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Selling Federal Reserve
Payment Services:
One Price Fits All?
John A. Weinberg

n a large modern economy, there is a vast and constant movement of funds
in the conduct of commerce and finance. The channels through which
these funds move constitute the payment system, which, ultimately, forms
a network connecting all participants in the economy. In dollar value, the bulk
of this movement is not in cash but in the form of instructions for the crediting
and debiting of accounts held with public or private financial institutions.1 As
a network for sending and receiving instructions, the payment system bears a
resemblance to transportation and, especially, communication systems. Accordingly, many of the issues and questions that arise in discussions of markets for
payment services have parallels in discussions of these other markets.
Markets that are characterized as networks are often thought to be driven
by the existence of economies of scale. In the presence of scale economies, the
average cost of providing services declines with the size of the network and the
volume of traffic it carries. The belief in such economies has motivated a long
history of direct government involvement and intervention in network markets,
from the operation of the postal service to the regulation of telecommunications
and transportation networks.
Much of the evolution of the structure of markets for payment services has
been driven by the desire of participants to take advantage of the economies
of network expansion. The most fundamental example is the replacement
of a system in which payments are made in currency directly between individuals to one in which payments are made through accounts with financial
intermediaries. Specifically, a check-based payment system opened the door to
This paper has benefited from the helpful comments of Bill Cullison, Jeffrey Lacker, Bruce
Summers, John Walter, and Tom Humphrey. The views expressed herein are the author’s and
do not represent the views of the Federal Reserve Bank of Richmond or the Federal Reserve
System.
1 For

a detailed description of the payment system, see Blommestein and Summers (1994).

Federal Reserve Bank of Richmond Economic Quarterly Volume 80/4 Fall 1994

Federal Reserve Bank of Richmond Economic Quarterly

network efficiencies to be gained through the centralized exchange of checks
among banks in clearinghouses.2 More recently, some payments have moved
from checks into electronic forms of transmission. For instance, the use of
Automated Clearinghouse (ACH) payments, for such purposes as payroll direct
deposit, tripled in the number of transactions processed annually (from around
800 million to around 2.4 billion) from 1986 to 1992.3
In addition to technological factors, the evolving market structure in the
payment system has been greatly influenced by the policy of the Federal
Reserve System. Prior to 1980, many payment services were provided free of
charge by the Federal Reserve to its member banks. As a result, a majority
of payments cleared through the Federal Reserve, either directly or through
correspondent banks. The Monetary Control Act of 1980, among its provisions, required Federal Reserve services to be made available, at a price, to all
institutions. The Reserve Banks were instructed to set prices to cover all direct
and indirect costs incurred in the provision of services. Since the institution of
pricing, the Reserve Banks have experienced losses in market share to private
providers. In check processing, for instance, renewed growth has occurred in
the activities of clearinghouses on local, regional and, most recently, national
levels. The resulting loss of market share by the Reserve Banks has been most
significant among larger institutions.4
In the provision of ACH services, the Fed’s position is somewhat more
dominant than in check services. The Federal Reserve processed about 94
percent of all transactions in 1992 (McAndrews 1994). Private alternatives
continue to develop, however. As in the case of check processing, new competition and the potential for institutions to engage in direct (nonintermediated)
exchanges are focused on large-volume ACH users.
In the changing payment services environment, there have been a number
of proposals for the restructuring of Fed pricing. Proposals for market-sensitive
pricing tend to suggest advantageous pricing terms to large-volume users of
services. Any such scheme amounts to some form of price discrimination.
This term is purely descriptive: it applies to any pricing other than the setting
of a single price per unit sold that is available to all buyers. The simplest
example, referred to as two-part pricing, involves charging all buyers the same
combination of a fixed fee and a per-unit price. When two-part pricing does
not “discriminate enough,” more complex schemes can be used. Examples include a per-unit price that varies with the quantity purchased and a schedule of
combinations of fixed and per-unit charges among which buyers can choose.
2 Goodfriend

(1990) discusses this change and how banks developed institutions for enhancing payments efficiency and dealing with the resulting credit risk.
3 McAndrews (1994) describes the growth in ACH payments.
4 The General Accounting Office (1989) found that between 1983 and 1987 the Federal
Reserve lost market share only among banks with over $750 million in assets.

J. A. Weinberg: Selling Federal Reserve Payment Services

Price discrimination in response to market competition raises some important questions about Federal Reserve pricing policy. For instance, are the
Reserve Banks’ “business interests” in conflict with their public policy responsibilities? Additional questions arise from the fact that price discrimination has
the tendency to favor some institutions, particularly larger institutions, over
others. Should the equal treatment of all banks be part of Fed pricing policy?
Of course, at the most basic level is the question of whether the Fed should
participate at all as a competitor with private providers of payment services.
This article argues that the public interest may be best served by a Federal
Reserve pricing policy that is responsive to competition, within certain limits.
This argument is based on the presumption that an important goal for Federal
Reserve policy is the resource efficiency of the payment system. An efficiency
perspective dictates that a loss of market share by the Federal Reserve is neither
good nor bad per se. What matters is the overall cost efficiency of the market.
If the Federal Reserve is replaced by providers with lower costs, then such a
change should be accommodated. The goal of pricing policy, however, should
be that only efficiency-enhancing losses are experienced.5
The central concept employed in this article is that of sustainable prices.6
Sustainable prices are prices designed to sustain an efficient allocation of production by giving no buyer an incentive to seek to obtain the product from
an alternative source. The following section briefly describes the organization
and pricing in the markets for check clearing and ACH services. These two
markets can be broadly characterized by a high volume of low-value transactions. As such, they make relatively intensive use of resources in transmitting
payment instructions and constitute large markets for transmission services.
The subsequent sections develop the notion of sustainable prices and use it to
draw conclusions about Fed pricing policy. In particular, sustainable pricing
can provide a guide for determining when market-sensitive pricing by the Fed
is and is not in the public interest.
It is important to note that resource efficiency is not the Federal Reserve’s
only public policy interest in the payment services market. Indeed, the Fed’s
primary concern is with the overall safety and reliability of the system. This
concern is expressed in the Fed’s regulatory oversight of arrangements used for
payment settlement. It is along the dimension of efficiency, however, that the
Fed’s role as a provider of many payment services should be evaluated. The
Fed’s participation should be determined by its ability to provide services in a
cost-effective manner.

5 While this article focuses on pricing, the terms of competition among alternative providers
are affected by a variety of other factors. For instance, in 1994 the Board of Governors adopted
a requirement of same-day settlement of checks presented by private collecting banks that put
private-sector processing on a more equal footing with Fed processing.
6 See Spulber (1989).

Federal Reserve Bank of Richmond Economic Quarterly

TWO PAYMENT SERVICES MARKETS IN BRIEF:
CHECKS AND ACH

The concept of sustainable prices, as developed below, applies to concentrated
markets.7 Hence, it is useful to establish at the outset that markets for payment
services tend to be fairly concentrated. In most of these markets, the Federal
Reserve has a significant market share, while in some markets, the Fed’s share
is dominant. A brief description of the structure of two markets follows.
In 1992, over 72 billion noncash payments were made in the United States.
Of these, 80 percent were made by check.8 Checks are written on more than
15,000 banks and other depository institutions. In about 30 percent of all transactions made with checks, the recipient deposits the payment in an account in
the bank on which the check is written. The clearing of these “on-us” items is a
simple matter; the bank merely debits the account of the payor and credits the
account of the payee (subject, of course, to the payor’s account having sufficient funds). The remaining 70 percent of check payments must clear between
banks. This clearing can proceed directly: a payee bank can send the check to
a payor bank in exchange for funds. Alternatively, check clearing can make
use of one or more of a number of intermediary services.9 One such service
is that provided by a clearinghouse. In a clearinghouse arrangement, a number
of institutions agree to exchange checks drawn on each other at a specified
place and time. Hence, a clearinghouse resembles multilateral direct exchange,
except in the way that payments are cleared. With each exchange of checks, a
clearinghouse member pays its net debit position or receives its net credit.
If a bank participates in a clearinghouse of any size or if it engages in
direct exchange with a large number of banks, it must have the capacity to sort
the checks it receives by payor bank. This task is performed by specialized
equipment, reader-sorter machines. If a bank chooses not to invest in sorting
capacity, it can, instead, send unsorted or incompletely sorted checks to an
intermediary institution that completes the collection process. Both the Federal
Reserve Banks and private collecting banks play this role. The collecting bank,
private or Fed, may sort and send checks to payor banks or to subsequent
collecting banks. For instance, a Federal Reserve office sends within-district
checks to payor banks and out-of-district items to their respective Fed offices. In
1992, the Fed handled over 19 billion checks, about half of all checks requiring
interbank clearing.
The resource costs in the check-collection process are dominated by two
cost categories: the sorting and transportation of checks. Direct, bilateral
7 For

a treatment of the wide variety of theories of behavior in concentrated markets, see
Tirole (1989).
8 The data cited in this section are from the Bank for International Settlements (1993).
9 The various paths for check clearing are reversed when a payor bank sends a “return item”
(a check returned because of insufficient funds).

J. A. Weinberg: Selling Federal Reserve Payment Services

exchange of checks is the most costly means of clearing since it requires
the payee bank to sort and ship to a large number of endpoints. Concentration
of both activities can lead to cost savings. A group of banks that regularly
receive checks drawn on each other can economize through a clearinghouse
arrangement. Hence, the typical clearinghouse is composed of relatively large
institutions within a metropolitan area. When an institution does not internalize
the economies of concentration, it can instead purchase sorting and transportation services from entities that can take advantage of the cost efficiencies
available.
The use of Automated Clearinghouse transactions is relatively new. In an
ACH payment, the payor (or the payee with preauthorization by the payor)
gives direct instructions to the payor’s bank for the transfer of funds. Modern
electronic information technology has made this means of transfer particularly
cost-effective for recurring payments of set value. Accordingly, a growing fraction of the work force has wage and salary payments directly deposited into
bank accounts by ACH. Other payments that might be made by ACH include
mortgage payments and insurance premiums.
As with checks, ACH payments must clear between banks when the payor
and the payee do not have accounts with the same institution. Clearing is
facilitated if the payor and payee bank share an electronic connection over
which instructions can be sent. Transactions can be made by direct bilateral
exchange, through a private clearinghouse, or through the Fed. The first two
options are likely to be used primarily by pairs or groups of banks that share a
large number of payments. That is, private ACH transactions have been carried
out primarily within geographic regions, while for interregional payments, the
Fed has been the dominant provider. This market structure may be subject
to change, however, as a private, national ACH initiative has recently begun
competing with the Fed. In 1992, 94 percent of approximately 1.8 billion ACH
transactions were made through the Fed.
Current pricing of Federal Reserve check and ACH services is a form of
two-part pricing, a combination of a fixed fee and a per-unit price. In check
services, the fixed charge is the cash letter charge. A cash letter is a collection
of checks deposited with the Fed. The cash letter charge and the per-item fee
vary with the amount of sorting that has already been done by the depositing
bank and with the locations of the banks on which the deposited checks are
drawn. The Federal Reserve Bank of Richmond’s price structure for 1994 includes cash letter charges between $2 and $3 for most checks, while per-item
fees range from less than 1¢ to 6¢.10 These different fee combinations apply to
varying amounts of sorting that may be necessary.

10 Larger

cash letter and per-item charges are assessed for some special categories of checks.

Federal Reserve Bank of Richmond Economic Quarterly

The prices for ACH services also vary with the particular services provided. The basic fee structure in the Richmond Fed’s 1994 price list includes a
participation fee of $20 per account per month and transaction (per-item) fees
of 1¢ per intradistrict item and 1.4¢ per interdistrict item. In addition, a bank
must have electronic access to the system. Access is priced with a monthly fee
that ranges from $30 to $1000, depending on the type of connection maintained.
While electronic access allows institutions to receive other services as well, at
least part of the access fee can be considered the fixed cost of engaging in
ACH transactions.

NATURAL MONOPOLY11

The main concepts to be employed can be demonstrated with a simple example
of a single service that can be provided by one or more sellers. Let qi be the
quantity provided to the ith out of N buyers. Denote by q the array of quantities
provided to all the buyers, q = (q1 , q2 , . . . qN ), and let Q be the sum of the qi .
The total cost incurred by a single seller in providing the service is given by
C(Q) = F +

fi + v(Q).

(1)

The fixed cost has two components. A general cost of F, the common fixed cost,
is incurred by any seller providing any quantity of the service (e.g., the cost
of maintaining an accounting and communication system for ACH transfers).
In addition, there may be a cost of fi specific to the relationship with buyer
i (the cost of an individual bank’s electronic connection to the system). The
variable-cost function, v(Q), is increasing and convex.12
The basic ideas can be presented for the simple case in which only the
common fixed cost, F, is present in equation (1). In this case, the relationship
between total cost and output might be represented as in Figure 1. The corresponding relationship between average cost and output is shown in Figure
2. This U-shaped average-cost curve exhibits economies of scale as long as

11 The case of natural monopoly is developed for expository purposes. The concept of
sustainable pricing can be extended to any market structure. The application to concentrated,
nonmonopoly markets closely parallels the case of natural monopoly. For instance, if all sellers
can operate at minimum average cost, then that minimum cost is the sustainable price.
12 It is worth pointing out that the N quantities (q ) specified above could just as easily
i
be interpreted as quantities of N different products. In that case, the variable-cost function v(Q)
might be replaced by a sum of separate cost functions, v(qi ), for each of the individual products.
The concepts developed here to analyze pricing of a single product in the presence of economies
of scale are directly applicable to the pricing of a set of products in the presence of economies
of scope. Economies of scope are said to exist when the costs of joint production of a set of
products is less than the sum of the costs of separate production.

J. A. Weinberg: Selling Federal Reserve Payment Services

Figure 1 Total Cost Curve
Costs

C(Q) = F + v(Q)

Quantity

Figure 2 Average Cost Curve
Average
Costs

C(Q)
Q
AC'
AC

Quantity

Note: Figure 1 displays a total cost curve with fixed cost F and convex variable-cost function
v(Q). Figure 2 shows the corresponding average-cost function. The quantity Qe is the “efficient
scale” at which minimum average cost ACe is achieved.

Federal Reserve Bank of Richmond Economic Quarterly

total output is less than the level labeled Qe .13 This level of output, at which
average cost is minimized, is referred to as the efficient scale for the production
of the service. Above the efficient scale, as average cost rises, there are diseconomies of scale. For now, it is assumed that all sellers and potential sellers
have identical cost structures.
As in any market, pricing is affected by the structure of the market—e.g.,
the number and relative sizes of sellers. Market structure is, in turn, affected by
the nature of the cost function for producing the service. If the total quantity
demanded in this market was very large relative to Qe , then competitive pricing
and free entry among providers of the service would tend to result in a market
composed of a large number of providers, each producing about Qe . The price
in this competitive market would tend toward ACe in Figure 2. That is, when
efficient scale is small relative to the size of the market, the invisible hand of
competition works well; production costs are minimized and price just covers
costs.
At the opposite extreme is the case in which a single seller’s efficient scale
(Qe ) is at least as large as the total quantity of service demanded by the market.
In this case, competition among active providers cannot enhance the efficiency
of production. Any division of output among sellers will only serve to raise
the overall economic costs of providing the service, by duplicating the fixed
costs. This is a case of natural monopoly. Under the belief that competition is
infeasible, price regulation is often imposed on industries which are thought to
operate under the conditions of natural monopoly.
A natural focus for the pricing of the product sold by a natural monopoly,
subject to the requirement that revenues just match costs, is to set a per-unit
price equal to the average cost of producing the total industry output. Suppose,
in Figure 2, that this output level is Q . Suppose further that the quantity
demanded is independent of price. This assumption is not essential but allows
us to focus on the issue of whether or how the market quantity is divided
among sellers. The price that just covers costs is AC . Note that this price is
greater than the marginal cost of production, since average cost is declining
at Q ; when average cost is declining, marginal cost is less than average cost.
Since price deviates from marginal cost, average-cost pricing in such cases is
sometimes referred to as second-best pricing; “first-best” pricing would equate
price to marginal cost, but would result in revenues less than costs. Secondbest pricing maximizes net social benefits subject to the constraint that total
revenues from the sale of the product just equal total costs.

13 The average-cost curves should be understood as long-run average-cost curves. Although
all factors of production are variable in the long-run, fixed costs are possible in the long-run if
a minimum (positive) level of some input is necessary for production of any positive amount of
output. For instance, to send telephone messages between two points, one must have, at least,
one telephone line connecting those points. This represents a fixed cost, even in the long run.

J. A. Weinberg: Selling Federal Reserve Payment Services

Clearly, average-cost pricing in Figure 2 leaves no opportunity for a competitor to attract some piece of the market and at least cover its costs. Any
piece of the market will involve average production costs greater than AC .
In order to win customers, however, a competitor would have to offer a price
below AC . In this case, uniform average-cost pricing (a per-unit price equal
to AC available to all buyers) is not vulnerable to the entry of competitors.
There is another case that falls into the category of natural monopoly for
which pricing is more problematic. This case can be illustrated by a simple
example in which there are two buyers, Big (B) and Small (S). Buyer B uses
qB units of the service, while S uses qS . The total market quantity, then, is
qB +qS = QM . Again, in the present example, quantity demanded is independent
of price, except that each buyer seeks the lowest-cost supplier. The situation is
depicted in Figure 3. Market quantity lies in the range of diseconomies of scale,
and the average cost of serving the whole market is greater than the cost of
serving just buyer B (ACM > ACB ). Although market quantity exceeds efficient
scale, the market is still a natural monopoly; any division of the market would
result in higher total production costs. The average cost of serving only buyer
S is greater than the average cost of serving the whole market (ACS > ACM ).

Figure 3 Natural Monopoly with Quantity Greater than Efficient Scale

Average
Costs

C(Q)
Q

ACM
ACB

Quantity

Note: Although market quantity, QM = qS + qB , is greater than efficient scale, the market is still a
natural monopoly; the cost of serving the entire market is less than the combined cost of serving
the market in any set of separate “pieces.”

Federal Reserve Bank of Richmond Economic Quarterly

In this example, a simple price structure would set a uniform price equal to
ACM , the average cost of serving the entire market. If there are no legal barriers
to entry, however, this price will induce a competitor to seek to gain a portion
of the market. Specifically, a competitor can target buyer B, offering a price
between ACM and ACB , the average cost of serving just buyer B. This strategy
allows the competitor to take advantage of the economies of scale available in
serving the large-volume user. Indeed, if no competitor were forthcoming and
if buyer B had access to the necessary technology, then the buyer would be
prompted to provide the service in-house.
A couple of comments on the competitor’s pricing strategy are useful to
bear in mind. First, the competitor must have reason to believe that the incumbent monopolist cannot or will not rapidly adjust prices in response to the
competitor’s move. Such a belief might be justified if the incumbent’s pricing
is subject to a cumbersome administrative procedure. Second, the competitor
must be able to offer the lower price to a restricted set of buyers. If targeting a
segment of the market requires making private deals with individual buyers, the
competitor’s task will be simpler if it is possible to identify a relatively small
number of buyers with large enough volume to take substantial advantage of
available economies of scale.
If the large-volume user defects to a competing source for the service,
what becomes of the small-volume user? If the incumbent continues to offer
the service at the price ACM , then buyer S is just as well off as before. This
price, however, no longer covers costs, which are now ACS . Assuming the
incumbent must cover costs, its price must rise. If it is resigned to serving
only the remaining customer, S, then the incumbent must set its price at ACS .
Note that the end result may be an inefficient market structure. If there are
two sellers operating, one serving buyer B and the other serving buyer S, then
the duplication of fixed costs in serving the market constitutes social waste.
The story may not end here. The incumbent may seek to win back some or all
of the market share lost. This counterattack may ultimately succeed, but even
temporary production by more than the efficient number of sellers is socially
inefficient.

SUSTAINABLE PRICES

Are there pricing strategies for the incumbent that leave no room for encroachment by competitors? In the above example, the incumbent was vulnerable,
because one buyer was charged a price that was greater than the cost of serving that buyer alone. The cost of serving only some subset of the buyers in a
market is referred to as the stand-alone cost for those buyers. Accordingly, a
set of buyers will be receptive to alternative sources of a service unless they
face a price that is no greater than their stand-alone cost. A pricing scheme
that meets this requirement for all sets of buyers is called a sustainable pricing

J. A. Weinberg: Selling Federal Reserve Payment Services

scheme. Sustainable prices leave no opportunity for a competitor with identical
costs to capture any segment of the market.
How should one set prices that just cover costs and result in efficient
production? In the case of natural monopoly, efficient production requires a
single producer. In this case, the task is to find prices that recover costs and
are sustainable. When market quantity is smaller than efficient scale, as in
Figure 2, a uniform (per-unit) price equal to the average cost of producing the
market quantity does the job. When market quantity is greater than efficient
scale, as in Figure 3, there is no uniform (nondiscriminating) price that can
satisfy both sustainability and cost recovery. On the other hand, a variety of
nonuniform price structures can achieve the desired goals. One simple form for
such pricing would be to give each buyer (or class of buyers) a distinct price.
While this approach may not be practical in all circumstances, it is used here
for illustrative purposes.
As defined above, sustainable prices generate total revenue that is necessarily no greater than total cost, since total cost is the stand-alone cost for
the whole market. Sustainability, however, does not rule out prices that yield
total revenue less than total cost. The Federal Reserve Banks operate under
the requirement, from the Pricing Principles developed by the Board of Governors pursuant to the Monetary Control Act, that revenues be sufficient to at
least cover all costs (the cost-matching requirement). Adding this condition to
sustainability necessarily results in revenues that exactly match total costs.
One implication of cost-matching, sustainable pricing is that at least one
buyer must be given a price lower than stand-alone cost. Suppose, in the example of Figure 3, that buyer B is charged its stand-alone cost, in the form of
a per-unit price of ACB = [F + v(qB )]/qB . If both buyers are to be served, the
revenue that needs to be collected from buyer S in order to just recover total
costs is
[F + v(qB + qS )] − [F + v(qB )].

