive pressures could
artificially tilt users through nonprice incentives toward an ECP service offered
by the Fed.
Because the paying bank has the right to insist on presentment of the paper
check, a key issue for ECP is inducing the paying bank to accept electronic
presentment. Stavins’ (1997) estimates indicate that while paying banks realize
significant cost savings from ECP, check writers incur increased costs and lose
the benefits of receiving canceled checks. Although her estimates suggest a
small net gain to paying banks and their customers, there will undoubtedly
be some instances in which ECP would raise the net cost to paying banks and
their customers. If the total benefits of ECP exceed the total cost for payors and
payees combined, then it ought to be possible for paying banks and their customers to be compensated by other participants. Such compensation could take
the form of fees for checks presented electronically, or alternatively, charges to
paying banks that wish to receive paper checks.
Net revenues from ECP services should cover the full incremental cost
of ECP if it is to be implemented without subsidization. In the absence of
barriers to competition, the Fed could not systematically violate this bound.
Theoretically, the six-hour monopoly gives the Fed the capability to subsidize
ECP; paying banks could be induced to adopt ECP before it is efficient to do
so. Eliminating barriers to competition like the six-hour monopoly would help
ensure that ECP will succeed if and only if it is truly beneficial to society.
One frequent suggestion by ECP advocates is that the Federal Reserve
alter its check presentment regulations so that paying banks are required to
accept presentment in electronic form as well as paper. Paying banks could
no longer insist on presentment of the paper check. This change is consistent
with a competitive market approach as long as paying banks who prefer to receive paper presentment are able to compensate collecting banks. If the paying
bank’s willingness to pay to receive paper exceeds the cost to collecting banks
of presenting paper, then the paying bank ought to be able to stay with paper.
Otherwise, the paying bank will receive presentment electronically.26
26 ECP

was implemented quite rapidly in Switzerland under just such a scheme. Paying
banks must pay a substantially higher fee to receive paper checks.

J. M. Lacker and J. A. Weinberg: Payment System Innovator

21

Simply mandating participation by paying banks would short-circuit the
competitive discipline imposed by the need to enlist voluntary cooperation.
Then an ECP plan that marginally lowers the costs of collecting banks as a
whole might succeed, even though it imposes greater additional costs on paying
banks and their customers. Such a scheme would not be in society’s interests,
and yet it might be adopted if acceptance by paying banks of electronic presentment were mandated with no opt-out provision.
What about Access?
We have interpreted access in terms of the costs of check collection to small
and remote banks. Fed participation in the check collection system is intended,
in part, to make the cost to these banks lower than it otherwise would be. This
interpretation is consistent with two alternative hypotheses. First, the Fed’s
priced services could be free of cross-subsidies, and therefore efficient, even
though its allocation of common costs might favor small and remote banks.
Second, the Fed’s pricing could involve cross-subsidies. In order to maintain
prices below incremental costs, the Fed would need to rely on market privileges
such as the six-hour monopoly.
If the six-hour monopoly is essential to achieving the Fed’s access goals,
then its continued presence could distort the implementation of ECP or other
innovations in check clearing. If current pricing involves cross-subsidies, then
the revenue from customers paying more than their stand-alone costs could be
used to push ECP prices below incremental cost. If the Fed’s current pricing
does not involve cross-subsidization, then the six-hour monopoly is not essential to the status quo price structure. In this last case it should be possible for
the Fed to implement ECP efficiently without sacrificing universal access.
Which of these two hypotheses is correct? As we noted above, available
data cannot discriminate between the two, and the Fed’s floor-cost methodology
may not guarantee the absence of subsidies. Moreover, it will always be difficult
to objectively verify the absence of cross-subsidies. As long as cross-subsidies
are possible, there will be those who question the Fed’s actions, particularly
with regard to new product offerings. How can the public be confident that
the Fed’s innovative efforts in the payment system enhance efficiency? The
simplest and most transparent measure would be to eliminate artificial barriers
to competition like the six-hour monopoly.

6.

CONCLUSION

We have drawn lessons for Federal Reserve payment system policy from the
history of other communications industries. Government intervention in these
industries has been driven largely by the desire to allocate common costs in
order to enhance access for some users. We have argued that Federal Reserve
Banks’ provision of check collection services fits the same pattern.

22

Federal Reserve Bank of Richmond Economic Quarterly

Providing access conflicts with technological progress when access is supported by subsidized prices and barriers to competition. In the telecommunications industry rapid innovation was stimulated by deregulation that required
a retreat from universal access. The U.S. Postal Service provides a contrasting
example in which protected markets were maintained but at an apparent cost in
foregone efficiency-enhancing innovation. The lesson for the Federal Reserve
seems clear: a pursuit of access that makes use of cross-subsidization interferes
with the efficient implementation of payment system innovations. Subsidies
erode market discipline and distort choices among competing technologies.
Let us emphasize that it is not at all clear that the Fed currently subsidizes
any segment of the check collection market. Federal Reserve policy explicitly
seeks to prevent subsidization and promote payment system efficiency. With its
efforts to promote ECP, the Fed seeks to establish itself as a leader in payment
system innovation. The Fed is well suited to understand, evaluate, and help
implement new technologies in this area. For the Fed to be an effective leader,
however, the public must be confident that its choices are in the public interest.
Eliminating any remaining competitive advantages would deny the Fed the
capacity to subsidize and thus would enhance the credibility of the Federal
Reserve’s commitment to payment system efficiency.

GLOSSARY OF COST-RELATED TERMS
Common costs: Costs that cannot be attributed to a particular individual
or group. Note that there can be costs that are attributable to a group
but common among the members of the group.
Attributable costs: Costs that arise directly from the provision of services
to a particular individual, group, or market segment.
Fixed costs: Costs that do not vary with the quantity of a service produced.
Fixed costs can be common among all users or attributable to a subset
of users.
Network effects: The benefits that one group’s participation creates for other
users of a communication service.
Incremental costs: The additional cost of extending a given amount of a
service to a particular individual, group, or market segment, given that
others are already being served. Incremental costs are attributable costs
(fixed and variable) less any network benefits created for others by
extending service to the particular individual or group.
Stand-alone costs: The cost of providing a free-standing service to an individual or group, in isolation from other users. Stand-alone costs include
the value of the network benefits that the group loses by not sharing joint
services with other users.

J. M. Lacker and J. A. Weinberg: Payment System Innovator

23

Subsidization: When the payments received from a group are less than the
incremental cost of providing service to that group.
Cross-subsidization: When the deficit created by subsidizing one group is
made up for by charging another group more than its stand-alone cost.

APPENDIX
Electronic Check Presentment
While many payment system innovations take the form of new payment
instruments, electronic check presentment (ECP) is simply a means of bringing
modern information technology to bear on the clearing and settlement of a
very old payment instrument. The standard method of clearing and settlement
begins when the person or firm receiving a check deposits the check in his
or her bank. If the check is drawn on a different account at the same bank,
the check stays there and is paid with a bookkeeping transfer. Otherwise, the
check is physically transported to the bank on which it is drawn (the paying
bank). After physical presentment of the check takes place, funds are sent from
the paying bank to the collecting bank. Often this process is intermediated by
other banks (correspondents), Federal Reserve Banks, or by private contractors
(courier services, for example). A check that is not honored for some reason—
because of insufficient funds in the check writers’ account, for example—is
returned to the bank at which it was initially deposited.
With electronic check presentment, consumers and businesses still conduct
transactions using paper checks. At some point in the process of clearing the
check, the relevant payment information is transferred into electronic form and
then sent on to the paying bank. The check itself may or may not continue
on its path to the paying bank. If the check is not sent to the paying bank,
it is called check truncation. Although truncation is not a necessary part of
ECP, many proponents believe that ECP can make its greatest contribution
to payment system efficiency in combination with truncation. Indeed, to the
extent that there are savings associated with substituting the flow of electronic
information for a paper flow, it would seem to make sense to have paper items
truncated as early as possible in the clearing process. On the other hand, the
occasional need to inspect the physical check suggests that it might be economical for truncation to occur at a more central point in the process in order
to concentrate the storage of paper items.
All Reserve Bank offices currently offer paying banks the option of receiving electronic check presentment. Slightly less than 14 percent of the checks
processed by the Fed in 1997 were presented electronically. For about another 9
percent, information was sent electronically to the paying bank, although actual

24

Federal Reserve Bank of Richmond Economic Quarterly

presentment was made with paper checks. Reserve Bank representatives are
actively involved in several collaborative efforts with industry representatives
aimed at finding ways of increasing the use of ECP.

REFERENCES
Bank for International Settlements. Statistics on Payment Systems in the Group
of Ten Countries. Basle, Switzerland: Bank for International Settlements,
1996.
Board of Governors of the Federal Reserve System. “Collection of Checks
and Other Items by Federal Reserve Banks and Availability of Funds and
Collection of Checks” (Docket No. R–1009), Federal Register, vol. 63
(March 16, 1998), pp. 12700–06.
. “Proposed Rule” (Docket No. R–0723), Federal Register, vol. 56
(February 6, 1991), pp. 4743–57.
. “The Federal Reserve in the Payments System,” Federal Reserve
Bulletin, vol. 76 (May 1990), pp. 293–98.
Bornholz, Robert, and David S. Evans. “The Early History of Competition in
the Telephone Industry,” in David S. Evans, ed., Breaking Up Bell. New
York: North-Holland, 1983.
Brock, Gerald W. “The Regulatory Change in Telecommunications: The
Dissolution of AT&T,” in Leonard W. Weiss and Michael W. Klass, eds.,
Regulatory Reform: What Actually Happened. Boston: Little, Brown and
Company, 1986.
Committee on the Federal Reserve in the Payments Mechanism. The Federal
Reserve in the Payments Mechanism. Washington: Board of Governors of
the Federal Reserve System, January 1998.
Economides, Nicholas. “The Economics of Networks,” International Journal
of Industrial Organization, vol. 14 (October 1996), pp. 673–99.
Gilbert, R. Alton. “Did the Fed’s Founding Improve the Efficiency of the
United States Payments System?” Manuscript. Federal Reserve Bank of
St. Louis, January 1998.
Jessup, Paul F. The Theory and Practice of Nonpar Banking. Evanston, Ill.:
Northwestern University Press, 1967.
Sidak, Gregory J., and Daniel F. Spulber. Protecting Competition from the
Postal Monopoly. Washington: AEI Press, 1996.

J. M. Lacker and J. A. Weinberg: Payment System Innovator

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Spahr, Walter Earl. The Clearing and Collection of Checks. New York: Bankers
Publishing Company, 1926.
Stavins, Joanna. “A Comparison of Social Costs and Benefits of Paper Check
Presentment and ECP with Truncation,” Federal Reserve Bank of Boston
New England Economic Review (July/August 1997), pp. 27– 44.
Stevens, Ed. “Non Par Banking: Competition and Monopoly in Markets for
Payments Services.” Manuscript. Federal Reserve Bank of Cleveland,
Financial Services Research Group, January 14, 1998.
. “The Founders’ Intentions: Sources of the Payments Services
Franchise of the Federal Reserve Banks,” Working Paper No. 03–
96. Cleveland: Federal Reserve Bank of Cleveland, Financial Services
Research Group, December 1996.
U.S. General Accounting Office. Check Collection: Competitive Fairness is
an Elusive Goal. Washington: U.S. General Accounting Office, 1989.
Weinberg, John A. “The Organization of Private Payment Networks,” Federal
Reserve Bank of Richmond Economic Quarterly, vol. 83 (Spring 1997),
pp. 25–43.

The Bond Rate and
Actual Future Inflation
Yash P. Mehra

I

t is widely believed that bond yields contain useful information about
expected inflation. Many have empirically investigated this issue by examining whether the slope of the term structure has any predictive content
in forecasting future inflation. That research, however, has produced disparate
results. In a series of papers, Mishkin (1990a, 1990b, 1991) and Jorian and
Mishkin (1991) report evidence that indicates the slope has predictive content
at long horizons but not at short horizons.1 In contrast, Engsted (1995) investigates whether the spread between the long-term interest rate and the one-period
inflation rate predicts future one-period inflation. While this spread does help
predict future inflation for a number of countries, it does not for the United
States.2
In this article, I provide new evidence on the predictive content of the bond
rate for future inflation using cointegration and error-correction modeling. The
empirical work here corrects for two possible shortcomings of the previous
research that may account for the disparate results described above. First, I
relax the assumption made in previous studies that the ex ante real interest
rate is constant. If the ex ante real rate is variable, then short-run movements

The views expressed are those of the author and not necessarily those of the Federal Reserve
Bank of Richmond or the Federal Reserve System. The author thanks Alex Wolman, PierreDaniel Sarte, and Wenli Li for many helpful comments.
1 In this research the horizon forecasts of inflation match that of the slope of the term
structure. Hence, the result that the slope has predictive content at long horizons but not at short
horizons should be interpreted to mean long-term bonds help predict inflation at long horizons,
but short-term bonds do not help predict inflation at short horizons. In this article, by contrast,
there is no such matching. In fact, I explore the predictive content of the long bond rate at short
and long inflation horizons.
2 Though this spread does Granger-cause the U.S. inflation rate, the sum of coefficients that
appear on lagged values of the spread in the inflation equation is small in magnitude. Engsted,
however, does not test whether the sum of these coefficients is different from zero.

Federal Reserve Bank of Richmond Economic Quarterly Volume 84/2 Spring 1998

27

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Federal Reserve Bank of Richmond Economic Quarterly

in the bond rate do not necessarily reflect movements in its expected inflation
component. In that environment the predictive content of the bond rate for
future inflation should be investigated controlling for the influences of variables that capture movements in the real rate of interest. The empirical results
indicate that inferences regarding the predictive content of the bond rate for
future inflation are sensitive to such conditioning. Second, the empirical work
in this article examines whether the predictive content has changed over time,
in particular between pre- and post-1979 periods. Recent research reported in
McCallum (1994) and Rudebusch (1995) indicates that the term structure’s ability to predict future economic variables may be influenced by the way the Fed
conducts its monetary policy.3 Most economists would agree that since 1979,
the Fed has made repeated attempts to bring down the trend rate of inflation
and contain inflationary expectations. In that environment an increase in the
current bond rate, even if it correctly signals an increase in long-term expected
inflation, may not necessarily translate into higher actual future inflation.
The results here focus on the behavior of the nominal yield on ten-year U.S.
Treasury bonds over the period 1959Q1 to 1996Q4. The economic variables
that appear in the cointegration and error-correction modeling are the bond
rate, the actual inflation rate, the nominal federal funds rate, and the output
gap. The last two variables control for variations in the real component of
the bond rate that are due to funds rate policy actions and the state of the
economy. The test results indicate that the bond rate is cointegrated with the
actual inflation rate during the full sample period, implying that the bond rate
and the inflation rate move together in the long run. Permanent movements in
the inflation rate are associated with permanent movements in the bond rate.
The estimated error-correction model, however, indicates that a change has
occurred in the way these two variables have adjusted in the short run. In the
pre-1979 period, when the bond rate rose above the current inflation rate, actual
future inflation accelerated. In the post-1979 period, however, the rise in the
bond rate was reversed, and actual future inflation did not accelerate. Thus the
bond rate signaled an acceleration in future inflation in the period before 1979
but not thereafter.
The results indicate that the above-noted change in the predictive content of the spread for future inflation may be due to change in Fed policy
since 1979. In the post-1979 period, future inflation is inversely related to the
current stance of Fed policy measured by the real funds rate, indicating Fed
policy was geared towards reducing inflation. No such effect is found prior to
1979. Together these results are consistent with the hypothesis that after 1979,
Fed policy prevented any increase in inflationary expectations (evidenced by
3 In the context of rational expectations hypothesis tests, McCallum (1994) shows how the
reduced-form regression coefficients depend upon the Fed’s policy rule when the Fed smooths
interest rates and responds to movements in the long-short spread.

Y. P. Mehra: Bond Rate and Future Inflation

29

the rise in the bond rate spread) that would have become embodied in higher
actual future rates of inflation. As markets understand and believe in such Fed
behavior, increases in inflationary expectations will be less common. The bond
rate will then increasingly reflect phenomena other than expected inflation,
thereby undermining its usefulness as a precursor of actual future inflation.

1.

