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FEDERAL RESERVE BANK OF DALLAS
DECEMBER 1998

FINANCIAL INDUSTRY

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Concentration, Technology, and Market Power
in Banking: Is Distance Dead?
Robert R. M o o r e

Benchmarking the Productive Efficiency of U.S. Banks
Thomas F. Siems arid Richard S. Barr

This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (FedHistory@dal.frb.org)

Financial Industry Studies
Federal Reserve Bank of Dallas

Robert D. McTeer, Jr.
President and Chief Executive Officer

Helen E. Holcomb
First Vice President and Chief Operating Officer

Robert D. Hankins
Senior Vice President

W. Arthur Tribble
Vice President

Economists
Jeffery W. Gunther
Robert R. Moore
Kenneth J. Robinson
Thomas F. Siems
Sujit "Bob" Chakravorti
Financial Analysts
Robert V. Bubel
Robert F. Mahal ik
Karen M. Couch
Kelly Klemme
Edward C. Skelton
Kory A. Killgo
Graphic Designer
Candi Aulbaugh
Editors
Jeffery W. Gunther
Robert R. Moore
Kenneth J. Robinson
Publications Director
Kay Champagne
Copy Editor
Jennifer Afflerbach
Design & Production
Laura J. Bell

Financial Industry Studies is published by the
Federal Reserve Bank of Dallas. The views expressed
are those of the authors and should not be attributed
to the Federal Reserve Bank of Dallas or the Federal
Reserve System.
Articles may be reprinted on the condition that
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Reserve Bank of Dallas.
Financial Industry Studies is available free of
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Reserve Bank of Dallas, P.O. Box 655906, Dallas, Texas
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Dallas Fed's web site, www.dallasfed.org.

Contents
Concentration,
Technology, and
Market Power
in Banking:
Is Distance Dead?

Advancing technology is reducing the barrier that distance
has traditionally posed between potential buyers and sellers for a
variety of goods and services. To what extent will technology
overcome distance as a barrier in banking? Consistent with distance becoming less of a barrier and banking markets becoming
larger in geographic scope, I find that the presence of nearby
competitors helps explain bank profitability in 1986 and 1987 but
not in 1996 and 1997. Hence, while it may be premature to pronounce distance dead in banking, its role does appear to be
diminishing.

Robert R. Moore

Page 1

Benchmarking the
Productive Efficiency of
U.S. Banks
Thomas F. Siems and Richard S. Barr

Page 11

Effective benchmarking allows comparisons among similar
business units to discover best practices and incorporate process
and product improvements into ongoing operations. Most current
benchmarking analyses are limited in scope by taking a onedimensional view of a service, product, or process and by ignoring any interactions, substitutions, or trade-offs between key
variables. In this study, we use a constrained-multiplier, inputoriented, data envelopment analysis (DEA) model to benchmark
the productive efficiency of U.S. banks. We find that the most
efficient banks effectively control costs and hold a greater percentage of earning assets than the least efficient banks. Performance measures for the most efficient banks indicate that they
earn a significantly higher return on average assets, hold more
capital, and manage less risky and smaller loan portfolios. We find
a close association between a bank's relative efficiency score
derived from the DEA model and its examination (CAMEL) rating.

Concentration,
Technology,
and Market Power
in Banking:
Is Distance Dead?

Advancing technology is breaking down
the barrier that distance has traditionally posed
between potential buyers and sellers. For example, residents in remote rural areas once would
have had to travel great distances to shop at a
large bookstore, but using the Internet, they can
now browse through bookstores offering millions of titles without leaving their homes. But
the extent to which distance will become irrelevant in other types of transactions will depend
on the nature of the transaction. Imagining a
world in which it would be as easy to enjoy the
cuisine of a restaurant a thousand miles away as
that of a restaurant a block away is difficult. At
the other extreme, downloading software from
a company on the other side of the world can
be as easy as downloading software from a
company next door. Where does banking fit
into this spectrum?

Robert R. Moore

Consistent with distance

becoming less important in
banking, I find that although
operating in a market with few
nearby competitors boosted
profitability a decade ago,
more recently it does not.

The answer is taking on heightened importance in light of the recent frenzied pace of
bank mergers that have brought about a conspicuous decline in the number of U.S. banking
organizations. One potential effect of banking
consolidation is a reduction in the competitiveness of banking markets. Reflecting the traditional view that the presence of nearby competitors is essential for competitive outcomes,
markets for banking services often have been
thought to be confined to relatively limited geographic areas. If an abundance of nearby competitors is essential for competition, then banking consolidation might threaten competition if
it reduced the number of competitors in some
local markets.

But although the number of U.S. banking
organizations is declining, other factors are
heightening competition in the industry. Deregulation has reduced geographic restrictions
on banking, allowing the banking organizations
that remain to have a physical presence in a
larger number of areas and fostering greater
competition among those organizations. Nonbank competitors have become a more important source of competition. And although traditional antitrust analysis considers physical
presence in a market essential for competing in
that market, competing in distant markets is
becoming less difficult than it once was. Advancements in communications are making it
easier and less expensive to exchange information over great distances through the telephone
and Internet. Also, with banking innovations
such as credit scoring and telephone banking,
transactions that once required face-to-face conRobert R. Moore is a senior economist and policy advisor tact can now be conducted at a distance.
at the Federal Reserve Bank of Dallas.
Whether distance remains a significant

FEDERAL RESERVE BANK OF DALLAS

FINANCIAL INDUSTRY STUDIES SEPTEMBER 1998

few competitors. Higher HHI values imply a
greater concentration of market share among a
few competitors. The HHI would attain its highest possible value (10,000 = 100 2 ) in a monopolistic market and would approach zero in a
market divided equally among an infinite number of competitors. In merger analysis, mergers
proposed in markets with high initial HHI values or mergers that would increase the HHI
substantially are considered potentially anticompetitive. In particular, Department of Justice
guidelines view bank mergers as potentially
anticompetitive if they would result in a postmerger HHI above 1,800 and would increase
the HHI by 200 or more (Rhoades 1993).2

barrier to competition in light of these innovations has important ramifications for banking
market competitiveness. If distance is a formidable barrier to competition, then a bank operating in a market without nearby competitors
might be able to set lower-than-competitive
deposit rates and higher-than-competitive loan
rates, as it would be difficult for a customer to
transact with a distant bank, even if that bank
offered more competitive rates. But if technology has made it easier for distant banks to compete, then operating in a market with little
competition nearby would not boost profits.
To see whether distance has become less
of a barrier to competition in banking, I examine the relationship between the profitability of
banking markets and the physical presence of
competitors in those markets. Consistent with
distance becoming less important in banking, I
find that although operating in a market with
few nearby competitors boosted profitability a
decade ago, more recently it does not.

Calculating the HHI requires a definition
of the banking market. In practice, banking
markets are defined to be relatively small geographic areas for antitrust purposes.3 In an
urban area, the banking market would typically
be defined as the Census Bureau's metropolitan
statistical area (MSA); outside urban areas, the
county (or parish in Louisiana) is typically used
as the definition of the banking market (Radecki
1998). I refer to these definitions as "local"
banking markets.4
The traditional focus on relatively small
geographic areas is linked to the historical
importance of distance as a barrier in banking;
to the extent that it was historically difficult to
transact with distant banks, they were excluded
from the market definition. Consistent with
banking markets being confined to local areas,
two recent surveys find that only a small fraction of consumers and small businesses use
commercial banks outside their local area (Kwast,
Starr-McCluer, and Wolken 1997). Cyrnak (1998)
finds, however, that lenders outside the local
market play an important role in making loans
to small businesses, especially in rural areas.
The differences between these studies' findings
highlight the challenge of defining banking markets in today's environment.

TRADITIONAL ANTITRUST POLICY
See United States v. Philadelphia
National Bank, 374 U.S. 321 (1963).
These guidelines are supplemented with
a consideration of mitigating factors,
including, but not limited to, potential
competition, the competitive viability of
the target firm, economic conditions in
the market, market shares of leading
firms, economies of scale in small
mergers, and the importance of nonbank competitors.
Various academic studies have examined the scope of banking markets.
Osborne (1988) examines loan rates in
various regions and among various loan
sizes and concludes that banking is an
integrated, national market. In contrast,
Hannan (1991) examines the relationship between local market concentration
and the terms of bank lending to businesses and finds significant local-market effects. Jackson and Eisenbeis
(1997) find that consumer deposit rates
in different regions are cointegrated,
supporting the idea that banking is an
integrated, national market.
While these definitions serve as reasonable proxies for the local markets used
in antitrust analysis, the actual definition of the banking market for antitrust
analysis is more complicated and
involves market-by-market analysis of
commuting patterns, location of
schools, shopping facilities, advertising,
and other factors (Amel 1997).
The focus here is on the geographic
definition of the banking market.
Additional questions concerning the
definition of the relevant products and
providers are beyond the scope of this
article.

Competition has long been viewed as
essential for market forces to work in the best
interest of an economy. In recognition of the
importance of maintaining competition, the
United States enacted various laws near the turn
of the twentieth century that were intended to
ensure adequate competition. One such law
was the Clayton Act of 1914, which prohibited
mergers if they would substantially reduce
competition. Some uncertainty existed about
the applicability to banking of the turn-of-thecentury antitrust laws and their subsequent
amendments, but the Philadelphia National
Bank case of 1963 made it clear that banks were
subject to those laws.1
To provide a concrete framework for
quantifying the impact of bank mergers on competition, in 1982 the Department of Justice published guidelines for merger approval based on
the Herfindahl-Hirschman Index (HHI), with
some subsequent revisions to the guidelines.
The Federal Reserve uses these guidelines as an
initial step in evaluating the competitive impact
of a proposed bank merger (Rhoades 1993).
The HHI equals the sum of the squared
market shares of the firms in the market, based
on deposits. If, for example, the deposits in a
market are equally divided between two competitors, then that market would have an HHI of
5,000 = 50 2 + 50 2 . The HHI measures the concentration of the market, that is, the degree to
which market shares are concentrated among a

Changing the definition of the banking
market will change the numerical value of the
HHI.5 As an extreme example, suppose banking
markets were defined as blocks within a large
city that had one bank on each block. The HHI
would then count each bank as having a
monopoly in its market, when in practice bank
customers in the city could readily transact with
any bank in town, implying that the banks were
not monopolists. While that example is unrealistic, it does make an important point: if markets
are defined too narrowly, the HHI will be artificially high. Moreover, if an artificially high HHI
is used in the regulatory decision of whether to

approve a merger, some mergers would he
rejected as anticompetitive when they actually
are not.

vice, and pay for the purchase. Each step of this
process would have been more difficult to complete with distant sellers than with nearby sellers.
Consequently, nearby sellers had an advantage
relative to distant sellers. And if there were only
a few nearby sellers, those sellers could use the
advantage conferred by their proximity to the
buyers as a source of monopoly power; that is,
the sellers could set prices above those that
would prevail in a competitive market.6
Technological advancement is making distance a less formidable barrier than it once was.
Cairncross (1997) discusses the "death of distance," arguing that technological advancements
are on their way to making distance virtually
irrelevant in economic transactions. The competitive ramifications of this would be profound:
a seller down the block would no longer have
a distance-based advantage over a seller on the
other side of the country, or even the world.
Banking is largely an information-based
business. Traditionally, customers brought information to the bank in person. Because the cost
of traveling to the bank depended on the distance between the customer and the bank, distance served as a barrier to competition. But
information can flow into a bank through other
means, such as by telephone. As advancements
in communication technology make it easier to
communicate from afar, distance as a barrier to
competition in banking could be eroded.
Two statistics are suggestive of the decline
in communication costs from 1987 to 1997.7
First, the price index for telephone services
decreased by an inflation-adjusted 21 percent
during that time. Second, in 1987 the price of a
very long (2,455-mile) call was 47 percent higher than the price of a short (39-mile) toll call,
but by 1997 the price of the two calls was equal
(Waldon 1998).8 Thus, the overall cost of communicating by telephone has dropped, and the
price of very long-distance calls has declined
relative to the price of shorter calls. Banking by
phone allows customers to interact with their
bank without visiting the bank in person. To the
extent that the cost of going to the bank has
remained roughly constant, the decrease in
communication costs has lowered the cost of
transacting at a distance relative to the cost of
transacting in person.9 While some impediments
to conducting business at a distance may remain, the relative cost has in all likelihood declined, thus reducing the barrier to competition.