(2)

Here, the first term is the total cost of serving both customers, while the second
term is the stand-alone cost of serving the large-volume customer. The difference between these two terms is referred to as the incremental cost of serving
customer S. This cost is denoted by ICS in Figure 4. Hence, the revenue needed
from buyer S can be collected with a per-unit price equal to ICS /qS . If buyer S
is charged anything less than this price, then in order to recover costs, the seller
must charge more than ACB . If B is charged more than ACB , a competitor will
take B’s business.
It is important to note that incremental cost, as the term is used here, is
not the same as marginal cost. The former, as indicated by equation (2), is the
cost of providing a particular quantity to a particular buyer, given the quantity
being provided to other buyers. The latter is simply the cost of providing an
additional unit of the product, without regard to the identity of the recipient. It

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Incremental Cost

Costs
C(Q )
M

C(qB)

Quantity

Note: C(qB ) is the stand-alone cost of serving buyer B, while C(QM ) is the total cost of serving
the entire market. The difference between the two, denoted ICS , is the incremental cost of serving
buyer S.

is possible to have a pricing structure in which the (marginal) price charged to
some buyers is less than marginal cost while no buyer’s average price is less
than its average incremental cost.
The price discrimination just described requires that buyers be segmented
into groups according to some observable characteristic. This task may not
always be straightforward. For instance, the quantity of services used by an
institution may be subject to significant change over time. In that case, setting
a price to a buyer based on the buyer’s previous behavior may not yield the
desired results of tailoring prices to current demand conditions. Fortunately,
the desired segmentation can typically be achieved by pricing schedules that
allow buyers to self-select into groups. One example is “option pricing,” in
which buyers are given a choice between a schedule with a high fixed charge
and low fee per unit and a schedule with a low fixed charge and high fee
per unit. For the two-buyer example, Figure 5 illustrates the total expenditure

J. A. Weinberg: Selling Federal Reserve Payment Services

Figure 5 Option Pricing
Costs,
Expenditures
C(Q)
C(Q )
M

EB
C(qB)

ICS

Quantity
qS

+
Note: The lines labeled ES and EB give the total expenditures (as a function of quantity purchased)
resulting from buying services under the two alternative options. Under one option, given by ES ,
the buyer pays no fixed fee and pays a per-unit price of PS = ICS /qS , which is the slope of the
line ES . This price generates expenditures by buyer S equal to incremental cost. The other option,
given by EB , includes a positive fixed fee and a lower per-unit price (slope). The key features
of the schedule EB are that it meets the total cost curve C(Q) at the quantity qB and that it lies
below ES at qB . Hence, buyer B prefers the schedule EB and has a total expenditure equal to
stand-alone cost, C(qB ). The fixed fee in the schedule EB must be (and is, as drawn) high enough
so that buyer S prefers the schedule ES .

schedules generated by such pricing options. In this example, the low fixed fee
is actually set at zero and combined with a per-unit price of PS = ICS /qS . An
individual buyer will choose the option for which its own total expenditures
are the smallest. Hence, the low-volume buyer selects the low fixed charge and
high per-unit fee, which is constructed so that total expenditures by buyer S
just cover incremental costs. Buyer B selects the other schedule, resulting in
expenditures equal to stand-alone cost.
The desired results also could be achieved by a pricing schedule with
volume discounts, in which the per-unit fee varies with the quantity purchased.

Federal Reserve Bank of Richmond Economic Quarterly

The total expenditure schedule from one such price structure is given in Figure
6. This price schedule sets a price of ICS /qS for the first qS units purchased.
For each additional unit purchased beyond that threshold, the buyer pays the
lower price of [C(qB ) − ICS ]/(qB − qS ). As Figure 6 indicates, this volumediscounting scheme is designed to collect exactly stand-alone cost from buyer
B and incremental cost from buyer S.
An option pricing scheme, like that presented in Figure 5, has recently
been adopted on a trial basis by some Federal Reserve Banks for some checkprocessing services. Most prices for Reserve Bank services, as discussed in
Section 1 above, are a simpler form of two-part pricing, including a single
fixed fee and a single per-item charge. This form of pricing is not as flexible

Figure 6 Volume Discount
Costs,
Expenditures
C(Q)
C(QM)

E
C(q )
B

Quantity

+
Note: Like Figure 5, Figure 6 presents a pricing arrangement that results in expenditures equal
to stand-alone cost for buyer B and incremental cost for buyer S. This arrangement involves no
fixed fee. The per-unit price is ICS /qS on the first qS units purchased. For each subsequent unit
purchased, a lower price is charged. This lower price is equal to [C(qB ) − ICS ]/(qB − qS ). The
resulting total expenditure, as a function of quantity purchased, is given by the kinked line, E.

J. A. Weinberg: Selling Federal Reserve Payment Services

as an option pricing schedule. Accordingly, sustainability may or may not be
achievable with simple two-part pricing.
In summary, sustainability requires that no buyer (or set of buyers) faces
prices greater than stand-alone costs. Adding the cost-matching condition requires that no buyer (or set of buyers) faces prices less than incremental costs.
That is, each buyer must face a price between stand-alone and incremental cost.
Within these restrictions, the relative pricing to different buyers can be treated
in a variety of ways. In the examples above, buyer B is charged stand-alone
cost and buyer S is charged incremental cost. Consequently, all of the fixed
costs of production are allocated to buyer B. This allocation could be reversed,
charging stand-alone cost to buyer S and incremental cost to buyer B. Price
schedules that allocate some fixed costs to each buyer face both buyers with
prices in between stand-alone and incremental costs. The concept of sustainability, by itself, gives no guide to the choice among these alternatives. The
next section suggests that the possibility of technological differences among
alternative providers of a service can help to sharpen the choice.

BYPASS AND TARGETED COMPETITION

The forgoing development of sustainable prices assumes that the same technology is available both to the incumbent firm (the Fed) and to any potential or
actual competitors. Hence the relevant cost standard for deterring entry is the
stand-alone cost of a market segment. There may be instances in which some
segment of the market can be served with a technology different from that used
by the incumbent seller. In such cases, the term “stand-alone cost,” as defined
above, is somewhat of a misnomer. This cost is the cost to a buyer, or group
of buyers, of obtaining services from a source with a cost structure identical to
the incumbent’s. When the alternative to the incumbent’s network involves a
substantially different technology, the buyer’s option is not so much to “stand
alone” as to “bypass” the network.
An example, as described by Einhorn (1987), is in the provision of longdistance telephone services. Most long-distance calls are routed through the
local telephone company, for which a charge is assessed. Large-volume callers,
however, may exercise the option to bypass the local company and connect
directly with their long-distance provider. The technology for bypassing the
local network and, therefore, the costs associated with doing so are different
from those associated with connecting through the network.
One can also think of obtaining payment services from alternative sources
as bypassing the Federal Reserve network. For instance, a local check clearinghouse utilizing centralized exchange of items involves a different pattern of
sorting and transportation expenditures from that arising in the use of the Fed’s
check-clearing services. Of course, in this regard, the most stark example of
bypassing the Fed’s network is direct bilateral exchange of payments.

Federal Reserve Bank of Richmond Economic Quarterly

The presence of a bypass alternative places additional constraints on the
pricing choices facing the incumbent seller. Continuing with the example of
Section 2, suppose that there are two buyers with quantities demanded of qS and
qB and the sum of these quantities is denoted QM . Buyers B and S can bypass
the incumbent and receive the service at a cost of C∗B and C∗S , respectively. The
incumbent seller’s total cost of serving the entire market is CM = F + v(QM ),
while buyer B (S) alone can be served by the incumbent for the stand-alone cost
of CB = F + v(qB ) (CS = F + v[qS ]). Suppose that the bypass technology is potentially attractive only to a large-volume buyer, so that C∗B < CB but C∗S > CS .
On the other hand, suppose that the market is still a natural monopoly. This is
so if when buyer B bypasses the system, total costs rise, or CM < CS +C∗B . This
last statement is equivalent to saying that the incumbent’s incremental cost of
serving buyer B is less than the bypass cost, since ICB = CM − CS < C∗B .
Under the conditions just described, the incumbent is limited in how much
of the common fixed costs can be allocated to buyers with a viable bypass
option. Recall that allocating all of the (common) fixed costs to a single buyer
amounts to charging that buyer its stand-alone cost. Here, such a price to
buyer B would induce B to bypass the incumbent, to the detriment of market
efficiency.
The incumbent’s pricing problem is further complicated if there is some
uncertainty about the viability of the bypass technology. Suppose, for instance,
that the incumbent is reasonably sure that C∗S > CS but is uncertain as to
the value of C∗B . If buyer B’s bypass cost is so low that it is less than the
incremental cost of serving B, then it is efficient to let buyer B bypass. Indeed,
in this case, there are no prices that the incumbent can set to cover costs and
guarantee against the loss of buyer B. On the other hand, it is still possible
to price in such a way that buyer B will be lost only if bypass is efficient.
Specifically, pricing to buyer B at incremental cost and buyer S at stand-alone
cost will succeed in covering costs regardless of whether B is retained. Further,
by comparing its bypass and incremental costs, B makes its choice in a way
that minimizes the total (social) costs of serving the market.
To summarize, the presence of bypass options that are potentially attractive
to some individual buyers or groups of buyers limits the ways in which fixed
costs can be recovered from buyers. Especially when the value of the bypass
option is not fully known by the incumbent, prices to segments of the market
that are likely to have the most attractive bypass options should be pushed
down to the incremental cost of serving those segments. Such an allocation of
fixed costs is likely not to coincide with the allocations implied by standard
accounting practices, and it may strike some (especially other buyers) as inequitable. It is important, however, to consider the alternative. If the incumbent
seeks to recover some of the fixed cost from likely candidates for bypass, those
buyers may turn to alternative sources even when it is socially inefficient to
do so. If their business is lost, the incumbent will still have to recover fixed

J. A. Weinberg: Selling Federal Reserve Payment Services

costs from the remaining buyers. This result would be less cost-efficient and
no more equitable than the result of sustainable pricing that recovers all fixed
costs from those buyers with the least attractive alternatives.

ADDITIONAL COMMENTS ON SUSTAINABLE PRICES

While this article has presented sustainable pricing as a tool for evaluating pricing from a public policy point of view, the concept originated as a predictive
notion in the theory of “contestable markets.”14 Contestable markets theory
holds that in the presence of potential competition, incumbent firms will not
be able to charge anything other than sustainable prices; any attempt to charge
unsustainable prices would quickly prompt entry of and loss of market share
to a competing seller. In other words, even in a natural monopoly, there are no
economic rents earned by an incumbent monopolist. This is a strong conclusion
that has not been broadly accepted without qualification. Most importantly, one
cannot discuss the effects of potential entry without considering the likely response to entry by the incumbent seller. In its purest form, contestable markets
theory assumes that the incumbent can alter its price in response to entry only
with some lag. The incumbent’s inability to respond quickly leaves an opportunity for an entrant to capture, at least temporarily, some part of the market
should the incumbent’s prices be unsustainable. Ultimately, the incumbent may
regain the market, but the absence of sunk costs implies that even temporary
profit opportunities will be exploited by entrants.
In an unregulated market populated only by private firms, there is little reason to suppose that firms do not have a great deal of flexibility in
adjusting their prices to competitive conditions. The situation of a Reserve
Bank, however, may come closer to that imagined by the contestable markets
theory. Clearly, the process necessary to adjust pricing policy is timeconsuming. Reserve Banks must set and publish prices once each year. Further,
the Board of Governors’ Pricing Principles, adopted pursuant to the Monetary
Control Act, state that substantive changes in the structure of prices or services
offered shall be made subject to public comment. Volume-based pricing for
check services (on a limited basis) was approved by the Board in November
1993 and became effective in January 1994, “subject to additional staff analysis
and public comment” (Board of Governors of the Federal Reserve 1994a).
When price adjustment is subject to lags, then prices that are not sustainable can attract entry, even if the market cannot efficiently support the
additional seller(s) in the long run. Hence, the use of unsustainable prices can
attract excessive entry when entrants can take advantage of an incumbent’s
administrative delays in responding to competition.
14 See

Baumol, Panzar, and Willig (1982).

Federal Reserve Bank of Richmond Economic Quarterly

It is also useful to compare sustainable prices to a pricing concept often
used in discussions of regulatory price setting. In such discussions, one approach is to seek prices that maximize social welfare, subject to a zero-profit
constraint for the seller. The “social welfare” to be maximized is a measure of
the benefits (e.g., utility or profits) received by buyers. The resulting prices are
referred to as Ramsey prices, because their derivation follows Ramsey’s (1927)
formulation of optimal taxation. Sustainability is a stronger constraint than zero
profits. Hence, Ramsey prices will not, in general, coincide with sustainable
prices. Accordingly, the former might be more applicable to the problem of
setting prices in the public interest when an incumbent seller is protected from
competition by legal barriers to entry.
Unlike Ramsey prices, the notion of sustainability used here is entirely
cost-based; it does not take into account a measure of the benefits generated by
the provision of payment services. A cost-based specification of sustainability
is exact when demands for services are assumed to be perfectly inelastic. The
more general specification would require that the net value provided to any
group of buyers (benefits to buyers less payments to seller) be no less than the
greatest net value those buyers could obtain from an alternate source. While
this generalization is a direct extension of the basic idea, measures of benefits
on the demand side of a market may be difficult to obtain. Hence, the costbased notion of sustainability may remain useful as a practical approximation
to the more general concept.

ARE PAYMENT SERVICES MARKETS
NATURAL MONOPOLIES?

Sustainable pricing is presented above in the context of a market that is a
natural monopoly. Neither of the markets discussed above, check and ACH
services, is a monopoly, although the ACH market comes close. Even the
market for check services, however, is fairly concentrated; in any given geographic region, the Federal Reserve serves a significant share of the market for
intraregional processing. Market structure is determined in part by the degree
of scale economies relative to the size of the market. Hence, a concentrated
market is likely to be one in which demand and technology conditions are such
that only a small number of sellers is viable. In such a market, the analysis of
sustainable pricing closely parallels that of natural monopoly.
The analysis offered in this article does assume that a seller’s efficient scale
is at least a sizeable fraction of the size of the market. Hence the applicability
of the pricing principles proposed above is partly an empirical matter. Specifically, what evidence exists on the significance of scale economies? There have
been a number of studies of the Federal Reserve’s check-collection services,

J. A. Weinberg: Selling Federal Reserve Payment Services

aimed at addressing this question.15 These studies tend to find fairly weak scale
economies in the observed range of production levels.16 Such findings might
seem at odds with the narrative description of the experience in check processing (and in ACH services), which seems to parallel the analysis of Section
2; average-cost pricing to the market as a whole led to the defection of highvolume users of the services. One possible conclusion is that the alternative
means used by defecting customers do, in fact, deliver the services with lower
real resource costs. That is, these users may have access to a superior bypass
technology. In that case, the Fed’s loss of market share would be efficiencyenhancing. On the other hand, the analysis of Figure 3 refers to a case in which
the incumbent operates above efficient scale. If this case were an accurate description of the Fed priced-services environment, then one would not expect to
find empirical evidence of widespread, unexploited economies of scale.
Aside from economies associated with check processing, there may be
scale efficiencies in the distribution and transportation of processed checks.
Fixed costs that are specific to each endpoint served may result in markets
where efficient scale is a sizeable fraction of the relevant market.
There is also the possibility that economies exist less in increasing the
scale of production of any given service than in the joint provision of multiple
services. This is the most common use of the term “economies of scope.”
For instance, a single electronic connection to a Reserve Bank can allow a
customer to use ACH services and other electronic services, including new
electronic check-collection options. To the extent that scope economies exist, it
may not make sense to talk about market structure, pricing, and cost recovery
on a product-by-product basis. The concept of sustainable prices, however, can
be directly extended to an environment with economies of scope. Consider the
pricing of an array of services. For such pricing to be both sustainable and
cost-matching, no service to any buyer or group of buyers can be priced above
stand-alone cost or below incremental cost. Here, stand-alone cost is the cost
of providing only a specific subset of the services to a specific subset of the
buyers. Similarly, incremental cost refers to the added cost of a specific subset
of services to a subset of buyers, given the services already being provided to
other buyers. As before, choices among sustainable price configurations amount
to choices among possible allocations of common fixed costs across buyers
and services. If a particular service is targeted for competition (for instance,
because of the availability of a bypass technology specific to that service), then
that service’s price should be set at incremental cost.
Even if the structure of cost and demand is such that these markets are not
natural monopolies, the concept of sustainable prices can still provide a useful
15 A

recent example is Bauer and Hancock (1992).
as these studies suggest, the average-cost curve is relatively flat at its minimum, then
average-cost pricing should be close to sustainability.
16 If,

Federal Reserve Bank of Richmond Economic Quarterly

benchmark for Reserve Bank pricing policy. The cost structure in a market
might be such that the efficient number of sellers is greater than one but still
small. For instance, if the market quantity sold tends to be about three times the
efficient scale of production, then the efficient number of sellers is three. In such
a “natural oligopoly,” pricing behavior tends to be the result of a complicated
dynamic game. Here, the administrative structure that governs Reserve Bank
pricing can be advantageous in that it may give the Federal Reserve the ability
to precommit to a pricing strategy over a long horizon.17 When the Fed is
one of several competitors, it can contribute to the efficiency of the market by
adopting a clear pricing policy to which other sellers can react. Specifically,
the Fed could make it known that it stands ready to sell to any market segment
at no greater than stand-alone cost and no less than incremental cost. Within
these bounds, it will adjust pricing to respond to competition, moving prices
in more competitive segments toward incremental cost. Such a strategy makes
it clear that market gains by competitors that reduce overall social costs will
not be contested, while those that raise costs will not be accommodated. Under
sustainable pricing, a seller cannot preserve market share that is not justified
by its technological capabilities.

SUSTAINABLE PRICING AND
THE MONETARY CONTROL ACT

The move toward market-sensitive pricing that responds to competitive conditions might raise questions about the role of the Federal Reserve in the provision
of payment services. To what extent should a Reserve Bank behave like a
private business? Does an attempt by a Reserve Bank to maintain its share
of the market interfere with its public policy objectives with regard to the
payment system? To the latter question, the discussion in this article suggests
the answer, “Not necessarily.” By letting its prices be guided by the notion
of sustainability, the Federal Reserve establishes a benchmark for the market
place. If competition targets a particular segment of the market, that segment
should be served by the Federal Reserve at incremental cost. Then, any gains
in market share by competitors will also be in the public interest. It is also
worth noting that no market segment is being subsidized by another as long as
no price is less than incremental cost.
It is important to note that the pricing behavior suggested herein is, in many
cases, not the behavior one would expect from a private business. That is, the
resulting pricing is not the pricing that would prevail in the market if the Fed
played no operational role. Private businesses are motivated by long-run profit
17 A

treatment of the benefit of precommitment in oligopoly pricing games can be found in
Tirole (1989).