THE MODEL AND THE METHOD

The Fisher Relation, the Bond Rate, and Future Inflation
In order to motivate the empirical work, I discuss what the Fisher relation
implies about the predictive content of the bond rate for future inflation. The
Fisher relation for the m-period bond rate is
˙t
BR(m) = rrt(m) + pe(m) ,
t

(1)

˙
where BR(m) is the m-period bond rate, pe(m) is the m-period expected inflation
rate, and rr(m) is the m-period expected real rate of interest. The Fisher relation
(1) relates the bond rate to expectations of inflation and the real rate over the
maturity (m) of the bond.
If the expected real interest rate is constant and if expectations of inflation
are rational, then the Fisher relation above can be expressed as in (2) or (3):
˙
BR(m) = rr + pt+m −
t

(2)

t+m

or
˙
p
˙
BR(m) − pt = rr + (˙ t+m − pt ) −
t

t+m ,

(3)

˙
where rr is the constant real rate, pt+m is the m-period future inflation rate, pt
˙
is the one-period current inflation rate, and t+m is the m-period future forecast
error that is uncorrelated with past information. Equation (2) indicates that the
bond rate contains information about the (m-period) future inflation rate, and
equation (3) similarly shows that the spread between the bond rate and the
current inflation rate has information about a change in the future inflation rate.
Testing the Predictive Content of the Bond Rate for Future Inflation
Previous Studies
Equations (2) and (3) above form the basis of empirical work in most previous
studies of the predictive content of the bond rate for future inflation. Previous researchers have investigated the term structure’s ability to predict future
inflation by running regressions that are of the form
˙
(˙ t+m − pt+n ) = a + b (BR(m) − BR(n) ) +
p
t
t

1t

(4)

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Federal Reserve Bank of Richmond Economic Quarterly

and
˙
˙
(˙ t+m − pt ) = c + d (BR(m) − pt ) +
p
t

2t ,

(5)

˙
where BR(n) is the n-period bond rate, pt+n is the n-period future inflation rate,
and other variables are as defined before. As can be seen, these regressions are
merely rearranged versions of Fisher relations (2) and (3).4 In (4) the spread
between the m-period and n-period nominal interest rates is used to predict
the difference between the m-period and n-period inflation rates, and in (5)
the spread between the m-period bond rate and the (one-period) inflation rate
is used to predict change in future inflation. Regressions like (4) appear in
Mishkin (1990a, 1990b, 1991) and those like (5) appear in Engsted (1995). If
b = 0 in (4) or d = 0 in (5), then that result indicates that the slope of the term
structure does help predict future inflation.
But, as noted before, equations (2) and (3) (or regressions [4] and [5])
embody the assumption that the expected real interest rate is constant. This is a
questionable assumption. Plosser and Rouwenhorst (1994) in fact present evidence that indicates that the long end of the term structure does seem to contain
information about the real economic activity and therefore about the real rate
of interest. If the expected real rate is not constant, then the disturbance term
in these regressions ([4] or [5]) may be correlated with the spread.5 In that case
ordinary least squares may provide inconsistent estimates of parameters b and
d, biasing inferences concerning the predictive content of the term structure
for future inflation. Hence, in order to examine robustness to change in the
assumption about the real rate, the predictive content should be investigated
conditioning on variables that may control for potential short-term movements
in the real rate.
Another issue not investigated fully in previous research is that slope parameters in (4) and (5) are likely to be influenced by the way the Fed conducts
its monetary policy (McCallum 1994). For example, if the Fed has in place
a disinflationary policy, then higher actual inflation may not follow a current
increase in the bond rate spread (as in [5]). This could happen if current widening in the bond rate spread causes the Fed to raise the funds rate, leading to
slower real growth and lower actual inflation in the future. In this scenario a
current increase in the bond rate spread still reflects expectations of rising future
4 That

is, we get (2) and (3) if we impose the restrictions a = 0, b = 1, c = −rr, and

d = 1.
5 To explain it further, assume the real rate c in (5) is not constant but in fact moves
systematically with certain economic factors as follows:

ct = c0 + c1 Zt + ut ,
where Z is a set containing determinants of the real rate. If we replace c in (5) by ct as above,
then the disturbance term in (5) contains terms like c1 Zt + ut . If the spread variable in (5) is
correlated with the determinants Zt , then the spread will be correlated with the disturbance term.

Y. P. Mehra: Bond Rate and Future Inflation

31

inflation. However, the ensuing Fed behavior prevents those expectations that
would have been embodied in higher actual inflation. Therefore, in regressions
like (5), the estimate of the slope parameter (d) may be small in periods during
which the Fed has been vigilant. Those considerations suggest that parameters
that measure the predictive content of the term structure for future inflation
may not be stable during the sample period.
Cointegration and Error-Correction Modeling
The empirical work here examines the predictive content of the bond rate using cointegration and error-correction modeling. This empirical procedure, as I
illustrate below, yields regressions that are similar in spirit to those employed
in some previous research but differ in that it includes additional economic
variables that control for potential movements in the real rate of interest.
As indicated before, the Fisher relation (1) for interest rates relates the bond
rate to expectations of future inflation and the real interest rate. If one assumes
that those expectations can be proxied by distributed lags on current and past
values of actual inflation and other fundamental economic determinants, then
the Fisher relation implies the following regression (6):
k

BRt = a +

k

bs pt−s +
˙
s=0

cs Xt−s + Ut ,

(6)

s=0

where pt is the actual inflation rate, Xt is the vector containing other economic
˙
determinants of the real rate, and Ut is the disturbance term. The presence of the
disturbance term in (6) reflects the assumption that distributed lags on actual
values of economic determinants may be good proxies for their anticipated
values in the long run but not necessarily in the short run.6
If levels of the empirical measures of these economic determinants, including the bond rate, are unit root nonstationary, then the bond rate may be
cointegrated with these variables as in Engle and Granger (1987). Under those
assumptions, regression (6) can be reformulated as in (7):
˙
BRt = d0 + d1 pt + d2 Xt + et .

(7)

Equation (7) is the cointegrating regression. The coefficients that appear on pt
˙
and Xt in (7) then measure the long-run responses of the bond rate to inflation
and its other real rate determinants. I investigate the question whether the bond
rate incorporates expectations of future inflation by testing whether the bond
rate is cointegrated with the actual inflation rate. My analysis thus views the
positive relationship between the bond rate and actual inflation as a long-run
phenomenon.
6 The

mean.

only assumption I make about the random disturbance term in (2) is that it has a zero

32

Federal Reserve Bank of Richmond Economic Quarterly

The cointegrating bond rate regression defines the long-run equilibrium
value of the bond rate. Should the bond rate rise above its long-run equilibrium
value, then either the bond rate should fall, the economic determinants including
inflation should adjust in the direction needed to correct the disequilibrium, or
both. I examine such short-run dynamic adjustments by building a vector errorcorrection model that consists of short-run inflation and bond rate equations.
The behavior of the error-correction variable, defined below, then provides
information about ways the bond rate and inflation adjust in the short run.
Therefore, if the error-correction term is positive and statistically significant in
the short-run inflation equation, then that evidence can be interpreted to mean
that the bond rate signals future inflation.7
To illustrate, assume that the bond rate depends only on the inflation rate in
the long run and that the expected real rate is mean stationary. The cointegrating
regression is then defined by the relation
˙
BRt = a + b pt + Ut ,

(8)

where Ut is the short-term error. This variable, defined as the error-correction
variable, measures the extent to which the bond rate differs from its long-run
equilibrium value in the short run. The presence of cointegration implies the
following error-correction model in ∆BR and ∆˙ :
p
k

∆BRt = c0 +

k

c2s ∆˙ t−s + λ1 Ut−1 +
p

c1s ∆BRt−s +
s=1

1t

(9a)

2t ,

(9b)

s=1

and
k

∆˙ t = d0 +
p

k

d2s ∆˙ t−s + λ2 Ut−1 +
p

d1s ∆BRt−s +
s=1

s=1

where Ut−1 is the lagged value of the error-correction variable from (8) and
where all other variables are as defined above. The presence of cointegration
˙
between BRt and pt implies that in (9) either λ1 = 0, λ2 = 0, or both. Thus,
if λ2 is positive and statistically significant, then a rise in the spread (Ut =
BRt − a − b pt ) signals higher actual future inflation. Since the real interest rate
˙
is assumed to be mean stationary, not constant, the error-correction equations
should be estimated including other (stationary) short-run determinants of the
real interest rate.8
7 Miller

(1991) has used this methodology to investigate short-run monetary dynamics.
is worth pointing out that Engsted (1995) uses an equation like (9b) to investigate
whether the spread between the bond rate and the actual inflation rate (Ut−1 in [8] here) helps
predict future inflation. He, however, derives this implication of the Fisher hypothesis under the
assumptions that expectations of inflation are rational and forward-looking and that the expected
real interest rate is constant. To explain it further, consider the following version of the Fisher
8 It

Y. P. Mehra: Bond Rate and Future Inflation

33

Data and Definition of Economic Determinants in the
Multivariable Analysis
The empirical work here examines the dynamic interactions between the bond
rate and the inflation rate within a framework that allows for movements in the
real component of the bond rate. The descriptive analysis of monetary policy in
Goodfriend (1993) and the error-correction model of the bond rate estimated in
Mehra (1994) indicate that the real component of the bond rate is significantly
influenced by monetary policy actions and the state of the economy. Therefore,
the economic variables that enter the analysis here are the bond rate, the actual
inflation rate, the nominal federal funds rate, and the output gap that measures
the state of the economy.
The empirical work uses quarterly data that spans the period 1959Q1 to
1996Q4. The estimation period, however, begins in 1961Q2, the earlier observations being used for lags. In addition, the sample is broken in 1979Q3, and
results are provided for subperiods 1961Q2 to 1979Q3 and 1979Q4 to 1996Q4.
The bond rate is the nominal yield on ten-year U.S. Treasury bonds (BR). Inflation as measured by the behavior of the consumer price index (excluding food
and energy) is the actual, annualized quarterly inflation rate (˙ ). The measure
p
of monetary policy used is the nominal federal funds rate (NFR), and the output
gap (gap) is the natural lag of real GDP minus the natural log of potential GDP;
the latter is generated using the Hodrick-Prescott filter (Hodrick and Prescott
1997).9 The interest rate data are for the last month of the quarter.
Tests for Unit Roots and Cointegration
Cointegration and error-correction modeling involves four steps. First, determine the stationarity properties of the empirical measures of economic
hypothesis (1) for the long-term bond rate:
∞

BR(t) = rr + (1 − b)

b j Et pt+j ,
˙

(a)

j=1

where rr is the constant real rate and b = e i ≈ (1 + rr) is the discount factor (Engsted 1995).
¯
That is, the long bond rate is given as the constant real rate plus a weighted average of expected
˙
˙
future one-period inflation rates (Et pt+j , j ≥ 1). If BRt and pt are nonstationary and expectations
are rational, then the above equation can be reformulated as
∞

BRt − b pt ≡ St = rr +
˙

bj Et ∆˙ t+j .
p

(b)

j=1

˙
˙
Equation (b) implies that BRt and b pt are cointegrated and that the spread St = BRt − b pt is an
optimal predictor of future changes in inflation. Engsted (1995) examines the second implication
by estimating a VAR in S and ∆˙ and then testing whether S Granger-causes ∆˙ .
p
p
9 I have examined the sensitivity of results to some changes in specification. For example,
alternatively defining output gap relative to a linear trend produces qualitatively similar results.

34

Federal Reserve Bank of Richmond Economic Quarterly

determinants suggested above. Second, test for the presence of cointegrating
relationships in the system. Third, estimate the cointegrating regression and
calculate the residuals. Fourth, construct the short-run error-correction equations.
In order to determine whether the variables have unit roots or are mean
stationary, I perform both unit root and mean stationarity tests. The unit root
test used is the augmented Dickey-Fuller test, and the test for mean stationarity
is the one advocated by Kwiatkowski, Phillips, Schmidt, and Shin (1992). Thus
a variable Xt is considered unit root nonstationary if the hypothesis that Xt has a
unit root is not rejected by the augmented Dickey-Fuller test and the hypothesis
that it is mean stationary is rejected by the mean stationarity test.
The test used for cointegration is the one proposed in Johansen and Juselius
(1990), and the cointegrating relations are identified by imposing restrictions
as in Johansen and Juselius (1994). Also, the cointegrating relations are estimated using an alternative estimation methodology, Stock and Watson’s (1993)
dynamic OLS procedure.

2.

EMPIRICAL RESULTS

Unit Root and Mean Stationarity Test Results
As indicated before, the economic variables that enter the analysis are the bond
rate (BR), the inflation rate (˙ ), the nominal funds rate (NFR), and the output
p
gap (gap). The output gap variable by construction is stationary. Table 1 reports
test results for determining whether other variables have a unit root or are mean
stationary. As can be seen, the t-statistic (tρ ) that tests the null hypothesis that
ˆ
a particular variable has a unit root is small for BR, p, and NFR. On the other
˙
hand, the test statistic (ˆ u ) that tests the null hypothesis that a particular variable
n
is mean stationary is large for all these variables. These results indicate that
BR, p, and NFR have a unit root and are therefore nonstationary in levels.
˙
Cointegration Test Results
Table 2 presents test statistics for determining the number of cointegrating relations in the system (BR, p, NFR, gap). Trace and maximum eigenvalue statistics
˙
presented in the table indicate that there are three cointegrating relations in the
system.10 This result holds in both the sample periods 1961Q2 to 1996Q4 and
1961Q2 to 1979Q3.
10 The

lag length parameter (k) for the VAR model was chosen using the likelihood ratio
test described in Sims (1980). In particular, the VAR model initially was estimated with k set
equal to a maximum number of eight quarters. This unrestricted model was then tested against a
restricted model, where k is reduced by one, using the likelihood ratio test. The lag length finally
selected in performing the Johansen-Juselius procedure is the one that results in the rejection of
the restricted model.

Y. P. Mehra: Bond Rate and Future Inflation

35

Table 1 Tests for Unit Roots and Mean Stationarity
Panel A
Series
X
BR
p
˙
NFR

Panel B
Test for Mean
Stationarity

Test for Unit Roots
ρ
0.96
0.89
0.89

tρ
ˆ
−1.7
−2.4
−2.8

k
5
2
5

x2 (2)
1.6
2.1
1.1

x2 (4)
1.3
1.8
0.40

nu
ˆ
0.80∗
0.39∗∗
0.46∗

∗ Significant

at the 5 percent level.
at the 10 percent level.
Notes: BR is the bond rate; p is the annualized quarterly inflation rate measured by the behavior
˙
of the consumer price index excluding food and energy; and NFR is the nominal federal funds
rate. The sample period studied is 1961Q2 to 1996Q4. ρ and t-statistics (tρ ) for ρ = 1 in panel
ˆ
A above are from the augmented Dickey-Fuller regressions of the form

∗∗ Significant

k

Xt = a0 + ρ Xt−1 +

as ∆Xt−s ,
s−1

where X is the pertinent series. The series has a unit root if ρ = 1. The 5 percent critical value is
2.9. The lag length k is chosen using the procedure given in Hall (1990), with maximum lag set at
eight quarters. x2 (2) and x2 (4) are Chi-squared statistics that test for the presence of second-order
and fourth-order serial correlation in the residual of the augmented Dickey-Fuller regression,
respectively. The test statistics nu in panel B is the statistic that tests the null hypothesis that the
ˆ
pertinent series is mean stationary. The 5 percent critical value for nu given in Kwiatkowski et
ˆ
al. (1992) is 0.463 (10 percent critical value is 0.347).

Table 3 presents estimates of the cointegrating relations found in the system. I first test the hypothesis that the three-dimensional cointegration space
contains cointegrating relations that are of the form (10) through (12):
˙
BRt = a0 + a1 pt + u1t ; a1 = 1,

(10)

˙
NFRt = b0 + b1 pt + u2t ; b1 = 1,

(11)

gapt = c0 + u3t .

(12)

and

Equation (10) can be interpreted as the Fisher relation for the bond rate and
equation (11) as the Fed reaction function. Equation (12) simply states that the
output gap variable is stationary. As shown in Johansen and Juselius (1994),
these cointegrating relations can be identified imposing restrictions on long-run
parameters in the cointegrating space.
In the full sample period, the hypotheses that cointegrating relations are of
the form (10) through (12) and that a1 = b1 = 1 are consistent with data (the
2
x1 statistic that tests those restrictions is small; see Table 3, panel A). However,
in the subsample 1961Q2 to 1979Q3, the restrictions that a1 = b1 = 1 are

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Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Cointegration Test Results

System
(BR, p, NFR, gap)
˙

System
(BR, p, NFR, gap)
˙

Panel A: 1961Q2 to 1996Q4
Trace
Maximum Eigenvalue
H0
H0 vs H1
r = 0 8.9∗
r ≤ 1 40.3∗
r ≤ 2 16.3∗
r ≤ 3 4.6

r=0
r=1
r=2
r=3

vs
vs
vs
vs

r ≤ 1 : 28.6∗
r ≤ 2 : 23.9∗
r ≤ 3 : 11.7∗
r ≤ 4 : 4.6

Panel B: 1961Q2 to 1979Q3
Trace
Maximum Eigenvalue
H0
H0 vs H1
r = 0 66.2∗
r ≤ 1 32.8∗
r ≤ 2 13.0∗
r ≤ 3 2.5

r=0
r=1
r=2
r=3

vs
vs
vs
vs

r ≤ 1 : 33.4∗
r ≤ 2 : 19.8∗
r ≤ 3 : 10.6∗
r ≤ 4 : 2.5

k
8

k
5

∗ Significant

at the 10 percent level.
Notes: Trace tests the null hypothesis that the number of cointegrating vectors (r) is less than
or equal to a chosen value, and maximum eigenvalue tests the null hypothesis that the number
of cointegrating vectors is r, given the alternative of r + 1 vectors. The VAR lag length (k) was
chosen using the likelihood ratio test in Sims (1980).

rejected by data, and the cointegrating relations are thus estimated without
such restrictions.11 As can be seen, estimates indicate that the bond rate is
cointegrated with the inflation rate, but the bond rate does not adjust one-forone with inflation. Therefore, inflation is the main source of the stochastic trend
in the bond rate.
The estimation procedure in Johansen and Juselius (1990, 1994) is a system
estimation method. In order to check the robustness of estimates, I also present
estimates of the cointegrating relations (10) and (11) using a single equation
estimation method. Panel B in Table 3 presents results using the dynamic
OLS procedure given in Stock and Watson (1993). As shown in the table, this
procedure yields estimates that are remarkably close to those reported above.
Results on the Error-Correction Coefficient in the Error-Correction Model
The cointegration test results described in the previous section are consistent
with the presence of cointegrating relations that are of the form
11 In

estimating error-correction equations for the pre-1979 period, I consider cointegrating
regressions with a = b = 1. This restriction implies that the bond rate does adjust one-for-one
with inflation. The basic results do not change if instead this restriction is not imposed (see
footnote 15).