STRUCTURE, CONDUCT, AND PERFORMANCE
Much of the basis for traditional antitrust
analysis—for banking and other industries—
stems from the structure-conduct-performance
(SCP) paradigm. As summarized by Tirole
(1988), the SCP paradigm argues that the structure of a market (which includes factors such as
market concentration, product differentiation
among sellers in the market, and cost structure)
influences firms' conduct in the market (which
includes factors such as pricing, advertising, and
research and development), and conduct influences performance (which includes such factors
as profitability, efficiency, and price relative to
marginal cost).
Empirical tests of the SCP paradigm in
banking have often found that the structure of
the market—especially market concentration—
has influenced conduct and performance.
Gilbert (1984) reviews the banking literature
and concludes that the majority of the evidence
supports the idea that bank market structure
influences bank performance. He also concludes
that the evidence supports measuring concentration at the local market level to explain performance.
Additional studies have been conducted
since Gilbert's review. Berger and Hannan
(1989) find that higher local market concentration is associated with banks paying lower rates
on deposits. Hannan (1991) finds that higher
local market concentration is associated with
higher interest rates on loans. More recently,
however, Radecki (1998) looks at the relationship between interest rates paid by a bank and
the concentration of the market in which the
bank operates. When examining data from
1996, he finds no link between local market
concentration and the rates paid on deposits; he
does find, however, a link between concentration of a state's banking market and deposit
rates paid in that state, suggesting that the state
may now be the relevant definition of the banking market.

THE CHANGING RELEVANCE OF DISTANCE
Distance has historically been a barrier
between buyers and sellers in many markets. To
conduct a transaction, a buyer would need to
gather information about the seller and the seller's product, take possession of the good or ser-

FEDERAL RESERVE BANK OF DALLAS

Concurrent advancements in financial
technologies have also worked to reduce the
obstacle of distance in banking. Credit scoring
approaches allow decisions that once would

FINANCIAL INDUSTRY STUDIES SEPTEMBER 1998

When distance is a barrier between
potential buyers and sellers, buyers in a
market where nearby sellers are sparse
can be viewed as having a high search
cost, as in Stigler (1961). In such models, higher search costs make the buyer
more willing to accept high prices.

The decline in communication costs
from 1987 to 1997 is part of a much
longer trend. From 1928 to 1997, the
inflation-adjusted price of a 10-minute,
2,752-mile daytime call on AT&T regular
rates fell by 98.9 percent. Data on AT&T
rates from Waldon (1998).

The relative prices are for AT&T basic
residential daytime rates. Discount flatrate calling plans have also made the
relative price of very long-distance calls
equal to the price of short toll calls.

By allowing documents to move quickly
and cheaply over long distances via
telephone lines, the fax machine also
reduces the importance of distance.

have been made using information obtained in
a face-to-face transaction to now be made using
information obtained elsewhere. Credit scoring
uses statistical analysis to evaluate the riskiness
of loan applicants based on the historical relationship between borrower characteristics and
borrower performance.10 Also, the adoption of
banking by personal computer has the potential to downplay distance even further. Already,
231 U.S. banks offer services over the Internet
(Online Banking Report 1998). For interaction
over the Internet, the physical distance between
the customer and the bank is irrelevant.

median level and profitability in markets with
concentration above the median level are used
to provide some evidence on that relationship.
Second, regressions that control for additional
market characteristics provide more evidence
on the relationship. I conduct these tests for
1986, 1987, 1996, and 1997. If distance is becoming less relevant in banking, then local market concentration should be a less important
determinant of profitability in the latter years
than in the earlier years.
Past studies tend to use the interest rates
paid on deposits or the interest rates paid on
loans as the measure of banking outcomes. One
potential shortcoming of using these measures
is that they may not capture differences in the
underlying bank products that could account for
differences in rates charged or paid. If, for
example, a bank paid a lower interest rate on
deposits than its competitors did, the bank
might nevertheless attract depositors in a competitive market if the bank maintained a larger
staff that provided better service than the other
thinly staffed banks. Some customers might be
willing to accept a lower interest rate on deposits
if they were compensated with better service.

Cairncross (1997) reports that when the
telephone spread to villages in Sri Lanka, farmers in outlying areas received prices for their
crops that were 80 percent to 90 percent of
those in Colombo, the capital; before use of the
telephone allowed village farmers to know
prices in Colombo, farmers were receiving only
40 percent to 50 percent of the Colombo price.
Similarly, when bank depositors are able to
learn easily the interest rates offered on deposits
by distant banks, using the Internet or other
sources, local banks may have a heightened
incentive to offer more competitive rates.

As a measure of banking outcomes, profitability avoids this shortcoming. Under competitive conditions, paying lower rates while
providing a larger staff would leave profitability
unchanged: although paying lower rates on
deposits would increase profitability, that boost
to profitability would be offset by the cost of
maintaining the larger staff. In addition, more
banks can be included in a study based on profitability than in a study based on interest rates
because all banks report profitability on the
Report of Condition and Income ("call report"),
whereas reliable interest-rate information must
be obtained from more limited survey data.
Although profitability has some advantages
as a performance measure, it also has some
drawbacks. First, the accounting conventions
that are used to compute profitability may introduce imprecision into the measurement of profitability itself. Second, while the rate paid or
charged by a bank is a fairly direct measure of
the link to the customer, profitability is a larger,
less immediate concept subject to various influences that may be difficult to control for statistically. Because profitability lacks immediacy as a
measure of the terms of banking services that
customers receive, the results of a study based on
profitability may be interpreted in several ways.

MEASURING THE IMPACT OF LOCAL AREA MARKET
CONCENTRATION ON BANK CUSTOMERS

See Mester (1997) for a review of credit
scoring. Peek and Rosengren (1998)
argue that the adoption of credit scoring
is promoting small businesses' access
to credit trom new sources.

One difficulty in linking banking performance in a market to conditions in that
market is that some banks have branches located in more than one market.
Because the Report of Condition and
Income ("call report") does not provide
income data at the branch level, assigning income to individual branches
would be problematic. To avoid this
problem, I limit attention to banks that
have all of their operations confined to
a single market. Such banks accounted
for 88.4 percent of all banks by number
and held 46.3 percent of bank assets
in June 1987. In June 1997, those
percentages were 75.3 and 28.2,
respectively.

The arguments above suggest that distant
banks are a more important source of competition than in the past. Suppose a local banking
market were highly concentrated and banks in
that market offered monopolistic terms to their
customers. In the past, it would have been difficult for banks outside the local market to offer
services at more competitive terms to customers
in that market. But today, with the decline in
communication costs and the ability to conduct
long-distance transactions that once required
face-to-face contact, distant banks would be
able to compete for those customers; that additional source of competition would drive the
terms on bank products toward competitive
rates. These arguments imply that high concentration in a local banking market is not as likely
to result in noncompetitive effects today as in
the past. If distant banks are an important
source of competition, then the traditional definition of local banking markets is too narrow.
To examine that claim empirically, I examine the relationship between profitability in a
local market and the concentration of the market using two approaches.11 First, simple univariate tests that compare profitability in
markets with concentration at or below the

Under an interpretation rooted in the SCP
paradigm, finding that higher market concentration is associated with higher profitability would

Table 1

Univariate Tests of the Relationship Between
Profitability and Market Concentration

be taken as a sign of anticompetitive practices:
high concentration implies that competition is
limited, allowing firms in the market to exercise
pricing power that results in monopoly profits.
As Peltzman (1977) discusses, however, a
positive correlation between profitability and
concentration could emerge for reasons other
than anticompetitive practices. If a market has a
firm that grows large because of cost advantages, that market would exhibit high profitability and high concentration, even in the absence
of anticompetitive practices. Results of earlier
studies (e.g., Berger and Hannan 1989, Hannan
1991) of the banking industry, however, suggest
that a positive relationship between concentration and profitability would reflect market
power, given that those studies found that higher concentration was associated with less competitive terms on loans and deposits.

Year and market type
1986

Average profitability in
markets with HHI
above median

.83
.76

1.01**

Rural

.85

Urban

.82

.94*
1.36

Rural
Urban

1987

1996
Rural
Urban

1997
Rural
Urban

1.09

1.29
1.23

1.34
1.29

1.25
1.21

1.31
1.05

N O T E S : ** a n d * d e n o t e m a r k e t c a t e g o r i e s w h e r e return o n a s s e t s is significantly different in the
high H H I m a r k e t s t h a n in the low HHI m a r k e t s at the 1 - p e r c e n t a n d 5 - p e r c e n t levels,
respectively. Statistical significance of differences in m e a n s w a s tested using a two-tailed
t-test.

The particular measure of profitability
used is the return on average assets (ROA) lor
banks within the local market, where local markets are approximated as MSAs for metropolitan
statistical areas and as counties for nonmetropolitan areas. For each market, ROA is the ratio
of net income of the banks in the market to the
average over the year of the banks' assets.
Market concentration is measured by the
HHI. As discussed above, the HHI is used in
antitrust analysis. Higher values of the HHI are
associated with a more concentrated market.
Also, in computing the HHI, thrift deposits were
included but were weighted by 50 percent,
reflecting some, but presumably imperfect, substitutability between bank and thrift deposits.12

significant. Finally, in 1997, average profitability
was higher in concentrated rural markets than
in unconcentrated rural markets, but in urban
markets, average profitability was actually lower
in concentrated markets; none of the differences
in profitability in 1997 is statistically significant,
however.
The univariate results thus support the idea
that operating in a market with few nearby competitors tended to boost profitability—at least
for rural markets—a decade ago. More recently,
however, operating in a market with few nearby
competitors is not associated with higher profitability. These results are consistent with distant
competitors becoming more important over the
past decade; that is, the results are consistent
with distance declining as a barrier in banking.