J. A. Weinberg: Selling Federal Reserve Payment Services

maximization. This may lead to deviations from sustainable prices in a number
of ways. First, an incumbent firm facing potential entry can set prices to any
market segment above stand-alone cost, as long as the incumbent has adequate
flexibility to adjust its prices in response to entry. In other words, revenues
can more than cover costs. Second, there may be situations in which a private
firm will be willing and able to set prices that fail to recover all costs in the
short run. Suppose, for example, that two firms find themselves in competition
in a market that has the cost and demand structure of a natural monopoly.18
In the long run, only one of the firms can remain in the market. To determine
which firm will survive, the two might engage in a “war of attrition” in which
prices are below costs and losses are incurred until one firm chooses to exit.
The short-run pricing would necessarily involve some prices to some market
segments below incremental cost. While the Monetary Control Act does allow
the Fed to have revenues that fall below costs in the short run, the Board of
Governors has adopted the policy of setting prices each year with the aim of
recovering all anticipated costs for that year (Board of Governors of the Federal
Reserve 1994b).
Unlike the pricing behavior of a private business, market-sensitive, sustainable pricing is motivated not by profit maximization, but by an interest in the
overall efficiency of the market for payment services. This motivation drives
pricing as close as possible to the “first-best” result of marginal-cost pricing
of all products to all buyers. The constraints that keep pricing away from that
goal are the need to cover costs and the need to ensure that market share is lost
only when the loss results in lowering the resource costs of serving the entire
market.
Does a pricing policy that results in disparate treatment of banks conflict
with the goals of Congress in writing the pricing requirement into the Monetary Control Act? The language of the Act instructs the Federal Reserve to
“give due regard to . . . the adequate level of [services] nationwide.” Since
the sustainable pricing schemes outlined above tend to involve average and
marginal prices that decline with the volume of services purchased, it appears
that such pricing will favor large institutions, because small banks would pay a
higher average price. Hence, disparate treatment, in the form of higher average
prices, might be thought of as impeding smaller institutions’ access to services.
The language in the Monetary Control Act could conceivably be interpreted as
prohibiting pricing that faces some institutions with a greater cost of access to
services. In the presence of economies of scale or scope, pricing that achieves
equal treatment of all buyers and just recovers costs is typically not sustainable. Hence, if the Monetary Control Act is interpreted strictly as mandating

18 For

instance, a market that could previously support two firms might experience a permanent decline in demand.

Federal Reserve Bank of Richmond Economic Quarterly

equal treatment, the Federal Reserve could find itself in an intractable bind; if
uniform, unsustainable prices result in significant loss of business, the Reserve
Banks could have difficulty covering costs without raising prices to remaining
buyers. The result would be equal treatment by the Fed but disparate treatment
by the market as a whole.
While the language of the Monetary Control Act may or may not be read
as providing a mandate for equal treatment, it does seem to dictate a continued
role for the Fed in the provision of payment services. Without such a legislated
dictum, one might legitimately wonder whether there is a necessary role for
the Fed in these markets. Indeed, the central result in the theory of contestable
markets, as noted above, is that the force of potential competition among private
businesses is sufficient to yield sustainable prices. On this point, experience in
deregulated transportation and telecommunication markets has been inconclusive. These markets tend to be highly concentrated, and strategic interaction
may tend to result in fluctuation between collusive and aggressively competitive
behavior. In such an environment, it is conceivable that a single large provider
committed to a sustainable pricing policy could provide a stabilizing influence
on the market while promoting an efficient market structure.

CONCLUSION

This article proposes a general principle for evaluating Reserve Bank pricing
strategies. The concept of sustainable pricing under conditions of scale and
scope economies appears to be a useful tool. Sustainable prices that just cover
total costs price all services to all customers in between their stand-alone and
incremental costs. When competition from private-market providers is focused
on a subset of services and customers, sustainability retains enough flexibility to
respond to competitive pressures by pushing some prices down to incremental
cost. This response is particularly appropriate in conditions of uncertainty about
competitors’ costs.
A strategy of market-sensitive sustainable pricing would result in loss of
business to competitors only when such loss is efficient. Hence, this strategy
provides a guideline for responding to competition in a way that respects the
requirements of the Monetary Control Act while promoting efficiency in the
delivery of payment services. If the Federal Reserve is going to be in the payment services business, it should use its position as a provider motivated by the
public interest to guide the market in the direction of efficiency. Sustainable
prices provide market participants with a benchmark for assessing the cost effectiveness of alternative modes of service delivery. Following this benchmark
may or may not stem the Fed’s loss of market share, but maintaining market
share should not be a goal of Fed policy. The Fed’s market share should be
whatever is consistent with the efficient operation of the payment system.

J. A. Weinberg: Selling Federal Reserve Payment Services

REFERENCES
Bank for International Settlements. Payment Systems in Eleven Developed
Countries. Bank Administration Institute, 1993.
Bauer, Paul, and Diana Hancock. “The Efficiency of the Federal Reserve
Payments System,” Working Paper. Washington: Board of Governors of
the Federal Reserve, 1992.
Baumol, William J., John C. Panzar, and Robert D. Willig. Contestable
Markets and the Theory of Industry Structure. New York: Harcourt Brace
Jovanovic, 1982.
Blommestein, Hans J., and Bruce J. Summers. “Banking and the Payments
System,” in Bruce J. Summers, ed., The Payment System: Design,
Management and Supervision. Washington: International Monetary Fund,
1994.
Board of Governors of the Federal Reserve System. 80th Annual Report, 1993.
Washington: Board of Governors, 1994a.
. Federal Reserve Regulatory Service, Vol. III. Washington: Board
of Governors, 1994b, locator number 7-134.
Einhorn, Michael A. “Optimality and Sustainability: Regulation and Intermodal
Competition in Telecommunications,” Rand Journal of Economics, vol.
18 (Winter 1987), pp. 550–63.
Goodfriend, Marvin S. “Money, Credit, Banking and Payment System Policy,”
in David B. Humphrey, ed., The U.S. Payment System: Efficiency, Risk and
the Role of the Federal Reserve. Boston: Kluwer Academic Publishers,
1990, pp. 247–277.
McAndrews, James. “The Automated Clearinghouse System: Moving Toward
Electronic Payment,” Federal Reserve Bank of Philadelphia Business
Review, July/August 1994, pp. 15–23.
Ramsey, Frank P. “A Contribution to the Theory of Taxation,” Economic
Journal, vol. 37 (March 1927), pp. 47–61.
Spulber, Daniel F. Regulation and Markets. Cambridge, Mass.: MIT Press,
1989.
Tirole, Jean. The Theory of Industrial Organization. Cambridge, Mass.: MIT
Press, 1989.
United States General Accounting Office. “Check Collection: Competitive
Fairness Is an Elusive Goal,” Report to Congressional Committees, May
1989.

Were Bank Examiners Too
Strict with New England
and California Banks?
Robert M. Darin and John R. Walter

Massachusetts Gov. Michael Dukakis accused the Comptroller of the Currency
of “enforcing stricter standards in New England than in the rest of the country.”
. . . New England’s elected officials are . . . concern[ed] that regulators are
pushing their once vibrant region into a recession by forcing banks to increase
loan reserves [emphasis added], which, in turn, is causing them to tighten
credit standards.
[T]here is widespread concern that the medicine might be worse than the
disease. Bankers fear that regulators who were heavily criticized for not
acting quickly when Texas banks were collapsing are now overreacting in
New England.
In a reprise of the kind of regulatory crackdown already experienced in the
East, California bankers report that federal agencies . . . have been harsh
this year.
American Banker

uring the early 1990s bank examiners were frequently accused of
being too strict with banks in New England, thereby contributing to
a credit crunch in the region.1 If supervisors of New England banks
were being unusually strict, they may have been reacting to public complaints
of lax supervision of the savings and loan industry in the 1980s. Such complaints were rife as New England banks’ loan problems were surfacing. As
California’s economy began a slowdown and banks there began to experience
significant loan losses, examiners of California banks also were accused of
being too strict. Unusually strict examination practices could have contributed
The views expressed are those of the authors and do not necessarily represent those of the
Federal Reserve Bank of Richmond or the Federal Reserve System.
1 For reports of examiner strictness, see American Banker, April 20, 1990, p. 1; April 25,
1990, p. 1; and August 16, 1991, p. 1; The Economist, April 7, 1990, p. 94; or The Wall Street
Journal, April 12, 1990, p. A16.

Federal Reserve Bank of Richmond Economic Quarterly Volume 80/4 Fall 1994

Federal Reserve Bank of Richmond Economic Quarterly

to the large declines in bank loans and the severity of the economic downturns
in New England and California.2 Several studies have found evidence that the
large declines in bank lending in New England were, in part, the result of
constraints on bank lending imposed by regulatory capital standards (Peek and
Rosengren 1992, 1993; Bernanke and Lown 1991).3 These studies focus on
whether capital constraints faced by New England banks during that region’s
economic troubles produced declines in bank lending. The capital constraints
in many cases resulted from large additions to reserves for loan losses. The
studies make no attempt to determine if bank examiners were inappropriately
strict in the amount of additions to reserves for loan losses they required of
banks, though Bernanke and Lown (1991) do briefly examine supervisory strictness and conclude that New England banks were not subject to overzealous
supervision.
This article looks for evidence of excessive examiner strictness as manifested in the amount of reserves for loan losses New England and California
banks were required to maintain. Here, strictness refers to the required level of
reserves for loan losses relative to expected loan losses. While requiring banks
to maintain a certain level of reserves for loan losses is only one of several
ways examiner strictness can manifest itself, it is one of the most important.
Allowing banks to hold reserves for loan losses that are too small relative
to expected future losses, or, equivalently, allowing them to overvalue their
loan portfolios, may increase bank failure costs borne by the deposit insurance
fund. On the other hand, excessive strictness may lead to unnecessary cutbacks
in bank lending. Such indeed is the contention of those criticizing examiners
of New England and California banks. To test for loan loss reserve account
strictness, we compare the ratio of reserves for loan losses to nonperforming
loans for New England and California banks to the average ratio for all U.S.
banks. If examiners were being unusually strict in the amount of loan loss
reserves they required of New England and California banks, the ratio for
these banks should have exceeded that of the average U.S. bank at the time
of the hypothesized strictness. We also examine how the average ratio for
New England and California banks changed in the periods before and during
the hypothesized strictness. If examiners were unusually strict, the ratios for
these banks should have increased to unusually high levels compared with past
years. Last, we compare the ratio for banks in New England and California
to the ratio for banks affected by oil-industry problems of the mid-1980s. If

2 According to a 1991 survey, 56 percent of surveyed small banks in northern and central
California indicated that they had denied loans during the year because of the strict regulatory
environment. The Western Independent Bankers Association and the Secura Group conducted the
survey, and the American Banker reported the results in its November 20, 1991, issue.
3 Peek and Rosengren (1993) go so far as to conclude that their evidence suggests that “New
England did suffer from a regulatory-induced credit crunch” (p. 28).

R. M. Darin and J. R. Walter: Were Bank Examiners Too Strict?

examiners were unusually strict with New England and California banks during
the 1990s, the ratios for New England and California banks should exceed those
of banks in the oil-industry-dependent region during economic difficulties. We
also broaden our measure of supervisory strictness beyond the simple reservesto-nonperforming ratio and test again for signs of examiner strictness.
Section 1 deals with bank problem-loan accounting and notes how examiner strictness may influence reported results. In Section 2 we describe our
measures of examiner strictness. In Section 3 we report the results of our analysis using the measures mentioned above. According to such measures, we find
little evidence that supervisors were too strict with banks in New England and
California. To the contrary, we find that banks in New England and California
seem to have received relatively lenient treatment. Finally, in Section 4 we
examine some possible reservations to our analysis.

EXAMINER STRICTNESS AND BANK ACCOUNTING
FOR PROBLEM LOANS

One category of problem-loan data is reserves for loan losses. Reserves for
loan losses are reported by all banks to federal regulators in quarterly financial
statements known as “call reports,” more technically named “Consolidated Reports of Condition and Income,” which consist of a balance sheet, an income
statement, and other financial information. The primary function of the reserve
for loan losses account is to adjust the reported value of the loan portfolio for
expected future credit losses. A bank’s reserve for loan losses should equal
its, or its examiner’s, best estimate of the dollar value of expected losses of
principal on its portfolio of loans. If a bank maintains its reserve account at a
level equal to this estimate, then total loans less reserves, or net loans, is the
best estimate of the collectible value of the loan portfolio. On bank financial
statements, net loans are added to other assets to arrive at total assets. The reserve account is established and maintained by periodic charges to an expense
account denoted “provision for loan losses.”4
Additions to the loan loss reserve account, like other expenses, reduce net
income. Under normal circumstances, a bank’s operating income is sufficient
to cover additions to loan loss reserves and other expenses. Sometimes, as
occurred at many New England banks during the late 1980s, additions to loan
loss reserves exceed income. In such cases, adding to loan loss reserves reduces
capital.
It seems likely that pressures on examiners to be strict or lenient will
manifest themselves in reserves for loan losses required of banks. During bank
examinations, examiners verify the adequacy of loan loss reserves and often
require banks to increase the size of the account. Examiners exercise a good deal
4 See

Walter (1991) for further discussion of loan loss reserves.

Federal Reserve Bank of Richmond Economic Quarterly

of judgment and discretion when determining what constitutes an adequate level
of loan loss reserves. Such judgment is necessary because many bank loans are
heterogeneous and the signals of impending loan losses vary from loan to loan.
But it leaves scope for examiner decisions to be influenced by pressures to be
strict or lenient. New England bank examiners were criticized for excessive
strictness in the early 1990s. Such strictness was attributed to fears of repeating past mistakes. On the other hand, throughout much of the 1980s, many
observers expressed concerns that examiners were being too lenient with banks
that held nonperforming less-developed-country (LDC) loans. Such banks were
seen as holding loan loss reserves that were low relative to expected losses on
the loans. Bank supervisors may have thought that by giving them additional
time to collect nonperforming loans or to supplement reserves for loan losses,
the banks would be able to avoid shrinking their loan portfolios or even failing.
Supervisors also may have been under some political pressure to “go easy” on
LDC-exposed banks. Had examiners forced the LDC-exposed banks to quickly
add reserves to cover expected loan losses, the necessary additions to reserves
could have virtually eliminated the equity of some of these banks (Mengle and
Walter 1991). Ultimately, the exposed banks made large additions to reserves
for LDC loans beginning in 1987.
Another category of banks’ problem-loan data is nonperforming loans.
According to federal bank regulatory definitions, nonperforming loans (“pastdue and nonaccrual loans” on bank call reports) are those for which the borrower is 30 days or more late on contracted interest or principal payments and
those on nonaccrual status. Loans 30 days or more late are further classified
as 30 to 90 days past due and 90 days or more past due. Regulators require
banks to stop accruing interest on loans, or place them on nonaccrual status,
if the borrower’s financial condition has deteriorated, if payment in full is not
expected, or if the loan has been in default 90 days or more.5 Few loans are
placed on nonaccrual status unless they are past due, since the first sign that
the financial condition of the borrower has deteriorated or that payment in full
is not expected generally is the failure to make timely interest or principal
payments.
Verifying the appropriateness of the loan loss reserve account during examinations typically involves a significant amount of examiner judgment and
discretion. Little discretion, however, is involved in determining whether or
not a loan should be reported as nonperforming. For most loans, if the borrower is current on interest and principal payments, the loan is not reported as
nonperforming. If, on the other hand, the borrower is more than 30 days past
5A

loan 90 days or more late generally must be placed on nonaccrual status unless (1) it is
a consumer installment loan, (2) it is secured by a mortgage on a one- to four-family property, or
(3) it is well secured and in the process of being collected. Loans that are 90 days or more late
that fall under one of the excluded categories are reported as “loans past due 90 days or more.”

R. M. Darin and J. R. Walter: Were Bank Examiners Too Strict?

due, the loan will be reported as nonperforming. Occasionally loans may be
placed on nonaccrual status even though they are not past due. The examiner
or bank may believe that even though the borrower is current on payments,
the borrower may be unable ultimately to repay the entire loan. In such cases,
nonperforming loans will be enlarged based on examiner or bank discretion.
The final category of problem-loan data discussed is loan charge-offs. When
it is apparent that all or a portion of a loan will be uncollectible, the loan is
charged off. The amount of the charge-off will equal the book value of the loan
when the bank or its examiner believes the loan is likely to be a total loss.
The charge-off will be less than book value when the bank or its examiner
believes that some of the loan’s principal value will be recovered, say, from
foreclosure on collateral. When a charge-off is taken, some or all of the book
value is removed from the bank’s books and the same amount is deducted from
the reserve for loan losses account. In most cases, loans more than 180 days
past due are charged off. On the other hand, there is a good deal of bank or
examiner judgment involved in charging off a loan that is less than 180 days
past due. Any recovery of an amount previously charged off is added to the
reserve balance upon its collection.

MEASURES OF EXAMINER STRICTNESS

As discussed earlier, examiners have considerable latitude to determine the
appropriate level of loan loss reserves, so that pressures to be more or less
strict may influence the amount of reserves held. Ideally, a test for excessive
examiner strictness would compare the bank’s loan loss reserve to a knowledgeable but impartial party’s estimate of future loan losses. Using this test, the
examiner’s strictness would be measured by the ratio of the bank’s reserves to
the impartial party’s loss estimate. If the ratio is significantly less than one, the
bank has underreported reserves and its examiner may have been too lenient.
If the ratio is approximately one, then the bank has properly reported reserves
and its examiner has been fair. If the ratio is significantly greater than one, then
the bank has overreported reserves, possibly because the bank’s examiner has
been too strict. While bank financial statements report loan loss reserve figures,
they do not report impartial loan loss estimates. In our analysis, we use banks’
reported nonperforming loans as a proxy for the impartial party’s estimate of
future loan losses.6

6 While many researchers count as nonperforming only those loans past due 90 days or more
and those in nonaccrual status, our measure of nonperforming loans also includes loans past due
30 to 90 days. We have chosen to be more inclusive because we believe that the component
consisting of loans 30 to 90 days past due provides additional information about future loan
losses. Our empirical results are not dependent on including this component.

Federal Reserve Bank of Richmond Economic Quarterly

We choose the nonperforming loans figure as a proxy because it is unlikely
to be influenced by examiner strictness yet is likely to be highly correlated with
an impartial party’s estimate of future loan losses. As discussed earlier, the
amount of reported nonperforming loans is subject to little examiner judgment.
Thus, like the impartial party’s loan loss estimate, it is unlikely to be influenced
by pressures on examiners to be lenient or strict. Since nonperforming loans
are known to be troubled, when the amount of such loans held by the bank
increases, an impartial party would increase his estimate of eventual loan losses
for most banks. For all U.S. banks, from 1983 to 1993, nonperforming loans
and net charge-offs (charge-offs less recoveries on previously charged-off loans)
during the following four quarters were highly correlated, with a correlation
coefficient of 0.87. Other research supports the hypothesis that nonperforming
loans have power in predicting future losses. Berger, King, and O’Brien (1991)
regress charge-offs on loan loss reserves and nonperforming loans, using data
for all U.S. banks from 1982 through 1989. They conclude that “the nonperformance measures [nonperforming loans] add significantly to the information
about future bank performance beyond loan loss reserves” (p. 769).7 In related
work, Avery, Hanweck, and Kwast (1985), Hirschhorn (1986), and Cole and
Gunther (1993) find that nonperforming loans help predict bank failures.
Unfortunately, we cannot simply examine the average ratio of reserves to
nonperforming loans for a region and conclude that if the ratio is greater than
one, the region’s examiners were unusually strict, and if the ratio is less than
one, they were unusually lenient. Typically the ratio is significantly lower than
one because a portion of nonperforming loans is likely to be completely or
partially repaid and only the remainder will result in a loss. A priori, we do
not know what levels of the reserves-nonperforming loans ratio indicate that
examiners have been “lenient,” “fair,” or “strict” for a given bank or group of
banks. Instead, to draw conclusions regarding examiner strictness we analyze
the reserves-nonperforming loans ratio for New England and California banks
relative to the ratio for three control groups. First, we compare the ratio for New
England and California banks to the ratio for all U.S. banks in the same time
period. We assume that examiners were fair for the average of all U.S. banks.
Second, we compare the reserves-nonperforming loans ratio for New England
and California banks to past years’ average levels of the ratio. In doing so, we

7 The Berger, King, and O’Brien measure of nonperforming loans differs slightly from our
measure of nonperforming loans. Berger, King, and O’Brien include as nonperforming loans those
past due 90 days or more, those on nonaccrual status, and renegotiated loans. Renegotiated loans
are those loans for which the bank has reduced interest or principal payments because of the
deterioration of the financial position of the borrower. We exclude from our analysis renegotiated
loans but include loans past due 30 to 90 days. Any differences in results should be minor because
Berger, King, and O’Brien estimate that renegotiated loans have a relatively small, and in some
of their regressions insignificant, influence on later loan charge-offs, and because, as noted earlier,
our results are largely unchanged by the inclusion of loans past due 30 to 90 days.