Y. P. Mehra: Bond Rate and Future Inflation

37

Table 3 Estimates of Restricted Cointegrating Vectors
Panel A: Johansen-Juselius Procedure
Sample Period
Sample Period
1961Q2 to 1996Q4
1961Q2 to 1979Q3
A1
A2

BRt = 3.1 + pt + U1t
˙
NFRt = 2.3 + pt + U2t
˙
2
x1 (3) = 0.92 (0.82)

BRt = 3.2 + 0.67 pt + U1t
˙
NFRt = 2.7 + 0.66 pt + U2t
˙
2
x2 (1) = 0.01 (0.91)

Panel B: Dynamic OLS
1961Q2 to 1996Q4
A1
A2

BRt = 2.9 + 1.0 pt + U1t
˙
NFRt = 2.2 + 1.0 pt + U2t
˙

1961Q2 to 1979Q3
BRt = 3.2 + 0.66 pt + U1t
˙
NFRt = 2.5 + 0.67 pt + U2t
˙

Notes: Panel A above reports two of the three cointegrating vectors that lie in the cointegration
space spanned by the four-variable VAR (BR, p, NFR, gap). The cointegrating vectors A1 and
˙
2
2
A2 are the Fisher relation for the bond rate and the funds rate. x1 (3) and x2 (1) are Chi-squared
statistics (degrees of freedom in parentheses) that test the null hypothesis that the identifying
restrictions imposed are consistent with data (Johansen and Juselius 1994).
Panel B above reports the same cointegrating vectors estimated using the dynamic OLS procedure
(eight leads and lags are used).

BRt = a0 + a1 pt + U1t
˙

(13)

˙
NFRt = b0 + b1 pt + U2t ,

(14)

and

where U1 and U2 are stationary disturbance terms. I now examine the behavior
˙
of the error-correction term U1t = BRt − a0 − a1 pt in short-run equations of the
form
k1

∆BR = b0 +

k2

b1s ∆BRt−s +
s=1

k3

b2s ∆˙ t−s +
p
s=1

b3s ∆NFRt−s
s=1

k4

b4s gapt−s + λ1 U1t−1 + δ1 U2t−1

+

(15a)

s=1

and
k1

∆˙ t = c0 +
p

k2

c1s ∆BRt−s +
s=1

k3

c2s ∆˙ t−s +
p
s=1

c3s ∆NFRt−s
s=1

k4

c4s gapt−s + λ2 U1t−1 + δ2 U2t−1 ,

+
s=1

(15b)

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Federal Reserve Bank of Richmond Economic Quarterly

where all variables are as defined before. The short-run equations include first
differences of the bond rate, inflation, and the funds rate and level of the output
gap, even though the last two variables do not enter the long-run bond equation
(13). These variables capture the short-run impacts of monetary policy and the
state of the economy on the bond rate and other variables. As indicated before,
the parameters of interest are λ1 , λ2 and the sums of coefficients that appear
on the bond rate in equation (15b). The expected signs of the error-correction
p
term U1t−1 are positive for ∆˙ and negative for ∆BR.
Following Campbell and Perron (1991), the lag lengths used in the errorcorrection model are chosen using the procedure given in Hall (1990). This
procedure starts with some upper bound on lags, chosen a priori for each
variable (eight quarters here) and then drops all lags beyond the lag with a
significant coefficient. I do present tests of the hypothesis that excluded lags
are not significant, however.
Table 4 reports the error-correction coefficients (t-values in parentheses)
when the long-run bond equation is (13). In addition, it also reports the sums
of coefficients that appear on (first differences of) the bond rate in the inflation
equation. Parentheses that follow contain t-statistics for the sum of coefficients,
whereas brackets contain Chi-squared statistics for exclusion restrictions. Panel
A reports results for the full sample 1961Q2 to 1996Q4 and panels B and C for
the subperiods 1961Q2 to 1979Q3 and 1979Q4 to 1996Q4.12 In full sample regressions the error-correction coefficient is negative and statistically significant
in the bond equation (∆BR), but in inflation equations (∆˙ ), it is generally small
p
and not statistically different from zero.13 Furthermore, individual coefficients
that appear on two lagged values of the bond rate in the inflation equation are
0.50 and −0.33. These coefficients are individually significant, but their sum
is not statistically different from zero, indicating that ultimately, increases in
the bond rate have not been associated with accelerations in actual inflation.14
Together, these results indicate that the short-run positive deviations of the
bond rate from its long-run equilibrium values were corrected mainly through
reversals in the bond rate. Actual inflation did not accelerate.
The results for the first subperiod 1961Q2 to 1979Q3 reported in panel
B of Table 4 are, however, strikingly different. As can be seen, the errorcorrection coefficient is negative and significant in the bond rate equation but
is positive and significant in the inflation equation. These results suggest that

12 Inflation

equations include dummies for President Nixon’s price and wage controls.
error-correction coefficients are in fact negative in the inflation equation that includes
other determinants of the real rate. In the inflation equation that includes only lagged values of
inflation, the coefficient that appears on the error-correction term is positive, small in magnitude,
and not statistically different from zero. The latter result is similar in spirit to the one in Engsted
(1995).
14 This result, of course, means that the bond rate Granger-causes inflation.
13 The

Y. P. Mehra: Bond Rate and Future Inflation

39

Table 4 Granger-Causality Results from Error-Correction Equations:
General to Specific, Using Hall Approach
Panel A: Cointegrating Regressions, 1961Q2 to 1996Q4
˙
˙
BRt = 2.9 + pt + U1t ; NFRt = 2.2 + pt + U2t
k1

Equation

∆BRt−s

U1t−1
−0.20 (3.5)
−0.13 (1.3)

∆BRt
∆˙ t
p

s=1

0.17 (0.6) [10.2]∗

(k1 , k2 , k3 , k4 )

x2 (sl)

(7,7,8,1)
(2,8,8,8)

9.5 (0.39)
5.3 (0.51)

Panel B: Cointegrating Regressions, 1961Q2 to 1979Q3
˙
˙
BRt = 1.7 + pt + U1t ; NFRt = 1.0 + pt + U2t
k1

Equation

−0.24 (3.5)
0.32 (3.2)

∆BRt
∆˙ t
p

s=1

(k1 , k2 , k3 , k4 )

x2 (sl)

(8,7,6,1)
(0,0,0,0)

∆BRt−s

U1t−1

8.9 (0.54)
38.4 (0.24)

Panel C: Cointegrating Regressions, 1979Q4 to 1996Q4
˙
˙
BRt = 4.2 + pt + U1t ; NFRt = 2.5 + pt + U2t
k1

Equation

∆BRt−s

U1t−1
−0.39 (2.9)
−0.01 (0.4)

∆BRt
∆˙ t
p

s=1

(k1 , k2 , k3 , k4 )

x2 (sl)

(7,0,6,8)
(0,6,8,8)

14.5 (0.21)
11.4 (0.33)

Notes: The coefficients reported are from error-correction regressions that include the bond rate
(BR), the inflation rate (˙ ), the nominal federal funds rate (NFR), and the output gap (gap) (see
p
equation [15] of the text). In addition, the model has two error-correction variables (U1t and U2t ).
(k1 , k2 , k3 , k4 ) refers to lag lengths that are chosen for BR, p, NFR, and gap. Parentheses contain t˙
statistics for the error-correction variable (U1t−1 ) or for the sum of coefficients that appear on the
k1

∆BRt−s . For the latter, brackets contain the Chi-squared statistic for the null

bond rate
s=1

hypothesis that every coefficient in this sum is zero. x2 (sl) tests the null hypothesis that remaining
lags are not significant (significance levels follow in parentheses).

positive deviations of the bond rate from its long-run equilibrium value were
eliminated partly through declines in the bond rate and partly through increases
in actual inflation. Consequently, in the pre-1979 period, actual inflation did
accelerate when the spread between the bond rate and the one-period inflation
rate rose.15
15 I

get similar results if cointegrating regressions (13) and (14) are estimated without restrictions b1 = a1 = 1. In particular, over the sample period 1961Q2 to 1979Q3, the error-correction
variable U1t−1 has a positive coefficient in the inflation equation, indicating that actual inflation
did accelerate following an increase in the bond rate spread.

40

Federal Reserve Bank of Richmond Economic Quarterly

In the aforementioned result, the fact that the spread signaled an increase
in inflation in the pre-1979 period but not in the full sample period implies that
the spread must have lost its predictive content in the post-1979 period. This
implication is consistent with the subperiod results reported in panel C of Table
4: the error-correction term is no longer significant in the inflation equation.
Comparison with Previous Studies
The full sample results discussed in the previous section indicate that the spread
between the bond rate and the one-period inflation rate does not help predict
one-quarter-ahead changes in the rate of inflation. Since inflation is a unit root
process, the results above also imply that the spread has no predictive content
for long-horizon forecasts of future inflation. The latter implication is in contrast
with the finding in Mishkin (1990a, 1990b, 1991) that at long horizons the long
end of the slope of the term structure does help predict future inflation.
As indicated before, an important assumption implicit in the regressions
used by Mishkin is that the ex ante real rate of interest is constant. This assumption may not be valid. Therefore, the predictive content of the spread
for future inflation should also be investigated conditioning on variables that
capture changes in the short-run determinants of the real rate.
In order to illustrate whether results are sensitive to such conditioning, I
also investigate the predictive content of the spread between the bond rate and
the (one-period) inflation rate for future inflation by estimating regressions of
the form
(ln[Pt+m /Pt ]/m) − ln(Pt /Pt−1 ) = a0 + λc U1t + V1t ,

(16)

k1

(ln[Pt+m /Pt ]/m) − ln(Pt /Pt−1 ) = a0 + λd U1t +

a1s ∆˙ t−s
p
s=1

k2

+

k3

a2s ∆NFRt−s +
s=1

k4

a3s ∆BRt−s +
s=1

a4s gapt−s + V2t ,

(17)

s=1

and
k1

(ln[Pt+m /Pt ]/m − ln(Pt /Pt−1 ) = a0 + λe U1t + δU2t +

a1s ∆˙ t−s
p
s=1

k2

+

k3

a2s ∆NFRt−s +
s=1

k4

a3s ∆BRt−s +
s=1

a4s gapt−s + V2t ,
s=1

where
˙
U1t = BRt − a0 − a1 pt ,
˙
U2t = NFR − b0 − b1 pt ,

(18)

Y. P. Mehra: Bond Rate and Future Inflation

41

and where m is the number of quarters, and other variables are as defined.16
U1 measures the spread between the bond rate and the (one-period) inflation
rate and U2 the spread between the nominal funds rate and the inflation rate.
Regression (16) examines the predictive content of the spread for long-horizon
forecasts of future inflation without controlling for variations in the spread
due to real growth, monetary policy actions, and inflation. Regressions (17)
and (18), however, control for such variations. Regression (18) is similar to
regression (17) except in that it also includes the current stance of short-run
monetary policy measured by the funds rate spread (U2t ). The regressions are
estimated over the full sample period as well as over subperiods 1961Q2 to
1979Q3 and 1979Q4 to 1996Q4 and for horizons up to four years in the future.
In addition, I consider the subperiod 1983Q1 to 1996Q4, during which inflation
has remained relatively low.
In Tables 5 and 6, I present estimates of the coefficient (t-values in parentheses) that appears on the bond rate spread variable (λc in [16]), λd in [17], and
λe in [18]).17,18 I also report the coefficient on the funds rate spread variable
(δ in [18]). In Table 5 the results are for the full sample period and the first
subperiod and in Table 6 for two post-1979 subperiods. If we focus on pre-1979
regression estimates, we will see that they indicate that the bond rate spread
does help predict future inflation (see t-values on λc , λd , and λe in Table 5,
panel B). This result holds at all forecast horizons and is not sensitive to the
inclusion of other variables in regressions. Furthermore, the funds rate spread
variable that controls for policy-induced movements in the real component of
the bond rate is never significant in those regressions, indicating that at the
time the current stance of monetary policy had no predictive content for future
inflation. Therefore, the widened bond rate spread was followed by higher
actual future inflation during this subperiod.

16 These

regressions differ from those reported in Mishkin (1990a, 1990b, 1991). Mishkin
uses zero-coupon bond data, derived from coupon-bearing bonds that have actually been traded.
So, he is able to match the horizon of the inflation forecast with that of the term spread. The
empirical work here instead uses yield-to-maturity data on coupon bonds and the inflation forecast
horizon does not match with that of the term spread. These differences, however, do not reduce the
importance of examining the potential role of additional variables that may provide information
about movements in the real rate of interest.
17 The t-values were corrected for the presence of moving-average serial correlation generated due to overlap in forecast horizon. The degree of correction in the moving-average serial
correlation was determined by examining the autocorrelation function of the residuals. This procedure generated the order of serial correlation correction close to the value given by (m − 1), where
m is the number of quarters in the forecast horizon. Furthermore, the use of realized multi-period
inflation in these regressions led to the loss of observations at the end of the sample, so that the
effective sample sizes are 1961Q2 to 1996Q4-m and 1961Q2 to 1979Q3-m.
18 All regressions are estimated including four lagged values of other information variables.
Furthermore, those lagged values are always statistically significant as a group in regressions (17)
and (18).

42

Federal Reserve Bank of Richmond Economic Quarterly

Table 5 Long-Horizon Inflation Equations
Panel A: 1961Q2 to 1996Q4
˙
˙
Cointegrating Regressions: BRt = 2.9 + pt + U1t ; NFRt = 2.2 + pt + U2t
Equation (Dc )
Equation (E)
Horizons in
Equation (C)
λe (t-value)
δ (t-value)
Quarters (m)
λc (t-value)
λd (t-value)
4
8
12
16

0.16 (1.5)
0.20 (1.5)
0.24 (1.6)
0.25 (1.7)

0.09 (1.0)
0.04 (0.4)
0.01 (0.1)
−0.07 (0.6)

0.02 (0.2)
0.14 (0.9)
0.21 (1.2)
0.22 (1.2)

0.07 (0.6)a
−0.12 (1.0)a
−0.26 (1.4)a
−0.33 (1.7)a

Panel B: 1961Q2 to 1979Q3
˙
˙
Cointegrating Regressions: BRt = 1.7 + pt + U1t ; NFRt = 1.0 + pt + U2t
c)
Equation (D
Equation (E)
Horizons in
Equation (C)
λe (t-value)
δ (t-value)
Quarters (m)
λc (t-value)
λd (t-value)
4
8
12
16

0.56 (5.4)
0.81 (7.9)
0.96 (7.9)
0.99 (9.1)

0.61 (7.4)
0.80 (6.5)
0.89 (12.6)
0.99 (13.2)

0.62 (3.3)
1.0 (4.4)
0.94 (3.4)
0.77 (2.8)

−0.00 (0.0)b
−0.25 (0.8)b
−0.10 (0.2)b
0.33 (0.9)b

a The

restriction λe + δ = 0 is consistent with data.
restriction λe + δ = 0 is not consistent with data.
c Additional variables included in equations (D) and (E) are always statistically significant as a
group.
Notes: The coefficients reported are from regressions of the form
b The

p(t, m) = f0 + λc U1t ,

(C)

k1

p(t, m) = g0 + λd U1t +

g1s ∆BRt−s

(D)

s=1
k2

+

k3

g2s ∆˙ t−s +
p
s=1

k4

g3s ∆NFRt−s +
s=1

g4 gapt−s
s=1

and
p(t, m) = λe U1t + δ U2t + other variables as in (D),

(E)

where p(t, m) is (log[Pt+m /Pt ])/m − log(Pt /Pt−1 ), m is the number of quarters in the forecast
horizon, and the rest of the variables are as defined before. All regressions are estimated setting
k1 = k2 = k3 = k4 = 4.

The full sample regression estimates, however, suggest strikingly different
results. The coefficient that appears on the bond rate spread variable is now
about one-third the size estimated in subsample regressions.19 For forecast
19 Mishkin

(1990a) also finds that in full sample regressions the coefficients that appear
on term spreads are generally smaller in size than those in pre-1979 regressions. Nonetheless,

Y. P. Mehra: Bond Rate and Future Inflation

43

Table 6 Long-Horizon Inflation Equations
Cointegrating Regressions: BRt = 4.2 + pt + U1t ; NFRt = 2.5 + pt + U2t
˙
˙
Panel A: 1979Q4 to 1996Q4
Horizons in
Equation (C) Equation (Da ) Equation (E)
λe (t-value)
δ (t-value)
λd (t-value)
Quarters (m)
λc (t-value)
4
8
12
16

Horizons in
Quarters (m)
4
8
12
16

0.21 (2.0)
0.31 (2.1)
0.35 (2.0)
0.42 (2.2)

0.18 (3.0)
0.28 (3.6)
0.31 (4.1)
0.37 (6.1)

0.29 (2.7)
0.58 (3.7)
0.61 (5.9)
0.73 (6.3)

Panel B: 1983Q1 to 1996Q4
Equation (C) Equation (Da ) Equation (E)
λe (t-value)
λd (t-value)
λc (t-value)
0.08 (0.4)
0.08 (0.9)
0.11 (0.9)
0.14 (0.7)

0.14 (2.0)
0.17 (2.7)
0.21 (3.9)
0.28 (4.4)

0.08 (0.3)
0.10 (4.4)
0.30 (3.6)
0.42 (6.2)

−0.10 (1.1)b
−0.26 (2.2)b
−0.28 (2.9)b
−0.35 (3.5)b

δ (t-value)
0.07 (0.07)b
0.10 (1.1)b
−0.11 (1.7)b
−0.22 (2.9)b

a Additional variables included in equations (D) and (E) are always statistically significant as a
group.
b The

restriction λe + δ = 0 is not consistent with data.

Notes: The cointegrating regressions are estimated over the period 1979Q4 to 1996Q4. The
coefficients reported above are from regressions like those given in Table 5. See notes in
Table 5.

horizons up to three years in the future, this coefficient is not statistically significant, and for somewhat longer horizons, it is marginally significant at the 10
percent level (see t-values on λc , λd , or λe in Table 5, panel A). Those estimates
suggest there had been a significant deterioration in the predictive content of
the bond rate spread for future inflation in the period since 1979. Furthermore,
results are now sensitive to variables included in the conditioning set. If we
ignore the current stance of Fed policy measured by the funds rate spread, then
the bond rate spread has no predictive content for actual future inflation at any
forecast horizon (see λd in Table 5, panel A). However, when the funds rate
spread variable is included in the conditioning set, then in long-horizon inflation
regressions, the bond rate spread variable appears with a positive coefficient.
Yet in those same regressions the coefficient that appears on the funds rate
spread is negative though barely statistically significant (see δ in Table 5, panel
his regressions pass the conventional test of parameter stability. The regressions estimated here,
however, do not depict such parameter constancy.