Univariate Approach
If operating in a local market with few
nearby competitors confers pricing power on
the banks operating in those markets, then local
markets with a high HHI should have high profitability. Table 1 shows the average profitability
of markets with an HHI at or below the median
in a given year and those with an HHI above the
median. This analysis is conducted separately
for urban and rural markets. Table 1 also displays the results of statistical tests run to detect
significant differences in profitability between
markets with high and low concentration.
As Table 1 shows, in 1986 and 1987, average profitability was higher for concentrated
markets as expected in both urban and rural
markets; the difference in profitability was only
statistically significant in rural markets, however.
In 1996, average profitability was higher in concentrated markets for both urban and rural markets, but the differences were not statistically

FEDERAL RESERVE BANK OF DALLAS

Average profitability in
markets with HHI at
or below median

Regression Approach
Although the univariate analysis above is
consistent with local area concentration no
longer being an important determinant of local
market profitability, that analysis does not control for factors beyond concentration that could
influence profitability. The regression approach
below attempts to isolate the relationship
between profitability and the HHI by controlling
for additional factors that could influence profitability. Table 2 provides formal definitions of
the variables used in the model.
Similar to the idea for univariate analysis,
under the hypothesis that higher concentration
allows banks to earn monopoly profits, the
regression coefficient on HHI should be positive. However, to the extent that it has become
easier for financial service providers to compete

FINANCIAL INDUSTRY STUDIES SEPTEMBER 1998

The degree of substitutability between
thrifts and banks is debatable, so thrifts
were allowed to enter the concentration
figures in two other ways. First, thrifts
were excluded entirely, reflecting nonsubstitutability between banks and
thrifts. Second, thrifts were included
with their deposits weighted by 100
percent, reflecting complete substitutability between banks and thrifts.
The results shown in Tables 3a-3d are
based on thrift deposits being weighted
at 50 percent. Weighting thrift deposits
at zero and 100 percent produced qualitatively similar results.

Table 2

Variable Definitions
Variable

states and zero for markets located in other
states; this leaves states with limited branching
as the base case. Branching restrictions increase
the cost of entering a market. By making it more
difficult to enter, restrictions on branching could
make it possible for high profitability to persist;
in the absence of restrictions, a highly profitable
market would be likely to attract outside competition. With the entry of additional competitors, bank customers would obtain terms that
are more favorable, and the profitability of
banks in that market would decline. To the
extent that branching restrictions impede that
dynamic, I would expect branching restrictions
to be associated with greater profitability; that
is, I would expect a negative sign for BRANCH
and a positive sign for UNIT. However, if distance is not a barrier in banking in 1996 and
1997, the effects of branching restrictions would
be zero; if distance no longer impedes transactions, then barriers to establishing a physical
presence in a distant location would no longer
affect profitability.

Definition

ROA

Return on average assets, percent

HHI

( S u m of squared market shares of all banks in market)/100,000

POP

Population of market in hundreds of millions of people

BRANCH

Equals 0.01 if market is in a state with unrestricted branching,
zero otherwise

UNIT

Equals 0.01 if state is a unit banking state, zero otherwise

PINCOME

Per capita personal income in market, $100,000

DEPGROW

Ratio of change in deposits to prior year deposits in market

TAR

Ratio of troubled assets to total assets

CONSUMER

Ratio of c o n s u m e r loans to total assets

AGRI

Ratio of agricultural loans to total assets

Ratio of commercial and industrial loans to total assets

REALEST

Ratio of real estate loans to total assets

SECURITIES

Ratio of securities to total assets

SUBCHS

Fraction of assets in market held by Subchapter S banks

NOTES: The variables ROA, TAR, CONSUMER, AGRI, CI, REALEST, SECURITIES, and
SUBCHS are computed using the subset of banks that have all their operations confined
to a single geographic area.

in distant markets, I would expect any positive
relationship between local area concentration
and profitability to be weaker in 1996 and 1997
than in 1986 and 1987.
While the relationship between profitability and the HHI is the primary focus, factors
other than HHI could influence the profitability
of a market. The first control factor is the size of
the market, measured by the popLilation within
the local area (POP). A market with a small
population might not attract entrants even
though existing banks in the market were highly
profitable, if the gains from entering the market
could not be justified by the cost. To the extent
that the cost of competing from afar has declined over time, entering small markets would
have become easier over time, making it less
likely for a small size to be associated with higher
profitability in 1996 or 1997 than in 1986 or 1987.

The model includes other control factors
that could affect profitability. Per capita personal income (PINCOME) controls for a potential
influence of affluence on profitability. Yearover-year deposit growth (DEPGROW) measures the growth in deposits in the market. To
the extent that rapid growth is demand-driven, I
would expect DEPGROW to be associated with
higher profits. TAR, the troubled asset ratio, is
the ratio of loans past due 90 days or more,
nonaccrual loans, and other real estate owned
to total assets. A high vahie of TAR reflects
banking problems that would make it difficult
for banks in the market to be profitable. The
variables CONSUMER, AGRI, CI, REALEST, and
SECURITIES are included to control for any
effect of portfolio composition on profitability;
these variables measure the fraction of assets
that are held in consumer loans, agricultural
loans, commercial and industrial loans, real
estate loans, and securities, respectively.

Restrictions on banks' ability to expand
into new markets through branching could also
influence market profitability. The model
includes two variables that reflect such legal
restrictions. First, the variable BRANCH identifies states where intrastate branching is freely
permitted; in states where intrastate branching is
freely permitted by merger, acquisition, or on a
de novo basis, BRANCH equals one; otherwise
BRANCH equals zero.13 In addition, in 1986 and
1987, a few states were unit banking states,
" Data on states'branching regulations
were obtained from Amel (1993) and
Conference of state Bank Supervisors

(1986,1996).

Finally, a recent change in tax law allows
certain banks to be organized as "Subchapter S"
corporations (Greef and Weinstock 1996). Because banks structured as Subchapter S corporations avoid corporate income tax, those banks
would be expected to report higher profitability
than other banks. To capture the influence of
Subchapter S status on the profitability of a market, I include a variable SUBCHS, the fraction of
the assets in a market that are held by Subchapter S banks. Because Subchapter S status
was not available until 1997, this variable is only
included in the 1997 regressions.

where no branching was allowed at all. To capt u r e
t h e p o s s i b l e effect of these more Stringent
restrictions, I include a variable UNIT that
equals one for markets located in unit banking

Table 3 a

Table 3 b

Estimation Results for Rural
Markets for 1986 and 1996:
Dependent Variable ROA
Intercept
HHI
POP

1986

Estimation Results for Rural
Markets for 1987 and 1997:
Dependent Variable ROA

1996

.08
(-35)

-1.10
(1.81)

5.05**
(1.24)

(1.10)

1.35

103.30
(107.33)

-49.97
(85.03)

BRANCH

14.55
(8.74)

4.57
(4.01)

UNIT

9.10
(5.71)

PINCOME

1987
Intercept
HHI

-3.47
(4.09)

4.54**
(1.20)

-1.68
(2.84)

-5.21
(181.56)

488.39
(354.23)

BRANCH

10.07
(5.49)

6.28
(8.08)

UNIT

3.80
(5.75)

POP

—

1997

-.97
(.69)

—

-3.78**
(1.09)

-.09
(.55)

.61**
(.19)

.42
(.23)

-27.37**
(2.27)

-13.86*
(6.53)

CONSUMER

1.64**
(.54)

3.38
(2.15)

CONSUMER

AGRI

1.86**
(.50)

2.86
(2.05)

AGRI

1.85**
(.57)

3.03
(1.84)

REALEST

2.34**
(.46)

2.82
(1.98)

REALEST

3.00**
(.95)

6.80
(5.13)

SECURITIES

2.10**
(.39)

2.47
(2.00)

SECURITIES

2.84**
(.83)

6.61
(5.05)

DEPGROW
TAR

R2
Chi-square statistic
for overall
significance

.38
542.2**

PINCOME
DEPGROW
TAR

.09
61.9**

-7.24
(4.83)

.35
(.19)

1.06
(.96)

-19.23**
(2.57)

-10.34*
(4.26)

3.06**
(1.13)

5.60
(5.66)

3.03**
(.92)

7.66
(5.56)

1.48
(1.06)

SUBCHS

—

.25

Chi-square statistic
for overall
significance

NOTES: ** and * denote statistical significance at
the 1-percent and 5-percent levels, respectively. Heteroskedasticity-consistent
standard errors are shown in parentheses.
Coefficient estimates were obtained by
ordinary least squares. Sample size was
2,003 for 1986 and 1,927 for 1996.

-1.73
(1.03)

389.3**

7.25
(5.52)

.87*'
(.16)
.11
77.0**

RESULTS
Tables 3 a - 3 d show the results from estimating the following equation relating market
profitability to market characteristics:
ROA =
+
+
+
+

Tables 3a and 3b show the results for rural
areas. For both 1986 and 1987, ROA in rural
markets has a significant, positive relationship
with HHI. Thus, in the earlier years examined,
higher concentration is associated with higher
profitability in rural markets; this result is consistent with traditional antitrust policy that views
concentration in local banking markets as influencing the terms that consumers of banking services receive. The rural markets in 1996 and
1997, in contrast to the earlier years, do not

a 0 + a ! HHI + a 2 POP + a 3 BRANCH
a 4 UNIT + a 5 PINCOME + a 6 DEPGROW
a 7 TAR + a 8 CONSUMER + ou> AGRI
a 1 0 CI + a n REALEST + a 1 2 SECURITIES
a, 3 SUBCHS

The regressions are run separately for urban
and rural areas.

FEDERAL RESERVE BANK OF DALLAS

FINANCIAL INDUSTRY STUDIES SEPTEMBER 1998

show a statistically significant relationship between the concentration measures and market
profitability; although not statistically significant,
the estimated sign on HHI is actually negative in
1997.14 Moreover, the coefficients on HHI are
significantly different in the statistical sense
when comparing 1997 with 1987 and when
comparing 1997 with 1996.15
The 1996 and 1997 results cast doubt on
the notion that concentration in local banking
markets continues to affect the terms that consumers of banking services receive. The finding
that a market's profitability is no longer tied to
its concentration is consistent with the argument
that geographic distance is becoming less relevant in banking. Measures of concentration that
are based on physical presence in local banking
markets ignore the role of distant competitors;
to the extent that distance is becoming a lower
barrier to competition, ignoring distant competitors by defining banking markets locally is
becoming increasingly misleading.

The significance of HHI in 1986 and
1987 and its insignificance in 1996 and
1997 do not change when the HHI is
calculated under the alternative ways of
including thrifts mentioned earlier. Also,
the results shown were obtained using
all markets for which the relevant data
were available; a similar pattern of
results occurs when extreme observations are excluded by limiting the sample
to markets with an ROA between -20
percent and 10 percent.
The statistical test for differences
across years also showed that the
effects of PINCOME differed in rural
markets when comparing 1986 and
1996, and that the effects of TAR differed in urban markets when comparing
1987 and 1997. The differences in
effects across years for the other variables were not statistically significant.
The insignificance of HHI might also
stem from multicollinearity of the explanatory variables. To reduce multicollinearity concerns, I estimate a model
where HHI is the only explanatory variable. The results of these parsimonious
regressions agree with those of the
regressions with the control factors
included: HHI is positive and significant
only in the 1986 and 1987 rural equations.

Table

Estimation Results for Urban
Markets for 1986 and 1996:
Dependent Variable ROA
1986
Intercept

HHI

1996

3.18

.47

(6.58)

(.83)

20.00

6.24

(13.88)

(3.97)

-5.22

POP

BRANCH

-1.08

(17.43)

(2.08)

-2.74

19.75

(19.54)

(15.36)

-24.27

UNIT

—

(22.66)
PINCOME

DEPGROW

.68
(.79)

2.51

.57

(1.59)

(.43)
-6.57

-20.96*

TAR

The control variables in the rural models
entered with mixed significance. BRANCH and
UNIT are never significant. TAR is always significant with the expected negative sign. SUBCHS
was significant with the expected positive sign
in 1997. All the portfolio variables are individually significant in 1986, but none is individually
significant in 1996; however, in both years the
portfolio variables are jointly significant. In
1987, all the portfolio variables except CI are
individually significant, and in 1997, none is; the
portfolio variables are jointly significant in 1987
but not in 1997. The reduction in the significance of the portfolio shares as determinants of
bank profitability may reflect the tranquility of
bank credit markets in 1996 and 1997 relative to
the oil-price-induced decline in asset quality
that occurred in 1986 and 1987.