R. M. Darin and J. R. Walter: Were Bank Examiners Too Strict?

assume that before troubled times, examiners were fair with New England and
California banks. Finally, we compare the ratio for New England and California
banks to the ratio for banks in the “oil region” during the period of that region’s
economic difficulties. We compute these ratios relative to the U.S. average. As
for oil-region banks, we assume their examiners were fair, or at least not strict,
since no complaints of such strictness were heard at the time of distress. Now
any one of these assumptions alone may be subject to question. But if all three
comparisons point to the same conclusion about examiner strictness, then we
can be fairly confident of our conclusions. We would conclude that there is
evidence that examiners in New England or California were unusually strict
if the loan loss ratio for banks in these regions was significantly above (1)
the ratio for all U.S. banks, (2) past levels of the ratio for New England and
California, and (3) the ratio for the oil region.
We also test for examiner strictness using a second measure, the ratio of
loan loss reserves to loan charge-offs occurring later (RESt /COt+i ). The ratio
allows us to avoid a potential bias caused by a change in the definition of nonperforming loans. Approximately when loan problems of New England banks
reached their peak, examiners began to require more frequently that banks
place loans current on principal and interest payments on nonaccrual status.
Before then, examiners only infrequently required banks to report any current
loans on nonaccrual status. Current loans placed on nonaccrual status were
commonly referred to as “performing nonperforming loans.” Typically, such
loans were suspect because collateral values had fallen significantly or because
there was some indication that the borrower would be unable to make continued
payments. Examiners generally required extra reserve backing for these loans.
Because a performing borrower is more likely than a nonperforming borrower
to repay a loan, the amount of loan loss reserves for performing nonperforming
loans should be somewhat lower than for other nonperforming loans. Thus, the
reserves-nonperforming loans ratio may have a downward bias beginning when
examiners increased the frequency with which they declared performing loans
nonperforming. Unfortunately, bank financial statements do not segregate performing nonperforming loans, so we cannot adjust for the bias. The RESt /COt+i
measure avoids this bias since it does not employ nonperforming loans at all.
The RESt /COt+i ratio also allows us to test the robustness of our conclusions regarding nonperforming loans. That is, it provides a measure that
requires no proxy of an impartial party’s estimate of loan losses. This could be
important because when using nonperforming loans as a proxy for an impartial
party’s estimate of loan losses, we in effect assume that a dollar of nonperforming loans always leads an impartial examiner to require each and every bank
to hold approximately the same level of reserves. If this is not true—in other
words, if a dollar in nonperforming loans leads an impartial examiner to require
fewer reserves in one region than in others—then our reserves-nonperforming
loans ratio may give us biased results. One can imagine, for example, that in a

Federal Reserve Bank of Richmond Economic Quarterly

region that has experienced a perceived temporary economic shock, impartial
examiners might require lower loan loss reserves per dollar of nonperforming
loans than in other regions. Since we cannot directly test the accuracy of nonperforming loans as a proxy, testing for examiner strictness with a measure that
is not dependent on this proxy provides the best opportunity to test the robustness of our strictness conclusions. If RESt /COt+i -based strictness conclusions
confirm those from the reserves-nonperforming loans measure, then we can be
more certain of the robustness of our conclusions.

ANALYSIS USING MEASURES OF
EXAMINER STRICTNESS

Figure 1 displays weighted-average reserves-nonperforming loans ratios for
banks in New England (Federal Reserve District 1), in the “oil region” (FR
District 11 and Oklahoma), in California, and throughout the United States
(observations are quarterly).8 The weighted average is the sum of loan loss
reserves for all banks in a region divided by the sum of all nonperforming
loans for all such banks.9 The figure shows that during the periods when
examiners were supposedly too strict, New England and California banks’
average reserves-nonperforming loans ratios were not unusually high relative
to (1) the U.S. average, (2) past levels achieved in the two regions, or (3)
the experience of the oil region. On the contrary, New England and California
reserves-nonperforming loans ratios were somewhat low.
Figure 1 shows that after remaining above the U.S. average ratio from 1983
until 1987, New England’s reserves-nonperforming loans ratio fell below the
U.S. average ratio and remained well below it until 1991, when it rose slightly
above it. The period when the ratio was low relative to the U.S. average
corresponds with New England’s economic troubles, which were worst between 1987 and 1992. Therefore, New England banks’ reserves-nonperforming
loans ratio was low for some years before examiners were criticized for unusual strictness (mostly in 1990). Even after the New England ratio rose above
the U.S. average ratio, it tracked that average fairly closely. Figure 1 also shows
that as economic difficulties were hitting California in 1990, the California
8 Our “oil region” (FR District 11 and Oklahoma in Figure 1) includes banks in Oklahoma,
from Federal Reserve District 10, and banks in Federal Reserve District 11. This combination
means that banks in states most affected by petroleum-industry problems are grouped together.
9 We display weighted results in these graphs because displaying the average of individual
banks’ ratios produces results that might be distorted by a small number of banks with very few
nonperforming loans. The reserves-nonperforming loans ratios of these banks are extremely high
because they had almost no nonperforming loans but over time maintained a significant amount
of loan loss reserves, producing ratios as high as 1700.

R. M. Darin and J. R. Walter: Were Bank Examiners Too Strict?

Figure 1 Ratio of Reserves to Nonperforming Loans

1.0

FR District 1
FR District 11 and Oklahoma

0.8

California
U.S. Average

0.6

0.4

0.2

0.0
1983:1

reserves-nonperforming loans ratio fell below the U.S. average ratio. It remained slightly below the U.S. average ratio through 1993.10
In 1990, at the time of the hypothesized strictness, New England banks’
reserves-nonperforming loans ratio was below its 1987 level and only about
equivalent to the level reached in 1985 and 1986. The ratio did begin to increase
rapidly in 1991, but it did not regain its 1987 level until late 1991. Likewise,
California banks’ average reserves-nonperforming loans ratio did not return to
10 The dips in the FR District 11 and Oklahoma line in Figure 1 beginning in the first
quarter of 1989 and in the FR District 1 line beginning in the first quarter of 1991 are the result
of the fairly unique way the FDIC handled some large bank failures in the late 1980s and early
1990s. Failures of large banking companies in Texas and New England (First Republic Bank
Corp. of Texas, MCORP of Texas, Texas American, First American Bank and Trust of Texas, and
Bank of New England) were handled for an interim period, usually less than a year, by placing
the assets and deposits of failed banks in “bridge banks” set up and owned by the FDIC, until
a buyer could be found. These bridge banks included on their books most of the failing banks’
nonperforming loans but minimum loan loss reserves, so that their presence in our Figure 1 data
set causes the reserves-nonperforming loans ratio to be low for the periods of their existence.
Removing bridge banks from the data used to construct Figure 1 eliminates most of the 1989
dip in the FR District 11 and Oklahoma line and all of the 1991 dip in the FR District 1
line and causes the FR District 1 line to rise above the U.S. Average line one quarter earlier
(second quarter rather than third quarter 1991) than shown in Figure 1. Other than these changes,
eliminating the “bridge bank effect” leaves Figure 1 essentially unchanged.

Federal Reserve Bank of Richmond Economic Quarterly

levels attained in 1990 until 1993, well after examiner strictness was supposed
to have occurred. Therefore, at the time of the hypothesized strictness, banks
in New England and California had fairly low reserves-nonperforming loans
ratios relative to pre-recession levels.
The oil region’s economic problems were worst in the 1984 through 1989
period. As shown in Figure 1, the reserves-nonperforming loans ratio of the
region’s banks did not fall until 1989, one year after nonperforming loans
reached their peak. In contrast to the experience of banks in New England
and California, oil-region banks showed little decline in the ratio of reserves
to nonperforming loans during troubles in the region. Though their reservesnonperforming loans ratio was below the U.S. average ratio throughout much
of the latter half of the 1980s, they maintained a fairly consistent increase
throughout the 1980s and early 1990s.
One of the most dramatic features of Figure 1 is the increase in the reservesnonperforming loans ratio in the second quarter of 1987. Virtually all of the
increase is accounted for by $18 billion of additions to loan loss reserves made
by large banks to provide for anticipated losses on LDC loans (McLaughlin and
Wolfson 1988). These additions began on May 20, 1987, when Citicorp added
$3 billion to loan loss reserves to cover expected LDC loan losses. Following
the Citicorp addition, other large banks throughout the country made sizable
additions to loan loss reserves to cover expected future losses on LDC loans.
As shown in Figure 1, the ratios for New England banks and California banks
also jumped in the second quarter of 1987, as banks in these areas also made
large additions for LDC loans. The ratio did not increase significantly in the
oil region because exposure to LDC debt was minimal in that region.
Even though New England and oil-region banks were in similar shape in
terms of the percentage of loans that were troubled, banks in these two regions
displayed very different behavior as nonperforming loans first began to increase.
Figure 2 displays the dollar amount of (1) nonperforming loans and (2) reserves
for loan losses for New England and the oil region. On average, oil-region banks
added substantially to reserves as soon as nonperforming loans began to rise
in 1984. In New England, by contrast, loan loss reserves remained essentially
unchanged as nonperforming loans almost doubled between mid-1987 and late
1989. In the first seven quarters of that period, these loans increased 82 percent
in New England while reserves rose only 2 percent. Conversely, comparable
seven-quarter figures for the oil region show that nonperforming loans relative
to assets rose 63 percent while reserves rose 62 percent. Banks in New England
did not add significantly to reserves for almost two years after the onset of rising problem loans. As a fraction of nonperforming loans, New England banks’
large quarterly additions to reserves in late 1989 and 1990 were significantly
greater than any quarterly additions made by oil-region banks. Additions made
by banks in New England were viewed as evidence that examiners were being
too stringent. But they only brought the reserves to nonperforming loans ratio

R. M. Darin and J. R. Walter: Were Bank Examiners Too Strict?

Figure 2 Loan Loss Reserves and Nonperforming Loans

16
14
12
10
8
6
4
2
0
1983:1

Nonperforming Loans (left scale)

Loan Loss Reserves (right scale)

4
3
2
1

Billions of Dollars

0
84

Oil Region
6
Nonperforming Loans
(left scale)

Loan Loss Reserves
(right scale)

4
3
2

Billions of Dollars

New England
16
14
12
10
8
6
4
2
0
1983:1

1
84

at New England banks up to the level of oil-region banks at a comparable point
in that region’s fortunes.
Differing reactions in New England and the oil region may have resulted
from different signals of future losses available to the two regions. The collapse
of OPEC and oil prices in the early 1980s may have given oil-region banks
and their examiners early and clear warning of long-lasting loan problems in
that region, leading them to make early additions to loan loss reserves. In New
England, on the other hand, signs of persistent loan problems may have become
clear only as more and more loans became nonperforming.
When compared to the average of all U.S. banks, weighted-average
reserves-nonperforming loans ratios for New England and California banks
provide no evidence of unusual examiner strictness. Indeed, they give some
indication of examiner lenience, especially in the period before the hypothesized strictness. Likewise, there is no evidence of unusual examiner strictness
when comparing reserves-nonperforming loans ratios for New England and
California during the periods of hypothesized examiner strictness to the average

Federal Reserve Bank of Richmond Economic Quarterly

ratios generated by banks in these regions before the onset of their economic
troubles. Finally, in comparison to results produced by banks in the oil region,
New England and California banks do not appear to have been treated strictly.
Figure 1 seems to point fairly consistently to the conclusion that New
England and California banks were not forced to add excessively to reserves
and might have even been treated leniently by examiners. Seeking additional
confirmation, we employed regression analysis to determine whether regions
were statistically significantly different from the average for all U.S. banks.
We ran regressions using as dependent variables the log of the quotient of two
ratios, namely, reserves to nonperforming loans for individual banks and for
the average of all U.S. banks. We employed as independent variables dummies
for banks’ regions. Expressed this way, our regression counts each bank’s individual reserves-nonperforming loans ratio equally, regardless of the size of
the bank. The regression equation appears as follows:
log(RATIOit /RATIOU.S.t ) = B1 ∗ RG1 + B2 ∗ RG2 + · · · + B13 ∗ RG13 + eit
RATIOit =

(RESQ1 + RESQ2 + RESQ3 + RESQ4 )
(NPLQ1 + NPLQ2 + NPLQ3 + NPLQ4 )

= Bank i’s average reserves-nonperforming loans ratio in year t.11
RATIOU.S.t = Arithmetic average of all U.S. banks’ RATIOi in year t.
The independent variables are all dummy variables: RGd is a dummy variable
equal to one if a bank is in Federal Reserve District number d and zero otherwise. The state of California is entered as regional dummy 13 (and is excluded
from Federal Reserve District 12) because California was especially plagued
by the recession of the early 1990s, while other Twelfth District states were
relatively better off. d = 1, 2, . . . 13.
The regression equation was run once for each year 1983 through 1993.
Because banks, or their supervisors, may take several quarters to adjust the
reserve account in response to a change in nonperforming loans, reservesnonperforming loans ratios were calculated using annual averages. Since every
region was represented by a dummy, constants were omitted from the regression. Table 1 displays the results of these regressions. The coefficient on each
region’s dummy is a measure of how location influences the deviation of a
bank’s reserves-nonperforming loans ratio from the U.S. average ratio. The
t-statistics are test statistics for the hypothesis that the region dummy coefficients equal zero. In other words, they test the hypothesis that there is
11 Banks that do not produce call reports for all four quarters in a year, either because of
failure, merger, or de novo entry, are removed from the regression calculation for the year. The
“bridge bank effect” (discussed in footnote 10) therefore does not influence our regression results.

R. M. Darin and J. R. Walter: Were Bank Examiners Too Strict?

no relationship between location in the region and the deviation of a bank’s
reserves-nonperforming loans ratio from the comparable U.S. average ratio.
The regression results corroborate the trends apparent in Figure 1. Banks
in New England and California had low reserves-nonperforming loans ratios
compared to banks nationwide around the time of their economic troubles and
during and after the periods examiners were criticized for being excessively
strict. Specifically, the regressions show very large (in absolute value) and
statistically significant negative coefficients for New England and California
during these periods. Banks in Federal Reserve District 1 (New England) had
a coefficient of −.68 in 1990, near the trough of the New England recession.
This was by far the largest absolute coefficient of any region in any year. The
reserves-nonperforming loans ratio for banks in New England fell significantly
below the average ratio for all U.S. banks in 1988, soon after loan troubles began to surface in New England. The ratio then declined further through 1990.
It began recovering in 1991 but remained significantly below the U.S. average
through 1993. The coefficients for California also became very highly negative
in the early 1990s. In contrast, the lowest coefficient registered in the oil region
(Federal Reserve District 11 and Oklahoma) was −.23. Until 1987 the reservesnonperforming loans ratio for banks in the oil region was significantly above
or only slightly below the U.S average. From 1987 through 1990, the reservesnonperforming loans ratio for oil-region banks was statistically significantly
lower than the average ratio for all U.S. banks, although the absolute value of
the coefficient for the oil region was much smaller than that of coefficients for
New England and California.12
The regression analysis provides evidence that New England and California
banks were not forced by excessively strict examiners to overreserve. It shows
that New England and California banks had much lower reserves relative to
nonperforming loans than average for all U.S. banks before, during, and after
the time examiners were being criticized for excessive strictness. The analysis
also shows that relative to the U.S. average, underreserving was much greater
in New England and California than it had been earlier in the oil region. The
regressions do indicate that some underreserving during economic troubles may
be normal, since it seems to have occurred in New England, California, and
in the oil region. Such could be the case because it may take some time for
banks to recognize and set aside income for problem loans, or for examiners
to examine banks and force them to increase reserves for loan losses.
When we further investigate examiner strictness using our second strictness
measure, the ratio of loan loss reserves today to loan charge-offs tomorrow
12 One

might conjecture that different size banks may reserve for loan losses in different
ways, on average. If this is the case, then our results may have been influenced by differences in
the size distribution of banks across the regions. To test for this, we regressed our ratio on size
dummies and found no consistent relationships.

Table 1
Regression equation: log(RATIOit /RATIOU.S.t ) = B1 ∗ RG1 + B2 ∗ RG2 + · · · + B13 ∗ RG13 + eit
Regional Dummies

1983

1984

1985

1986

1987

1990

1991

1992

1993

Fed Reserve District 1

0.12
(2.19)b

0.19
(3.62)c

0.21
(4.08)c

0.23
(4.54)c

0.19
(3.64)c

−0.23
(−4.10)c

−0.62
(−10.96)c

−0.68
(−11.71)c

−0.56
(−9.09)c

−0.41
(−6.10)c

−0.35
(−4.99)c

Fed Reserve District 2

0.15
(2.68)c

0.17
(3.09)c

0.28
(5.44)c

0.27
(5.57)c

0.15
(3.08)c

−0.10
(−1.91)a

−0.29
(−5.59)c

−0.43
(−8.35)c

−0.35
(−6.83)c

−0.38
(−7.05)c

−0.41
(−7.35)c

Fed Reserve District 3

−0.18
(−3.40)c

−0.08
(−1.69)a

0.01
(0.20)

0.04
(0.81)

−0.04
(−0.94)

−0.16
(−3.15)c

−0.23
(−4.66)c

−0.35
(−7.21)c

−0.38
(−7.87)c

−0.29
(−5.97)c

−0.34
(−6.51)c

Fed Reserve District 4

−0.15
(−4.00)c

−0.08
(−2.04)b

−0.04
(−1.08)

−0.05
(−1.51)

−0.10
(−2.97)c

−0.18
(−4.88)c

−0.23
(−6.15)c

−0.23
(−6.08)c

−0.23
(−6.03)c

−0.18
(−4.67)c

−0.13
(−3.23)c

Fed Reserve District 5

0.06
(1.47)

0.10
(2.86)c

0.10
(2.83)c

0.11
(3.40)c

0.01
(0.36)

−0.05
(−1.33)

−0.14
(−3.93)c

−0.20
(−5.87)c

−0.26
(−7.60)c

−0.19
(−5.55)c

−0.18
(−4.88)c

Fed Reserve District 6

0.07
(3.11)c

0.07
(3.26)c

0.03
(1.22)

0.00
(0.02)

−0.08
(−3.59)c

−0.11
(−4.86)c

−0.17
(−7.16)c

−0.23
(−9.89)c

−0.24
(−10.68)c

−0.16
(−7.07)c

−0.11
(−4.56)c

0.11
(6.61)c

0.20
(11.98)c

0.22
(12.51)c

0.19
(10.61)c

0.18
(9.91)c

0.12
(6.39)c

0.06
(2.96)c

0.03
(1.45)

0.03
(1.30)

0.00
(0.14)

−0.03
(−1.38)

−0.02
(−0.92)

−0.10
(−4.18)c

−0.11
(−4.68)c

−0.06
(−2.49)b

0.01
(0.30)

−0.16
(−6.93)c

−0.01
(−0.32)

0.04
(1.56)

0.08
(3.11)c

0.09
(3.66)c

0.10
(3.78)c

Fed Reserve District 7

−0.03
(−1.42)

−0.04
(−2.38)b

0.00
(0.12)

Fed Reserve District 8

−0.04
(−1.46)

−0.04
(−1.74)a

−0.02
(−0.94)

Fed Reserve District 9

−0.26
(−10.26)c

−0.32
(−13.70)c

−0.34
(−15.30)c

−0.31
(−14.48)c

1988

1989

0.07
(2.60)c

Fed Reserve District 10
(excluding Oklahoma)

0.16
(7.45)c

0.07
(3.26)b

0.10
(5.13)c

0.11
(6.20)c

0.18
(9.72)c

0.27
(13.22)c

0.35
(16.79)c

0.38
(18.23)c

0.45
(21.32)c

0.40
(18.59)c

Fed Reserve District 11
(including Oklahoma)

0.15
(7.71)c

0.19
(10.65)c

0.08
(4.99)c

−0.07
(−4.31)c

−0.20
(−12.12)c

−0.23
(−12.27)c

−0.18
(−8.68)c

−0.05
(−2.36)b

0.04
(2.07)b

0.03
(1.22)

Fed Reserve District 12
(excluding California)

−0.48
(−9.40)c

−0.40
(−8.30)c

−0.38
(−8.17)c

−0.31
(−6.88)c

−0.29
(−6.02)c

−0.29
(−5.54)c

−0.17
(−3.20)c

−0.03
(−0.53)

0.08
(1.61)

0.14
(2.61)c

0.29
(5.36)c

California

−0.24
(−4.81)c

−0.08
(−1.93)a

0.04
(1.05)

0.01
(0.24)

0.06
(1.50)

0.04
(1.01)

0.10
(2.36)b

0.05
(1.16)

−0.26
(−6.42)c

−0.43
(−10.15)c

−0.45
(−10.16)c

F-Statistic

29.76

33.96

31.60

32.74

39.76

45.79

58.94

68.67

72.26

54.70

46.24

0.00

13,889

13,841

13,870

13,715

13,221

12,643

12,269

11,925

11,556

11,140

10,674

F-Significance
Number of Observations
a

Significant at the 10 percent level.

Significant at the 5 percent level.

Significant at the 1 percent level.

0.38
(16.80)c
−0.03
(−1.36)

Notes: Banks that did not produce call reports for all four quarters in a year were removed from the regression calculation for the year. Otherwise, regressions include
all U.S. banks. t-statistics are in parentheses.