44

Federal Reserve Bank of Richmond Economic Quarterly

A). This result is consistent with the presence of policy-induced movements in
the real component of the funds rate and their subsequent negative effects on
future inflation rates. In fact, the coefficients that appear on the bond rate and
the funds rate spreads are equal in size but opposite in signs. Those estimates
suggest that increases in the bond rate spread accompanied by equivalent increases in the funds rate spread have had no effect on actual future inflation
rates.20
The first subperiod and full sample results discussed above suggest the
presence of considerable subperiod instability. In order to gain more insight into
subperiod differences, Table 6 presents estimates from long-horizon inflation
equations for two post-1979 subperiods, 1979Q4 to 1996Q4 and 1983Q1 to
1996Q4. Those estimates permit the following inferences about the predictive
content of the spread for future inflation in the post-1979 period. First, the
predictive content of the spread for future inflation has deteriorated in the post1979 period. The size of the coefficient that appears on the bond rate spread
variable is not only small relative to its value found in the pre-1979 period,
but its size declines further during the relative low inflation period of the late
1980s and the 1990s (compare values of λc in Tables 5 and 6). Second, the
marginal predictive content of the spread for future inflation is now sensitive
to variables included in regressions (compare values of λc and λe in panels
A and B of Table 6). Third, the current stance of monetary policy measured
by the funds rate spread correlates negatively with future inflation, indicating
Fed policy was geared towards reducing inflation in the post-1979 period. In
those regressions the bond rate spread variable remains significant, indicating
the bond rate spread does contain information about future inflation. However,
the results also indicate that actual future inflation may not accelerate following
the rise in the bond rate spread if the Fed reacts aggressively by raising the
funds rate (see estimates of λe and δ in Table 6).
The descriptive analysis of monetary policy in Goodfriend (1993) in fact
indicates that since 1979 the Fed has had a disinflationary policy in force to
reduce the trend rate of inflation and contain inflationary expectations. Accordingly, this Fed behavior may be at the source of deterioration in the predictive
content of the bond rate for actual future inflation. To the extent that rising
long-run inflationary expectations evidenced by the rise in the bond rate were
triggered in part by news of strong actual or anticipated real growth, the Fed
may have calmed those expectations by raising the funds rate. The induced
tightening of monetary policy may have reduced inflationary expectations by
reducing actual or anticipated real growth, thereby preventing any increase in
actual inflation. Given such Fed behavior, observed increases in the bond rate

20 This

result is similar in spirit to the finding reported using cointegration and errorcorrection methodology.

Y. P. Mehra: Bond Rate and Future Inflation

45

do not necessarily indicate that actual inflation is going to accelerate in the
near term.

3. CONCLUDING OBSERVATIONS
This article views the Fisher hypothesis as a long-run relationship with shortrun variation in the real interest rate. The findings show that the bond rate is
cointegrated with the inflation rate over the 1962Q2 to 1996Q4 period, which
indicates that in the long run, permanent movements in actual inflation have
been associated with permanent movements in the bond rate.
The short-run error-correction equations help identify ways in which the
bond rate and inflation adjust in the short run. In the pre-1979 period, increases
in the bond rate were followed by an acceleration in actual inflation, whereas
that did not happen in the post-1979 period. In the latter period, short-run
increases in the bond rate have usually been reversed, with no follow-up in
actual inflation.
In the period since 1979, the Fed has made serious attempts to reduce the
trend rate of inflation and contain inflationary expectations. Such Fed behavior
may have prevented the short-run increases in inflationary expectations, as
evidenced by increases in the bond rate, from finally producing higher actual
inflation. These results imply that if the Fed retains its hard-won credibility
for inflation stability, then the bond rate may reflect phenomena other than
expected inflation, thereby undermining its usefulness as a precursor of actual
future inflation.

REFERENCES
Campbell, John Y., and Pierre Perron. “Pitfalls and Opportunities: What
Macroeconomists Should Know about Unit Roots,” in Olivier J. Blanchard and Stanley Fischer, eds., NBER Macroeconomics Annual 1991.
Cambridge, Mass.: MIT Press, 1991, pp. 141–201.
Engle, Robert F., and C. W. Granger. “Cointegration and Error-Correction:
Representation, Estimation, and Testing,” Econometrica, vol. 55 (March
1987), pp. 251–76.
Engsted, Tom. “Does the Long-Term Interest Rate Predict Future Inflation? A
Multicountry Analysis,” The Review of Economics and Statistics, vol. 77
(February 1995), pp. 42–54.
Goodfriend, Marvin. “Interest Rate Policy and the Inflation Scare Problem:
1979 to 1992,” Federal Reserve Bank of Richmond Economic Quarterly,
vol. 79 (Winter 1993), pp. 1–24.

46

Federal Reserve Bank of Richmond Economic Quarterly

Hall, Alastair. “Testing for a Unit Root in Time Series with Pretest Data-Based
Model Selection,” Journal of Business and Economic Statistics, vol. 12
(October 1994), pp. 461–70.
Hodrick, Robert J., and Edward C. Prescott. “Postwar U.S. Business Cycles:
An Empirical Investigation,” Journal of Money, Credit, and Banking, vol.
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Johansen, Soren, and Katarina Juselius. “Identification of the Long-Run and
the Short-Run Structure: An Application to the ISLM Model,” Journal of
Econometrics, vol. 63 (July 1994), pp. 7–36.
. “Maximum Likelihood Estimation and Inference on
Cointegration—With Applications to the Demand for Money,” Oxford
Bulletin of Economics and Statistics, vol. 52 (May 1990), pp. 169–210.
Jorion, Philippe, and Frederick Mishkin. “A Multicountry Comparison of Term
Structure Forecasts at Long Horizons,” Journal of Financial Economics,
vol. 29 (March 1991), pp. 59–80.
Kwiatkowski, Denis, Peter C. B. Phillips, Peter Schmidt, and Yongcheol Shin.
“Testing the Null Hypothesis of Stationarity against the Alternative of a
Unit Root: How Sure Are We That Economic Time Series Have a Unit
Root?” Journal of Econometrics, vol. 54 (October–December 1992), pp.
159–78.
McCallum, Bennett T. “Monetary Policy and the Term Structure of Interest
Rates.” Manuscript. Carnegie-Mellon University, June 1994.
Mehra, Yash P. “An Error-Correction Model of the Long-Term Bond Rate,”
Federal Reserve Bank of Richmond Economic Review, vol. 80 (Fall 1994),
pp. 49–68.
Miller, Stephen M. “Monetary Dynamics: An Application of Cointegration
and Error-Correction Modeling,” Journal of Money, Credit, and Banking,
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Mishkin, Frederic S. “A Multicountry Study of the Information in the Shorter
Maturity Term Structure about Future Inflation,” Journal of International
Money and Finance, vol. 10 (March 1991), pp. 2–22.
. “The Information in the Longer Maturity Term Structure about
Future Inflation,” Quarterly Journal of Economics, vol. 105 (August
1990a), pp. 815–28.
. “What Does the Term Structure Tell Us about Future Inflation?”
Journal of Monetary Economics, vol. 25 (January 1990b), pp. 77–95.
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and Real Economic Growth,” Journal of Monetary Economics, vol. 33
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Rudebusch, Glenn D. “Federal Reserve Interest Rate Targeting, Rational
Expectations, and the Term Structure,” Journal of Monetary Economics,
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Inventory Investment
and the Business Cycle
Andreas Hornstein

W

hen reporting on the current state of the economy, the business press
gives considerable attention to changes in inventory investment. The
reason for the media attention appears to be related to three issues.
First, changes in inventory investment apparently account for a substantial fraction of changes in gross domestic product (GDP). Second, current changes in
inventory investment are assumed to convey useful information about the nearterm future of the economy. Third, there is a view that the inherent dynamics
of inventory investment are destabilizing the economy. In this article I review
some of the empirical regularities of inventory investment over the business
cycle taking the first issue as a starting point.1 The empirical regularities I
choose to study are to some extent determined by particular theories of inventory investment, but any theory of inventory investment should be consistent
with these regularities.
The argument that inventory investment is important for the business cycle
is often based on the close relationship between changes in inventory investment and GDP during recessions. For example, Blinder (1981) and Blinder
and Maccini (1991) argue that, in a typical U.S. recession, declining inventory
investment accounts for most of the decline in GDP. In support of this claim,
Table 1 documents the peak-to-trough decline of GDP and inventory investment
during postwar U.S. recessions. This same peak-to-trough decline is apparent

I would like to thank Michelle Kezar and Andrew Olmem for research assistance and Mike
Dotsey, Bob Hetzel, Tom Humphrey, and Alex Wolman for helpful comments. Any opinions
expressed are mine and do not necessarily reflect those of the Federal Reserve Bank of
Richmond or the Federal Reserve System.
1 When appropriate, I will make some comments on the second issue, namely, whether
inventory investment is useful for forecasting GDP. In the conclusion, I will remark briefly on
the third issue, namely, whether inventory investment is destabilizing the economy.

Federal Reserve Bank of Richmond Economic Quarterly Volume 84/2 Spring 1998

49

50

Federal Reserve Bank of Richmond Economic Quarterly

Table 1 GDP and Inventory Investment in Postwar Recessions

GDP Peak to Trough
1948:4
1953:2
1957:3
1960:3
1969:3
1973:4
1980:1
1981:3
1990:2

to
to
to
to
to
to
to
to
to

1949:4
1954:2
1958:1
1960:4
1970:4
1975:1
1980:3
1982:3
1991:1

Change
in GDP
−24.4
−48.8
−81.4
−40.7
−20.3
−146.2
−116.7
−140.9
−124.1

Change in
Inventory
Investment
−33.3
−20.0
−18.4
−47.9
−38.4
−77.0
−52.7
−43.4
−60.7

Notes: “Dates correspond to the largest peak-to-trough decline in GDP associated with each
postwar recession. Each date is within one quarter of the quarter containing the peak or trough
month as defined by the National Bureau of Economic Research.”
Source: Fitzgerald 1997, Table 1, p. 12.

during the 1980–97 period, as shown in Figure 1.2 Figure 1 also shows that
inventory investment is a very noisy time series. During that period, inventory
investment not only declines dramatically during recessions, it also declines
substantially during expansions. For example, in the expansion years 1986 and
1988, inventory investment declined by almost as much as it did during the
1990 recession. This experience suggests that, while the observation that during
recessions declining inventory investment accounts for much of declining GDP
is interesting, it might not be very useful when we want to evaluate the role of
inventory investment over the complete business cycle.3
Rather than study the behavior of inventory investment for a particular
phase of the business cycle, I choose to document the stylized facts of such
investment over the entire business cycle using standard methods.4 A stylized
2 Shaded

areas in Figure 1 represent National Bureau of Economic Research (NBER) recessions. We display only the last two NBER business cycles so that the graph is not overcrowded.
The behavior of inventory investment and GDP from 1980 to the present is not qualitatively
different from the earlier part of the postwar period.
3 Because inventory investment is such a noisy time series, it is also unlikely that it contains
useful information to forecast GDP growth. There are two additional pieces of evidence which
suggest that inventory investment is not a particularly good predictor of future GDP growth. First,
the Conference Board (1997) does not include inventory investment in its widely distributed list
of leading economic indicators. Only the inventory/sales ratio is included and then as a lagging
indicator. Second, if we forecast GDP growth using lagged GDP growth alone, we do better than
if we include lagged GDP growth and changes in lagged inventory investment. That is, we do
better in the sense that the first procedure has a lower mean squared forecast error.
4 For the most part I review earlier work on inventory investment by Blinder (1981) and
Blinder and Maccini (1991), using a different method to extract the business cycle components
of time series.

A. Hornstein: Inventory Investment and the Business Cycle

51

Figure 1 Changes in GDP and Inventory Investment

120
GDP

1992 Dollars

80
40
0
-40

Inventory Investment

-80
-120
1980

+

1982

1984

1986

1988
Year

1990

1992

1994

1996

fact is an observed empirical regularity between particular variables, which is
of interest because economic theory predicts a certain pattern for it. One cannot
look for stylized facts without the guidance of economic theory, but economic
theory is also developed from the stylized facts uncovered. Since inventory
investment ∆N is the difference between production Y and sales X, that is
∆N = Y − X, the stylized facts discussed involve the behavior of these three
interrelated variables.

1.

MODELS OF INVENTORY INVESTMENT

The two leading economic theories of inventory investment are the productionsmoothing model and the (S, s) inventory model. Both theories start with a single firm that solves a dynamic constrained-profit-maximization problem using
inventory investment as one of the firm’s decision variables.5 The
theories differ in how the implications for inventory investment, derived
for an individual firm, are applied to the study of aggregate inventory
investment.6
5 These theories differ from the early behavioral models of inventory investment that are not
explicitly based on fully specified dynamic optimization problems (Metzler 1941).
6 For an extensive survey of theories of inventory investment, see Blinder and Maccini
(1991).

52

Federal Reserve Bank of Richmond Economic Quarterly

A simple production-smoothing model starts with the assumption that a
firm’s production is subject to increasing marginal cost and that sales are exogenous. If the firm’s sales are changing over time but its marginal cost schedule is
constant, then the firm minimizes cost by smoothing production, and it reduces
(increases) inventories whenever sales exceed (fall short of) production. Thus
production is less volatile than sales, and inventory investment and sales tend
to be negatively correlated. A firm with increasing marginal cost wants to use
inventories to smooth production regardless of whether or not the changes in
demand are foreseen. If demand changes randomly and the firm has to decide
on current production before it knows what current demand is, the firm also
uses inventories as a buffer stock and accordingly reduces (increases) inventory
stocks whenever demand is unexpectedly high (low). This buffer-stock motive
then reinforces the negative correlation between inventory investment and sales.
The previous argument assumes that the firm faces only demand variations.
If, on the other hand, the firm predominantly faces supply shocks in the form
of a changing marginal cost schedule, then the implications for inventory investment, production, and sales are very different. In order to minimize costs,
the firm now increases (decreases) production and accumulates (reduces) inventories during times when marginal cost is low (high). Thus production is
more volatile than sales, and inventory investment and production tend to be
positively correlated.
So far the production-smoothing model described above applies to the behavior of an individual firm, rather than the behavior of aggregate variables. To
understand the aggregate variables, one often uses the concept of a representative agent and interprets the behavior of aggregate variables in terms of the
behavior of a large number of identical individual decision units. The simple
production-smoothing model then predicts that production will be more (less)
volatile than sales if supply shocks are more (less) important than demand
shocks.7
A simple (S, s) inventory model assumes that the seller of a good does
not himself produce the good. Instead, the seller orders the good from some
producer and incurs a fixed cost when he places the order. Suppose that the
marginal cost of ordering one more unit of the good is constant and that sales
are exogenous. A seller who chooses the order size that minimizes total cost
faces the following tradeoff. On the one hand, increasing the order size reduces
the average or per-unit order cost because it spreads the fixed cost over more
units of the good. On the other hand, an increased order size means that the
seller forgoes additional interest income on the funds that have been used to
finance the larger order. Given the optimal order size, the seller places an order
7 Further work has studied the effects of serial correlation in demand shocks, stock-out
avoidance, etc. Again, for a survey on this work, see Blinder and Maccini (1991) or Fitzgerald
(1997).

A. Hornstein: Inventory Investment and the Business Cycle

53

whenever the inventory falls below a critical lower level s and the order brings
inventories up to the higher level S. After that, sales reduce the inventory until
the critical lower level s is reached again. If orders equal production, then
production will be more volatile than sales. The relationship between sales and
inventory investment is unclear.
Like the production-smoothing model, the (S, s) inventory model applies to
an individual decision unit. Unlike the production-smoothing model, however,
the notion of a representative agent cannot be used in order to understand the
behavior of aggregate variables. The problem is that in the (S, s) inventory
model, a firm’s behavior is characterized by long periods of inactivity interrupted by short bursts of activity. While one may observe such discontinuous
behavior for individual decision units, one does not observe it for aggregate
variables. For this theory, aggregation has to be studied explicitly, and aggregate
variables will not necessarily behave the same way as do the corresponding
variables of individual decision units. In particular, in a model where individual
firms follow (S, s) inventory policies, one cannot a priori say whether aggregate
production or aggregate sales is more volatile or how aggregate inventory investment is correlated with aggregate sales. Fisher and Hornstein (1997) study
the effects of technology and preference shocks on aggregate production, sales,
and inventory investment in a general equilibrium model with a trade sector
where individual firms use (S, s) inventory policies.8 They find that for both
types of shocks (1) production is more volatile than sales, and (2) inventory
investment tends to be positively correlated with sales. They also find that
preference and technology shocks differ in their effect on retail-price markups.
In particular, retail-price markups are procyclical for technology shocks and
countercyclical for preference shocks.

2.

CYCLICAL COMPONENTS OF INVENTORY
INVESTMENT

Up to this point I have used economic theory to identify potential stylized facts
pertaining to inventory investment. To further evaluate the role of inventory
investment over the business cycle, I will need an operational definition to
identify business cycle movements in the data. Usually business cycles are
identified with recurring expansions and contractions in economic activity that
occur simultaneously over a wide range of sectors. Burns and Mitchell (1946,
p. 3) state that
8 In

a general equilibrium model, shocks cannot be unambiguously classified as demand
or supply disturbances. Usually shocks that affect the production technology are interpreted as
supply disturbances, and shocks that affect the preferences of agents are interpreted as demand
disturbances.