2.20
(7.31)

CONSUMER

(10.10)

(5.13)

-2.24

1.47

(8.71)
AGRI

(.88)

-.10

-.18

(8.22)

(1.37)

-5.58

.85

(11.56)
REALEST

(1.13)

-2.95

.60

(10.17)

(.69)
-.37

-3.66

SECURITIES

(8.37)

(.53)

.07

R2
Chi-square

.14

statistic

for overall

93.3**

37.8**

significance
N O T E S : ** a n d * d e n o t e statistical s i g n i f i c a n c e at
the

1-percent and 5-percent

spectively.

levels,

re-

Heteroskedasticity-consistent

s t a n d a r d e r r o r s a r e s h o w n in p a r e n t h e s e s .
Coefficient

estimates

were

obtained

o r d i n a r y least s q u a r e s . S a m p l e s i z e w a s

Tables 3c and 3d show the results for
urban markets. Unlike in the rural markets, profitability in the urban markets does not show a
significant relationship with HHI in any of the
years examined; moreover, the estimated sign
on HHI is negative in 1997. In all the years
examined, the average level of concentration is
much lower in urban markets than in rural markets. Hence, it is possible that concentration is
low enough in urban markets for competitive
outcomes to have been obtained in all periods
of examination. Also, difficulties in controlling
for all potential influences on profitability may
have obscured the relationship between profitability and concentration. Finally, given that
ROA is only as precise as the accounting
assumptions that underlie it, it is possible that

3 4 2 for 1 9 8 6 a n d 3 5 8 for 1 9 9 6 .

an underlying relationship between profitability
and concentration exists but is masked by
imprecision in the data.16
The control variables included in the
urban models entered with mixed significance.
BRANCH and UNIT, the variables included to
capture the potential effect of geographic
branching restrictions on profitability, are
insignificant in all equations estimated. TAR is
statistically significant for 1986 and 1987, but not
in 1996 and 1997.
Overall, these results are consistent with
distance declining in importance in banking.

Table 3d

relevant in banking, then local market concentration should be a less important determinant
of profitability. The evidence presented here is
consistent with the presence of nearby competitors influencing the competitiveness of rural
banking markets in 1986 and 1987. In 1996 and
1997, however, the data are no longer consistent
with that view: the presence of nearby competitors no longer helps to explain the profitability
of the banking market, suggesting that markets
for banking services are now geographically
broader than before.

Estimation Results for Urban
Markets for 1987 and 1997:
Dependent Variable ROA
Intercept

1987

1997

13.12
(11.95)

-1.70
(3.44)

HHI

39.37
(28.47)

-17.76
(10.56)

POP

-25.09
(20.85)

-.72
(3.09)

BRANCH

82.08
(63.93)

16.29
(13.33)

UNIT

6.34
(27.65)

PINCOME

13.51
(10.61)

DEPGROW

.18
(1.06)

—

3.88*
(1.97)
.003
(.002)

TAR

-64.21*
(31.87)

10.24
(10.46)

CONSUMER

-15.28
(15.45)

3.35
(3.93)

-9.74
(10.61)

3.16
(3.78)

-23.14
(21.85)

2.47
(5.20)

REALEST

-17.13
(15.87)

1.79
(3.55)

SECURITIES

-16.63
(16.07)

2.73
(3.93)

AGRI

SUBCHS
R2
Chi-square statistic
for overall
significance

—

.18
37.3**

The change in the relationship between
local market concentration and profitability over
the past ten years accords with recent changes
in technology. Falling communication costs are
making distant competitors increasingly important, since lower communication costs make
obtaining information about and transacting
with distant banks more economical. Moreover,
banking innovations are enabling long-distance
transactions that once required face-to-face
contact.
While the results presented here are not
sufficient to pronounce distance dead in banking, they are consistent with a weakening of its
role. Banks continue to maintain and grow
extensive branch networks, suggesting that a
substantial number of customers still value geographic proximity. However, the conduct and
performance of banks appear to depend less
now on the physical presence of competitors in
local markets, suggesting that linkages between
local areas and the broader banking market are
stronger now than in the past. This finding is
consistent with the eroding impact of distance as
a barrier to competition in banking. The benefits of vigorous competition under a free market
system have long been recognized. Advancing
technology is promoting competition in new
ways by diminishing the barrier of distance.

.44
(.35)
.07
17.0

REFERENCES
Amel, Dean F. (1993), "State Laws Affecting the Geographic Expansion of C o m m e r c i a l Banks," Board of
Governors of the Federal Reserve System, u n p u b l i s h e d

While concentration of local markets helped to
explain profitability in rural markets a decade
ago, it no longer does.

manuscript, September, 1 - 4 3 .
(1997), "Antitrust Policy in Banking: Current Status
a n d Future Prospects," Proceedings

ference

CONCLUSION

of the 1997 Con-

and Competition

(Chicago:

Federal Reserve Bank of Chicago).

The traditional approach to antitrust enforcement in banking is to view the market for
banking services as local and geographically
limited. However, if distance is becoming less

FEDERAL RESERVE BANK OF DALLAS

on Bank Structure

Berger, Allen N., a n d Timothy H. Hannan (1989), "The
Price-Concentration Relationship in Banking," Review of

Economics

and Statistics

71 (May): 2 9 1 - 9 9 .

FINANCIAL INDUSTRY STUDIES DECEMBER 1998

Cairncross, Frances (1997), The Death of Distance:

the Communications

Revolution

Will Change

How

Online Banking Report (1998), "True U.S. Internet Banks,"

Our Lives

<http://www.onlinebankingreport.com/fulserv2/shtml>,

(Boston: Harvard Business School Press).

visited O c t o b e r 1, 1998.

Conference of State Bank Supervisors (1986, 1996),

O s b o r n e , Dale K. (1988), "Competition a n d G e o g r a p h i c a l

/A Profile of State Chartered

Integration in C o m m e r c i a l Bank Lending," Journal

Banking.

Banking

and Finance

12 (March): 8 5 - 1 0 3 .

Cyrnak, Anthony W. (1998), "Bank Merger Policy a n d the
New CRA Data," Federal

Reserve

Peek, Joe, a n d Eric S. Rosengren (1998), "The Evolution

Bulletin 84, September,

of Small Bank L e n d i n g to Small Businesses," Federal

703-15.

Reserve Bank of Boston New England
Competition: A Survey," Journal

Banking

of Money, Credit

Economic

Review,

March/April: 2 7 - 3 6 .

Gilbert, R. Alton (1984), "Bank Market Structure a n d

and
Peltzman, Sam (1977), "The Gains a n d Losses from

16 (November): 6 1 7 - 4 5 .

Industrial Concentration," Journal

of Law and

Economics

20 (October): 2 2 9 - 6 3 .

Greef, Charles E „ a n d Peter G. Weinstock (1996), "Tax
Freedom Day C o m e s E a r l y — S u b S Status Now Available
for Banks," The Texas Independent

Banker 23 (October):

Radecki, Lawrence J. (1998), "The E x p a n d i n g Geo-

16-18.

g r a p h i c Reach of Retail Banking Markets," Federal

Hannan, Timothy H. (1991), "Bank C o m m e r c i a l Loan

June, 1 5 - 3 4 .

Reserve Bank of N e w York Economic

Policy

Review,

Markets a n d the Role of Market Structure: Evidence from
Surveys of C o m m e r c i a l Lending," Journal

Finance

of Banking

and

Rhoades, Stephen A. (1993), "The Herfindahl-Hirschman
Index," Federal

15 (February): 1 3 3 - 4 9 .

Reserve

Bulletin 79, March, 1 8 8 - 8 9 .

J a c k s o n , William E., a n d Robert A. Eisenbeis (1997),

Stigler, G e o r g e (1961), "The E c o n o m i c s of Information,"

" G e o g r a p h i c Integration of Bank Deposit Markets a n d

Journal

of Political

Economy

69 (June): 2 1 3 - 2 5 .

Restrictions on Interstate Banking: A Cointegration
A p p r o a c h , " Journal

of Economics

and Business

Tirole, Jean (1988), The Theory of Industrial

(July/August): 3 3 5 - 4 6 .

( C a m b r i d g e , Mass.: MIT Press).

Kwast, Myron L., Martha Starr-McCluer, a n d John D.

Waldon, Tracy (1998), The Industry

Wolken (1997), "Market Definition a n d the Analysis of

Reference

Antitrust in Banking," Antitrust

tures for Telephone

Bulletin 42 (Winter):

Mester, Loretta J. (1997), "What's the Point of Credit
Scoring?," Federal Reserve Bank of Philadelphia

Business

Services

Review, S e p t e m b e r / O c t o b e r : 3 - 1 6 .

and

Division's
Expendi-

(Washington, D.C.: Federal

C o m m u n i c a t i o n s Commission).

973-95.

Analysis

Book of Rates, Price Indices,

Organization

Benchmarking the
Productive Efficiency
of U.S. Banks

The U.S. banking industry is highly competitive. Conventional wisdom holds that in
competitive industries the strongest institutions
survive and that those institutions are among
the most efficient and effective. Success in competitive markets demands achieving the highest
levels of performance through continuous
improvement and learning. It is therefore imperative that managers understand where they
stand relative to competitors and best practices
regarding their productivity.
Comparative and benchmarking information can provide impetus for significant improvements and can alert institutions to new
practices and new paradigms. Uncovering and
understanding best practices, however, is often
limited by the simplicity of the analytical framework and the difficulty in collecting and analyzing vast quantities of data for large-scale
problems.
Simple gap analyses—probably the most
commonly used technique for benchmarking—
can provide important insights but are somewhat limited in scope because they take a
one-dimensional view of a service, product, or
process and because they ignore any interactions, substitutions, or trade-offs between key
variables. For the U.S. banking industry,
DeYoung (1998) provides evidence that simple,
one-dimensional accounting ratios give an
incomplete picture. DeYoung found that wellmanaged banks often incur significantly higher
raw (accounting-based) unit costs than poorly
managed banks. DeYoung reports that blind
pursuit of accounting-based cost benchmarks
actually might reduce a bank's cost-efficiency by
cutting back on expenditures essential to a wellrun bank. Thus, a more inclusive multiple-input,
multiple-output framework for evaluating productive efficiency and providing benchmarking
information on how to become a well-managed
bank seems essential to improving decision
making at poorly managed banks.

Thomas F. Siems and Richard S. Barr

I ore efficient banks

tend to be higher performers
and safer institutions.

We use a constrained-multiplier, inputoriented, data envelopment analysis (DEA)
model to create a robust quantitative foundation
to benchmark the productive efficiency of U.S.
banks. DEA is an alternative and a complement
to traditional central-tendency (statistical regression) analyses, and it provides a new approach
to traditional cost-benefit analyses and frontier
(or best-practices) estimation. DEA is a linearThomas F. Siems is a senior economist and programming-based technique that converts
policy advisor at the Federal Reserve Bank of Dallas. multiple inputs and multiple outputs into a
scalar measure of relative productive efficiency.
Richards. Barr is an associate professor
of computer science and engineering
In this study, we are interested in benchat Southern Methodist University. marking the productive efficiency of U.S. banks.