Federal Reserve Bank of Richmond Economic Quarterly

(RESt /COt+i ), our nonperforming loans-based results are confirmed. Analysis
using RESt /COt+i indicates that New England and California banks might have
received lenient treatment at the hands of their examiners, or at least did not
receive overly strict treatment.
Figure 3 displays the weighted-average RESt /COt+i ratio graphed by region. The figure shows that New England banks’ ratio fell below the U.S.
average ratio beginning in 1988 and remained below it until early 1991, when
New England’s ratio moved slightly above the U.S. average ratio.13,14 The
figure also shows that the average ratio for California banks remained significantly above the U.S. average ratio until mid-1990, but then fell below. The
average ratio for New England banks began falling in 1986, remained until
1992 well below levels maintained between 1983 and 1986, and never rose
above the early 1986 level. California banks’ average RESt /COt+i ratio shows
a similar pattern across time. In the oil-industry region, the ratio remained
well below the U.S. average ratio until 1988. Then it either conformed to the
average or rose above it throughout the remainder of the region’s difficulties.
These graphs indicate that compared to their U.S. and oil-region counterparts,
as well as themselves in better times, New England and California banks may
have been underreserved during much of each region’s slowdown.
Table 2 displays results from regressions using RESt /COt+i instead of
RES/NPL but otherwise equivalent to the RES/NPL regression presented earlier.
As was the case with the earlier regressions, the largest negative coefficients
are associated with the economic difficulties experienced in New England and
California in the late 1980s and early 1990s. Significantly negative coefficients
continued even as complaints were surfacing of excessive examiner strictness
in these regions. Banks in the oil region had RESt /COt+i ratios well below the
U.S. average ratio throughout the study period, though negative coefficients for
the oil region were never as large as they were for New England and California
at their worst. These results corroborate results from the nonperforming loans
regressions and graphs.

CAVEATS

Our regression analyses presented in Tables 1 and 2, and our comparisons of
ratios for New England and California banks to the average ratio for all U.S.
banks, could incorrectly classify regional examiners as more lenient than they
were. If examiners were inappropriately strict in their standards for determining
13 In our calculations, we excluded any bank that was not operating in all of the five quarters
(one quarter when reserves are observed plus the following four quarters when charge-offs for
the bank are observed) used to calculate a ratio.
14 We also compared reserves to charge-offs over the next eight quarters and found similar
results.

R. M. Darin and J. R. Walter: Were Bank Examiners Too Strict?

Figure 3 Ratio of Reserves to Eventual Net Charge-Offs

FR District 1
FR District 11 and Oklahoma

California
U.S. Average

0
1983:1

reserves with all U.S. banks, New England and California banks might seem
to have received lenient treatment by comparison even though they too were
subject to inappropriately strict treatment. Bizer (1993) finds evidence that
U.S. bank supervisors, on average, became stricter in their confidential bank
ratings after 1989 as compared with before 1989. No studies exist of examiner
strictness in standards for determining loan loss reserves. However, stories appearing around 1990 in the banking press reported a perception among bankers
and borrowers that these standards were made stricter for banks throughout the
country, not just in New England and California. We believe it unlikely that our
measures incorrectly indicate lenient treatment of New England and California
banks.
For one thing, our data do not support the conclusion that examiners
throughout the United States became stricter in loan loss reserves standards in
1989 or 1990. To be sure, the U.S. average reserves-nonperforming loans ratio
line shown in Figure 1 reaches a local minimum in the first quarter of 1991 and
rises consistently afterward. But it does not rise to unusually high levels until
1993. Similarly, in Figure 3 the U.S. average RESt /COt+i line reaches a local
minimum in 1989, remains relatively flat until 1991, and then begins rising.
True, as of the end of 1992, it does rise above the previous highs achieved
in 1987 and 1988, but not far above. It therefore seems unlikely that unusual
examiner strictness occurred for the average U.S. bank before late 1992.

Table 2
Regression equation: log(RATIOit /RATIOU.S.t ), where RATIO = (loan loss reserves)t /(net charge-offs)t+i
Regional Dummies

1983

1984

1985

1986

1987

1988

1991

1992

Fed Reserve District 1

1.11
(13.23)c

1.35
(16.78)c

1.31
(16.48)c

0.99
(12.10)c

0.61
(7.36)c

−0.42
(−5.07)c

−1.19
(−14.10)c

−1.14
(−12.35)c

−0.71
(−7.34)c

−0.55
(−5.23)c

Fed Reserve District 2

0.75
(9.09)c

1.12
(14.28)c

1.10
(14.42)c

0.76
(9.56)c

0.38
(4.87)c

0.04
(0.53)

−0.64
(−8.30)c

−0.64
(−8.34)c

−0.47
(−5.95)c

−0.56
(−6.66)c

Fed Reserve District 3

1.05
(13.10)c

1.22
(16.09)c

1.31
(17.87)c

0.99
(13.06)c

0.82
(10.80)c

0.52
(7.21)c

0.10
(1.42)

−0.13
(−1.82)a

−0.16
(−2.22)b

−0.05
(−0.58)

Fed Reserve District 4

0.40
(6.98)c

0.55
(10.26)c

0.50
(9.50)c

0.36
(6.72)c

0.15
(2.77)c

−0.09
(−1.55)

−0.11
(−1.99)b

−0.16
(−2.82)c

−0.13
(−2.04)b

Fed Reserve District 5

0.67
(11.79)c

0.74
(14.08)c

0.74
(14.61)c

0.46
(9.01)c

0.34
(6.56)c

0.12
(2.27)b

−0.15
(−2.91)c

−0.25
(−4.94)c

−0.23
(−4.47)c

−0.02
(−0.31)

Fed Reserve District 6

0.14
(3.95)c

0.15
(4.52)c

0.10
(3.06)c

−0.08
(−2.27)b

−0.21
(−6.01)c

−0.29
(−8.41)c

−0.37
(−10.87)c

−0.43
(−12.46)c

−0.28
(−8.01)c

−0.22
(−5.87)c

Fed Reserve District 7

0.16
(5.91)c

0.05
(1.84)a

0.19
(8.03)c

0.46
(17.93)c

0.53
(19.26)c

0.50
(17.56)c

0.46
(15.69)c

0.32
(10.88)c

0.27
(9.08)c

0.18
(5.31)c

Fed Reserve District 8

0.05
(1.34)

0.04
(1.12)

0.11
(3.38)c

0.22
(6.41)c

0.22
(6.04)c

0.18
(4.88)c

0.13
(3.36)c

0.09
(2.33)b

0.08
(2.13)b

0.13
(2.92)c

Fed Reserve District 9

−0.08
(−2.25)b

−0.22
(−6.62)c

−0.28
(−8.61)c

−0.12
(−3.58)c

0.07
(1.90)a

0.17
(4.54)c

0.27
(6.89)c

0.42
(10.72)c

0.37
(8.89)c

0.35
(7.65)c

−0.05
(−0.90)

1989

1990

Fed Reserve District 10
(excluding Oklahoma)

−0.50
(−15.98)c

−0.53
(−18.32)c

−0.35
(−12.59)c

−0.25
(−8.71)c

−0.10
(−3.08)c

0.04
(−1.14)

Fed Reserve District 11
(including Oklahoma)

−0.39
(−13.91)c

−0.32
(−12.66)c

−0.55
(−23.00)c

−0.71
(−28.93)c

−0.79
(−29.55)c

Fed Reserve District 12
(excluding California)

−0.06
(−0.84)

0.05
(0.78)

0.03
(0.45)

−0.18
(−2.47)b

California

−0.28
(−3.87)c

0.03
(0.45)

0.16
(2.66)c

0.18
(2.97)c

F−Statistic

87.61

124.13

150.51

141.73

0.00

12,363

12,744

12,726

F−Significance
Number of Observations
a

Significant at the 10 percent level.

Significant at the 5 percent level.

Significant at the 1 percent level.

0.16
(4.68)c

0.26
(7.46)c

0.31
(8.19)c

0.16
(3.84)c

−0.64
(−22.33)c

−0.31
(−10.07)c

−0.09
(−2.84)c

−0.07
(−2.00)b

−0.08
(−2.17)b

−0.25
(−3.36)c

−0.17
(−2.19)b

−0.14
(−1.63)

−0.04
(−0.44)

−0.05
(−0.63)

−0.01
(−0.12)

0.13
(2.01)b

0.32
(4.97)c

0.29
(4.43)c

−0.25
(−3.89)c

−0.68
(−10.97)c

−1.03
(−15.22)c

122.36

79.76

65.31

55.90

41.83

35.16

0.00

11,718

10,750

10,400

10,106

9,860

9,172

8,109

Notes: Banks that did not produce call reports for all five quarters (one quarter when reserves are observed plus the following four quarters when charge-offs are
observed) used to calculate a year’s ratio and banks that had no net charge-offs were removed from the regression calculation for the year. Otherwise, regressions
include all U.S. banks. Year indicates time period when reserves were held. t-statistics are in parentheses.

Federal Reserve Bank of Richmond Economic Quarterly

Second, in comparing ratios for New England and California banks to ratios
for control groups other than the U.S., we find that our measures also indicate
no unusual strictness, and possibly lenience, for New England and California banks. As noted earlier, the reserves-nonperforming loans and RESt /COt+i
ratios achieved by New England banks in the late 1980s and early 1990s remained at or below the levels produced by New England banks before the
1987 decline. This indicates that unless examiners were inappropriately strict
with New England banks in 1986 and 1987, they apparently were not in
1990 and 1991. A similar argument may be made for California banks. The
reserves-nonperforming loans ratios for the oil region and New England were
approximately equivalent at similar times during their difficulties. (Nonperforming loans peaked in the third quarter of 1988 for the oil region and the first
quarter of 1991 for New England.) So, unless examiners were inappropriately
strict in reserve standards for oil-region banks, they apparently were not with
New England banks.
While it seems unlikely that comparisons with U.S. bank averages bias our
analysis, our reserves-nonperforming loans ratio may understate the degree of
examiner strictness in another way. A bank with an unusually large ratio of
loan charge-offs to nonperforming loans could have a low ratio of reserves to
nonperforming loans even though it is not underreserved and has not undergone unusually lenient examination. The high charge-off bank is likely to have
a relatively low reserves-nonperforming loans ratio for two reasons. First, if the
nonperforming loans charged off tend to be those with the greatest expected
losses and therefore those with the greatest proportion of reserves, it is likely
that charge-offs will lower the proportion of reserves to nonperforming loans.
Second, when a portion of a nonperforming loan is charged off, the remainder
of the nonperforming loan may have a lower-than-normal expected loss and
require few loan loss reserves.
The bias in the reserves-nonperforming loans measure that can occur
when loan charge-offs are unusually large can be minimized by modifying the
reserves-nonperforming loans ratio. Loan charge-offs are added back to reserves
for loan losses and to nonperforming loans so that the measure of examiner
strictness becomes (RES+CO)/(NPL+CO). This modification reverses the bias
introduced by loan charge-offs on reserves and nonperforming loans. When the
regressions presented in Table 1 were rerun with the (RES + CO)/(NPL + CO)
ratio substituted for the reserves-nonperforming loans ratio as the dependent
variable, coefficients and their significance levels were virtually identical to
those generated with the simpler reserves-nonperforming loans ratio. This result indicates that our original reserves-nonperforming loans ratio suffered from
little if any bias from unusually large charge-offs. It follows that the reservesnonperforming loans ratio probably underestimates examiner strictness little.
The RESt /COt+i ratio also may understate examiner strictness because
of examiner charge-off procedures. Since examiners have some discretion in

R. M. Darin and J. R. Walter: Were Bank Examiners Too Strict?

determining the required amount of loan charge-offs, it is possible that a tendency to be excessively strict might show up in the amount both of loan loss
reserves and banks’ charge-offs. If so, then COt+i in the RESt /COt+i ratio
would increase, causing that ratio to indicate either a decline or no change in
examiner strictness when in fact examiners increased strictness.
Charged-off loan recovery data for New England and California banks,
however, provides no evidence that examiners were excessively strict in the
amount of charge-offs they required. As noted earlier, funds collected on loans
previously charged off (for example from the sale of foreclosed properties or
from repayments made by delinquent borrowers) are called recoveries. Their
dollar amounts are reported in quarterly call reports. Excessive charge-off strictness means that examiners are forcing banks to charge off loans that ultimately
will be repaid, or to charge off greater proportions of loans than ultimately
will be lost on these loans. Therefore, an inappropriate increase in charge-off
strictness should lead to an increase in later recoveries. Figure 4 graphs one
year’s average charge-offs divided by the following year’s average recoveries
(COt /RECt+i ) for New England, California, and the United States. Suppose the
decline in the New England RESt /COt+i line in Figure 3, or the rise in the line

Figure 4 Ratio of Charge-Offs to Eventual Recoveries

New England
California
8

U.S. Average

2
1983:4

84:4

85:4

86:4

87:4

88:4

89:4

90:4

91:4

92:4

+
Notes: Each charge-off figure is the four-quarter sum of charge-offs in the current quarter and
three previous quarters. Each recovery figure is the four-quarter sum of recoveries beginning in
the following quarter.

Federal Reserve Bank of Richmond Economic Quarterly

to levels only slightly higher than the U.S. average after 1990, was the result of
examiners being unusually strict in charge-off procedures. If so, then one would
expect the COt /RECt+i line in Figure 4 also to fall after 1987 and be unusually
low relative to the U.S. average. Figure 4, however, shows that New England
banks’ COt /RECt+i line increased from 1987 through 1990. Then, consistent
with the U.S. average line, the New England line peaked in mid-1990 and
declined for several quarters before leveling off well above the U.S. average
line. California banks follow the same pattern as New England banks and U.S.
banks, though from a lower level. The consistently lower-than-U.S.-average
COt /RECt+i ratio exhibited by California banks could indicate that California
banks’ examiners consistently applied stricter charge-off requirements than the
average for all U.S. banks. It is unlikely then that New England and California
banks’ RESt /COt+i ratio was artificially depressed during economic difficulties
in those regions, since examiners apparently were not unusually strict in the
charge-offs they required during those periods.

CONCLUSIONS

We have developed and examined several measures of supervisory strictness.
We find little evidence that bank supervisors were too strict with New England
and California banks. To the contrary, by our measures, examiners treated New
England and California banks less strictly in times of trouble than the average
U.S. bank. Moreover, examiners treated the former banks less strictly than before their economic troubles and less strictly than oil-region banks that suffered
similar economic difficulties. These measures, however, provide no evidence
that any such leniency by examiners was intentional. Perhaps examiners were
surprised by the severity of the New England and California problems, but
were less surprised by the severity of problems in the oil region.
It is probably true that the large additions to reserves for loan losses made
by banks in New England and California in the early 1990s may have diminished these banks’ ability to lend. But our data indicates that those additional
reserves at best only made up for an extended period when reserves were
too low relative to expected loan losses. It seems unlikely, therefore, that
inappropriate action by bank examiners exacerbated the effects of the 1990–91
recession in these regions.

R. M. Darin and J. R. Walter: Were Bank Examiners Too Strict?

REFERENCES
Avery, Robert B., Gerald A. Hanweck, and Myron L. Kwast. “An Analysis of
Risk-Based Deposit Insurance for Commercial Banks,” in Proceedings of
a Conference on Bank Structure and Competition (Federal Reserve Bank
of Chicago, May 1985), pp. 217–50.
Berger, Allen N., Kathleen Kuester King, and James M. O’Brien. “The Limitations of Market Value Accounting and a More Realistic Alternative,”
Journal of Banking and Finance, vol. 15 (September 1991), pp. 753–83.
Bernanke, Ben S., and Cara S. Lown. “The Credit Crunch,” Brookings Papers
on Economic Activity, 2:1991, pp. 205–39.
Bizer, David S. “Regulatory Discretion and the Credit Crunch,” Working
Paper. Washington: U.S. Securities and Exchange Commission, April
1993.
Cole, Rebel A., and Jeffrey W. Gunther. “Separating the Likelihood and
Timing of Bank Failure,” Finance and Economics Discussion Series, no.
93-20. Washington: Board of Governors of the Federal Reserve System,
Division of Research and Statistics, June 1993.
Hirschhorn, Eric. “Developing a Proposal for Risk-Related Deposit Insurance,”
Banking and Economic Review, September/October 1986, pp. 3–10.
McLaughlin, Mary M., and Martin H. Wolfson. “The Profitability of Insured
Commercial Banks in 1987,” Federal Reserve Bulletin, vol. 74 (July
1988), pp. 403–18.
Mengle, David L., and John R. Walter. “How Market Value Accounting Would
Affect Banks,” in Rebuilding Banking, Proceedings of the 27th Annual
Conference on Bank Structure and Competition (Federal Reserve Bank of
Chicago, May 1991), pp. 511–33.
Peek, Joe, and Eric S. Rosengren. “Bank Regulation and the Credit Crunch.”
Unpublished manuscript. February 1993.
. “The Capital Crunch in New England,” Federal Reserve Bank of
Boston New England Economic Review, May/June 1992, pp. 21–31.
Walter, John R. “Loan Loss Reserves,” Federal Reserve Bank of Richmond
Economic Review, vol. 77 (July/August 1991), pp. 20–30.

An Error-Correction Model
of the Long-Term Bond Rate
Yash P. Mehra

ost recent studies of long-term interest rates have emphasized term
structure relations between long and short rates. They have not,
however, looked behind these relations to find the basic economic
factors that affect the overall level of interest rates.1 In this article, I examine
empirically the role of economic fundamentals in explaining changes in the
long-term U.S. Treasury bond rate.
The economic determinants of the bond rate are identified by building on
the loanable funds model used by Sargent (1969), among others.2 The bond
rate equation estimated here, however, differs from the one reported in Sargent
in two major respects. First, it uses the federal funds rate rather than the money
supply to capture the influence of monetary policy actions on the real component of the bond rate. As is now widely recognized, financial innovations and
the deregulation of interest rates have altered the short-run indicator properties
of the empirical measures of money. Hence, it is assumed that the impact of
monetary policy actions on the real bond rate is better captured by changes in
the real funds rate than in the real money supply. Second, it uses cointegration
and error-correction methodology, which is better suited to distinguish between
the short- and long-run economic determinants of the bond rate than the one
used in Sargent and elsewhere.

The views expressed are those of the author and not necessarily those of the Federal Reserve
Bank of Richmond or the Federal Reserve System.
1 The main reason for this neglect is that the studies in question have been interested primarily in testing the validity of the expectations theory of the term structure of interest rates. One
recent exception is the study by Goodfriend (1993), who has attempted to look at fundamentals.
In Goodfriend, the long bond rate is viewed as an average of expected future short rates, the latter
in turn depending on monetary policy actions and the expected trend rate of inflation. Goodfriend
then uses a narrative approach to discuss the interactions between the bond rate and its economic
determinants, including monetary policy and expected inflation. He does not, however, formally
test for or estimate the impact of these economic determinants on the bond rate.
2 For example, see Echols and Elliot (1976) and Hoelscher (1986), who have employed
variants of this model to study the behavior of the long-term bond rate.

Federal Reserve Bank of Richmond Economic Quarterly Volume 80/4 Fall 1994

Federal Reserve Bank of Richmond Economic Quarterly

The empirical work presented here suggests several results. First, inflation
rather than the deficit appears to be the major long-run economic determinant
of the bond rate. The long-run deficit-interest rate link found here in the data is
fragile.3 Second, monetary policy actions measured by the real funds rate have
substantial short-run effects on the real bond rate. Third, the bond rate equation
estimated here is consistent with the bond rate’s actual, long-run behavior from
1971 to 1993. Nevertheless, it fails to explain some large, short-run upswings
in the bond rate that have occurred during the subperiod 1979Q1 to 1993Q4.
Those upswings in the bond rate are most likely due to short-run swings in its
major long-run economic determinant—expected inflation—and hence may be
labeled as reflecting inflation scares as in Goodfriend (1993).
The plan of this article is as follows. Section 1 presents the model and the
method used in estimating the bond rate equation. Section 2 presents empirical
results, and Section 3 contains concluding observations.

THE MODEL AND THE METHOD

A Discussion of the Economic Determinants of the Bond Rate:
A Variant of the Sargent Model
The economic determinants of the nominal bond rate are identified here by
specifying a loanable funds model employed by Sargent (1969), among others.
In this model, the nominal interest rate is assumed to be composed of a real
component, a component reflecting inflationary expectations, and a component
reflecting the influence of monetary policy actions on the real rate. In particular,
consider the identity (1) linking real and nominal components:
Rn(t) = Re(t) + [Rm(t) − Re(t) ] + Rn(t) − Rm(t) ,

(1)

where Rn is the nominal interest rate, Re is the equilibrium real rate, and Rm is
the market real rate. The nominal interest rate equation estimated here is based
on hypotheses used to explain each of the three terms on the right-hand side
of (1).
The first term, Re, is the real rate that equates ex ante saving with investment and the government deficit. Assume that savings (S) and investment (I)
depend upon economic fundamentals as in (2) and (3):
I(t) = g0 + g1 ∆y(t) − g2 Re(t)

(2)

S(t) = s0 + s1 y(t) + s2 Re(t) ,

(3)

3 This result is consistent with the Ricardian hypothesis that neither consumption nor interest
rates are affected by the stock of government debt or by the deficit. In an extensive survey, Seater
(1993) also concludes that the Ricardian hypothesis is approximately consistent with the data.