54

Federal Reserve Bank of Richmond Economic Quarterly
. . . a cycle consists of expansions occurring at about the same time in many
economic activities, followed by similarly general recessions, contractions,
and revivals which merge into the expansion phase of the next cycle; this
sequence of changes is recurrent but not periodic; in duration business cycles
vary from more than one year to ten or twelve years; they are not divisible
into shorter cycles of similar character with amplitudes approximating their
own.

The business cycle is thus different from long-term trend and short-term
irregular movements in the economy. Yet many of the economic variables are
growing over time (GDP, sales) or are very erratic (inventory investment).
Furthermore, since inventories can serve as a buffer stock to compensate for
short-term movements in demand or supply, one may want to study the business
cycle component and the short-term irregular component separately.
Bandpass filters, which essentially are moving averages, separate the time
series of a variable into components with different periodicities (see Baxter and
King [1995]).9 Using this method, I construct the business cycle components of
inventory investment, GDP, and final sales as displayed in Figure 2. First, one
can see that, for business cycle movements, inventory investment contributes
only a small part to GDP volatility. Second, GDP is more volatile than final
sales, and final sales and inventory investment tend to increase and decrease
together. Figure 3 plots the irregular components of inventory investment. Consistent with Figure 1’s depiction of changes in GDP and inventory investment,
Figure 3 shows that inventory investment accounts for a substantial fraction of
the short-term volatility of GDP.
The two inventory models discussed above capture different features of
the inventory holding problem. In any one sector of the economy, one of the
features will play a bigger role. For example, when firms in the manufacturing
sector choose the size of their finished goods inventories, the productionsmoothing model seems to be more appropriate. But when firms in the trade
sector make their order decisions, or firms in the manufacturing sector decide
on the size of their material inventories, the (S, s) inventory model seems to be
more appropriate. Our study of disaggregated data shows two things. On the
one hand, it is difficult to attribute aggregate inventory investment volatility
to particular sectors because inventory investment moves much the same in
each sector. On the other hand, we find that although important features of
the inventory holding problem differ systematically across sectors, the properties of inventory investment, production, and sales are remarkably similar
across sectors; for business cycle movements, production is more volatile than
sales, and inventory investment and sales are positively correlated. The only
9 In

Appendix A I describe the basic idea underlying the decomposition of a time series
using bandpass filters.

A. Hornstein: Inventory Investment and the Business Cycle

55

Figure 2 Business Cycle Components of GDP, Final Sales,
and Inventory Investment

150
GDP

100

1992 Dollars

50
0
Inventory
Investment

-50

Final
Sales

-100
-150
-200
-250

1963

+

1966

1969

1972

1975

1978
Year

1981

1984

1987

1990

exception concerns the behavior of retail-price markups, which are not consistently procyclical or countercyclical across sectors.

3.

STYLIZED FACTS OF INVENTORY INVESTMENT

The organization of the stylized facts is suggested by the predictions of the two
basic models of inventory investment, the production-smoothing and the (S, s)
inventory models. First, I document the behavior of aggregate variables, GDP,
final sales, and inventory investment. Then I decompose aggregate inventory
investment into sectors according to whether it is more likely that inventory
decisions are influenced by the production-smoothing motive or the fixed order
cost motive. Next, I examine the relative volatilities of production and sales
and the correlation between inventory investment and sales. Finally, I study the
behavior of the retail price index relative to the producer price index, that is,
the retail-price markup.10

10 Appendix

B describes the time series used and how the business cycle and irregular
component of each time series is constructed.

56

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Irregular Components of GDP and Inventory Investment

60
GDP

1992 Dollars

40
20
0

-20
Inventory
Investment

-40
-60

+

1963

1966

1969

1972

1975

1978
Year

1981 1984

1987

1990

Inventory Investment at the Aggregate Level
For quarterly changes in aggregate values of GDP, final sales, and inventory
investment, Table 2 quantifies some of the observations made earlier in the
introduction using Figure 1. The table shows that GDP is more volatile than
final sales and that final sales and inventory investment are essentially uncorrelated (the correlation coefficient is 0.01). This observation is consistent with
properties of the simple production-smoothing model and the (S, s) model, and
for the former it implies that supply shocks must be relatively more important
than demand shocks. Note that, consistent with conventional wisdom, changes
in inventory investment account for a substantial part of the variance of changes
in GDP, about 30 percent.11
When distinguishing between the business cycle and irregular components
of a time series, one sees that GDP is more volatile than final sales for both
components, whereas inventory investment is positively correlated with final
sales for the business cycle component but negatively correlated for the irregular component. The correlation coefficients are, respectively, 0.54 and −0.2.
11 Given

that the variance of output is the sum of the variance of sales, the variance of
inventory investment, and the covariance of sales and inventory investment, we can attribute
output volatility to sales and inventory investment volatility because of the low sales/inventory
investment correlation.

A. Hornstein: Inventory Investment and the Business Cycle

57

Table 2 GDP, Final Sales, and Inventory Investment

NIA Component
GDP
Final sales
Inventory investment
Covariance of final
sales and inventory
investment

First Difference
of Levels
Variance Percent

Business Cycle
Component
Variance Percent

Irregular
Component
Variance Percent

1534.99
1085.94
439.11
9.94

5479.39
3961.99
315.63
1197.46

255.41
190.19
122.88
−57.92

70.7
28.6
0.6

72.3
5.8
21.9

74.5
48.1
−22.7

Again, the fact that production is more volatile than sales is consistent with
the simple production-smoothing model when supply shocks dominate demand
shocks, but now the model cannot easily account for the comovement of sales
and inventory investment. In particular, the model does not predict the strong
positive correlation between inventory investment and sales for the business
cycle component. Moreover, the weak negative correlation for the irregular
component seems to indicate that, over the short term, demand shocks dominate supply shocks, and inventories are used as a buffer stock. The (S, s) model
is consistent with the properties of the business cycle component but does not
predict the negative correlation between inventory investment and sales for the
irregular component.
For the business cycle component, it is difficult to attribute GDP volatility
to either sales or investment volatility since there is a strong positive correlation
between these two components of GDP. Furthermore, relative to GDP, inventory investment is much less volatile for the business cycle component than it
is for the irregular component. Inventory investment variance represents only
6 percent of GDP variance for the business cycle component but 50 percent
of GDP variance for the irregular component. Thus it appears that inventory
investment is less important for GDP volatility over the business cycle than it
is for short-term fluctuations.12
12 Since

the calculation of changes in a variable, that is, its first differences, and the calculation of business cycle and irregular components of the same variable represent different data
transformations, it is hardly surprising that they lead to different results. These observations are
not inconsistent; they only reflect different properties of the data and the transformation used.
Appendix A shows how the business cycle and irregular components of a variable represent
the frequency components of that same variable that fall within a particular frequency band and
where each frequency receives the same weight. Calculating changes in a variable, that is, first
differences, is another data transformation that includes all frequencies but gives more weight to
higher frequencies (Baxter and King 1995). Thus first differences emphasize components with
short periodicity relative to components with long periodicity, and therefore the properties of a
first-differenced variable are more closely related to the properties of the irregular component
than to the properties of the business cycle component of that variable.

58

Federal Reserve Bank of Richmond Economic Quarterly

Disaggregating Inventory Investment
Most of the results from the study of aggregate variables also apply when
aggregate production, sales, and inventory investment are disaggregated into
their sectoral components: manufacturing and trade. It is useful to study the
sectoral components of inventory investment because the production-smoothing
and the (S, s) models seem to be more or less appropriate for different types
of inventories. For example, the production-smoothing model appears to be
more appropriate for finished goods inventories in the manufacturing sector,
whereas the fixed order cost model appears to be more appropriate for material
inventories in the manufacturing sector and inventories in the wholesale and
retail trade sector. This suggests that one should focus attention on the theory of
inventory investment that is most appropriate for the sector that contributes the
most to aggregate inventory investment volatility. Unfortunately, it turns out to
be difficult to attribute aggregate inventory investment volatility to individual
sectors.
Table 3 shows the variance of the components of total inventory investment:
manufacturing and trade inventories. Over the business cycle, finished goods
inventories in the manufacturing sector account for only about 10 percent of
the total variance of inventory investment. On the other hand, inventories in
the trade sectors and materials in the manufacturing sector account for about
a quarter of total inventory volatility. Note that, although inventory investment
in the trade sector accounts on average for more than half of total inventory
investment, it accounts for less than 20 percent of the volatility of inventory investment over the business cycle. Any attempt to attribute the variance
of total inventory investment to particular components, however, meets with
limited success because more than half of total inventory volatility is due to
the comovement of inventory investment components. In particular, within the
manufacturing sector about 50 percent of total volatility is due to the comovement of finished goods, goods-in-process, and materials inventories. For total
inventory investment volatility, about 40 percent of total volatility is due to the
comovement of the individual components: manufacturing, retail, and wholesale
trade. This observation is the main difference between our results and those
of Blinder and Maccini (1991). They find that, of manufacturing inventory
volatility, only 25 percent is due to the comovement of finished goods, materials, and goods-in-process inventories. And for total inventory investment, only
20 percent is due to covariance terms.
Blinder and Maccini (1991) define the business cycle component of a time
series as fluctuations around a linear trend. In effect, their definition of the
business cycle eliminates long-run growth components but not the irregular
component, or short periodicity movements, from consideration. Table 3 reveals
as much. It shows that these high-frequency movements are not highly correlated across sectors; that is, the results of Blinder and Maccini (1991) represent

A. Hornstein: Inventory Investment and the Business Cycle

59

Table 3 Variance Decomposition of Inventory Investment

Inventory Component

Percent of
Total
Investment

Manufacturing and trade
Manufacturing
Finished goods
Goods-in-process
Materials and supplies
Covariance terms

Business Cycle
Component
Variance Percent
2.491

Irregular
Component
Variance Percent
4.753

43.5
15.2
14.7
13.6

1.035
0.107
0.249
0.150
0.535

41.6
10.3
23.9
14.4
51.4

1.538
0.443
0.487
0.556
0.072

32.4
28.4
31.3
35.7
4.6

Wholesale trade

26.5

0.172

6.9

0.924

19.4

Retail trade

30.0

0.312

12.5

1.990

41.9

0.973

39.1

0.301

6.3

Covariance terms

a mixture of the properties of business cycle and irregular components. Also,
for the irregular component, inventory investment in the trade sector accounts
for a much bigger share of overall inventory investment variance.
Production, Sales, and Inventory Investment at the Sectoral Level
The behavior of production, sales, and inventory investment is remarkably similar in the different sectors. In all sectors, production tends to be more volatile
than sales, substantially so in the retail and wholesale trade sector. This is
true for both the business cycle components and the irregular components (see
Table 4), thus confirming Blinder and Maccini’s (1991) results. Note also that
over the business cycle, the durable goods sectors are much more volatile than
the nondurable goods sectors. This is consistent with other work on sectorally
disaggregated data (Hornstein and Praschnik 1997).
Table 5a documents the pattern of comovement between inventory investment and sales for the business cycle components. Over the business cycle,
inventory investment and sales are positively correlated. What is of interest
is that there are different patterns of lead-lag relationships between inventory
investment and sales in the various sectors. For example, in the manufacturing
sector, inventory investment in nondurable manufacturing is essentially uncorrelated with sales, but such investment in durable manufacturing bears a
strong contemporaneous correlation with sales. In the wholesale trade sector,
inventory investment in the durable sector is also contemporaneous with sales,
but inventory investment in the nondurable sector leads sales by three months.
Furthermore, in retail trade, inventory investment leads sales by three months,

60

Federal Reserve Bank of Richmond Economic Quarterly

Table 4 Relative Variance of Production Y and Sales X

Sector
Manufacturing

Business Cycle Component
Var(Y)
Var (X)
Var (Y)

Var(X)

43.2
47.9
20.0
23.2
4.9
4.9

41.9

Wholesale trade
Durables
Nondurables

11.49
6.0
1.6

Retail trade
Durables
Nondurables

9.9
3.9
1.5

Durables
Nondurables

Irregular Component
Var(Y)
Var (Y)
Var (X)

Var(X)

1.03
1.14
1.04
1.21
1.02
1.01

6.84
7.36
3.59
3.92
1.31
1.38

10.3
5.0
1.6

1.12
1.19
1.03

1.48
2.14
1.45

1.74
0.50
0.90

1.11
1.18
1.01

8.1
3.1
1.2

1.23
1.28
1.18

1.64
1.43
2.35

1.78
1.08
0.27

1.21
1.26
1.17

19.2
4.8

6.66
3.37
1.18

1.03
1.11
1.07
1.16
1.11
1.17

Note: For the manufacturing sector, the first row refers to the narrow inventory definition (finished
goods inventories only) and the second row refers to the broad inventory definition (finished goods
and goods-in-process inventories).

Table 5a Comovement of Inventory Investment ∆N and Sales X for
Business Cycle Components
Correlation coefficient for Xt and ∆Nt+s , where s =
−4
Manufacturing
Durables
Nondurables

−3

−2

−1

0.09
0.15
0.20
0.25
0.47
0.51
0.54
0.57
0.23
0.28
0.32
0.36
0.59
0.62
0.65
0.66
−0.13 −0.08 −0.03
0.01
−0.11 −0.08 −0.04 −0.01

0

1

2

3

4

0.30
0.60
0.39
0.67
0.05
0.01

0.33
0.61
0.41
0.67
0.08
0.03

0.36
0.61
0.43
0.66
0.10
0.04

0.38
0.60
0.43
0.64
0.12
0.04

0.38
0.58
0.43
0.61
0.12
0.03

Wholesale trade
Durables
Nondurables

0.43
0.49
0.19

0.44
0.51
0.17

0.44
0.53
0.14

0.43
0.53
0.09

0.39
0.34
0.29
0.23
0.16
0.52
0.50
0.47
0.43
0.37
0.03 −0.04 −0.12 −0.20 −0.27

Retail trade
Durables
Nondurables

0.55
0.54
0.35

0.54
0.54
0.34

0.53
0.53
0.32

0.50
0.51
0.30

0.47
0.48
0.28

Note: See Note to Table 4.

0.43
0.44
0.25

0.37
0.38
0.22

0.31
0.32
0.18

0.24
0.25
0.14

A. Hornstein: Inventory Investment and the Business Cycle

61

Table 5b Comovement of Sales X and Inventory Investment ∆ N for
Irregular Components
Correlation coefficient for Xt and ∆Nt+s , where s =
−4
−0.14
−0.11
Durables
−0.11
−0.06
Nondurables −0.16
−0.17
Wholesale trade −0.01
Durables
−0.00
Nondurables −0.02
Retail trade
−0.01
Durables
−0.02
Nondurables −0.02

Manufacturing

−3

−2

−1

−0.23
−0.14
−0.13
−0.07
−0.17
−0.13
0.08
0.04
0.11
−0.05
−0.03
0.07

−0.15
−0.06
−0.07
−0.02
−0.09
−0.04
0.01
−0.13
0.11
−0.03
0.06
−0.15

−0.06
0.04
0.02
0.09
−0.05
0.01
0.11
0.04
0.11
−0.04
−0.07
0.02

0

1

2

3

−0.08
0.18
0.13
0.15
0.20
−0.06
0.18
0.15
0.09
0.11
0.04
0.18
0.09
0.03 −0.02
−0.02
0.17
0.14
0.02
0.01
−0.10
0.10
0.10
0.14
0.21
−0.08
0.10
0.11
0.10
0.16
−0.04 −0.06 −0.06 −0.09 −0.00
−0.09 −0.03
0.08
0.08
0.01
0.02 −0.18 −0.13 −0.05 −0.06
−0.23
0.05
0.18
0.07
0.06
−0.34
0.01
0.15
0.05
0.07
−0.10
0.02
0.11 −0.05
0.04

Note: See Note to Table 4.

both for durable and nondurable goods.13 This observation might be useful to
differentiate between models of inventory investment across sectors.
For the irregular component, inventory investment and sales are essentially
uncorrelated, with a tendency towards negative correlations (see Table 5b). In
particular, for the retail trade sector, sales and inventory investment are somewhat negatively correlated. As for aggregate data, it appears as if inventory
stocks are used to buffer unforeseen short-term fluctuations in sales.
The Cyclical Behavior of the Retail-Price Markup
One last variable, the retail-price markup, is of interest because extensions of
simple (S, s) inventory models suggest that sellers have some control over the
prices they set. Such control means that decisions on inventory investment,
sales, and prices are interrelated. Fisher and Hornstein (1997) describe such
an (S, s) inventory model for the retail sector. They argue that the cyclical
behavior of the retail-price markup depends on whether supply or demand
shocks are more important for a market. In particular, their model predicts that
if productivity shocks to the suppliers of the retailers are predominant, then
the retail-price markup should be positively correlated with sales. On the other
13 The

4

fact that inventory investment leads sales over the business cycle does not mean that
inventory investment can be used to predict future sales. The reason is simply that the business
cycle component of a variable represents a moving average of past and future values of the
variable.