FEDERAL RESERVE BANK OF DALLAS

FINANCIAL INDUSTRY STUDIES SEPTEMBER 1998

We would like to thank Kory Killgo,
Kelly Klemme, and Sheri Zimmel for
outstanding research assistance. The
second author acknowledges that this
work was supported in part by the
National Science Foundation, grant
DMII 93-13346, and the Texas Higher
Education Coordinating Board,
Advanced Technology Program, grant
ATP-003613-023.

customer-oriented measures for evaluation purposes. Banks can benchmark all kinds of things,
although the most valuable generally fall into
the following four categories: business results,
cycle time, quality assurance, and assets.
Steps 2 and 3 are the organizational steps
necessary for information and data collection. It
is useful to form a benchmarking team with
employees from many different parts of the
bank and to develop efficient data collection
and information gathering systems.
Step 4 uses the measures drawn from all
relevant information sources to assess the bestpractice organizations, and one's standing relative to them, both at present and projected into
the future. The U.S. banking industry reports
balance sheet and income statement data to federal banking regulators on a quarterly basis.
These data are often used to assess performance
relative to peer groups.
Finally, once the best practices are identified and understood, step 5 uses these results to
formulate action plans for improvement.

This is accomplished by comparing the volume
of services provided and resources used by
each bank with those of all other banks. To further evaluate our results and demonstrate their
usefulness as a complementary off-site monitoring tool for regulators, we compare our DEA
results with bank examination (CAMEL) ratings.
We find that the most efficient banks are
relatively successful in controlling costs and also
hold a greater amount of earning assets. The
more efficient banks also earn a significantly
higher return on average assets, hold more capital, and manage less risky and smaller loan
portfolios than less efficient institutions. To validate our results, we compare the relative efficiency scores derived from the DEA model with
the examination ratings assigned by bank supervisors. We find a close association between our
efficiency scores and bank examination ratings,
suggesting that our model could be useful to
regulators as a complementary off-site monitoring tool.

WHAT IS BENCHMARKING?

LIMITATIONS OF CURRENT
BENCHMARKING METHODS

Benchmarking is the search for best practices to improve an organization's products and
processes. The word "benchmark" comes from
geographic surveying and means "to take a measurement against a reference point." Benchmarking
has become the darling of the continuousprocess-improvement movement; in fact, in
1991 it became an integral part of the Malcolm
Baldrige National Quality Award guidelines.1
Xerox Corp.'s pioneering use of benchmarking
led to its reclamation of leading market share
from overseas competitors. Xerox cites 40 percent to 50 percent lower production costs, increased quality, 25 percent to 50 percent reduction in product-development cycle time, and
inventory reductions of 75 percent (Finein 1990).
Such radical improvements have not been lost
on those organizations eager to excel.

The Malcolm Baldrige National Quality
Award was established in 1987 through
passage of the Malcolm Baldrige Quality
Improvement Act. The award was created to stimulate American companies to
improve quality and productivity, recognize their achievements, and establish
criteria to evaluate quality improvement
efforts. See U.S. Department of
Commerce (1993) and Hart and Bogan
(1992).
See Camp (1989), Harrington (1991),
and Spendolini (1992).
See Sammon, Kurland, and Spitalnic
(1984).

Every documented benchmarking study
contains a data analysis component. In Camp's
(1989) seminal book on benchmarking, data
analysis involves determining the current performance "gap" and then projecting future
performance levels. However, benchmarking
analysts are often left to their own devices as to
how to actually analyze the data, characterize
and measure gaps, and project future performance levels.
One of the earliest approaches to competitor assessment consists of simple time-series
plots and projections of each measure identified
for the benchmarking organization and its perceived best competitor.3 While these analyses
can be useful (mostly for financial performance
measures like return on assets or relative stock
price movements), they are somewhat limited in
scope; that is, simple gap analyses are onedimensional views of a service, product, or
process that ignore any interactions, substitutions, or trade-offs between key variables.
For example, a negative correlation between two or more desired qualities will be
disregarded using simple gap analyses. An automobile manufacturer designing a new car
would like both "high fuel economy" and "low
time from 0 to 60 miles per hour." But improvement on one quality measure will have a negative impact on the other. And a complete

Virtually every documented benchmarking
analysis has the following steps: (1) determine
what to benchmark, (2) form a benchmarking
team, (3) identify benchmarking targets, (4) collect and analyze information and data, and (5)
take action.2 The fundamental idea is to measure and compare the products, services, or work
processes of organizations that are identified as
representing best practices. From this, one can use
benchmarking to assess relative performance,
establish organizational targets and goals, and
monitor and learn from industry best practices.
Step 1 consists of choosing the items or
processes to be benchmarked and selecting

understanding of the process is aggravated further as more quality measures are considered,
such as vehicle safety. Simple gap analyses
examine only one measure at a time and ignore
any interactions between variables. Such analyses are difficult to interpret when trade-offs and
choices must be made between multiple measures.
The commonly employed analytical framework and surrounding theory and methodology
used to identify best-practice competitors and
contrast them within the reference population is
somewhat limited. In addition, the fundamental
fact remains that benchmarking in the service
sector is far more challenging than in manufacturing, primarily due to the difficulty in measuring services.4 Overcoming these limitations
requires an innovative approach.

tiple inputs and outputs. As a result, DEA was
first used to evaluate productive efficiency
among nonprofit entities. Its use then spread to
evaluate the relative productive efficiency of
branches in large networks and of individual
institutions in entire industries.6
In general, DEA focuses on technological,
or productive, efficiency rather than economic
efficiency.7 For our purposes, productive efficiency focuses on levels of inputs relative to
levels of outputs. To be productively efficient, a
firm must either maximize its outputs given
inputs or minimize its inputs given outputs.
Economic efficiency is somewhat broader in
that it involves optimally choosing the levels
and mixes of inputs and/or outputs based on
reactions to market prices. To be economically
efficient, a firm seeks to optimize some economic goal, such as cost minimization or profit
maximization. In this sense, economic efficiency
requires both productive efficiency and allocative efficiency.

DATA ENVELOPMENT ANALYSIS:
A NEW WAY TO ANALYZE DATA
Despite the paucity of tools available to
analyze best practices and compute relative
strengths and weaknesses, the success of
benchmarking underscores its inherent usefulness as a process and points to the dramatic
additional gains that are possible. A more useful
benchmarking paradigm should have the following attributes:

As discussed in Bauer et al. (1998), it is
quite plausible that some productively efficient
firms are economically inefficient, and vice
versa. Such efficiency mismatches depend on
the relationship between managers' abilities to
use the best technology and their abilities to
respond to market signals. Productive efficiency
requires only input and output data, whereas
economic efficiency also requires market price
data. Allocative efficiency is about doing the
right things, productive efficiency is about doing
things right, and economic efficiency is about
doing the right things right. DEA was developed
specifically to measure relative productive efficiency, which is our focus here.

• a solid economic and mathematical underpinning,
• alternative actual and composite/hypothetical best-practice units,
• the ability to take into account the
trade-offs and substitutions among the
benchmark metrics, and
• a means to suggest directions for improvement on the many organizational
dimensions included in the study.

According to microeconomic theory, the
concept of a production function forms the
basis for a description of input-output relationships in a firm; that is, the production function
shows the maximum amount of outputs that
can be achieved by combining various quantities of inputs. Alternatively, considered from an
input orientation, the production function describes the minimum amount of inputs required
to achieve the given output levels.
For a given situation, the production function, if it were known, would provide a description of the production technology. Efficiency
computations then could be made relative to
this frontier. Specifically, inefficiency could be
determined by the amount of deviation from
this production function, or frontier. In practice,
however, one has only data—a set of observations corresponding to achieved output levels
for given input levels. Thus, the initial problem

Data envelopment analysis, or DEA, is a
frontier estimation methodology with the above
attributes.5 DEA has proven to be a valuable tool
for strategic, policy, and operational decision
problems, particularly in the service and nonprofit sectors. Its usefulness to benchmarking is
adapted here to provide an analytical, quantitative benchmarking tool for measuring relative
productive efficiency.
DEA was originally developed by Charnes,
Cooper, and Rhodes (1978) to create a performance measure that managers could use when
conventional market-based performance indicators were unavailable. DEA computes the
relative technical (or productive) efficiency of
individual decision-making units by using mul-

FEDERAL RESERVE BANK OF DALLAS

FINANCIAL INDUSTRY STUDIES SEPTEMBER 1998

In many industries, the intangibility,
multiplicity, and heterogeneity of service
outputs make it difficult to construct
clear and uniform performance standards within an industry. And of those
measures in use, most are simple
ratios—return on investment, time per
transaction, cost per person served,
services delivered per hour, etc.—with
no synthesizing metrics commonly
accepted. Interested readers are directed
to Fitzgerald et al. (1991).

Frontier estimation methodologies are
mathematical approaches to determine
best-practice firms, that is, those firms
performing on the frontier. In the past
two decades, four main frontier
approaches have been developed to
assess firm performance relative to
some empirically defined best-practice
standard. DEA is a nonparametric linear
programming approach. The other
three approaches are econometric
approaches—the stochastic frontier
approach (SFA), thick frontier approach
(TFA), and distribution-free approach
(DFA). The approaches differ primarily
in their assumptions regarding the
shape of the efficient frontier and how
random error is handled. Interested
readers are directed to Berger and
Humphrey (1997), Bauer et al. (1998),
and the papers included in Fried, Lovell,
and Schmidt (1993).

See, for example, Banker and Johnston
(1994), Thompson et al. (1990),
Boussofiane, Dyson, and Thanassoulis
(1991), and Grosskopf et al. (forthcoming).

DEA can be adapted to examine economic efficiency by observing the costs
to produce a set of outputs given the
best-practice technology and input
prices. Interested readers are directed
to Bauer et al. (1998) and Fare,
Grosskopf, and Lovell (1994).

input. This is represented as:

Chart 1

Comparison of DEA and
Regression Approaches

EFFICIENCY^ = (Eurk OUTPUTrk)/(Evik INPUTik),
where urk is the unit weight placed on output r
and vik is the unit weight placed on input i by
the k'b firm in the population.
Now, how should the weights (the u's and
v's) be determined? DEA selects the weights
that maximize each firm's productive efficiency
score as long as no weight is negative and the
weights are universal; that is, any firm should be
able to use the same set of weights to evaluate
its own efficiency ratio, and the resulting ratio
must not exceed one. So, for each firm, DEA
maximizes the ratio of its own total weighted
output to its own total weighted input. In general, the model will put higher weights on those
inputs the firm uses least and those outputs the
firm produces most.

Output

Input

Parametric approaches require the
imposition of a specific functional
form—such as a regression equation
or production function—that relates the
independent variables to the dependent
variables. In contrast, as a nonparametric method, DEA requires no
assumptions about the functional form
and calculates a maximal performance
measure for each firm relative to all
other firms. Interested readers are
directed to Charnes et al. (1994).
In a study of hospital efficiency reported
by Banker, Conrad, and Strauss (1986),
regression analysis concluded that no
returns to scale were present, whereas
DEA uncovered the possibilities of
returns to scale in individual hospitals.
In another context, Leibenstein and
Maital (1992) used DEA to demonstrate
that gains from moving inefficient firms
onto the frontier can be more significant
than gains from moving efficient firms
to the optimal point on the frontier.
DEA was originally developed by
Charnes, Cooper, and Rhoades (1978),
who expanded on the concept of technical efficiency as outlined in Farrell
(1957).
See Ali (1992).