Y. P. Mehra: An Error-Correction Model

where y is real income. Equation (2) is an accelerator-investment equation
with interest rate effects, while equation (3) is a standard Keynesian savings
function. In equilibrium, the government deficit must be covered by an excess
of savings over investment. Hence, the equilibrium real rate is the rate that
solves equation (4):
RDEF(t) = S(t) − I(t),

(4)

where RDEF is the real government deficit. Substituting (2) and (3) into (4)
yields the following expression for the equilibrium real rate:
Re(t) =

1
[(g0 − s0 ) + g1 ∆yt − s1 yt + RDEF(t) ].
s2 + g2

(5)

The deficit and increases in the rate of growth of real income raise the demand
for funds and hence drive up the equilibrium real rate. In contrast, a higher
level of output generates a larger volume of savings and hence reduces the
equilibrium real rate.
The second term on the right-hand side of (1) is the deviation of the market
real rate from the equilibrium real rate. This interest rate gap arises in part
from monetary policy actions. The Federal Reserve can affect the real rate by
changing the supply of high-powered money. In the loans market, such changes
in the supply of money have effects on the demand and supply curves for funds
and hence the market real rate as in (6):
Rm(t) − Re(t) = −hi [∆rM(t) ],

(6)

where rM is the real supply of money. A rise in real money supply drives the
market rate downward with respect to the equilibrium real rate.
The third term on the right-hand side of (1) is the gap between the nominal
and real market rates of interest. Such a gap arises as a result of anticipated
inflation and is expressed as in (7):
Rn(t) − Rm(t) = β ṗet ,

(7)

where ṗe is anticipated inflation. Substituting (5), (6), and (7) into (1) produces
(8), which includes the main potential economic determinants of the bond rate
suggested in Sargent (1969).
Rn(t) = d0 + d1 ṗe(t) + d2 RDEF(t) − d3 y(t) − d4 ∆rM s(t) + d5 ∆y(t)

(8)

Equation (8) says that the nominal bond rate depends on anticipated inflation,
the deficit, changes in real money supply and income, and the level of income.
An Alternative Econometric Specification
Sargent (1969) estimates equations like (8) for one-year and ten-year bond
yields using annual data from 1902 to 1940. The bond rate equations estimated
here, however, differ from those reported in Sargent in two major respects. In

Federal Reserve Bank of Richmond Economic Quarterly

Sargent, changes in real money supply capture the impact of monetary policy
actions on the equilibrium real rate. As is now widely recognized, financial
innovations and the deregulation of interest rates have altered the short-run indicator properties of the empirical measures of money.4 However, the nominal
federal funds rate has been the instrument of monetary policy. Therefore, the
impact of monetary policy actions on the real rate is captured by including
the real funds rate in the bond rate equation.5 Secondly, the bond rate equation
here is based on cointegration and error-correction methodology, which is better
suited to distinguish between the short- and long-run economic determinants
of the bond rate than the one used in Sargent and elsewhere.
The nominal bond rate equation estimated here consists of two parts: a
long-run part and a short-run part. The long-run part that specifies the potential,
long-run determinants of the level of the bond rate is expressed in (9).
Rn(t) = a0 + a1 ṗe(t) + a2 RFR(t) + a3 RDEF(t)
− a4 ln ry(t) + a5 ∆ ln ry(t) + U(t) ,

(9)

where RFR is the real federal funds rate, RDEF is the real deficit, ln ry is
the logarithm of real income, and U is the disturbance term. Equation (9)
describes the long-run responses of the bond rate to anticipated inflation, the
real federal funds rate, the real deficit, changes in real income, and the level of
real income. The coefficients ai , i = 1 to 5, measure the long-run responses in
the sense that they are the sums of coefficients that appear on current and past
values of the relevant economic determinants. The term a1 ṗe in (9) captures the
inflation premium in the bond rate, whereas the remaining terms capture the
influence of other variables on the equilibrium real component of the bond rate.
If the nominal bond rate and anticipated inflation variables are nonstationary
but cointegrated as in Engle and Granger (1987), then the other remaining
long-run impact coefficients (a2 , a3 , a4 , and a5 in [9]) may all be zero.
Equation (9) may not do well in explaining short-run movements in the
bond rate for a number of reasons. First, it ignores the short-run effects of
fundamentals. Some economic factors, including those measuring monetary
policy actions, may be important in explaining short-run changes in the bond
rate, even though they may have no long-run effects. Second, the long-term
bond equation (9) completely ignores short-run dynamics. The presence of
expectations and/or adjustment lags in the effects of economic fundamentals
on the bond rate may cause the bond rate to differ from the value determined
in (9). Hence, in order to explain short-run changes in the bond rate, consider
the following error-correction model of the bond rate:
4 See

Hetzel and Mehra (1989) and Feinman and Porter (1992) for evidence on this issue.
(1993) also uses the funds rate to measure the impact of monetary policy
actions on the real component of the bond rate.
5 Goodfriend

Y. P. Mehra: An Error-Correction Model

∆Rn(t) = c0 + c1 ∆ṗe(t) + c2 ∆RFR(t) + c3 ∆RDEF(t) + c4 ∆ ln ry(t)
n

+ c5 ∆2 ln ry(t) +
c6s ∆Rn(t−s) + c7 U(t−1) + (t) ,

(10)

s=1

where U(t−1) is the lagged residual from the long-run bond equation (9), ∆2
is the second-difference operator, and other variables are as defined before.
Equation (10) is the short-run bond rate equation, and the coefficients ci , i = 1
to 5, capture the short-run responses of the bond rate to economic determinants
suggested here. The coefficients that appear on lagged first differences of the
bond rate, c6s , s = 1 to n, capture short-run dynamics. The equation is in an
error-correction form, indicating that the bond rate will adjust in the short run
if the actual bond rate differs from its long-run value determined in (9), i.e.,
if U(t−1) is different from zero in (10). The coefficient c7 that appears on the
lagged error-correction residual in (10) thus captures the short-run influence of
long-run dynamics on the bond rate.
Data and Definition of Variables
The main problem in estimating (9) or (10) is that long-run anticipated inflation
is an unobservable variable. The empirical work here first uses actual inflation
as a proxy for long-run anticipated inflation. In this case, the coefficient a1
that appears on actual inflation in the long-run bond equation (9) measures the
bond rate’s response to anticipated inflation, where the latter is modeled as a
distributed lag on current and past inflation rates. Hence, this specification is
similar in spirit to the one used in Sargent (1969), who had employed an infinite
(geometric) distributed lag as a proxy for inflationary expectations. I, however,
also examine results using one-year-ahead inflation rates from the Livingston
survey to proxy for long-run anticipated inflation.
The empirical work uses quarterly data from 1955Q1 to 1993Q4.6 The
bond rate is the nominal yield on 30-year U.S. Treasury bonds. Inflation is
measured by the behavior of the consumer price index. The real federal funds
rate is the nominal federal funds rate minus the actual, annualized quarterly
inflation rate. The real deficit variable is included in ratio form as federal
government deficits scaled by nominal GDP.7 Real income is real GDP. Hence,
the empirical specifications considered here are given in (11) and (12).
6 The data on the Livingston survey are provided by the Philadelphia Fed. All other data
series are from the Citibank data base.
7 This specification reflects the assumption that in a growing economy higher deficits result
in higher interest rates only if the deficit rises relative to GDP. Hence, the deficit is scaled by
GDP. This specification amounts to the restriction that the coefficients a3 and a4 in (9) are equal
in magnitude but opposite in sign. However, none of the results here qualitatively change if the
deficit (RDEF) and real GDP (ln ry) enter separately in regressions.

Federal Reserve Bank of Richmond Economic Quarterly

R30(t) = a0 + a1 ṗ(t) + a2 RFR(t) + a3 (DEF/y)(t) + a4 ∆ ln ry(t) + U(t)

(11)

∆R30(t) = c0 + c1 ∆ṗ(t) + c2 ∆RFR(t) + c3 ∆(DEF/y)(t)
+ c4 ∆2 ln ry(t) + c5 U(t−1) + (t) ,

(12)

where R30 is the bond rate, ṗ is actual inflation, and (DEF/y) is the ratio of
deficits to GDP. Equation (11) is the long-run bond rate equation and equation
(12) the short-run equation. The alternative specification investigated here replaces ṗ(t) in (11) and (12) with ṗe(t) , where ṗe is the Livingston survey measure
of inflationary expectations.
Estimation Issues: The Long-Run Bond Rate Equation
The stationarity properties of the data are important in estimating the longrun bond equation. If empirical measures of economic determinants including
the bond rate are all nonstationary variables but cointegrated as in Engle and
Granger (1987), then the long-run equation (11) can be estimated by ordinary
least squares. Tests of hypotheses on coefficients that appear in (11) can then be
carried out by estimating Stock and Watson’s (1993) dynamic OLS regressions
of the form
R30(t) = a0 + a1 ṗ(t) + a2 RFR(t) + a3 [DEF(t) /y(t) ] + a4 ∆ ln ry(t)
+

s=−k

a4s ∆ṗ(t−s) +

a5s ∆RFR(t−s)

s=−k

a6s ∆[DEF(t−s) /y(t−s) ] +

s=−k

a7s ∆2 ln ry(t−s) + (t) . (13)

s=−k

Equation (13) includes, in addition to current levels of economic variables,
past, current, and future values of changes in them.
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
tests are performed by estimating the augmented Dickey-Fuller regression of
the form
X(t) = m0 + ρX(t−1) +

m1s ∆X(t−s) + (t) ,

(14)

s=1

where X is the pertinent variable, is the random disturbance term, and k is
the number of lagged first differences of X necessary to make serially uncorrelated. If ρ = 1, X has a unit root. The null hypothesis ρ = 1 is tested using

Y. P. Mehra: An Error-Correction Model

the t-statistic. The lag length (k) used in tests is chosen using the procedure
given in Hall (1990), as advocated by Campbell and Perron (1991).8
The Dickey-Fuller statistic tests the null hypothesis of unit root against the
alternative that X is mean stationary. Recently, some authors including DeJong
et al. (1992) have presented evidence that the Dickey-Fuller tests have low
power in distinguishing between the null and the alternative. These studies
suggest that it would also be useful to perform tests of the null hypothesis of
mean stationarity to determine whether the variables are stationary or integrated.
Thus, tests of mean stationarity are performed using the procedure advocated
by Kwiatkowski, Phillips, Schmidt, and Shin (1992). The test, hereafter denoted
as the KPSS test, is implemented by calculating the test statistic
n̂u =

T
1 2 2
S /σ̂ ,
T 2 t=1 (t) k

where S(t) = ti=1 ei , t = 1, 2, . . . T, et is the residual from the regression
of X(t) on an intercept, σ̂k is a consistent estimate of the long-run variance of
X, and T is the sample size.9 The statistic n̂u has a nonstandard distribution
and its critical values have been provided by Kwiatkowski et al. (1992). The
null hypothesis of stationarity is rejected if n̂u is large. Thus, a variable X(t) is
considered unit root nonstationary if the null hypothesis that X(t) has a unit root
is not rejected by the augmented Dickey-Fuller test and the null hypothesis that
it is mean stationary is rejected by the KPSS test.
The test for cointegration used is the one proposed in Johansen and Juselius
(1990). The test procedure consists of estimating a VAR model that includes
differences as well as levels of nonstationary variables. The matrix of coefficients associated with levels of these variables contains information about the
long-run properties of the model. To explain the model, let Zt be a vector of time
series on the bond rate and its economic determinants. Under the hypothesis
that the series in Zt are difference stationary, one can write a VAR model as

∆Zt = Γ1 ∆Z(t−1) + · · · + Γ(k−1) ∆Z(t−k−1) + Π Z(t−k) + (t) ,

(15)

8 The procedure is to start with some upper bound on k, say k max, chosen a priori (eight
quarters here). Estimate the regression (14) with k set at k max. If the last included lag is
significant, select k = k max. If not, reduce the order of the estimated autoregression by one until
the coefficient on the last included lag (on ∆X in [14]) is significant. If none is significant, select
k = 0.
9 The residual e is from the regression X = a + e . The variance of X is the variance of
t
t
t
t
the residuals from this regression and is estimated, using the Newey and West (1987) method, as

σ̂k =

T
T
T

1 2
2
et +
b(s, k)
et et−s ,
T
T
t=1

s=1

t=s+1

where T is the sample size, the weighing function b(s, k) = 1 +
parameter. The lag parameter was set at k = 8.

S
,
1+k

and k is the lag truncation

Federal Reserve Bank of Richmond Economic Quarterly

where Γi , i = 1, 2, . . . k − 1, and Π are matrices of coefficients that appear
on first differences and levels of the time series in Zt .
The component ΠZt−k in (15) gives different linear combinations of levels
of the time series in Zt . Thus, the matrix Π contains information about the
long-run properties of the model. When the matrix’s rank is zero, equation
(15) reduces to a VAR in first differences. In that case, no series in Zt can
be expressed as a linear combination of other remaining series. This result
indicates that there does not exist any long-run relationship between the series
in the VAR. On the other hand, if the rank of Π is one, then there exists only
one linear combination of series in Zt . That result indicates that there is a
unique, long-run relationship between the series.
Two test statistics can be used to evaluate the number of the cointegrating
relationships. The trace test examines the rank of Π matrix and the hypothesis
that rank (Π) ≤ r, where r represents the number of cointegrating vectors. The
maximum eigenvalue statistic tests the null that the number of cointegrating
vectors is r, given the alternative of r + 1 vectors. The critical values of these
test statistics have been reported in Johansen and Juselius (1990).
OLS estimates are inconsistent if any right-hand explanatory variable in
the long-run bond equation (11) is stationary. In that case, the long-run bond
equation (11) can be estimated jointly with the short-run bond equation (12).
To do so, solve (11) for U(t−1) and then substitute for U(t−1) into (12) to
yield (16).
∆R30(t) = (c0 − c5 a0 ) + c1 ∆ṗ(t) + c2 ∆RFR(t) + c3 ∆(DEF(t) /y(t) )
+ c4 ∆2 ln ry(t) − c5 R30(t−1) − c5 a1 ṗ(t−1) − c5 a2 RFR(t−1)
− c5 a3 DEF(t−1) /y(t−1) − c5 a4 ∆ ln ry(t−1) + t

(16)

Equation (16) is the short-run bond rate equation that includes levels as well
as differences of the relevant economic determinants. The long-run coefficients
ai , i = 1, 2, 3, can be recovered from the reduced-form estimates of equation
(16).10 The equation can be estimated by ordinary least squares,11 or by instrumental variables if contemporaneous right-hand variables are correlated with
the disturbance term.

10 The long-run coefficient on inflation (a ) is the coefficient on ṗ(t − 1) divided by the co1
efficient on R30(t−1) ; the long-run coefficient on deficit (a3 ) is the coefficient on DEF(t−1) /y(t−1)
divided by the coefficient on R30(t−1) ; and the long-run coefficient on the real funds rate is the
coefficient on RFR(t−1) divided by the coefficient on R30(t−1) . The intercept a0 , however, cannot
be recovered from these reduced-form estimates.
11 Since lagged levels of economic determinants appear in (16), ordinary least squares estimates are consistent if some variables on the right-hand side of (16) are in fact stationary.

Y. P. Mehra: An Error-Correction Model

ESTIMATION RESULTS

Unit Root Test Results
Table 1 presents test results for determining whether the variables R30, ṗ, ṗe ,
and (DEF/y) have a unit root or are mean stationary. As can be seen, the
t-statistic (tp̂ ) that tests the null hypothesis that a particular variable has a unit
root is small for all these variables. On the other hand, the test statistic (n̂u ) that
tests the null hypothesis that a particular variable is mean stationary is large
for R30, ṗ, ṗe and (DEF/y), but small for RFR. These results thus indicate that
R30, ṗ, ṗe , and (DEF/y) have a unit root and are thus nonstationary in levels.
The results are inconclusive for the RFR variable.
As indicated before, a variable has a unit root if ρ = 1 in (14). In order
to indicate the extent of uncertainty about the point-estimate of ρ, Table 1
also contains estimates of ρ and their 95 percent confidence intervals. As can
be seen, the estimated intervals contain the value ρ = 1 for levels of these
variables. However, these intervals appear to be quite wide: their lower limits
are close to .90 for the series shown. These results indicate that the variables
may well be mean stationary. Hence, I also derive results treating all variables
as stationary.
Table 1 also presents unit root tests using first differences of R30, ṗ, ṗe ,
RFR, ln ry and (DEF/y). As can be seen, the t-statistic for the hypothesis ρ = 1
is fairly large for all these variables. The point-estimates of ρ also diverge away
from unity. These results indicate that first differences of these variables are
stationary.
Cointegration Test Results
Treating the bond rate, inflation, the real funds rate, and government deficits as
nonstationary variables, Table 2 presents test statistics for determining whether
the bond rate is cointegrated with any of these variables.12 Change in real
income (∆ ln ry) is not considered because it is a stationary variable. Trace
and maximum eigenvalue statistics, which test the null hypothesis that there is
no cointegrating vector, are large for systems (R30, ṗ), (R30, ṗe ), (R30, DEF/y),
(R30, ṗ, DEF/y) and (R30, ṗe , DEF/y), but are very small for the system
(R30, RFR). These results indicate that the bond rate is cointegrated with inflation (actual or expected) and deficits, but not with the real funds rate. That
is, the bond rate stochastically co-moves with inflation and the deficit variable,
but not with the real funds rate.
12 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 JJ procedure is the one that results in the rejection of the restricted
model.

Federal Reserve Bank of Richmond Economic Quarterly

Table 1 Tests for Unit Roots and Mean Stationarity
Panel A
Tests for
Unit Roots
Series X
R30
ṗ
ṗe
RFR
DEF/y
∆R30
∆ṗ
∆ṗe
∆RFR
∆DEF/y
∆ ln ry
∗

ρρ̂

tρρ̂

.97
.87
.97
.85
.93

−1.65
−2.74
−1.78
−2.38
−2.46

5
7
2
2
1

−5.47∗
−5.09∗
−6.33∗
−5.52∗
−6.18∗
−4.83∗

8
8
1
7
8
7

−.02
−.70
.38
−1.50
−.80
.20

Panel B
Tests for
Mean Stationarity

Confidence Interval
for ρ
(.93,
(.84,
(.92,
(.87,
(.87,

1.03)
1.01)
1.02)
1.02)
1.02)

n̂u
1.31∗
.53∗
1.02∗
.39
1.42∗

Significant at the 5 percent level.

Notes: R30 is the 30-year bond rate; ṗ is the annualized quarterly inflation rate measured by the
behavior of consumer prices; ṗe is the Livingston survey measure of one-year-ahead expected
inflation; RFR is the real federal funds rate; and DEF/y is the ratio of federal government deficits
to nominal GDP. ∆ is the first-difference operator. The sample period studied is 1955Q1 to
1993Q4. ρ and t-statistics (tρ̂ ) for ρ = 1 in Panel A above are from the augmented Dickey-Fuller
regressions of the form
X(t) = a0 + ρX(t−1) +

as ∆X(t−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 number of lagged first differences (k) included in these regressions are chosen using the
procedure given in Hall (1990), with maximum lag set at eight quarters. The confidence interval
for ρ is constructed using the procedure given in Stock (1991).
The test statistics n̂u in Panel B above is the statistic that tests the null hypothesis that the
pertinent series is mean stationary. The 5 percent critical value for n̂u given in Kwiatkowski et
al. (1992) is .463.

Table 3 presents the dynamic OLS estimates of the cointegrating vector
between the bond rate and its long-run determinants, inflation and the deficit.
Panel A presents estimates with actual inflation (ṗ) and Panel B with expected
inflation (ṗe ). In addition, the cointegrating vector is estimated under the restriction that the bond rate adjusts one for one with inflation in the long run. In
regressions estimated without the above-noted full Fisher-effect restriction, the
right-hand explanatory variables have their theoretically predicted signs and
are statistically significant. Thus, the bond rate is positively correlated with
inflation and deficits in the long run. The coefficient that appears on the

Y. P. Mehra: An Error-Correction Model

Table 2 Cointegration Test Results

Trace
Test

Maximum Eigenvalue
Test

(R30, ṗ)

23.7*

21.2*

(R30, ṗe )

20.6*

17.6*

(R30, RFR)

12.1

8.9

(R30, DEF/y)

30.4*

27.5*

(R30, ṗ, DEF/y)

46.8*

35.6*

(R30, ṗe , DEF/y)

48.3*

31.9*

System

The lag length k was selected using the likelihood ratio test procedure described in footnote 12
of the text.
* Significant at the 5 percent level.
Notes: Trace and maximum eigenvalue tests are tests of the null hypothesis that there is no
cointegrating vector in the system. For the two-variable system, the 5 percent critical value is
17.8 for the trace statistic and 14.5 for the maximum eigenvalue statistic. Critical values are from
Johansen and Juselius (1990). (For the three-variable system, the corresponding 5 percent critical
values are 31.2 and 21.3.)