62

Federal Reserve Bank of Richmond Economic Quarterly

Table 6 Comovement of Sales X and Retail Markups M at
Business Cycle Frequencies
Correlation coefficient for Xt and Mt+s , where s =
−4

−3

−2

−1

0

1

All retail
0.61
0.60
0.58
0.56
0.54
0.51
Durable goods
0.28
0.27
0.25
0.23
0.21
0.18
Autos
0.03
0.01 −0.00 −0.02 −0.03 −0.05
Furniture
0.13
0.09
0.04 −0.02 −0.07 −0.12
Building mat. −0.66 −0.70 −0.73 −0.75 −0.76 −0.76
Nondurable
0.50
0.53
0.56
0.58
0.60
0.61
Food
0.37
0.34
0.30
0.26
0.21
0.16
Apparel
0.17
0.09
0.02 −0.06 −0.14 −0.21
Others
0.48
0.42
0.35
0.28
0.21
0.15

2

3

4

0.48
0.15
−0.06
−0.18
−0.75
0.62
0.11
−0.27
0.09

0.45
0.11
−0.06
−0.23
−0.74
0.62
0.07
−0.33
0.03

0.41
0.07
−0.07
−0.27
−0.71
0.61
0.04
−0.38
−0.03

hand, if shocks to demand for the retailer’s product are predominant, then the
retail-price markup should be negatively correlated with sales.
The comovement over the business cycle between retail-price markups and
sales for a selected number of products is documented in Table 6. Apparently
there is no strong consistent pattern in the data. For nondurable goods, with
the exception of apparels, the markup tends to be positively correlated with
sales, and for durable goods the markup tends to be negatively correlated with
sales. Of interest is the absence of any strong comovement for cars. One note
of caution: the lack of correlation between markup and sales should not be
taken as evidence for inflexible prices. The markup is defined as the ratio of
retail prices to producer prices, both of which tend to be strongly correlated
with sales over the business cycle. In particular, the retail price is negatively
correlated with sales for all goods, and, with the exception of building materials,
the producer price indexes are negatively correlated with sales.
Finally, we have not presented results for the irregular component because
for these frequencies the markup is essentially uncorrelated with sales. In this
case the markup is uncorrelated with sales, because both the retail price and
the producer price index are uncorrelated with sales.

4.

CONCLUSION

The description of the data above suggests that it is important to distinguish between the irregular and the business cycle components of inventory investment,
production, and sales. Bearing this in mind, the findings can be summarized
as follows. First, inventory investment fluctuations are not important for output fluctuations over the business cycle, but they are important for short-term
output fluctuations. Second, over the business cycle, we cannot attribute total

A. Hornstein: Inventory Investment and the Business Cycle

63

inventory investment volatility to its individual components because all components are highly correlated. Third, inventory investment is positively correlated
with sales over the business cycle but tends to be uncorrelated or negatively
correlated with sales for short-term fluctuations. Fourth, production tends to be
more volatile than sales; this feature is common to all sectors, and it applies to
business cycle and short-term fluctuations.
How well do the existing models of inventory investment match these
stylized facts? The production-smoothing model is in principle consistent with
the finding that production is more volatile than sales in the particular case
where cost shocks are assumed to be more important than demand shocks.
Essentially the production-smoothing model is used in order to say something
about the relative importance of unobserved demand and supply shocks in the
economy. Unfortunately, with direct observations on cost and demand shocks,
the production-smoothing model often is no longer consistent with the stylized
facts, given the observed relative volatility of shocks (for some recent work,
see Durlauf and Maccini [1995]). Furthermore, the production-smoothing model
has problems accounting for the comovement of sales and inventory investment,
even if cost shocks are more volatile than demand shocks.
Less can be said about how well the (S, s) inventory framework conforms to
the stylized facts because only recently has work begun that tries to incorporate
this framework in quantitative general equilibrium models. For a simple general
equilibrium model with (S, s) inventory policies, Fisher and Hornstein (1997)
have shown that the model’s quantitative implications are consistent with the
stylized facts. But more work needs to be done.
Let me conclude with a remark on whether inventory investment can destabilize the economy.14 Obviously the stylized facts reviewed in this article by
themselves have nothing to say about this issue. Potential destabilization can
only be addressed within some theory of inventory investment. For example,
the fact that production appears to be more volatile than sales does not mean
that, because of inventory investment, production is excessively volatile. If one
believes that the production-smoothing model is a useful representation of the
economy, then at least for a firm, this outcome is optimal if marginal cost varies
over time.
Most inventory investment models, with few exceptions, are partial equilibrium in nature; that is, they describe the behavior of a firm/industry and take
the behavior of the rest of the economy as given. A complete analysis of the role
of inventory investment requires that the particular inventory investment model
is embedded in a general equilibrium model in order to study how inventory
investment affects the rest of the economy and vice versa. It is not clear that

14 This

is a well-known property of inventories in the traditional inventory-accelerator models
(Metzler 1941).

64

Federal Reserve Bank of Richmond Economic Quarterly

inventory investment will be destabilizing in such a general equilibrium model
or even what such destabilization means. One possible interpretation is that,
with inventories, the equilibrium of an economy is no longer determinate. In
this case, one could construct particular equilibria where output fluctuates even
though the fundamentals of the economy do not change at all; however, such
work remains to be done.15

APPENDIX A:
THE CYCLICAL COMPONENTS OF A TIME SERIES
The decomposition of a time series into business cycle and irregular components
using a bandpass filter is a statistical method based on the frequency domain
analysis of time series.16 Essentially, this method interprets a time series as the
sum of a very large number of sine and cosine waves, and it isolates groups of
waves within particular frequency bands. Rather than describing in detail this
technique and the underlying statistical theory, I simply want to provide some
insight on how it works. For an introduction to the analysis of time series in the
frequency domain, see Harvey (1993) or Hamilton (1994). For a description of
bandpass filters, see Baxter and King (1995).
Extracting Periodic Components from Deterministic Time Series . . .
In order to illustrate the problem, consider the following example. Define a
variable Yt as the sum of sine and cosine functions
3

[αi cos(ωi t) + βi sin(ωi t)].

Yt =
i=1

A sine (cosine) function has amplitude one and periodicity T = 2π. A function
is periodic with period T if the function repeats itself every T periods.17 For
a periodic function, its frequency 1/T denotes how many cycles are completed
within a unit of time. The transformation of the sine (cosine) function α cos(ωt)
[β sin(ωt)] has amplitude α (β), periodicity T = 2π/ω, and frequency ω =
2π/T.

15 See

Benhabib and Farmer (1997) for a survey on endogenous business cycle models.
methods have been used to identify the business cycle components of time series,
for example, stochastic trends or linear trends. One close relative of a bandpass filter for the
business cycle is the Hodrick-Prescott filter, also described in Baxter and King (1995).
17 The sine function satisfies sin(t + 2πj) = sin(t) for all t and j = . . . , −1, 0, +1, . . ..
16 Other

A. Hornstein: Inventory Investment and the Business Cycle

65

In the example, Yt is the sum of three periodic functions and is itself periodic. Assume that the unit of time is a month and that the first component has a
periodicity of 50 years (ω1 = 2π/(12 · 50)); the second component has a periodicity of five years (ω2 = 2π/(12 · 5)); and the third component has a periodicity
of one year (ω3 = 2π/(12 · 1)). For this example, the first component represents
long-run trends (low-frequency movements); the second component represents
a business cycle (medium-frequency movements); and the third component
represents short-run fluctuations (high-frequency movements), like seasonal
fluctuations. Suppose there is a finite number of observations on Yt as shown
in Figure A1: How can the three different components be extracted from Yt ?18
An ideal bandpass filter extracts the components of a time series whose
frequencies are within a given frequency band (Baxter and King 1995). This
filter assigns a weight of one to all frequencies that fall within the specified
band and zero weight to all frequencies outside the specified band. The ideal
bandpass filter is represented by a moving average with infinitely many leads
ˆ
and lags, Yt = s=−∞,. . .,∞ as Yt+s , and the filter is defined by its weights,
{as }s=−∞,. . .,+∞ , which depend on the frequency band to be extracted from
the time series. Since only a finite number of observations is available, the bandpass filter has to be approximated. It turns out that an approximate bandpass
filter has the same moving average representation except that the weights are
ˆ
truncated, YtS = s=−S,. . .,S as Yt+s , and the number of leads/lags S determines
the approximation quality. Because the bandpass filter is approximate, it will
pass some components with frequencies outside the specified frequency band,
and it will not assign all frequencies within the specified frequency band the
same weight. The approximation improves with the number of leads and lags
included in the moving average term.
I follow Baxter and King (1995) and identify the business cycle with periodicities between one and one-half years and six years, and for monthly
(quarterly) data I use an approximation involving 36 (12) leads and lags. The
irregular component (trend component) is identified with the periodicities of
less than one and one-half years (more than six years). When this procedure is
applied to the time series of Yt in Figure A1, the approximate bandpass filter
extracts its low-, medium-, and high-frequency components quite well.19
. . . and Stochastic Processes
The business cycle is not a deterministic process, which should be apparent
from the graphs of GDP growth. Definitions of the business cycle, such as
Burns and Mitchell’s (1946, p. 3) above, recognize this fact and refer to “. . .
18 I

have set α1 = 1, α2 = 0.1, α3 = 0.05, and βi = 0 for i = 1, 2, 3.
filtered series is not defined for the first and last S observations since the filter uses
S leads and lags.
19 The

66

Federal Reserve Bank of Richmond Economic Quarterly

Figure A1 A Sine Function and its Cyclical Components

1.5
Low Frequency
1.0

0.5

0

-0.5

Medium Frequency
High Frequency

-1.0

-1.5

+

5

10

15

20
25
Period

30

35

40

45

recurrent but not periodic . . .” movements. In particular, Lucas ([1977], 1989,
p. 217) states that “. . . movements about trend . . . can be well described by
a stochastically disturbed difference equation of very low order.” Yet, I have
discussed the bandpass filter as a way to extract periodic components from a
time series that is the sum of deterministic cycles.
This approach remains valid for the study of covariance stationary stochastic time series, because of the spectral representation theorem.20 The theorem
states that any covariance stationary time series can be written as the integral
of randomly weighted sine and cosine functions
π

Yt = µ +

[α(ω) cos(ωt + β(ω) sin(ωt)]dω,

(1)

0

where the random variables α(ω) and β(ω) are in a sense “mutually uncorrelated” with mean zero. The property that α and β are uncorrelated is useful
because it allows us to attribute the variance of Yt to its various components. Let
20 A stochastic process Y is covariance stationary if the first and second moments of the
t
process are time independent; that is, expected values are E[Yt ] = µ and E[Yt Yt−s ] = ρs for all
t, s.

A. Hornstein: Inventory Investment and the Business Cycle

67

0 ≤ ω L < ω H ≤ π and write the interval [0, π] as the union of a low-frequency
trend component ITR = [0, ω L ], a medium-frequency business cycle component
IBC = [ω L , ω H ], and a high-frequency irregular component IIR = [ω H , π]. The
bandpass filter can be applied to the stochastic process Yt and extract the components associated with each frequency band I = [ω0 , ω1 ]. Because the sine
and cosine functions at different frequencies are uncorrelated, the variance of
Yt is the sum of the variances of the nonoverlapping frequency components.
To get some idea of how a bandpass filter works for a stochastic process,
consider the following example. Suppose the stochastic process Yt is described
by a low-order stochastic difference equation, in particular, Yt is first-order
autoregressive (AR(1)),
Yt = 0.95Yt−1 + εt for t = 1, 2, . . . ,
where Y0 is given, and εt is an identically and independently distributed random
variable that takes on values −0.1 or +0.1 with a probability of one-half each.
Suppose that each time period represents a quarter. Make 120 independent
draws of the random variable εt and construct a particular 30-year time path of
this process {yt }t=0,. . .,30·4 . The result is something like Figure A2a. Recurrent
but not periodic movements are clearly recognizable in the time path. As a next
step apply a bandpass filter to this time path and extract the trend, business
cycle, and irregular components of the time series, shown in Figure A2a-c.
As is apparent from this figure, the business cycle component is quite smooth,
with cycles between two and six years, whereas the irregular component has
somewhat less amplitude and no particular cyclical pattern.
Finally, note that the spectral decomposition theorem applies to covariance
stationary stochastic processes. In particular, this means that there should be
no trend in the stochastic process; that is, the mean of the random variable
Yt should not change over time. As pointed out above, most of the economic
time series do have a trend. In this context it is useful to know that a bandpass
filter which excludes components with zero frequency, that is, infinite periodicity, also removes any linear and quadratic trend from a time series (Baxter
and King 1995).21 Thus a bandpass filter that isolates the business cycle and
irregular components also eliminates linear and quadratic trends.

21 It

also removes any components that are integrated of order one or two.

68

Federal Reserve Bank of Richmond Economic Quarterly

Figure A2 AR(1) Stochastic Process and its Cyclical Components

a. Trend Component
0.20
Low Frequency

0.10
0

Simulated AR(1)

-0.10
-0.20

0

5

10

15

20

25

30

35

25

30

35

25

30

35

b. Business Cycle Component
0.10
Medium Frequency

0.05
0
-0.05
-0.10

0

5

10

15

20

c. Irregular Component
0.04
High Frequency

0.02
0
-0.02

0

5

10

15

20

+

APPENDIX B: THE DATA
The data used in this article are taken from DRI U.S. Central Database. For
the study of aggregate inventory investment, I use quarterly data from 1960:1
to 1995:4 on GDP and the change in business inventories. Both series are

A. Hornstein: Inventory Investment and the Business Cycle

69

in billions of chained (1992) dollars, seasonally adjusted. For the study of
disaggregated inventory investment, I use monthly data from January 1960 to
December 1996 for manufacturing and trade sales and inventories. All series
are billions of chained (1992) dollars, seasonally adjusted. Inventories are end
of period.
Production is defined as sales plus inventory investment. For the manufacturing sector I follow Blinder and Maccini (1991) and consider two definitions
of output. For the narrow definition of output, I use only inventory investment
in finished goods, and for the broad definition of output, I include inventory
investment in goods-in-process as well.
The quantity index for a variable is usually obtained by deflating the nominal values with a price index. The quantity indexes for sales and inventories are
not directly comparable because they are measured in different units. In particular, nominal sales are deflated with a “market” price index, while inventories
are deflated with a “cost” price index. Since production in a sector is defined as
the sum of sales and inventory investment, either inventories or sales have to be
adjusted. For constant dollar quantity indexes, West (1983) suggests rescaling
the inventory series using the base-period ratio of (business receipts)/(costs of
goods sold) from corporate income tax returns. I follow West even though his
procedure is not quite appropriate for my data set: I use a chain-type quantity
index rather than the constant dollar quantity index that West uses. It does not
appear as if my decision to follow West significantly affects the results. Since
the scale factor is constant, the effects of a particular choice for the scale factor
are limited to the properties of production relative to other variables. However,
here I get similar results as Blinder and Maccini (1991).
For the study of the relative prices of retail goods to producer goods, I use
monthly data from January 1967 to December 1996 for retail sales, implicit
price deflators for retail sales, and the producer price index. All series are
seasonally adjusted; retail sales are in billions of chained (1992) dollars. The
commodity categories for retail data and producer price data are not the same,
and I follow Blinder (1981) in the way the categories are linked:

Commodity

Retail Sales/Prices

Producer Price Index

Durable goods
Cars
Furniture

Total durable goods
Automotive dealers
Furniture and audio
video group
Building materials group

Durable goods
Passenger cars
Furniture and household
durables
Lumber and wood products

Total nondurable goods
Food group
Apparel group
Other nondurable goods

Consumer nondurables
(less food)
Processed foods and feeds
Textile products and apparel
Consumer nondurables
(less food)

Building materials
Nondurable goods
Food
Apparel
Other nondurable goods

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Federal Reserve Bank of Richmond Economic Quarterly

The business cycle (irregular) component of a time series xt is calculated as
follows. Because production, sales, and inventory stocks are characterized by
geometric growth, that is, a log-linear trend, I start out with the log transformation of the variables. First, we extract the business cycle (irregular) component
ln xt from the log of the time series, then we define the business cycle (irreg˜
˜
ular) component as xt = xt − exp(ln xt − ln xt ). For inventory investment the
ˆ
business cycle (irregular) component is defined as the first difference of the
corresponding component of inventory stocks.

REFERENCES
Baxter, Marianne, and Robert G. King. “Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series,” Working Paper 5022.
Cambridge, Mass.: National Bureau of Economic Research, February
1995.
Benhabib, Jess, and Roger E. A. Farmer. “Indeterminacy and Sunspots in
Macroeconomics,” in Handbook of Macroeconomics. North Holland,
forthcoming.
Blinder, Alan S. “Retail Inventory Behavior and Business Fluctuations,”
Brookings Papers on Economic Activity, 2:1981, pp. 443–505.
, and Louis J. Maccini. “Taking Stock: A Critical Assessment of
Recent Research on Inventories,” Journal of Economic Perspectives, vol.
5 (Winter 1991), pp. 73–96.
Burns, Arthur F., and Wesley C. Mitchell. Measuring Business Cycles. New
York: National Bureau of Economic Research, 1946.
Conference Board. “Benchmark Revisions in the Composite Indexes,” Business
Cycle Indicators, vol. 2 (December 1997), pp. 3–4.
Durlauf, Stephen N., and Louis J. Maccini. ”Measuring Noise in Inventory
Models,” Journal of Monetary Economics, vol. 36 (January 1995), pp.
65–89.
Fisher, Jonas D. M., and Andreas Hornstein. “(S, s) Inventory Policies in
General Equilibrium,” Federal Reserve Bank of Richmond Working Paper
97–7. May 1997.
Fitzgerald, Terry J. “Inventories and the Business Cycle: An Overview,”
Federal Reserve Bank of Cleveland Economic Review, vol. 33 (Third
Quarter 1997), pp. 11–22.
Hamilton, James D. Time Series Analysis. Princeton, N.J.: Princeton University
Press, 1994.

A. Hornstein: Inventory Investment and the Business Cycle

71

Harvey, Andrew C. Time Series Models, 2d edition. Cambridge, Mass.: MIT
Press, 1993.
Hornstein, Andreas, and Jack Praschnik. “Intermediate Inputs and Sectoral
Comovement in the Business Cycle,” Journal of Monetary Economics,
vol. 40 (December 1997), pp. 573–95.
Lucas, Robert E. “Understanding Business Cycles,” Carnegie-Rochester
Conference Series on Public Policy, vol. 5 (1977), pp. 7–29, reprinted in
Robert E. Lucas, Studies in Business Cycle Theory. Cambridge, Mass.:
MIT Press, 1989, pp. 215–39.
Metzler, Lloyd A. “The Nature and Stability of Inventory Cycles,” Review
of Economics and Statistics, vol. 23 (Third Quarter 1941), pp. 113–29,
reprinted in Robert A. Gordon and Lawrence R. Klein, eds., Readings in
Business Cycles. Homewood, Ill.: Irwin, 1965.
West, Kenneth D. “A Note on the Econometric Use of Constant Dollar
Inventory Series,” Economic Letters, vol. 13 (Fourth Quarter 1983), pp.
337–41.