The specific DEA model incorporated here
is the constrained-multiplier, input-oriented ratio
model as described in Charnes et al. (1990) and
Charnes et al. (1989). 10 A constrained-multiplier
DEA model places restrictions on the range for
the weights, or multipliers. While unconstrained
DEA models allow each firm to be evaluated in
its best possible light, undesirable consequences
can result when firms appear efficient in ways
that are difficult to justify. More specifically, to
maximize a particular firm's efficiency score,
unconstrained models often assign unreasonably low or excessively high values to the
weights. In contrast, constrained multiplier
models incorporate judgment, or a
priori
knowledge, into the evaluation of each firm.
Upper and lower bounds are imposed on the
individual weights and used to transform the
data before the individual DEA efficiency scores
are computed. (See box titled "Mathematical
Foundations for DEA" for more details.)

is the construction of an empirical production
frontier based on the observed data.
DEA constructs such an empirical production frontier. More precisely, DEA is a nonparametric frontier estimation method that
involves applying linear programming to
observed data to locate the best-practice frontier.8 This frontier can then be used to evaluate
the productive efficiency of each of the organizational units responsible for the observed output and input quantities. As such, DEA is a
methodology directed to frontiers rather than
central tendencies. As shown by the singleinput, single-output representation in Chart 1,
instead of trying to fit a regression line through
the center of the data, DEA "floats" a piecewise
linear surface on top of the observations. The
focus of DEA is on the individual observations
in contrast to the focus on the averages and
estimation of parameters associated with regression approaches. Because of this unique orientation, DEA is particularly adept at uncovering
relationships that remain hidden from other
methodologies. 9

Key to the identification of such a frontier
from empirical observations is the solution of a
set of mathematical programming problems of
sizable proportions. Specifically, if one is to
evaluate and compare n different organizations
along a variety of criteria simultaneously, then n
separate, but related, mathematical programming problems must be optimized and the
results combined.
The computational capacity and speed for
these large-scale problems has only recently
improved. Until just a few years ago, the maximum number of units, or organizations, that
could be evaluated was in the hundreds.11 But
more recently, refined algorithms that employ
parallel-processing technology have produced a
capability to simultaneously consider tens of

DEA produces relative efficiency measures. The solid line in Chart 1 is the derived efficient frontier, or envelopment surface, which
represents the revealed best-practice production
frontier. The relative efficiency of each firm in
the population is calculated in relation to this
frontier. For each inefficient firm (those that lie
below the envelopment surface), DEA identifies
the sources and level of inefficiency for each of
the inputs and outputs.
Mathematically, the relative productive
efficiency of each firm is computed as the ratio
of its total weighted output to its total weighted

Table 1

Variable Definitions
thousands of units.12 While most benchmarking
studies narrow their scope to a small number of
units (most likely because of the computational
speed required and the difficulty in obtaining
vast quantities of data), global or world-class
benchmarking can now be performed with
these new algorithms and computational structures. As a result, large-scale analyses can be
used to distill the true leaders from a large pool
of competitors, and the entire U.S. banking
industry can now be analyzed using DEA.

Call Report item code
Inputs
Salary expense
Premises a n d fixed assets
Other noninterest expense
Interest expense
Purchased funds*
Outputs
Earning a s s e t s !

RIAD4135
RCFD2145
RIAD4093 - RIAD4135
RIAD4073
RCFD0278 + RCFD0279 + RCON2840 +
RCFD2850 + RCON6645 + RCON6646
R C F D 2 1 2 2 - ( R C F D 1 4 0 7 + RCFD1403) +
RCFD0390 + RCFD0071 + RCFD0276 +

Interest income
Noninterest income

USING DEA TO BENCHMARK PRODUCTIVE
EFFICIENCY OF BANKS

RCFD0277 + RCFD2146
RIAD4107
RIAD4079

* Purchased funds are federal funds purchased and securities sold under agreement to repurchase, demand notes issued to the U.S. Treasury, other borrowed money, time certificates of
deposit of $100,000 or more, and open-account time deposits of $100,000 or more.

To examine this analytical framework for
benchmarking, we focus on the U.S. commercial banking industry. Following earlier
research, we slightly modify a five-input, threeoutput DEA model that captures the essential
financial intermediation functions of a bank
(see Chart 2).13 The model approximates the
decision-making nature of bank management
by incorporating the necessary input allocation
and product mix decisions needed to attract
deposits and make loans and investments. In
general, the five inputs represent resources
required to operate a bank (i.e., labor costs,
buildings and machines, and various funding
costs). The three outputs represent desired outcomes: earning assets, interest income, and
noninterest income. The variable definitions and
Call Report item codes are shown in Table l.14
According to this model, productively efficient
banks—or best-practice banks—allocate resources and control internal processes by effectively managing their employees, facilities,
expenses, and sources and uses of funds while
working to maximize earning assets and
income.

t Earning assets are total loans less loans past due 90 days or more and loans in nonaccrual
status, plus total securities, interest-bearing balances, federal funds sold and securities purchased under agreements to resell, and assets held in trading accounts.

edge of factors that are important in judging
quality of bank management. The survey was
intended to identify the correct set of the most
important inputs and outputs and then evaluate
the importance of each variable in relation to
the others. Examiners were asked the following
four questions:
1. What publicly available data do you
think are important in judging the quality of bank management?
2. What publicly available data do you
think are important in influencing the
quality of bank management?
3. Which of the given list of criteria are
most important in judging and influencing the quality of bank management?
4. Evaluate the relative importance (via
pairwise comparisons) of the factors
given below using one of the following
indicators: the factors are equal in
importance (=); one factor is slightly
greater in importance (> or <); one factor is greater in importance (> or <);
one factor is much greater in importance ( » or « ) .

The upper and lower bounds for the unit
weights used in the constrained-multiplier
model were determined through a survey of
twelve experienced Federal Reserve Bank of
Dallas bank examiners regarding their knowl-

Chart 2

Questions 1 and 2 focus on the most important
outputs and inputs, respectively. Each criterion
was rated on a scale of 1 (not important) to 7
(extremely important). Questions 3 and 4 provide relative comparisons between the multiple
inputs and multiple outputs. The "given list of
criteria" and "factors given below" referenced in
questions 3 and 4, respectively, refer to the five
inputs and three outputs used in our model.

DEA Model

• Interest expense
• Purchased funds

FEDERAL RESERVE BANK OF DALLAS

FINANCIAL INDUSTRY STUDIES SEPTEMBER 1998

See Barr and Durchholz (1997).
Variables included in this model have
been shown to capture the importance
of management to a bank's survival.
See Barr, Seiford, and Siems (1993)
and Barr and Siems (1997) for discussion of a similar model used to evaluate
bank efficiency and then predict survivability.
Banks submit Call Reports to the federal
banking regulators on a quarterly basis
to capture balance sheet and income
statement information. Additional
variables as potential candidates for
inclusion in the model are numerous,
however, so we employ this relatively
parsimonious model because of its
value in previous research studies.

Table 2

Constraints for the Multipliers (Weights) in the DEA Model
Survey range
(percent)

Survey average
(percent)

Analytic hierarchy
process weights
(percent)

Inputs
Salary expense
Premises and fixed assets
Other noninterest expense
Interest expense
Purchased funds

15.8-35.9
3.1-15.7
15.8-35.9
17.2-42.8
12.1-34.0

23.1
9.6
22.7
25.9
18.8

25.2
11.4
19.8
23.5
20.2

Outputs
Earning assets
Interest income
Noninterest income

40.9-69.5
25.7-46.9
10.2-20.2

51.3
34.3
14.4

52.5
33.8
13.7

process and compared with the survey averages.15 As shown, four of the five publicly available input variables used in our model have
relatively equal importance; only premises/fixed
assets has a much lower average weight. For the
three publicly available output variables, earning assets is clearly the most important, followed by interest income and then noninterest
income.

MODEL RESULTS
Our DEA benchmarking model was
applied to year-end 1991, 1994, and 1997 data.
There were 11,397 banks in operation in 1991,
10,224 banks in 1994, and 8,628 banks in 1997
that conformed to our data requirements.16 To
evaluate the input and output factors driving the
efficiency results, the banks were divided into
quartiles for each of the three analysis periods
based on their DEA efficiency score. Table 3
shows the average values for each input and

As shown in Table 2, upper and lowrer
bounds on the values of the multipliers were
established from the survey results based on the
relative scores given by the bank examiners. To
verify the accuracy of these results and check
for robustness, the relative average weights
were also computed using the analytic hierarchy

Mathematical Foundations for DEA
strained-multiplier, input-oriented DEA model
construction is the reduction of the multiple-inputmultiple-output situation for each DMU to that of a
single "virtual" input and a single "virtual" output.
For a DMU, the ratio of this single virtual output to
single virtual input provides a measure of relative
efficiency that is a function of the multipliers. Thus,
each DMU seeks to maximize this ratio as its
objective function. The decision variables are the
unit weights (multipliers) for each of the inputs and
outputs, so that the objective function seeks to
maximize the ratio of total weighted output of
DMUfc divided by its total weighted input:

The mathematical programming approach of
DEA is a robust procedure for efficient frontier estimation. In contrast to statistical procedures based
on central tendencies, DEA focuses on revealed
best-practice frontiers. That is, DEA analyzes each
decision-making unit (DMU) separately; it then
measures relative productive efficiency with respect to the entire population being evaluated.
DEA is a nonparametric form of estimation; that is,
no a priori assumption on the analytical form of the
production function or distributional assumptions
are required.

The analytic hierarchy process is an
effective decision-making tool that
quantifies subjective judgments and
preferences. In essence, a hierarchy of
components is developed, numerical
values are assigned to subjective judgments using pairwise comparisons, and
then the judgments are synthesized to
determine which components have the
highest priority and influence in the
decision process. Interested readers are
directed to Saaty (1982) and Golden,
Wasil, and Harker (1989).
Banks that were chartered within three
years of the analysis date were excluded
from the analysis because de novo
banks typically have different cost
structures than more established banks
(see DeYoung, 1998). Also, banks
reporting nonpositive values for any
input or output variable (with the exception of purchased funds, which

In the discussion to follow, we assume there
are n DMUs to be evaluated. Each DMU consumes
varying amounts of m different inputs to produce s
different outputs. Specifically, DMU^ consumes
amounts Xk = {xik} of inputs (/'=
and produces amounts Yk = {yrk} of outputs ( r = 1,...,s).
We assume xik>0 and yrk > 0. The sx n matrix of
output measures is denoted by Y, and the m x n
matrix of input measures is denoted by X.
A number of different mathematical programming DEA models have been proposed in the
literature (see Charnes et al., 1994). Essentially
these various models each seek to establish which
of n DMUs determine an envelopment surface,
which defines the best-practice efficiency frontier.
The geometry of this envelopment surface is prescribed by the specific DEA model employed.
To be efficient, the point corresponding to DMU^
must lie on this surface. DMUs that do not lie on
the envelopment surface are termed inefficient.
The DEA results identify the sources and amounts
of inefficiency and provide a summary measure of
relative productive efficiency.

maximize EFFICIENCYk

= {Zurk yrk)/(Zvik

xik),

where urk is the unit weight selected for output yrk,
and Vjk is the unit weight selected for input x,k. For
the constrained-multiplier model, these weights
must be within the possible range specified by
incorporating expert information, managerial preference, or other judgment into the analysis.
The universality criterion requires DMU^to
choose weights subject to the constraint that no
other DMU would have an efficiency score greater
than one if it used the same set of weights, so that:

(.Iurk yn)l(Xvlk Xjj) < 1, for all j = 1

In addition, the selected weights cannot be
negative, so that urk > 0 for r = 1
s and vik > 0
for /'= 1,...,m. This fractional programming problem
is then transformed, following Charnes and Cooper
(1962), into an equivalent ordinary linear programming problem. A complete DEA solution involves
the solution of n such linear programs, one for
each DMU.