Table 3 Cointegrating Regressions; Dynamic OLS
(Leads,
Lags)

Without the Full FisherEffect Restriction

With the Full FisherEffect Restriction

Panel A: (R30, ṗ, DEF/y)
(−4, 4)

R30t = 2.0 + .61ṗt + .73(DEF/y)t
(.03) (.03) (.04)

R30t = 1.3 + 1.0ṗt + .30(DEF/y)t
(.10) (.03) (.05)

(−8, 8)

R30t = 2.0 + .60ṗt + .78(DEF/y)t
(.12) (.03) (.08)

R30t = 1.3 + 1.0ṗt − .13(DEF/y)t
(.10) (.03) (.03)

Panel B: (R30, ṗe , DEF/y)
(−4, 4)

R30t = 2.6 + .77ṗet + .46(DEF/y)t
(.13) (.03) (.03)

R30t = 2.1 + 1.0ṗet + .13(DEF/y)t
(.11) (.03) (.03)

(−8, 8)

R30t = 2.6 + .72ṗet + .57(DEF/y)t
(.15) (.06) (.13)

R30t = 2.8 + 1.0ṗet + .00(DEF/y)t
(.14) (.00) (.03)

Notes: All regressions are estimated by the dynamic OLS procedure given in Stock and Watson
(1993), using leads and lags of first differences of the relevant right-hand side explanatory variables. Parentheses contain standard errors corrected for the presence of moving average serial
correlation. The dynamic OLS regressions also include leads and lags of the real federal funds
rate.

Federal Reserve Bank of Richmond Economic Quarterly

inflation variable ranges between .6 and .8 and is less than unity, indicating
that the bond rate does not adjust one for one with inflation in the long run.
The coefficient that appears on the deficit variable ranges between .4 and .8,
indicating that a one percentage point increase in the ratio of deficits to GDP
raises the bond rate by 40 to 80 basis points.13 However, the coefficient that
appears on the deficit variable is sensitive to the restriction that there is a full
Fisher effect. If the cointegrating regression is reestimated with this restriction,
then the deficit variable coefficient becomes small and even turns negative in
some cases (see Table 3).
The full Fisher-effect restriction is in fact rejected by the data, indicating
that it should not be imposed routinely on the bond regression. Nevertheless,
it is a reasonable restriction to consider if one wants to carry out the sensitivity analysis. The finding that the long-run deficit-interest rate link weakens
when the restriction is imposed indicates that the deficit may be proxying the
information that is already in inflation. The deficit appears to raise the long
rate because of its positive effect on anticipated inflation rather than on the
real component of the bond rate. Hence, these results imply that inflation is the
main, long-run economic determinant of the bond rate.
The Short-Run Bond Rate Equation
Since unit root test results are inconclusive for some series, the short-run bond
equation is estimated jointly with the long-run part as in (16), which includes
lagged levels of the series. If the variables are stationary in levels, OLS estimates will still be consistent.
Table 4 presents instrumental variable estimates of the bond equation
(16).14 Panel A there reports regressions with actual inflation (ṗ), and Panel
B regressions with expected inflation (ṗe ). In addition, I estimate the equation
with and without the constraint that the bond rate adjusts one for one with
inflation in the long run (compare equations in columns A.1 and B.1 versus
A.2 and B.2, Table 4). As can be seen, the coefficients that appear on various
economic variables have their theoretically predicted signs and in general are
statistically significant. The results there indicate that in the short run the bond
rate rises if inflation increases, or if the real federal funds rate rises. Changes
13 These estimates are close to those reported in Hoelscher (1986). Hoelscher uses the tenyear bond rate and the Livingston survey measure as proxies for long-term expected inflation. He
estimates the bond regression from 1953 to 1984, using annual data. The coefficients that appear
on his inflation and deficit variables are .84 and .42, respectively. Hoelscher does not, however,
examine the sensitivity of results to the restriction that the bond rate adjusts one for one with
inflation in the long run.
14 I use instrumental variable estimates because contemporary values of changes in the
funds rate, inflation, and real income variables may be correlated with the disturbance term. For
example, the evidence in Mehra (1994) indicates that the Fed has responded to the information
in the bond rate about long-run expected inflation. Hence, the change in the funds rate may be
contemporaneously correlated with the disturbance term.

Y. P. Mehra: An Error-Correction Model

Table 4 Error-Correction Bond Rate Regressions

Explanatory
Variables
constant
R30t−1
ṗt−1
ṗet−1
(DEF/y)t−1
RFRt−1
∆ṗt
∆ṗet
∆RFRt
∆ ln rYt
∆R30t−1
∆R30t−2
SER
DW
Q(36)
n(ṗ, RFR, DEF/y)
n(ṗe , RFR, DEF/y)

Panel A
Regressions Using
Actual Inflation Data

Panel B
Regressions Using Livingston
Survey Inflation Data

A.1

A.2

B.1

B.2

.55 (2.1)
−.29 (4.7)
.20 (4.9)

−.01 (0.1)
−.18 (4.6)
.18 (4.6)

1.80 (2.4)
−.59 (3.2)

.59 (4.5)
−.30 (6.2)

.18 (3.2)
.19 (3.6)
.40 (3.7)

.06 (2.2)
.13 (2.9)
.32 (3.3)

.43 (4.2)
.24 (1.8)
.31 (2.9)

.30 (6.2)
.02 (0.8)
.15 (4.1)

.35
−.01
−.10
.16

(4.6)
(0.2)
(1.1)
(1.7)

.24
.05
−.24
.09

(4.0)
(1.4)
(3.2)
(1.0)

.451
2.0
35.3

.434
1.84
37.6

(.7, .7, .6)

(1.0, .7, .3)

.61
.31
−.10
.31
.10

(2.1)
(2.5)
(1.2)
(1.4)
(0.8)

.26
.14
.03
−.01
.03

(1.8)
(2.5)
(1.1)
(0.1)
(0.4)

.709
2.0
54.9

.504
1.95
46.3

(.7, .5, .4)

(1.0, .5, .1)

Notes: All regressions are estimated by instrumental variables. The instruments used are a constant, one lagged value of the bond rate, inflation, the real federal funds rate, and the ratio of
deficits to GDP and two lagged values of changes in inflation, the real funds rate, real GDP, and
the bond rate. Regressions in columns A.2 and B.2 above are estimated under the restriction that
coefficients on R30t−1 and ṗt−1 (ṗet−1 ) sum to zero (there is complete Fisher-effect), while those
in columns A.1 and B.1 are without this restriction. SER is the standard error of regression, DW
is the Durbin-Watson statistic, and Q(36) is the Lung-Box Q-statistic based on 36 autocorrelations
of the residuals. n(x1 , x2 , x3 ) indicates the long-run (distributed) responses of the 30-year bond
rate to x1 , x2 , and x3 , respectively.

in real GDP do not have much of an impact on the bond rate.15 The coefficients
that appear on contemporaneous values of these variables range from .3 to .6
for inflation and from .2 to .4 for the real funds rate. Thus, a one percentage
point increase in the rate of inflation raises the bond rate between 30 to 60
basis points, while a similar increase in the real funds rate raises it by 14 to 35
basis points in the short run.16
15 First differences of the deficit variable and second differences of real GDP when included
in regressions were generally not significant.
16 The point-estimates of the short-run, monetary policy impact coefficient found here are
close to those found or assumed in some other studies. For example, the empirical work presented
in Cook and Hahn (1989) indicates that a one percentage point rise in the funds rate target raises
the long rate by 10 to 20 basis points, whereas in Goodfriend (1993) such an increase in the funds
rate is assumed to raise the long rate by 25 basis points.

Federal Reserve Bank of Richmond Economic Quarterly

As indicated before, the bond rate’s long-run distributed-lag responses to
economic determinants here can be recovered from the reduced-form estimates
of the short-run bond equation presented in Table 4. As can be seen, the longrun coefficients that appear on these variables range from .7 to 1.0 for inflation,
.5 to .7 for the real funds rate, and .1 to .6 for the deficit variable. Moreover,
as before, the long-run coefficient on the deficit variable becomes small and
is statistically insignificant if the full Fisher-effect restriction is imposed on
the data (see equations A.2 and B.2 in Table 4). The long-run coefficient that
appears on the real funds rate, however, remains quite large and is statistically
significant. This result indicates that (stationary) movements in the real funds
rate can have substantial effects on the bond rate in the short run.17,18
Predictive Ability of the Bond Rate Equation
I now examine whether bond rate regressions presented in Table 4 can explain
the actual behavior of the bond rate. In particular, I examine one-year-ahead
dynamic forecasts of the bond rate from 1971Q1 to 1993Q4, using regressions
A.2 and B.2 of Table 4. Recall that regression A.2 uses actual inflation as a
proxy for long-run inflationary expectations and regression B.2 uses one-yearahead expected inflation as a proxy. Since the forecast performance of these
two regressions is similar, I discuss results only for the former.
Figure 1 charts the quarterly values of the bond rate, actual and predicted.
As can be seen, the regression captures fairly well broad movements in the
bond rate from 1971Q1 to 1993Q4. The mean prediction error is small, only
6 basis points, and the root mean squared error is .74 percentage points. This
regression outperforms a purely eight-order autoregressive model of the bond
rate. For the time series model, the mean prediction error is 13 basis points
and the root mean squared error is 1.2 percentage points.
I evaluate further the predictive performance from 1971Q1 to 1993Q4 by
estimating regressions of the form (17).
17 If all variables are stationary, then the long-run coefficient that appears on the funds
rate in the short-run bond equation measures the sum of coefficients associated with current and
past values of changes in the funds rate. Since permanent movements in the funds rate have
no permanent effects on the bond rate, this long-run coefficient in fact measures the short-run
response of the bond rate to changes in the funds rate.
18 The long-run coefficient that appears on the funds rate in the bond rate regression may
be an upwardly biased estimate of the impact of monetary policy actions on the real component
of the bond rate. The main source of this potential bias is the absence of the relevant longrun expected inflation variable in these regressions. If the Fed responds to variables that have
information about long-run expected inflation, then the funds rate may be picking up the influence
of expected inflation on the bond rate rather than the influence of monetary policy actions on the
real component of the bond rate. Some evidence that favors this view emerges in Table 4. As can
be seen, the magnitude of the long-run coefficient that appears on the funds rate declines from .7
to .5 if one-year-ahead expected inflation (Livingston) data are substituted for actual inflation in
the regression.

Y. P. Mehra: An Error-Correction Model

Figure 1 Actual and Predicted 30-Year Bond Rate

18
16

Actual
Predicted
Error

14
12
10
8
6
4
2
0
-2
-4
1971:1

75:1

80:1

85:1

90:1

Note: Predicted values are generated using the regression with actual inflation (regression A.2 in
Table 4).

A(t) = d0 + d1 P(t) ,

(17)

where A is the actual quarterly value of the bond rate and P is the value
predicted by the bond rate regression. If d0 = 0 and d1 = 1, then regression
forecasts are unbiased. The coefficients d0 and d1 take values .3 and .97, respectively, for regression A.219 and 1.7 and .8, respectively, for the time series
model. The hypothesis d0 = 0, or d1 = 1, is rejected for the time series model,
but not for the economic models.20
Unpredictable, Short-Run Upward Swings in the Bond Rate: Inflation
A look at Figure 1 indicates that the bond rate regression estimated here fails
to predict some large, short-run movements in the bond rate that have occurred
during the post-1979 period.21 Table 5 presents quarterly changes in the bond
rate from 1979Q1 to 1994Q2. It also presents changes predicted by the bond
19 For

regression B.2 of Table 4, d0 = .13 and d1 = 1.0.
regression A.2, the relevant Chi-squared statistics that test d0 = 0 and d1 = 1 are .3
and .2, respectively. The relevant statistics are .03 and 0.0 for regression B.2 of Table 4. For the
time series model, the relevant Chi-squared statistics take values 3.9 and 4.1. Each Chi-squared
statistic is distributed with one degree of freedom. The 5 percent critical value is 3.84.
21 Such large, short-term increases in the bond rate did not occur during the pre-1979 period.
20 For

Federal Reserve Bank of Richmond Economic Quarterly

Table 5 Actual and Predicted Quarterly Changes in the Bond Rate
1979Q1 to 1994Q2
Year/Qtr.

Actual

Predicted

Error

Year/Qtr.

1979Q1
1979Q2
1979Q3
1979Q4
1980Q1
1980Q2
1980Q3
1980Q4
1981Q1
1981Q2
1981Q3
1981Q4
1982Q1
1982Q2
1982Q3
1982Q4
1983Q1
1983Q2
1983Q3
1983Q4
1984Q1
1984Q2
1984Q3
1984Q4
1985Q1
1985Q2
1985Q3
1985Q4
1986Q1
1986Q2
1986Q3
1986Q4

.15
−.11
.25
.95
2.22a
−2.53
1.53a
1.06
.29
.27
1.71a
−1.22
.08
.39
−1.85
−1.53
.09
.30
.70a
.25
.50
1.06a
−1.15
−.77
.29
−1.36
.16
−1.07
−1.58
−.39
.05
−.25

.07
.06
.37
.49
.55
−.69
.74
1.09
−.63
1.32
−.32
−.14
.44
.53
−.69
.01
.42
.48
−.30
.06
.13
.01
−.35
−.37
−.11
−.59
.17
−.36
.50
.41
−.13
−.03

.07
−.17
−.12
.46
1.66
−1.84
.79
−.03
.92
−1.06
2.03
−1.07
−.36
−.14
−1.15
−1.54
−.33
−.18
1.00
.18
.36
1.05
−.79
−.40
.40
−.77
−.01
−.70
−2.10
.03
.18
−.21

1987Q1
1987Q2
1987Q3
1987Q4
1988Q1
1988Q2
1988Q3
1988Q4
1989Q1
1989Q2
1989Q3
1989Q4
1990Q1
1990Q2
1990Q3
1990Q4
1991Q1
1991Q2
1991Q3
1991Q4
1992Q1
1992Q2
1992Q3
1992Q4
1993Q1
1993Q2
1993Q3
1993Q4
1994Q1
1994Q2

Actual

Predicted

Error

.18
1.02a
1.02a
−.47
−.49
.37
.06
−.05
.16
−.90
−.12
−.25
.66
−.10
.57
−.79
.05
.18
−.52
−.25
.27
−.13
−.50
.10
−.62
−.01
−.81
.25
.35
.80a

.20
.16
−.07
−.22
−.25
.25
−.07
.22
.44
.03
−.10
.12
.55
−.31
−.01
−.80
−.67
−.47
−.50
−.64
−.36
−.45
−.50
−.17
−.60
−.51
−.51
.32
−.43b
.01b

−.02
.85
1.09
−.24
−.24
.12
.13
−.27
−.27
−.93
−.01
−.37
.11
.21
.58
.01
.72
.65
−.02
.39
.63
.32
.00
.27
−.02
.29
−.29
−.07
.78
.78

Mean Error
RmSE

−.004
.74

a This significant increase in the bond rate is not predicted by the bond rate regression A.2 of Table 4
(the prediction error is at least as large as the root mean squared error).
b This forecast assumes that during the first and second quarters the ratio of deficits to GDP equals the
value observed in 1993Q4.

Notes: The predicted values are generated using the bond rate regression A.2 of Table 4.

Y. P. Mehra: An Error-Correction Model

regression. If we focus on quarterly increases in the bond rate that are significantly underpredicted by the regression (that is, magnitudes of prediction errors
either equal or exceed the root mean squared error), the results then indicate
that the bond rate rose 2.2 percentage points in 1980Q1, 1.53 in 1980Q3, 1.71
in 1981Q3, .7 in 1983Q4, 1.1 in 1984Q2, 2.1 in 1987Q2 to 1987Q3, and .8 in
1994Q2 (see Table 5). Except for the latest episode, most of these short-run
upswings in the bond rate have been subsequently reversed, so that for the
period as a whole the bond rate is well predicted by the regression.
The bond rate equation here attempts to explain changes in the bond rate
using actual, not long-run anticipated, values of economic fundamentals. In the
long run, actual values of fundamentals may move with anticipated values, but
that may not be so in the short run. Hence, if the bond rate in fact responds to
anticipated fundamentals, then the bond rate regressions estimated here may not
explain very well short-run movements in the bond rate. These considerations
suggest one possible explanation of some unpredictable short-run upswings in
the bond rate that have occurred since 1979: namely, short-term movements in
its anticipated fundamentals. Since, as indicated by cointegration test results,
inflation, rather than the deficit or the real funds rate, is the main long-run economic determinant of the bond rate, the short-run increases in the bond rate may
then be due to short-run movements in its long-run determinant—anticipated
inflation.22 Thus, the bond rate may rise with anticipated inflation in the short
run even as actual inflation remains steady. Such upswings, however, are likely
to be reversed if they are not substantiated by the behavior of actual inflation.
As can be seen in Table 5, that in fact has been the case.
Following Goodfriend (1993), the periods during which large, unpredictable increases in the bond rate have occurred can be labeled as inflation scares.
Goodfriend uses a narrative approach to discuss the interactions among the
bond rate, the federal funds rate, and economic determinants such as inflation
and real growth. He assumes that inflation is the bond rate’s main long-run
determinant and that changes in the funds rate have minor short-run effects on
the bond rate. Hence, he calls a significant bond rate rise in the absence of
an aggressive funds rate tightening an inflation scare. The results from a more
formal bond rate equation here are in line with those in Goodfriend (1993).

22 Short-run changes in anticipated monetary policy actions and deficits cannot explain the
big increases in the bond rate either. As noted before, the bond rate is unrelated to short-term
changes in the deficit. Furthermore, the magnitudes of future funds rate increases needed to explain
the current increases in the bond rate are too big to be consistent with past Fed behavior. In the
past, the Fed has moved the funds rate in small increments most of the time.

Federal Reserve Bank of Richmond Economic Quarterly

CONCLUDING OBSERVATIONS

Using cointegration and error-correction methodology and building on the loanable funds model of interest rate determination given in Sargent (1969), this
article identifies the main long- and short-run economic determinants of the
bond rate. In the cointegrating regression, inflation and fiscal deficits appear as
two potential long-run economic determinants of the bond rate. That regression
indicates that the bond rate is positively correlated with inflation and the deficit
and that the bond rate does not adjust one for one with inflation in the long run.
However, if that regression is reestimated under the restriction that the bond rate
does in fact adjust one for one with inflation, then the long-run deficit-interest
rate link found here weakens. Those results imply that the positive effect of the
deficit on the real component of the bond rate found here is suspect. Hence,
inflation emerges as the main economic determinant of the long rate.
The results here also indicate that changes in the real federal funds rate have
substantial short-run effects on the bond rate, even though long-run stochastic
movements in the bond rate are unrelated to the real funds rate. In addition,
the bond rate rises if inflation accelerates. Surprisingly, current changes in real
GDP do not have much of an effect on the bond rate.
The bond rate regressions estimated here are broadly consistent with the
actual behavior of the bond rate from 1971 to 1993. However, these regressions fail to predict some large, short-run upswings in the bond rate that have
occurred during the subperiod 1979Q1 to 1994Q2. One possible explanation
of these results is that actual inflation may be a poor proxy for the long-run
expected rate of inflation, the main long-run economic determinant of the bond
rate. Hence, the bond rate may rise significantly in the short run if long-run
anticipated inflation increases, even though actual inflation may have been
steady.

REFERENCES
Campbell, J. Y., and P. Perron. “Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots,” in O. J. Blanchard and
S. Fischer, eds., NBER Macroeconomics Annual, 1991. Cambridge, Mass.:
MIT Press, 1991, pp. 141–200.
Cook, Timothy, and Thomas Hahn. “The Effect of Changes in the Federal
Funds Rate Target on Market Interest Rates in the 1970s,” Journal of
Monetary Economics, vol. 24 (November 1989), pp. 331–51.
DeJong, David N., and John C. Nankervis, N. E. Savin, and Charles H.
Whiteman. “Integration Versus Trend Stationarity in Time Series,”
Econometrica, vol. 60 (March 1992), pp. 423–33.

Y. P. Mehra: An Error-Correction Model

Dickey, D. A., and W. A. Fuller. “Distribution of the Estimators for Autoregressive Time Series with a Unit Root,” Journal of the American
Statistical Association, vol. 74 (June 1979), pp. 427–31.
Echols, Michael E., and Jan Walter Elliot. “Rational Expectations in a Disequilibrium Model of the Term Structure,” American Economic Review,
vol. 66 (March 1976), pp. 28–44.
Engle, Robert F., and C. W. Granger. “Cointegration and Error-Correction:
Representation, Estimation and Testing,” Econometrica, vol. 55 (March
1987), pp. 251–76.
Feinman, Joshua, and Richard D. Porter. “The Continuing Weakness in M2,”
Finance and Economic Discussion Paper #209. Washington: Board of
Governors of the Federal Reserve System, September 1992.
Fuller, W. A. Introduction to Statistical Time Series. New York: Wiley, 1976.
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.
Hall, A. “Testing for a Unit Root in Time Series with Pretest Data Based
Model Selection.” Manuscript. North Carolina State University, 1990.
Hetzel, Robert L., and Yash P. Mehra. “The Behavior of Money Demand in
the 1980s,” Journal of Money, Credit, and Banking, vol. 21 (November
1989), pp. 455–63.
Hoelscher, Gregory. “New Evidence on Deficits and Interest Rates,” Journal
of Money, Credit, and Banking, vol. XVII (February 1986), pp. 1–17.
Johansen, Soren, and Katarina Juselius. “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.
Kwiatkowski, Denis, Peter C. B. Phillips, Peter Schmidt, and Yoncheol 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.
Mehra, Yash P. “A Federal Funds Rate Equation,” Mimeo, Federal Reserve
Bank of Richmond, March 1994.
Newey, Whitney K., and Kenneth D. West. “A Simple, Positive Semi-Definite,
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,”
Econometrica, vol. 55 (May 1987), pp. 703–8.
Sargent, Thomas J. “Commodity Price Expectations and the Interest Rate,”
Quarterly Journal of Economics, vol. 83 (February 1969), pp. 127–40.