New Evidence Connecting
Exchange Rates to
Business Cycles
Alan C. Stockman

V

irtually every theoretical model of exchange rates predicts that the real
exchange rate between two countries (with floating nominal exchange
rates) is correlated with the ratio of business-cycle conditions in the
two countries. Yet almost no empirical evidence exists to support this prediction
of the models. In fact, there is little empirical evidence that ties real exchange
rates to any underlying economic conditions. Some well-known studies have
concluded that exchange rates appear to have “a life of their own,” perhaps
moving with speculators’ expectations far more than with changes in economic
fundamentals. (See Flood and Rose [1995] for a prominent example.)
Contrary to this widely held contention, this article presents new evidence
that exchange rates are connected with fundamentals, in particular with the
relative gross domestic product (GDP) of each of the two countries involved,
as predicted by nearly all exchange-rate theories. Moreover, they are related in
the direction predicted by standard models: a country’s currency tends to be
depreciated in real terms when that country’s real GDP is relatively high, and
vice versa.
Why have previous studies not found this relationship between real exchange rates and ratios of real GDP? The answer is that the relationship is hard
to detect with simple linear models, because it appears to be nonlinear and
conditional on persistent movements (rather than purely transitory movements)
in the data. Recent theoretical and empirical work has pointed to the potential
The author is the Marie C. and Joseph C. Wilson Professor of Economics, Chair of the
Department of Economics at the University of Rochester, and a Research Associate with the
National Bureau of Economic Research. The author thanks Mike Dotsey, Marvin Goodfriend,
Tom Humphrey, and Wenli Li for comments that significantly improved the article. The views
expressed are those of the author and do not necessarily reflect those of the Federal Reserve
Bank of Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 84/2 Spring 1998

73

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Federal Reserve Bank of Richmond Economic Quarterly

importance of nonlinearities in exchange-rate data and has pointed the way to
the evidence reported here.

1.

WHAT THEORETICAL MODELS SAY

A common feature of nearly all models of exchange rates is the prediction that
the real exchange rate between two countries is correlated with the real-GDP ratio between them.1 Define the real exchange rate as the exchange-rate-adjusted
ratio of price levels: if the nominal exchange rate e is the price of foreign money
(in units of home money) and if P and P∗ are the home and foreign price levels,
then the real exchange rate is q ≡ eP∗ /P. The real exchange rate measures the
relative price of a basket of foreign goods in terms of a basket of home goods.2
An increase in q means “real depreciation” of home currency (a decrease in
the relative price of home goods); a decrease in q means “real appreciation”
of home currency (an increase in the relative price of home goods). Define the
output ratio y as home real GDP divided by foreign real GDP. Most theoretical
models of exchange rates predict a positive relationship between y and q.
The economic reasoning behind this prediction is not difficult, though its
details differ depending on the model. First, consider an equilibrium model
of exchange rates as outlined in Stockman (1987). The real exchange rate in
that model, as in other equilibrium models3 and some sticky-price models,4
equals the marginal rate of substitution (MRS) in consumption between home
and foreign goods. Consider a model with two countries and two goods, one
produced exclusively in each country. A representative consumer in the home
country has the utility function U(x, y), where x and y represent consumption of
home and foreign goods by consumers in the home country. A representative
consumer in the foreign country has the utility function U∗ (x∗ , y∗ ), where x∗ and
y∗ represent consumption of home and foreign goods by foreign consumers.
Regardless of many other details of a model like this, an equilibrium will
usually entail a condition that says
MRS(x, y) = MRS∗ (x∗ , y∗ ) = 1/q,

(1)

MRS(x, y) = UX (x, y)/UY (x, y)

(2a)

where

1 Some models, such as in Stockman and Tesar (1995), do not necessarily make this prediction because they postulate demand shocks with flexible prices.
2 The baskets of goods are the baskets used to measure the price indexes P and P∗ .
3 See, for example, Stockman (1980, 1987), Lucas (1982), and Svensson (1985).
4 See, for example, Obstfeld and Rogoff (1995) and Kollmann (1997). The equilibrium
differs in other models, such as in Chari, Kehoe, and McGrattan (1998).

A. C. Stockman: Exchange Rates to Business Cycles

75

and
∗
∗
MRS∗ (x∗ , y∗ ) = UX (x∗ , y∗ )/UY (x∗ , y∗ )

(2b)

are the equilibrium marginal rates of substitution between home and foreign
goods, X and Y, for the home and foreign consumers. The difference between
the operations of most models with flexible or sticky prices lies in the behavior of the consumptions, x and y, inside the MRS function. Short-run price
stickiness affects consumption, so it affects the real exchange rate q.
First consider a model with flexible prices and suppose that production
of the home good, X, rises exogenously, holding fixed the production of the
foreign good, Y. This rise in the supply of the home good typically reduces its
equilibrium relative price; i.e., it typically depreciates the home real exchange
rate (it raises q). Therefore a rise in the ratio of home-country output to foreigncountry output is associated with home-currency real depreciation.
A simple example occurs when the utility functions are the same in both
countries and the elasticity of substitution between home and foreign goods is
unity. Then a 10 percent increase in production of X reduces its relative price
by 10 percent in equilibrium, and consumers in each country increase their
consumption of X by 10 percent and leave their consumption of Y unchanged.5
With any standard utility function, an increase in x, holding y fixed, reduces
MRS(x, y) and thereby causes home real depreciation (a rise in q).6 This discussion has assumed that home output rises exogenously with no change in foreign
output. However, the same reasoning and results apply when home and foreign
5 This occurs regardless of the asset market structure of the model—the result holds with
complete asset markets or no asset markets at all. See Stockman (1987) and Cole and Obstfeld
(1991). More generally, whether the increase in supply of X raises or reduces home consumption
of the foreign good Y depends on details of the model. For example, if the elasticity of substitution
between the two goods is very low, then the demand for X may be very inelastic, and a 10 percent
increase in the supply of X may reduce its price so much that home consumers reduce consumption
of Y.
6 The implication in this example that home output rises relative to foreign output may
appear to depend on the use of different units of measurement for the two outputs—with home
output measured in units of the home good X and foreign output measured in units of the foreign
good Y. However, the model continues to predict a positive relationship between the output ratio
and the real exchange rate if both outputs are expressed in common units, as long as the elasticity
of substitution between the goods is less than unity (so that demands for the goods are elastic).
For example, suppose both are measured in units of the home good X. The value of foreign
output, measured in units of the home good X, is qys , where ys denotes foreign output of good
Y. Letting xs denote home output of good X, the ratio of home-to-foreign output, expressed in
common units, is xs /qys . With unit-elastic demands, this ratio stays constant as xs and q move
together. When demands are less than unit-elastic, this ratio rises and falls together with xs and
q. So units of measurement of the output ratio become an important issue only if demands are
elastic. This article uses national GDP data with each country’s real GDP expressed in units of
its own production bundle to calculate the output ratio y, so this measurement issue does not
apply. However, the measurement issue would become important if a similar analysis calculated
the output ratio with an exchange-rate-adjusted ratio of nominal GDP series.

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Federal Reserve Bank of Richmond Economic Quarterly

output move together (as in the data) with output in one country exogenously
rising more than output in the other country.7
Not surprisingly, the model’s implication for comovements of the output
ratio and the real exchange rate is reversed for exogenous changes in demand.
After all, changes in supply generate negative comovements of the output of
a good and its price; changes in demand generate positive comovements. For
various reasons, most models of exchange rates of the type discussed above
have relied on productivity shocks rather than demand shocks to drive the
model.8 This reliance results partly from the relative success of real businesscycle models driven by technology shocks and partly from the difficult task
of identifying demand shocks in the data. (Fiscal policy changes appear to be
much too small and infrequent in the data to explain either business cycles
or exchange-rate changes; taste shocks are inherently unobservable, though
potentially measurable through their effects on the economy.)
Despite the small role of demand shocks in flexible-price models, they have
played the key role in another class of models—those with sluggish nominal
price adjustment. These models predict, even with demand shocks, that output
ratios and real exchange rates are positively correlated—a rise in home output
relative to foreign output (a rise in y) occurs together with real depreciation of
home currency (a rise in q). Again, the basic economic reasoning is straightforward and robust to many perturbations of details in the models.
When prices are sticky in the short run, a vast array of business-cycle
models generates the prediction that an increase in aggregate demand raises
real output in the short run. Corresponding models of open economies also
predict short-run home-currency depreciation (the nominal exchange rate, e,
rises), which translates into real depreciation (an increase in q) because of
sticky prices. Together, these two results imply that aggregate demand shocks
create a positive relationship between the output ratio y and real exchange
rate q.
Despite differences in detail across sticky-price models, the reasons for
their exchange-rate predictions share a common feature: in each model, the
exchange rate is determined through an uncovered-interest-parity condition.
7 This basic logic is not sufficient to generate an unambiguous prediction for the balance of
trade or the current account of the balance of payments, as Stockman (1990) explains. To see
why, imagine first that the increase in home production is temporary and that nothing that people
do can make it permanent. In that case, people in the home country will typically want to save
a large fraction of this temporary increase in income, and they will save by lending to (investing
in) people in foreign countries. This international lending creates a surplus in the balance of trade
and the current account. Now suppose instead that the increase in home production can be made
permanent (or at least longer lasting) through investment to expand the economy’s capital stock.
In this case, investment demand rises and the equilibrium increase in investment (in the short
run) may exceed the equilibrium increase in production; if so, the economy runs a deficit in its
trade balance and current account.
8 See Stockman and Tesar (1995) for a counterexample.

A. C. Stockman: Exchange Rates to Business Cycles

77

Uncovered interest parity says that the expected rate of change of the nominal
exchange rate equals the difference in nominal interest rates across countries.
This condition derives from two components: (1) the arbitrage condition of
covered interest parity, which states that the forward exchange rate relative to
the spot exchange rate equals the difference in interest rates (and which is well
substantiated in the data), and (2) the hypothesis that the forward exchange rate
equals the expected future spot exchange rate. The second component, unlike
the first, appears to be falsified in the data for reasons that economists do not
yet understand.9 Its falsification does not necessarily invalidate theories that
use it as a component (any more than quantum effects invalidate Newtonian
physics) because the violations (which appear to be either time-varying risk
premia or systematic forecast errors) could be small enough that they do not
materially affect the theory.
The common reasoning in these models states that the increase in aggregate
demand (perhaps resulting from a monetary shock) depreciates the expected future nominal exchange rate. Given the difference in nominal interest rates across
countries, uncovered interest parity then requires a corresponding depreciation
of the current nominal exchange rate. In some models, such as in Obstfeld
and Rogoff (1995), the shock to aggregate demand does not affect the interest
differential, so the current nominal exchange rate immediately depreciates to
its expected long-run level.10 In other models, such as in Dornbusch (1976) or
Chari, Kehoe, and McGrattan (1998), the shock to aggregate demand reduces
the home nominal interest rate relative to the foreign rate, requiring a shortrun depreciation in excess of the long-run depreciation. In both cases, nominal
depreciation implies real depreciation (a rise in q) in the short run because of
sticky prices.11 As a result, the models imply a positive correlation between
the output ratio y and real exchange rate q.12

9 With exchange rates expressed in logarithms, arbitrage would make this second component true in a world without uncertainty. Froot and Thaler (1990) discuss the puzzle of empirical
falsification of this component.
10 In the Obstfeld-Rogoff model, for example, the short-run response of the output ratio is
proportional to the short-run response of the nominal and real exchange rates, with the factor
of proportionality determined by the elasticity of substitution in consumption between various
goods.
11 Even a model in which the nominal interest rate rises in the short run (because the
expected-inflation effect of a monetary shock exceeds the fall in the real interest rate) would
predict currency depreciation if the increase in the home nominal interest rate were smaller than
the percentage increase in the long-run exchange rate.
12 For reasons similar to those explained in footnote 7, these models do not make unambiguous, robust predictions about the response of the trade balance or current account, or about
comovements between these and other variables.

78

2.

Federal Reserve Bank of Richmond Economic Quarterly

EMPIRICAL METHODS AND RESULTS

Data for the models consist of quarterly observations on exchange rates and
real GDP for Australia, Canada, France, Italy, Japan, the Netherlands, Spain,
Switzerland, the United Kingdom, and the United States, generally over the
period 1974:1 through 1996:4. These countries appear in the sample as representative of developed economies with some heterogeneity in geography and
circumstances, yet with consistent and reliable data. Germany is notable for
its absence in the sample. Its exclusion is due to data issues associated with
unification, which could play a particularly important role with our short sample
of less than 25 years per country.
Define the nominal exchange rate eab as the domestic price in country a of
the (foreign) currency of country b, and qab as the (natural) logarithm of the
relative price of country b’s goods in terms of country a’s goods:
qab = ln

eab pb
.
pa

An increase in qab indicates “real depreciation” of currency a and “real appreciation” of currency b. Define yab as the (natural) logarithm of the ratio of
output in country a relative to country b:
yab = ln

GDPa
,
GDPb

where GDPa indicates real GDP in country a.
As noted above, standard models with sticky prices, such as in Dornbusch
(1976) and its variants, including Obstfeld and Rogoff (1995) and Chari, Kehoe, and McGrattan (1998), imply a positive relationship between qab and yab .
Specifically, a monetary expansion in country a raises yab (above its long-run
equilibrium value) and raises qab (that is, it causes real depreciation of currency
a).
Simple correlations are not consistent with this prediction. For example,
simple correlations between qab and yab appear in Table 1, with the United
States as the comparison country for each exchange rate. They are negative
in seven out of eight cases. Only the correlation for Switzerland takes the
predicted positive sign, and that correlation is smaller than the absolute values
of four of the seven negative correlations.
While most empirical economic research involves linear methods, recent
empirical and theoretical work motivates an alternative nonlinear approach to
the data. Recent empirical papers present evidence of nonlinearities in univariate time-series models of exchange rates.13 These papers examine nonlinear
models of exchange rate adjustment toward purchasing-power-parity levels
13 See

O’Connell (1997); O’Connell and Wei (1997); Michael, Nobay, and Peel (1997);
Obstfeld and Taylor (1997); and Taylor and Peel (1997).

A. C. Stockman: Exchange Rates to Business Cycles

79

Table 1 Simple Correlations
Italy
Japan
U.K.
France
Switzerland
Spain
Netherlands
Australia

−0.48
−0.62
−0.23
−0.49
0.38
−0.15
−0.80
−0.17

when adjustment takes place only or mainly outside a band around the long-run
level of the exchange rate or when adjustment is simply more rapid because exchange rates begin farther from their long-run levels. Recent evidence strongly
indicates nonlinearities in exchange-rate behavior, with faster mean reversion in
exchange rates when they begin far from purchasing-power-parity levels. This
result means that the half-life of real exchange rates (the time it takes them to
return to their long-run levels following a one-time shock) is apparently lower
than previous research had indicated. Whether the half-life is small enough for
consistency with theoretical models remains unknown.14
Similarly, recent theoretical work suggests reasons for weaker adjustment
of exchange rates toward purchasing power parity when the economy is close
to its long-run equilibrium. Uppal and Sercu (1996) have explored a simple
model of international arbitrage costs in product markets that implies little or
no adjustment of real exchange rates toward long-run levels when the economy is close to long-run equilibrium. Proportional arbitrage costs create a
no-arbitrage band around a long-run equilibrium, in which the real exchange
rate can vary without tendency to return to a mean.15 Outside that band,
14 The theoretical models discussed above use the same shocks to generate business cycles
and changes in real exchange rates, so they predict not only correlations between the two but
similar half-lives of real exchange rates and output ratios. More research is required to test this
prediction of the models.
15 In a simple version of this model, countries are autarkic within the no-arbitrage band
and the real exchange rate is indeterminate within the limits of that band. Consider a simple
static model with a single homogeneous good randomly endowed and consumed in each of two
countries. Imagine that the countries are identical ex ante in every respect. Suppose there are
“iceberg” costs associated with shipping a good from one country to the other—when one unit
of a good is exported by either country, only k < 1 goods arrive in the other country. (This
situation resembles the commodity points discussed by Heckscher (1916) in analogy to the gold
points of the classical gold standard, or zones of inaction in models of irreversible investment,
or s-S inventory models.) Consider the equilibrium of such a model with complete markets in
which consumers trade in asset markets prior to knowing the levels of random endowments. The
equilibrium involves a no-arbitrage band—if endowments are sufficiently similar, then people
consume their endowments, while if endowments are sufficiently dissimilar, then people with high
endowments ship some of their goods to people with low endowments. Because of the “iceberg”
costs of shipping, consumers choose not to trade on asset markets and not to equate consumption

80

Federal Reserve Bank of Richmond Economic Quarterly

arbitrage opportunities lead the real exchange rate back toward the band. This
arbitrage-cost framework provides a loose interpretation of the recent empirical work mentioned above.16 Ohanian and Stockman (1997) have extended the
model developed by Uppal and his coauthors to a dynamic context.17 While
their model is directed at a different issue (explaining commonly suggested
connections between exchange rates and international portfolio adjustments),
it also implies that factors generating international portfolio adjustments inside
the no-arbitrage band could mask connections between real exchange rates and
other variables. As a result, connections between the real exchange rate and
other variables, such as the output ratio, may be stronger outside that band.
More generally, the signal-to-noise ratio may be larger when shocks are larger
and drive either the output ratio or real exchange rate farther from its long-run
equilibrium; we exploit this idea empirically below.
A key issue in analyzing exchange-rate data involves the choice of whether
and how to filter those data. The correlations in Table 1 would be meaningless
if either qab or yab were nonstationary. Unfortunately, standard statistical tests
are unable to distinguish between the two main alternative hypotheses about
these data: that they are trend-stationary or that they contain unit roots. This
inability to distinguish the form of the trend in these data is not unique to this
article—it plagues almost all analyses of real exchange-rate data and, indeed,
macroeconomic analysis more generally. The hypothesis of trend-stationarity in
qab means that the probability distribution of qab is stationary after a deterministic time trend has been removed from qab . The alternative hypothesis of a unit
root in qab means that qab has a random trend, in the sense that the probability
distribution of changes in qab is stationary. The same applies to trends in yab .
One can investigate these trends by testing for the presence of a unit root in a
standard unit-root test, such as the augmented Dickey-Fuller test. The results of
unit-root tests for qab or yab are available from the author; however, they share
a common characteristic with many unit-root tests in macroeconomic data in
that they yield ambiguous results.
in the two countries. While a modified version of purchasing power parity holds outside the band,
within the band, nominal and real exchange rates are indeterminate. With sticky prices or real
costs of arbitrage outside the band, the real exchange rate can deviate from the band with only a
slow tendency to return in the long run. It is this idea that forms the basis for the recent empirical
studies of nonlinearities in exchange-rate behavior.
This simple model leaves many questions open. What are the arbitrage costs? How large are
they? Evidence indicates that they are connected not only with distance but national borders—see
Engel and Rogers (1996)—without providing reasons for this connection. These questions pose
challenges for future research.
16 The interpretation is loose for several reasons. One reason is that most recent empirical
work uses linearly detrended (real or nominal) exchange-rate data. While changes in equilibrium
relative prices may create such trends, the statistical models do not take into account the effects of
this trend on the rate at which arbitrage would push the exchange rate back toward the (moving)
band.
17 See Uppal (1993); Uppal, Sercu, and Van Hulle (1995); and Uppal and Sercu (1996).