The essential characteristic of the con-

could equal zero) were removed from
the analysis.

Table 3

Bank Profiles by DEA Efficiency Quartile
DEA efficiency quartile

1991 data
Inputs

1
Most efficient

(percent)

Least efficient
(percent)

Most to
least efficie,
difference
(percent)

1.83
2.22

-.40*
-1.22*

2.41
4.62
16.07

-.87*
-9.78*

88.24

4.44*
.13*
-.05

Salary expense / total assets

1.43

1.54

1.65

Premises and fixed assets / total assets
Other noninterest expense / total assets
Interest expense / total assets

1.00
1.53
4.71

1.48
1.62

1.76
1.84

Purchased funds / total assets

6.29

4.70
8.17

4.66
11.12

Earning assets / total assets

92.68

91.67

Interest income / total assets

8.68

8.71

90.59
8.67

.95

.79

.89

8.55
1.00

Number of institutions

2,850

.7340
.6334

2,848
.5982

2,849

Average efficiency score
Lower boundary

.5387

.4611

.5665
.6334

.5092
.5664

0
.5091

1.59
1.56

1.70
1.77

1.95
2.14

1.61

1.72
2.62

2.13
2.68

10.89

12.88

-3.38*

91.54

90.36
6.67

2.23*
.37*

.08*

Outputs

Noninterest income / total assets

Upper boundary

1.0000

.2728*

1994 data
Inputs
Salary expense / total assets

1.57

Premises and fixed assets / total assets
Other noninterest expense / total assets

1.19

Interest expense / total assets

1.79
2.52

Purchased funds / total assets

9.50

2.58
10.29

92.59
7.04

92.08
6.91

1.30

.80

6.80
.85

Number of institutions

2,556

2,557

Average efficiency score

.7356
.6404

.5742

2,555
.5207

.5550

1.0000

.6150
.5932
.6404

.5932

.5550

Salary expense / total assets

1.67

1.60

Premises and fixed assets / total assets
Other noninterest expense / total assets
Interest expense / total assets

.98
1.85

1.55
1.31

1.64
1.94

1.75
2.44

3.29

3.30
12.33

-.38*
-.96*
-.34*
-.16*

Outputs
Earning assets / total assets
Interest income / total assets
Noninterest income / total assets

Lower boundary
Upper boundary

1.05

.25

.2149*

1997 data
Inputs

Purchased funds / total assets

10.46

-.08
-1.45*
-.07
.14*

1.50

1.92

3.27
13.63

3.15
15.32

-4.85*

91.83

90.65

2.33*

7.37
.84

7.33

.13t

.90

.90*

Outputs
Earning assets / total assets

92.99

Interest income / total assets

7.45

Noninterest income / total assets

1.80

92.60
7.41
.77

Number of institutions

2,157

Average efficiency score
Lower boundary

.6685
.4722

.4313
.3982

.3717

.3067

1.0000

.4721

.3451
.3981

0
.3450

Upper boundary
* Indicates significant difference at the .01 level.
t Indicates significant difference at the .05 level.

FEDERAL RESERVE BANK OF DALLAS

FINANCIAL INDUSTRY STUDIES SEPTEMBER 1998

.3617*

Table 4

Bank Performance Measures by DEA Efficiency Quartile
DEA efficiency quartile

M o s t t0

(percent)

4
Least efficient
(percent)

least efficien
difference
(percent)

1.00
8.81
53.34
1.65

.82
8.25
54.74
1.96

.01
7.76
56.56
2.93

1.22*
2.59*
-7.61*
-1.38*

2,850
.7340
.6334
1.0000

2,848
.5982
.5665
.6334

2,849
.5387
.5092
.5664

2,850
.4611
0
.5091

1994 data
Return on average assets
Equity / total assets
Total loans / total assets
Nonperforming loans / gross loans

1.52
11.19
53.22
1.00

1.26
9.62
55.58
.96

1.06
9.10
55.38
.99

.61
8.63
54.27
1.46

Number of institutions
Average efficiency score
Lower boundary
Upper boundary

2,556
.7356
.6404
1.0000

2,556
.6150
.5932
.6404

2,557
.5742
.5550
.5932

2,555
.5207
0
.5550

1997 data
Return on average assets
Equity / total assets
Total loans / total assets
Nonperforming loans / gross loans

1.57
12.42
54.78
1.04

1.31
10.19
59.06
.92

1.20
9.49
60.23
.94

.86
9.29
60.53
1.15

Number of institutions
Average efficiency score
Lower boundary
Upper boundary

2,157
.6685
.4722
1.0000

2,157
.4313
.3982
.4721

2,157
.3717
.3451
.3981

2,157
.3067
0
.3450

1
Most efficient
(percent)

(percent)

1991 data
Return on average assets
Equity / total assets
Total loans / total assets
Nonperforming loans / gross loans

1.23
10.35
48.95
1.55

Number of institutions
Average efficiency score
Lower boundary
Upper boundary

.2728*

.91*
2.56*
-1.06t
-.46*
.2149*

.72*
3.13*
-5.75*
—.lit
.3617*

* Indicates significant difference at the .01 level,
t Indicates significant difference at the .05 level.

output variable as a percentage of total assets.
Comparing the most efficient quartile of banks
with the least efficient quartile reveals some interesting differences. In 1991, the most efficient
banks had significantly lower salary expense,
premises and fixed assets, other noninterest expense, and purchased funds, and they had significantly higher relative levels of earning assets,
interest income, and interest expense. By 1997,
only interest expense, premises and fixed assets,
and purchased funds had statistically significant
differences among the input variables. On the
output side, significant differences still existed
for earning assets and interest income, and a
significant advantage for the most efficient banks
was found for noninterest income.

relative efficiencies for the time period under
analysis, the underlying trends regarding the
significance and strength that each variable contributes can help explain the changes that took
place in the banking industry. From 1991 to
1997, noninterest income became a significantly more important part of banking. In 1991,
noninterest income as a percentage of total
assets averaged 0.95 percent for the most efficient banks and 1 percent for the least efficient
banks. By 1997, the most efficient banks increased this percentage to 1.8 percent, whereas
the ratio for the least efficient banks dropped to
0.9. The increase in noninterest income as a
percentage of total assets for the most efficient
institutions is consistent with banks' increased
focus on earning greater fee income and participation in off-balance sheet activities. The tradi-

While DEA efficiency scores cannot be
compared from year to year because they reveal

tional role of U.S. hanks as strictly financial
intermediaries is widely viewed as changing, as
banks move beyond the balance sheet and
compete in other arenas (see Clark and Siems,
1997).
To see whether our productive efficiency
model correlates with performance, the average
values for a few important bank performance
measures are given in Table 4 by DEA efficiency
score quartile for each analysis period. As
shown, the most efficient banks earned a significantly higher return on average assets than the
least efficient institutions. In 1991, the most
efficient bank quartile earned an average 1.23
percent on average assets, whereas the least
efficient bank quartile earned just 0.01 percent.
In 1997, return on average assets increased for the
banking industry, with the most efficient bank
quartile earning an average 1.57 percent and the
least efficient bank quartile earning 0.86 percent.

In 1991, the largest institutions were found to be
significantly less efficient than the smallest
banks. For 1994 and 1997, there were no significant differences in productive efficiency
between the largest and smallest institutions,
suggesting no significant economies of scale.17

CLASSIFYING BANKS USING EXAMINER RATINGS
In the early 1970s, federal regulators
developed the CAMEL rating system to help
structure the bank examination process. In
1979, the Uniform Financial Institutions Rating
System was adopted to provide federal bank
regulatory agencies with a framework for rating
the financial condition and performance of individual banks. Since then, the use of the CAMEL
factors in evaluating a bank's financial health
has become widespread among regulators. The
evaluation factors are as follows:

More efficient banks also held significantly
higher equity capital. In 1991, the most efficient
bank quartile's capital-to-asset ratio averaged
10.35 percent, versus 7.76 percent for the least
efficient banks. Similar to gains in profitability,
capital levels substantially increased for the
entire banking industry by 1997, with the most
efficient bank quartile holding a capital-to-assets
ratio of 12.42 percent and the least efficient
bank quartile holding 9.29 percent.
More efficient banks also managed relatively smaller loan portfolios that tended to have
fewer risky assets, as evidenced by their lower
levels of nonperforming loans to gross loans. In
1991, the most efficient bank quartile had an
average ratio of total loans to total assets of
48.95 percent, which is significantly less than
the average 56.56 percent held by the least
efficient banks. Nonperforming loans to gross
loans for the most efficient banks in 1991 averaged 1.55 percent, versus 2.93 percent for the
least efficient banks.
By 1997, banking conditions had improved, but the significant differences in portfolio composition, asset quality, and risk levels
remained. The most efficient bank quartile in
1997 had a total loans-to-total assets ratio of
54.78, significantly less than the 60.53 percent
for the least efficient bank quartile. And, while
overall asset quality improved, nonperforming
loans to gross loans for the most efficient bank
quartile was 1.04 percent, significantly less than
the 1.15 ratio for the least efficient banks.
As shown in Table 5, when the data are
separated into asset-size quartiles, we find no
significant differences in efficiency between the
largest and smallest banks, with one exception.

FEDERAL RESERVE BANK OF DALLAS

•
•
•
•
•

Capital adequacy
Asset quality
Management quality
Earnings ability
Liquidity

Each of the five factors is scored from one to
five, with one being the strongest rating. An
overall composite CAMEL rating, also ranging
from one to five, is then developed from this
evaluation.18
As a whole, the CAMEL rating, which is
determined after an on-site examination, provides a means to categorize banks based on
their overall health, financial status, and management. The Commercial Bank
Examination
Manual produced by the Board of Governors
of the Federal Reserve System describes the five
composite rating levels as follows:
CAMEL = 1 An institution that is basically
sound in every respect.
CAMEL = 2 An institution that is fundamentally sound but has modest weaknesses.
CAMEL = 3 An institution with financial,
operational, or compliance
weaknesses that give cause
for supervisory concern.
CAMEL = 4 An institution with serious
financial weaknesses that
could impair future viability.
CAMEL = 5 An institution with critical
financial weaknesses that
render the probability of failure extremely high in the
near term.

FINANCIAL INDUSTRY STUDIES SEPTEMBER 1998

The literature on economies of scale in
banking is extensive; interested readers
are directed to Clark (1996) for a
review. The quartile approach here
should be viewed as tentative, because
quartiles are too broad to capture differences among the larger institutions.

Beginning in 1997, the CAMEL rating
system was revised to include a sixth
component: S—sensitivity to market
risk. This study uses the original
CAMEL rating system for the 1991 and
1994 samples, as it was the one in use
during those periods. Because market
risk had been implicitly considered in
the original CAMEL rating, its introduction to the revised rating, CAMELS, was
not expected to result in significant
changes to the composite rating.