Federal Reserve Bank of Richmond Economic Quarterly

Seater, John J. “Ricardian Equivalence,” Journal of Economic Literature, vol.
XXXI (March 1993), pp. 142–90.
Sims, Christopher A. “Macroeconomics and Reality,” Econometrica, vol. 48
(January 1980), pp. 1–49.
Stock, James H. “Confidence Intervals for the Largest Autoregressive Root in
U.S. Macroeconomic Time Series,” Journal of Monetary Economics, vol.
28 (December 1991), pp. 435–59.
, and Mark W. Watson. “A Simple Estimator of Cointegrating
Vectors in Higher Order Integrated Systems,” Econometrica, vol. 61 (July
1993), pp. 783–820.

Medical Care Price Indexes
Robert F. Graboyes

ealth care expenditures have grown from 4.4 percent of the U.S. economy in 1950 to over 13 percent in 1994. At the same time, medical
care prices have risen twice as fast as other prices, according to the
Consumer Price Index (CPI). That apparent increase in the price of medical
care (relative to other goods and services) would explain by itself the additional
spending for health care, though some research suggests that the numbers not
be taken at face value. The purpose of this article is to give an understanding
of how medical care price indexes are created and why some researchers have
expressed concerns about how these indexes are interpreted.
The article is organized as follows: Section 1 introduces the notion and
purpose of a price index. Section 2 explains what is meant by quality change
and focuses on areas such as the changing efficacy of a medical intervention,
the introduction of new goods, and the use of generic drugs. An additional subsection outlines several proposals for the difficult task of constructing a valid
price index when quality changes. Section 3 explains some index problems not
associated with quality change. Section 4 summarizes the concern that today’s
indexes may overstate medical inflation. Finally, the appendix gives details on
some currently published indexes.

LOGIC AND CONSTRUCTION OF PRICE INDEXES1

A price index measures the average price of a set of goods and services in
one period against the average price of the same goods in another period. The
central logic is that this basket of goods and services provides an adequate
measure of some average purchaser’s standard of living or level of satisfaction.
This article also appears in the third edition of Macroeconomic Data: A User’s Guide, Roy
Webb, ed. (Richmond: Federal Reserve Bank of Richmond, 1994). The views expressed are
those of the author and not necessarily those of the Federal Reserve Bank of Richmond or
the Federal Reserve System.
1 Wallace

and Cullison (1981) and Webb and Willemse (1994) describe in detail procedures
used and problems encountered in constructing any macroeconomic price index.

Federal Reserve Bank of Richmond Economic Quarterly Volume 80/4 Fall 1994

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R. F. Graboyes, Oct. 14, 1999;: Ch. 0, sheet 1, p. 69

Federal Reserve Bank of Richmond Economic Quarterly

As the price of the basket changes, the index changes proportionally. A 10
percent rise in a medical care price index thus implies a 10 percent increase in
the cost of a fixed quantity of medical care for some average purchaser, even
though some individual prices will have risen and others will have fallen.
The first task in creating these indexes is to define the limits of medical
care: Do we treat cough drops as medicine and include them, or do we call them
candy and exclude them? Do we include gymnasium membership dues, since
exercise helps prevent illness, or do we count the dues as recreational expenses
and exclude them? Once the medical sector or subsector is defined, individual
medical price data can be collected. Then these data must be averaged into an
index by using some set of arithmetic weights. These weights generally reflect
the relative amount spent on each product in some base period. In the CPI,
hospital services receive larger weights than aspirin because consumers spend
more on hospital services than on aspirin.

MEDICAL CARE PRICE INDEXES AND
QUALITY CHANGE

Technological progress has changed significantly the quality of medical care
in this century, and this is the fundamental complication in producing medical
care price indexes. Implicitly, a price index assumes that one’s consumption
basket does not change over time and a given basket provides a constant level
of satisfaction. While these assumptions are never strictly true for any set of
commodities, they are especially problematic in medicine. The treatments given
in 1944 barely resemble those given in 1994. And the health benefits of a given
treatment can change through the years as well.2
The productivity of medical care has advanced greatly over this century.
Some of the types of technological progress include the following: [1] Previously untreatable disease becomes treatable: In recent decades, heart transplants and coronary bypass operations have given years of life, whereas earlier
patients would have died. Therapies such as antibiotics, beta blockers, insulin
therapy, and kidney dialysis have effected similar improvements. [2] Previous
treatment replaced by new treatment: Laparoscopic techniques, using fiber
optics and tiny incisions, have largely replaced traditional open surgery in many
areas. For example, newer techniques for gallbladder removal require only one
to two days in the hospital, compared with three to seven days for traditional
surgery. The laparoscopic procedure also results in fewer postoperative complications, less pain, and a shorter convalescence. In addition, some patients for
whom traditional surgery is too risky can safely undergo the newer technique.3
2 For example, the expected benefit of a heart transplant is much higher in 1994 than it was
in 1970, when the operation was still experimental.
3 Legorretta et al. (1993).

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R. F. Graboyes: Medical Care Price Indexes

[3] Cheap prevention of costly diseases: Vaccines against polio, smallpox,
and other diseases have provided relatively inexpensive means to eradicate
diseases that, if contracted, would impose tremendous costs. [4] Decreased
resource requirements for an existing treatment: Electronic monitors allow
some conditions to be tracked at home rather than in a hospital bed, thus
reducing the need for hospital resources. Some cost reductions have resulted
more from a change in medical opinion than in any change in technology; for
instance, doctors now recommend shorter hospital stays following childbirth.
[5] Movement up the learning curve: Since the first coronary bypasses were
performed, practice and observation have made surgeons more adept at the
procedure, resulting in higher success rates.
In some areas of medicine, however, a given level of medical spending
may now provide fewer health benefits than in the past. Defensive medicine—
care that does not benefit the patient and whose purpose is to avoid malpractice
claims—has become a fixture of American medicine.4 The health benefits of
other procedures are hotly debated—prostate and breast cancer screenings are
examples. Heroic end-stage care for the terminally ill is another. A final complication in measuring the quality of medical care is that the population being
treated and the illnesses people suffer change over time. It is impossible to
neatly compare the productivity of a medical system pre- and post-AIDS, for
example.
Quality changes such as these complicate the construction and interpretation of medical care price indexes. Some examples discussed below illustrate
difficulties encountered when [1] the efficacy of a good or service changes,
[2] new goods are introduced, and [3] old goods are reintroduced under new
labels.
Change in Efficacy
Over time, the improved health from using a specific medical commodity often
increases (or decreases). This section uses a hypothetical example to demonstrate the analytical difficulties posed by changes in the quality of medical
care. Table 1a shows data on a hypothetical economy in which gross domestic
product (GDP) consists of two goods: medical procedures (say, an operation)
and food. From year 0 to year t, nominal GDP (the sum of spending on food
and medicine) grows from $9.5 million to $12.2 million. As the expenditures
index shows, total purchases have grown 28 percent.
Table 1b uses an alternative measure of medical output. Instead of defining
output as the number of procedures performed, this table defines it as the
number of lives saved (alternatively, we could use quality of life or some other
measure of medical outcome). According to these figures, there has been a
4 Brostoff

(1993) describes a study by Lewin-VHI, Inc., that estimated the costs of defensive
medicine to be $36 billion per year.

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Table 1a Measuring Aggregate Price and Quantity Changes:
Medical Procedures and Food
Medical
Procedures

Indexes
(year 0 = 100)

Food

Year 0
Expenditures
Quantity
Price
Share of economy

500,000
1,000
500
5.3%

9,000,000
100,000
90
94.7%

100
100
100

Year t
Expenditures
Quantity
Price
Share of economy

1,200,000
2,000
600
9.8%

11,000,000
110,000
100
90.2%

128
115
112

Interpretation: Index = 128 implies 28 percent growth over the period. Calculation of
year t indexes:
Expenditure:

128 ≈ 100 ×

1,200,000 + 11,000,000
500,000 + 9,000,000

Price: 112 ≈ 100 × (5.3% ×
Quantity: 15 ≈ 100 ×

600
500

+ 94.7% ×

100
)
90

Expenditure Index
Price Index

dramatic quality change in the medical procedure. Thirty percent of the patients
survive in year t (600 out of 2,000), compared with only 10 percent in year
0 (100 out of 1,000). Because of this, the price of one life saved has dropped
from $5,000 to $2,000, compared with an increase in the price per procedure
from $500 to $600.
Inflation is measured in Table 1b as 7 percent, compared with Table 1a’s
rate of 12 percent. Real economic growth is 15 percent in Table 1a and 20
percent in Table 1b. The practical effects of such measurement discrepancies
are not trivial. Throughout the economy, wage contracts, government benefits,
taxes, and other contractual arrangements tie payments to changes in the general
price level. It matters to a company whether its workers should be given a 12
percent or a 7 percent cost-of-living increase.
For most purposes, it would be better to measure growth as in Table 1b
rather than as in Table 1a, since it is lives saved and not procedures performed
that indicate economic well-being. We can guess, for example, that improvements in X-ray machines and in doctors’ abilities to read X-rays have led to a
greater efficacy in the use of X-rays. How much sooner, on average, are

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R. F. Graboyes: Medical Care Price Indexes

Table 1b Measuring Aggregate Price and Quantity Changes:
Lives Saved and Food
Lives
Saved

Indexes
(year 0 = 100)

Food

Year 0
Expenditures
Quantity
Price
Share of economy

500,000
100
5,000
5.3%

9,000,000
100,000
90
94.7%

100
100
100

Year t
Expenditures
Quantity
Price
Share of economy

1,200,000
600
2,000
9.8%

11,000,000
110,000
100
90.2%

128
120
107

Interpretation: Index = 128 implies 28 percent growth over the period. Calculation of
year t indexes:
Expenditure:

128 ≈ 100 ×

1,200,000 + 11,000,000
500,000 + 9,000,000

Price: 107 ≈ 100 × (5.3% ×
Quantity: 120 ≈ 100 ×

2,000
5,000

+ 94.7% ×

100
)
90

Expenditure Index
Price Index

cases of disease found in 1994 than in 1954 on a per-X-ray basis? How much
more does the average X-ray extend or improve life today? Even if we could
accurately answer these questions, what would be the dollar value of each
improvement? Since the answers are difficult to even approximate, analysts in
statistical bureaus with limited budgets usually shrug their shoulders and use
the number of X-rays to represent output, rather than using some measure of
abatement of disease or extension of life.
The difficulty in distinguishing quality, quantity, and price changes exists
for all goods and services. For example, a pound of chicken in 1994 is not the
same product as a pound of chicken was in 1924. The taste, consistency, and
nutritional characteristics have all changed. Also, the qualities of a computer in
1994 are vastly different from what they were in 1974. At least for these tangible products, one can imagine how quality might be defined. With services,
however, the difficulty in defining output makes it especially problematic to
measure changes in the quality of that output. In no service industry is the
effort more daunting than in medicine. Measuring medical care production in
terms of the means (procedures) rather than the ends (good health) is somewhat

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Federal Reserve Bank of Richmond Economic Quarterly

akin to measuring vegetable prices in dollars per acre planted rather than dollars
per bushel of yield. The former would lead us to mistakenly measure increased
yields per acre from added fertilizer as inflation.
New Goods Problem
Another serious indexing problem is that new products and technologies have
been introduced rapidly into medicine (and other industries) in the last 50 years.
Price index weights, however, are revised only infrequently. As a result, price
indexes may miss significant reductions in the cost of living. Gordon (1992)
writes that “penicillin entered the CPI in 1951, after it had already experienced
a 99 percent decline from its initial price” (p. 9). Berndt, Griliches, and Rosett
(1993) examined the new goods problem with respect to the introduction of new
pharmaceuticals. They found that the Bureau of Labor Statistics (BLS) tends
to give insufficient weight to newer products and that these products tend to
experience lower-than-average price increases. Together, these two tendencies
would bias the measured price increases upwards.
We can illustrate the mechanics of the new goods problem by departing
from medicine for a moment and considering two familiar products from the
electronics industry. Suppose a long-term price series used 1940 expenditure
weights. There would be no weight for the transistor, and the skyrocketing price
of vacuum tubes would appear to contribute to inflation. Of course, vacuum
tube prices are up largely because the production volumes have become small.
The invention of the transistor has greatly reduced the cost of devices that
amplify and rectify electronic signals.
While the BLS deals with the new goods problem in several ways, the
most common process is called “linking” in which, at some arbitrary point, one
good is dropped and the other added. Importantly, the new good is introduced
in such a way that this replacement leaves the price level unchanged.
The data in Table 2 provide a hypothetical example of linking. Suppose
drug A is replaced over time by drug B, but that for a time both are on the
market. The first two columns represent the prices of drug A and drug B in years
1 through 6. The price of drug A is rising due to general inflation and other
factors. New products like B frequently will decline in price after introduction
because [1] through experience the company entering the market improves its
manufacturing techniques, [2] the new company increases its market share and
can take advantage of economies of scale, and [3] close substitutes increasingly compete with profitable established products. The next-to-last column
represents a price index that, beginning in year 2, reflects changes in the price
of drug B. The last column represents an index that reflects drug A prices until
year 5 and then switches to drug B. The problem is deciding at what point
to drop drug A and to add drug B. This table shows that such a choice may
completely change the message sent by the price index. Again, this problem

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R. F. Graboyes: Medical Care Price Indexes

Table 2 Linking Old and New Goods in a Price Index

Year

(Old)
Drug A
Price

(New)
Drug B
Price

Price Index:
Drug B Added
in Year 2

Price Index:
Drug B Added
in Year 5

1
2
3
4
5
6

100
130
140
160
190
240

420
390
370
340
380
470

100 (base year)
93 ≈ 100 × 390 ÷ 420
88 ≈ 93 × 370 ÷ 390
81 ≈ 88 × 340 ÷ 370
90 ≈ 81 × 380 ÷ 340
112 ≈ 90 × 470 ÷ 380

100 (base year)
130 ≈ 100 × 130 ÷ 100
140 ≈ 130 × 140 ÷ 130
160 ≈ 140 × 160 ÷ 140
179 ≈ 160 × 380 ÷ 340
221 ≈ 179 × 470 ÷ 380

Notes: If drug B replaces drug A in the price index in year 2, the index shows a smaller price
rise than if B replaces A in year 5. This is because the year 5 link misses drug B’s price decline
in the first few years. Calculations are not exact due to rounding.

may be more serious in medicine than in most other sectors of the economy.
The relative costs and benefits of transistors and vacuum tubes can be defined
in fairly objective terms, while new drugs are rarely as easy to compare.
Old Goods, New Label Problem—Generic Drugs
A variant on the new goods problem is the case in which an existing good is
reintroduced to the market under a new label, as in the case of generic drugs.
Following is a hypothetical example illustrating the generic drug problem described by Scherer (1993). Suppose that [1] a name-brand drug X costs one
dollar per pill, [2] a biochemically identical generic drug Y is introduced at
fifty cents per pill, [3] half the market switches from X to Y. If one treats X
and Y as a single drug, then the average price has dropped by 25 percent, since
purchasers of the pills are now paying 25 percent less on average than they
used to.
In fact, this change will not normally show up in the CPI as a price reduction. First, weights in the CPI market basket are changed infrequently. CPI
data are collected on specific brands, like our drug X. Until the weights are
revised, the price of brand Y will not enter into the calculation of the CPI.
Second, when the generic drug Y is added to the CPI market basket, it will
be added into the index as a new product, separate from name-brand drug X.
Thus, the addition of Y to the basket will not show up as a decline in price.
Price indexes indicate generally that pharmaceuticals prices have risen at a
high rate compared with general inflation or even with other parts of the medical sector. Scherer (1993), Berndt, Griliches, and Rosett (1993), and Griliches
and Cockburn (1993) examine this trend and conclude that mismeasurement
is partly to blame. This mismeasurement occurs in part because of the way
generic drugs are introduced into indexes such as the CPI.

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Federal Reserve Bank of Richmond Economic Quarterly

Alternative Approaches to Measuring Medical Care Prices
Researchers have suggested alternative ways of measuring medical output that
might yield better estimates of medical prices than do current procedures.
Wilensky and Rossiter (1986) describe four ways of measuring medical care
output: the procedure (e.g., one day’s radiation therapy), the case (e.g., a cancer,
from diagnosis to conclusion of treatment), the episode (e.g., a particular period
of the illness), and per capita (e.g., the patient’s total health care, including the
cancer). Procedure-based indexes are the most commonly used today, but alternative indexes have been proposed that would use alternative units of output.
Health Insurance Premiums as Price Proxies
Some researchers have suggested that a good indicator of price increases might
be found in the premiums paid on a standard health insurance policy.5 The
logic is that an insurance policy represents a fixed bundle of medical goods and
services, and if quality remains constant, the price of the policy will represent
the price of that bundle. This idea found some favor in the late 1960s, when,
it can be argued, health insurance policies were fairly standardized. Problems
with that approach have become apparent, however, as policies have grown less
uniform, with broad differences in copayments, deductibles, payout limits, and
services provided. Technological and other changes in medicine mean that a
policy today provides very different care from an identical policy 30 years ago;
thus, quality changes are as big a problem as they are with a procedure-based
measure. Also, the real values of policies differ across states, since each state’s
regulatory practices partially determine the insurance companies’ liabilities.
Finally, the quantity of medical care demanded by the average policyholder
differs across localities.
Costs of Treatment of a Representative Group of Illnesses
Scitovsky (1964) proposed taking a group of illnesses and measuring how the
prices of treating those illnesses changed over time.6 Instead of measuring
inputs like hospital beds, operations, and drugs, this approach would take an
occurrence of a number of illnesses—say, a case of pneumonia, a brain tumor,
and a broken leg—and measure the total costs of treating this set of illnesses.
Quality change would still be a problem, though, since the means of treating
a particular disease changes over time. This proposal did suggest adjusting the
measured treatments for quality, using indicators like infant mortality and ageadjusted death rates per numbers of cases as proxies for quality. Scitovsky was
5 This idea is discussed in Feldstein (1993), pp. 71–72. Feldstein also refers readers to Reder
(1969), p. 98, and Barzel (1969).
6 This proposal is described in Feldstein (1993), pp. 64–71.

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concerned, however, that simple quality adjustments such as these would be
inadequate, given the complexity of measuring medical outcomes.
Hedonic Pricing
One method of adjusting for quality that has been used by statistical agencies
and academic researchers is hedonic pricing. Hedonic pricing values a good by
assuming that the good is really a bundle of characteristics and that there are
separate demands for each of these characteristics. In measuring price changes
in computers, for example, the Bureau of Economic Analysis uses a model that
breaks the computer down into a set of characteristics (e.g., number of calculations per unit of time), and then measures the prices of those characteristics.
Recombining these separate prices yields an estimated price for a computer,
holding quality constant (see Triplett [1986]). In this approach, quality is merely
the sum of a group of quantities.
An example of the hedonic approach applied to medical equipment is
Trajtenberg (1990). He compares three price indexes for Computerized Tomographic X-ray devices (CT or CAT scanners): [1] a standard index with no
adjustment for quality change; [2] a hedonic index, assuming that a CAT
scanner is really a bundle of four characteristics (head vs. body, scan time,
resolution, and image reconstruction time); and [3] a welfare-change index
based on the same four characteristics, but designed for a very different
objective—measuring the consumer’s well-being rather than the price of these
four characteristics. Over the period 1973 to 1982, the standard index increases
from 100 to 259.4, the hedonic price index decreases from 100 to 27.3, and
the welfare-change index decreases from 100 to .07. Thus, one methodology
produces a price index 3,700 times higher than does another price index. As
Getzen (1992) writes:
Differences of this magnitude in only a few items would be sufficient to
show that rather than being the fastest rising component of the [general price
level], the real quality-adjusted price of medical care is falling—a conclusion
that would be confirmed by most rational consumers given a choice of 1931
medicine at 1931 prices and the medical technology of 1991 at 1991 prices.
(P. 116)

Hedonic pricing may provide a promising approach for some goods. However,
the procedure adds markedly to the cost of data, and not all goods and services
are good candidates for the procedure.

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