A. C. Stockman: Exchange Rates to Business Cycles

81

Unit-root tests have many well-known problems. One serious problem is
that these tests have low power to reject unit roots (correctly, when the data
in fact do not have unit roots) in short samples like those available for the
current analysis, particularly when the true root is close to unity. For example,
the power to reject a unit root is low in a short sample when a series follows
a first-order autoregressive process, yt = αyt−1 + ut , where −1 < α < 1, but
the root α is 0.95 or some other number close to 1. The power of these tests
to reject unit roots correctly is also low when the data follow a more complicated (but stationary) time-series process, like the nonlinear processes studied
in the papers mentioned in footnote 13. For example, Taylor and Peel (1997)
show that nonlinear mean reversion can create a high probability of failing to
reject unit roots when using standard methods, even when the data are actually
stationary. For these reasons, this article follows most other research on real
exchange rates by treating real exchange rates q as trend-stationary. For similar
reasons, we also treat real-GDP ratios y as trend-stationary. This assumption
makes results in this article more easily comparable with the bulk of other
empirical work in the area.18
We begin with an examination of whether the detrended series, DTq and
DTy, is more strongly related when one of the series is large (in absolute value)
relative to its mean. Table 2 shows conditional correlations between detrended
GDP ratios (DTy) and detrended real exchange rates (DTq) when the absolute
value of the detrended real exchange rate is large. The first column of statistics
shows unconditional correlations; the second column shows the correlations
that are conditional on the absolute value of DTq > 0.1 (which means that the
detrended real exchange rate is at least 10 percent above or below its mean). The
interpretation of this table requires an economic model. One might think about
an arbitrage model with a no-arbitrage band of unknown size and interpret the
table as capturing situations in which the exchange rate is outside that arbitrage
band. Alternatively, one might think that many factors other than business-cycle
conditions affect the relationship between exchange rates and output ratios in
normal times and that when the exchange rate is close to its mean, this “noise”
makes it difficult to detect a consistent relationship. Under this interpretation,
larger deviations of exchange rates from their means may indicate times when
the “signal-to-noise” ratio is larger, allowing economists potentially to observe
the relationships predicted by the theories outlined earlier.

18 The usual assumption that the real exchange rate is trend-stationary, adopted here, implies
a failure of long-run absolute purchasing power parity (though not relative purchasing power
parity). The underlying assumption is that something—like differences in productivity growth
causing differences in the trend relative price of nontraded goods, which are part of the bundles
of goods included in the real exchange rate measure—cause the equilibrium real exchange rate
to show a trend. The data clearly support the presence of some trend, whether stochastic or (as
here) deterministic and linear.

82

Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Correlations between Detrended Exchange Rates and
GDP Ratios Conditional on Size of Exchange Rates

Country Pair
U.K., Japan
France, Japan
Italy, Japan
Switzerland, Japan
Australia, Japan
Netherlands, Japan
Spain, Japan
Canada, Japan
U.K., U.S.
France, U.S.
Italy, U.S.
Switzerland, U.S.
Australia, U.S.
Netherlands, U.S.
Spain, U.S.
Japan, U.S.

Unconditional
0.66
−0.21
0.15
0.08
0.18
−0.32
−0.03
0.41
−0.12
−0.21
0.01
0.16
−0.23
−0.47
−0.50
0.46

ABS(DTq)
> 0.1
0.78
−0.31
0.14
0.17
0.29
−0.45
0.05
0.50
−0.27
−0.69
0.01
0.27
−0.59
−0.64
−0.57
0.62

ABS(DTq)
> 0.15
0.79
−0.01
0.24
0.20
NA
NA
0.25
0.46
−0.42
NA
−0.15
0.38
0.21
−0.63
NA
0.68

ABS(DTq)
> 0.2
0.79
−0.02
0.34
NA
NA
NA
NA
NA
NA
NA
NA
0.63
0.26
NA
NA
0.69

NA = Not available due to insufficient number of observations.

Table 2 examines the connection between output ratios and real exchange
rates when the latter are far from their detrended means, measured as when the
absolute value of the detrended log real exchange rate—ABS(DTq)—exceeds
0.1, 0.15, or 0.2. The results show, at best, a very weak connection between
output ratios and exchange rates even when exchange rates are far from their
means. Half (eight of 16) of the unconditional simple correlations are positive;
only nine of 16 are positive when the absolute value of the detrended exchange
rate exceeds its mean by 10 percent or more.
Table 3 is analogous to Table 2 in that it shows conditional correlations
between detrended GDP ratios (DTy) and detrended real exchange rates (DTq).
While Table 2 conditions on a large real exchange rate, Table 3 conditions
on a large absolute value of the detrended output ratio. Again, one might use
the arbitrage model to interpret this table as capturing situations in which the
economy is outside the arbitrage band. Alternatively, one might think of large
output ratios as indicating times when the signal-to-noise ratio is large enough
that we could find evidence of the comovements predicted by the theories
outlined above.
Like the results of Table 2, those in Table 3 fail to show any strong connection between output ratios and exchange rates even when output ratios are far
from their means. The first column of statistics shows unconditional correlations
between real exchange rates and output ratios; the second column shows the

A. C. Stockman: Exchange Rates to Business Cycles

83

Table 3 Correlations between Detrended Exchange Rates and
GDP Ratios Conditional on Size of GDP Ratios

Country Pair
U.K., Japan
France, Japan
Italy, Japan
Switzerland, Japan
Australia, Japan
Netherlands, Japan
Spain, Japan
Canada, Japan
U.K., U.S.
France, U.S.
Italy, U.S.
Switzerland, U.S.
Australia, U.S.
Netherlands, U.S.
Spain, U.S.
Japan, U.S.

Unconditional
0.63
−0.19
0.23
0.10
0.18
−0.32
−0.03
0.54
−0.12
−0.21
0.03
0.15
−0.23
−0.47
−0.50
0.46

ABS(DTy)
> 0.01
0.67
−0.22
0.28
0.08
0.25
−0.34
−0.03
0.59
−0.14
−0.23
0.02
0.15
−0.28
−0.52
−0.55
0.63

ABS(DTy)
> 0.02
0.73
−0.32
0.23
0.18
0.34
−0.32
−0.06
0.75
−0.20
−0.22
0.10
0.18
−0.27
−0.53
−0.57
0.66

ABS(DTy)
> 0.03
0.78
−0.29
0.22
0.36
0.33
−0.38
−0.13
0.81
−0.10
−0.25
0.25
0.40
−0.11
−0.47
−0.64
0.66

correlations conditional on the absolute value of DTy > 0.01 (which means
that the detrended output ratio is at least 1 percent above or below its mean).
Other columns show the results for larger values of output ratios. Evidently,
the correlation is not much different when the real exchange rate is far from
its mean (as in the last three columns of Table 2) or when the output ratio is
far from its mean (as in the last three columns of Table 3) than when both are
close to their means.
Tables 2 and 3 address the issue of large versus small values of detrended
real exchange rates and output ratios but not issues of transitory versus more
persistent changes in these variables. Business cycles refer to changes in real
GDP that are sustained over at least several quarters. One might expect a
stronger relationship between exchange rates and real GDP over business cycles and longer periods than over short periods, which may see many unrelated,
transitory changes in output ratios and exchange rates.
We now turn to the connection between real exchange rates and output
ratios when changes in either are sustained for several quarters. Table 4 shows
that the results change substantially when we condition in a different way
to capture business cycles. Although the table focuses on Japan as the base
country, similar results appear when the United States is the base country. Column 1 shows the percentage of positive observations of a country’s detrended
real exchange rate over the entire sample. The numbers are all close to onehalf. Column 2 shows the percentage of positive observations of a country’s

84

Federal Reserve Bank of Richmond Economic Quarterly

Table 4 Percentage of Positive Detrended Real Exchange Rates
When Detrended GDP Ratios are Positive
1

Country Pair
U.K., Japan
Canada, Japan
Switzerland, Japan
U.S., Japan
France, Japan
Netherlands, Japan
Italy, Japan
Spain, Japan
Australia, Japan

2
3
4
5
6
Percent of Positive Observations
Marginal
if
if
if
probability
in whole
if
sample DTy > 0 DTy > 0 DTy > 0 DTy > 0 level for
for two for four for six
column 5
quarters quarters quarters
52
46
53
54
54
52
52
52
45

82
66
68
70
51
52
56
49
47

87
73
75
77
54
50
58
50
48

91
74
73
81
56
50
55
51
38

89
75
88
72
64
65
58
45
52

10−6
0.002
0.002
0.02
0.18
0.26
0.54
0.73
1

detrended real exchange rate conditional upon its detrended GDP ratio being
positive in the same quarter. In six of nine cases, the percentage of positive
observations of the detrended exchange rate is larger than in the entire sample
(column 1). Columns 3 through 5 show the same information conditional upon
detrended GDP ratios being positive for the next two, four, or six consecutive
quarters. The percentage of positive detrended exchange rates is generally larger
when we condition on positive GDP ratios. This result occurs in eight out of
nine cases in column 5, and in most cases the percentage is quite high. Column
6 shows the marginal probability level for rejecting the null hypothesis that
the numbers in column 5 arise purely by chance (such as when one draws
them randomly from a binomial distribution). This “sign test” (treating positive and negative observations as binomial draws) assumes that the underlying
distribution is symmetric, which appears to be roughly true in these data. (The
fact that the numbers in the first column are close to one-half is consistent
with this assumption). In four of the nine cases (the United Kingdom, Canada,
Switzerland, and the United States), we can strongly reject the null hypothesis
that the connection between detrended real exchange rates and detrended GDP
ratios arises purely by chance. Even in the five cases in which we cannot reject
that null hypothesis, more than half of the observations are positive in four
of the five cases (France, the Netherlands, Italy, and Australia). For example,
column 5 shows that almost two-thirds of the observations are positive for both
France and the Netherlands.
One can achieve greater statistical power by pooling the data; however,
the probability distribution is exceedingly complicated when one allows for
dependence across country pairs. Overall, nearly two-thirds of the observations

A. C. Stockman: Exchange Rates to Business Cycles

85

Table 5 Percentage of Positive Detrended GDP Ratios
When Detrended Real Exchange Rates are Positive
1

Country Pair
U.K., Japan
Canada, Japan
U.S., Japan
Australia, Japan
Switzerland, Japan
France, Japan
Spain, Japan
Netherlands, Japan
Italy, Japan

2
3
4
5
6
Percent of Positive Observations
Marginal
if
if
if
probability
in whole
if
sample DTq > 0 DTq > 0 DTq > 0 DTq > 0 level for
for two for four
for six
column 5
quarters quarters quarters
42
38
45
53
59
52
48
52
41

70
60
63
58
65
48
41
43
50

72
63
72
57
67
51
45
42
53

77
71
78
59
63
53
48
43
52

77
75
72
65
68
62
54
42
47

0.01
0.01
0.04
0.11
0.14
0.38
0.84
0.65
1

on the detrended real exchange rate in column 5 of Table 4 are negative (with
264 observations in that column, the detrended exchange rate is negative in
183 instances and positive in 81 instances). The probability that this occurs
purely by chance would be only three hundred-millionths of 1 percent if data
on detrended GDP ratios and exchange rates in each row of the table were
independent. Of course, the fact that Japan is involved in each comparison
means that the data are probably dependent. However, even with dependence
across observations, the results in this table show strong evidence that when
a country’s detrended GDP rises for six straight quarters relative to Japan, its
currency tends to take a low value on foreign exchange markets (q is high).
Table 5 shows analogous calculations that are conditional upon sustained
depreciation of real exchange rates. Column 1 of Table 5 shows the percentage
of positive observations of a country’s detrended output ratio over the entire
sample. Column 2 shows the percentage of positive observations of a country’s
detrended output ratio conditional upon its detrended real exchange rate being
positive in the same quarter. Except in the Netherlands (and Spain for durations
shorter than six quarters), exchange rates show real depreciation significantly
more often when the GDP ratio is high for several quarters (than in the overall
sample). Unfortunately, the number of observations available for calculations in
column 6 is sufficiently low that we can strongly reject the null hypothesis that
this result arises purely by chance for only three of the nine cases in column
5—for the United Kingdom, Spain, and the United States.
Tables 4 and 5 examine groupings of observations in these data that are
conditional upon whether one of the variables exceeds its mean for some
duration. Table 6 extends this evidence by testing the null hypothesis that

86

Federal Reserve Bank of Richmond Economic Quarterly

Table 6 Test Results: Means of Detrended Exchange Rates Conditional
on Signs of Detrended GDP Ratios

Country Pair
U.K., Japan
Canada, Japan
U.S., Japan
Italy, Japan
Australia, U.S.
Switzerland, Japan
Spain, Japan
France, Japan
Netherlands, Japan

1
2
3
Mean detrended
Mean detrended
t-statistic for null
(log) exchange rate (log) exchange rate hypothesis that the
if detrended GDP
if detrended GDP means in columns
ratio exceeds
ratio is less than
1 and 2 are equal
its median
its median
0.08
0.07
0.05
0.01
0.03
0.01
0.00
−0.01
−0.01

−0.08
−0.07
−0.05
−0.05
−0.02
−0.00
0.00
0.01
0.03

−11.0
−9.0
−6.4
−4.3
−3.0
−0.6
1.1
2.3
4.3

the mean detrended exchange rate does not depend on whether the detrended
GDP ratio is above or below its median value. The large absolute values of
the t-statistics in column 3 of Table 6 indicate rejection of that null hypothesis.
In seven of nine cases, we can reject the hypothesis that the means of the real
exchange rates do not depend on the GDP ratio. In five of those seven cases
the direction of the difference in means is the direction predicted by standard
models. The exceptions are France and the Netherlands. In most cases, the
evidence in this table, as in Tables 4 and 5, clearly indicates that high GDP
ratios and depreciated real exchange rates tend to occur together in the data.
Because the results of Tables 4 and 5 indicate that the connection between
real exchange rates and GDP ratios is strongest when one of the series shows
sustained movement away from its mean, Table 7 adds duration to the test
shown in Table 6. Specifically, it repeats the test in Table 6 with the condition that the detrended GDP ratio is above or below its median value for six
straight quarters. In every case we can reject the hypothesis that the means do
not depend on the GDP ratio; in six of the nine cases, the connection is in
the direction predicted by standard models. Spain now joins France and the
Netherlands as exceptions. Table 7 provides even stronger evidence that high
GDP ratios and depreciated real exchange rates tend to occur together.
Together, Tables 4 through 7 provide the strongest evidence currently available that changes in real exchange rates are connected to changes in real-GDP
ratios over periods of several quarters, as predicted by nearly all existing models
of exchange rates.

A. C. Stockman: Exchange Rates to Business Cycles

87

Table 7 Test Results: Means of Detrended Exchange Rates Conditional
on Signs and Duration of Detrended GDP Ratios

Country Pair
U.K., Japan
Canada, Japan
U.S., Japan
Italy, Japan
Australia, U.S.
Switzerland, Japan
Spain, Japan
France, Japan
Netherlands, Japan

3.

1
2
3
Mean detrended
Mean detrended
t-statistic for null
(log) exchange rate (log) exchange rate hypothesis that the
if detrended GDP
if detrended GDP
means in columns
ratio exceeds its
ratio is less than its 1 and 2 are equal
median for six
median for six
straight quarters
straight quarters
0.11
0.10
0.06
0.02
0.04
0.06
−0.03
0.01
−0.01

−0.13
−0.10
−0.05
−0.11
−0.07
−0.02
0.02
0.03
0.04

−15.9
−12.3
−6.9
−9.4
−6.8
−8.3
2.9
2.3
5.1

CONCLUSIONS

The inability of economists to find strong statistical relationships between exchange rates and underlying economic conditions has been a huge puzzle in
international economics. In particular, standard models of both the sticky-price
and flexible-price varieties predict that real depreciations of a country’s currency tend to occur along with increases in its output relative to foreign output.
The findings reported here are probably the strongest evidence yet that this
relationship appears in the data. The same findings show that the relationship
is nonlinear and conditional. These empirical results raise a set of new questions
for future research, particularly regarding related nonlinear and conditional connections between exchange rates and other variables. It appears that exchange
rates, after all, do not have lives of their own.

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