Table 5

Bank Profiles by Asset Quartile
Asset quartile
1
Largest
(percent)

(percent)

4
Smallest
(percent)

Largest to
smallest
difference
(percent)

1991 data
Inputs
Salary expense / total assets
Premises and fixed assets / total assets
Other noninterest expense / total assets
Interest expense / total assets
Purchased funds / total assets

1.49
1.64
1.90
4.63
13.69

1.52
1.62
1.73
4.70
10.46

1.61
1.63
1.82
4.71
9.51

1.82
1.57
1.95
4.66
7.99

-.33*
,07t
-.04
-.03
5.71*

Outputs
Earning assets / total assets
Interest income / total assets
Noninterest income / total assets

90.23
8.56
1.09

91.40
8.64
.84

91.01
8.68
.85

90.55
8.74
.86

-.32*
-.18*
.23*

Score
DEA efficiency score

.5661

.5826

.5867

.5965

-.0304*

Number of institutions

2,849

2,850

1994 data
Inputs
Salary expense / total assets
Premises and fixed assets / total assets
Other noninterest expense / total assets
Interest expense / total assets
Purchased funds / total assets

1.56
1.69
1.92
2.54
14.54

1.63
1.74
1.76
2.62
10.92

1.69
1.71
1.73
2.61
9.86

1.92
1.51
1.85
2.63
8.24

-.36*
.19*
.07
-.08*
6.30*

Outputs
Earning assets / total assets
Interest income / total assets
Noninterest income / total assets

91.29
6.72
1.21

91.99
6.84
.94

91.71
6.89
.86

91.59
6.98
.99

-.30*
-.26*
,23t

Score
DEA efficiency score

.6156

.6121

.6060

.6118

.0039

Number of institutions

2,556

1997 data
Inputs
Salary expense / total assets
Premises and fixed assets / total assets
Other noninterest expense / total assets
Interest expense / total assets
Purchased funds / total assets

1.54
1.73
1.72
3.23
16.03

1.61
1.87
1.57
3.27
13.37

1.63
1.79
1.63
3.28
12.22

1.87
1.52
1.66
3.23
10.13

-.33*
.21*
.05
.01
5.90*

Outputs
Earning assets / total assets
Interest income / total assets
Noninterest income / total assets

91.76
7.32
1.38

92.20
7.39
.98

92.12
7.41
.97

91.98
7.45
.98

-.22
-.13
.391

Score
DEA efficiency score

.4641

.4133

.4401

.4607

.0034

Number of institutions

2,157

* Indicates significant difference at the .01 level,
t Indicates significant difference at the .05 level.

Table 6

DEA Efficiency Scores by Strong/Weak CAMEL Rating
1991

Inputs

1994

1997

Strong

Weak

Strong

Weak

Strong

Weak

banks
(percent)

banks

(percent)

banks
(percent)

Salary expense / total assets

1.54

Premises and fixed assets / total assets
Other noninterest expense / total assets
Interest expense / total assets

1.53
1.64
4.64

Purchased funds / total assets

10.24

1.83*
1.97*

1.65
1.65

2.23*
1.98*

1.63
1.72

2.41*

1.71

2.92*

4.82*

2.61

11.39*

10.95

Currently, federal banking agencies
permit banks that have less than $250
million of assets, are well-capitalized, are
well-managed, have CAMELS ratings of
1 or 2, and have not experienced a
change of control during the previous

2.04*

12 months to be examined every 18
months. Problem banks—those with

1.43

1.941"
2.26*

2.73*

3.25

3.48*

are examined twice per year.

10.79

12.65

14.83*

CAMELS ratings of 4 or 5—typically

Cole and Gunther (1998) assess the
speed with which the information con-

Outputs
Earning assets / total assets

91.65

Interest income / total assets

8.55

87.85*
8.88*

.83

1.05*

6.83
.93

DEA efficiency score

.5942

.5235*

Number of institutions

5,641

1,846

Noninterest income / total assets

92.18

89.72*

1.38*

7.33
.85

7.88*
1.25*

.6137

.5532*

.4272

.3751*

7,188

491

4,273

221

91.92

88.11*
7.32*

tent of CAMEL ratings decays when
benchmarked against an off-site monitoring system. Applying a probit model
to publicly available accounting data,
Cole and Gunther found that their
econometric forecasts provide a more
accurate indication of survivability for
banks with examination ratings more

NOTE: Strong banks are those with CAMEL ratings of 1 or 2; weak banks are those with CAMEL ratings of 3, 4, or 5.

than one or two quarters old. Cargill

* Indicates significant difference between strong and weak banks at the .01 level,

(1989) found that CAMEL ratings are
primarily proxies for available market

t Indicates significant difference between strong and weak banks at the .05 level.

information. Berger and Davies (1994)
found that downgrades in CAMEL
ratings precede stock price reductions.
21

Commercial hanks are examined annually for
safety and soundness by one of the federal bank
regulatory agencies or a state regulator.19
The use of examiner ratings in research
studies has been limited.20 DeYoung (1998) uses
CAMEL ratings and a logit model to separate
banks into well-managed and poorly managed
samples and then estimates a thick cost frontier
model to measure X-inefficiency differences
between the two samples.21 DeYoung found that
the well-managed banks had significantly lower
estimated unit costs than the poorly managed
banks.22 Despite this significant cost-efficiency
difference, DeYoung also found that the wellmanaged banks incurred significantly higher
raw (accounting-based) unit costs than did the
poorly managed banks. This result is important
because it implies that cost-efficient bank management requires expenditures generally not
made by poorly managed banks.

with composite CAMEL ratings of 1 or 2; weak
banks are those rated 3, 4, or 5.
As shown in Table 6, for each of our
analysis periods, strong banks had significantly
higher efficiency scores than weak banks.23 For
the input variables, strong banks generally have
significantly lower (as a percentage of total assets)
salary expense, premises and fixed assets, other
noninterest expense, interest expense, and purchased funds than weak banks. For the output
variables, we find that strong banks hold significantly more earning assets than weak banks, as
one would expect; but, somewhat surprisingly,
they generate significantly less interest income
and noninterest income as a percent of total
assets than weak banks.
The higher relative interest and noninterest
income levels for the weak banks might be due to
their generally higher risk positions and poorer
asset quality. Weak banks might be earning
greater interest and noninterest income because
their investments have more risks. But the increased income levels do not make up for the
significantly higher input costs needed to monitor these investments and service these assets.
Chart 3 shows the percentage of banks
within each CAMEL-rating category that falls
into each efficiency score quintile. This analysis
uses the entire sample of banks for all three
years. If the DEA efficiency scores do not differentiate between strong banks and weak banks,

To further evaluate our DEA model, individual bank efficiency scores were compared
with confidential bank examiner ratings. For our
1991 sample, 7,487 U.S. commercial banks were
examined and given CAMEL ratings in 1992; for
our 1994 and 1997 samples, 7,679 and 4,494
banks were examined and given ratings in 1995
and 1998, respectively. To simplify our analysis,
we grouped the banks into two categories
based on their composite CAMEL rating: strong
and weak. Strong banks are those institutions

FEDERAL RESERVE BANK OF DALLAS

FINANCIAL INDUSTRY STUDIES SEPTEMBER 1998

The thick frontier approach is one of the
main parametric frontier methods used
by researchers to evaluate efficiency.
The thick frontier method compares
estimates of costs derived from a
best-practice cost function with those
derived from a cost function using data
from the worst-practice firms (see
Berger and Humphrey, 1997). In the
banking cost literature, X-inefficiency
describes any excess cost of production
not caused by suboptimal scale or
scope. While the methodology selected
has a great effect on the X-inefficiency
differences, most studies find X-inefficiencies equal to about 20 percent to
25 percent of costs. See Berger, Hunter,
and Timme (1993) and Evanoff and
Israilevich (1991) for thorough reviews
of this literature.

The relationship between management
quality and X-inefficiency has not been
explored as thoroughly as one might
expect, given the number of studies that
conclude that the quality of management is the most important factor in the
success or failure of a bank. For more
on the link between X-inefficiency and
management quality, interested readers
are directed to Peristiani (1997), who
found a statistically significant correlation between X-inefficiency and bank
examiners' numerical assessments of
"management quality," and Barr and
Siems (1997) and Wheelock and Wilson
(1995), who use an efficiency measure
as a proxy for management quality in
bank failure studies.

Our analysis was also carried out using
the M-rating instead of the composite
CAMEL rating and produced qualitatively
similar results to those presented here.

periods: 1991, 1994, and 1997. Interestingly, noninterest income became a significantly more important variable over time as banking conditions
improved and banks focused on generating more
fee income and offering a greater selection of
products. Our analysis also reveals that the most
efficient banks earn a significantly higher return
on average assets, hold significantly more capital, and manage relatively smaller loan portfolios with fewer troubled assets.
Consistent with previous empirical research, the results found here for U.S. commercial banks confirm the commonsense proposition that banks that receive better CAMEL ratings
by banking regulators are significantly more
efficient. Using our DEA model, we find that
strong banks (those rated 1 or 2) are significantly more efficient than weak banks (those
rated 3, 4, or 5). This result points to the potential usefulness of our DEA efficiency model as
an additional off-site monitoring tool for bank
examiners.
The development and extension of frontier estimation research has been limited historically by compLitational feasibility. Recent
breakthroughs in solving truly large-scale models, such as the one developed here, open up a
wide range of new possibilities and directions
for research. A benchmarking support system
could be developed to help individual institutions explicitly gauge their shortcomings and
formalize and prioritize action plans to improve
productive efficiency. Additionally, large-scale
efficiency analyses of the entire banking system
can be used to better understand the effects
of industry dynamics and structure changes—
mergers and acquisitions, local market concentration and competitiveness, regulatory changes,
technological improvements, and so forth.

Chart 3

Efficiency Score Quintiles by CAMEL Rating
Combined Data 1991,1994,1997
Percentage of banks in efficiency quintile
100

CAMEL rating
fCXj 1st quintile (highest DEA scores)

4th quintile

5th quintile (lowest DEA scores)

| 2nd quintile

| \ ' j 3rd quintile

then each CAMEL-rating category would be expected to contain 20 percent of the highest scoring banks, 20 percent of the second qLiintile
banks, etc. However, as shown in the chart, there
is a clear separation of efficiency quintiles: the
most efficient banks are overrepresented in the
CAMEL-1 group, while the least efficient banks
are overrepresented in the CAMEL-5 group. More
specifically, 30 percent of the CAMEL-1-rated
banks have efficiency scores in the highest
score quintile, while 57 percent of the 5-rated
banks have efficiency scores in the lowest score
qLiintile. The close association between efficiency
scores derived from the DEA model and bank
examiner CAMEL ratings suggests that the scores
may be useful as an additional off-site surveillance tool for bank regulators.

Overall, benchmarking the productive efficiency of U.S. banks can help bank managers
and regulators better understand a bank's productive abilities relative to competitors and
industry best practices. We have shown that
more efficient banks tend to be higher performers and safer institutions.

CONCLUSIONS AND DIRECTIONS
FOR FUTURE RESEARCH
In this study, we used a constrained-multiplier, input-oriented DEA model to evaluate the
relative productive efficiency of U.S. banks.
Using this measure, we can consider the sources
of inefficiency and possible paths to boost
productive efficiency. In addition, this productive efficiency measure provides an indicator to
benchmark performance and is conceptually
superior to measures produced using common
gap analysis methodologies.
Using our five-input, three-outpLit model,
we find that the most efficient bank quartile has
significantly higher DEA efficiency scores than
the least efficient quartile for all three analysis

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