Measuring Bank Cost Efficiency:
Don’t Count on Accounting Ratios
Robert DeYoung
This article explores the challenges and misconceptions of measuring cost efficiency at financial institutions.
We illustrate situations in which accounting-based expense ratios are misleading and show that statistics-
based “efficient cost frontier” approaches often measure cost efficiency more accurately. We also demonstrate
a less complicated “fix-up” technique that combines the best qualities of both approaches. Finally, we
summarize the existing literature on cost inefficiencies, scale economies, scope economies, and technological
change at commercial banks, and conclude that any thorough treatment of bank efficiency must analyze
revenues as well as expenses.
The deregulation of financial markets in the 1980s
led to a massive restructuring of the commercial
banking industry. Barriers to geographic expansion and
ceilings on interest rates were eliminated, and
commercial banks experienced dramatic increases in
actual and potential competition from in-state banks,
out-of-state banks, and non-bank rivals. Over 1,000
banks became insolvent after 1980, succumbing to the
combination of unfamiliar competitive conditions and
unfavorable macroeconomic events. Thousands more
were acquired by rival institutions, leaving the US
banking system with about 25% fewer banks today
than at the start of the 1980s.
These trends are likely to continue, and perhaps
accelerate, when the final provisions of the Riegle-
Neal Interstate Banking and Branching Efficiency Act
become law in 1997. What kind of banks are likely to
flourish, fail, or be acquired as the industry continues
to consolidate? If the past is pr elude to the future,
the banks that disappear will be those that are
inefficiently run. Inefficient banks have relatively
high costs and earn relatively low revenues, and as
a result generate smaller capital cushions to protect
Robert DeYoung is a Senior Financial Economist at the Office
of the Comptroller of the Currency, Washington, DC, 20219.
The opinions expressed in this article are those of the author
and do not necessarily reflect those of the Office of the
Comptroller of the Currency or the Department of the
Treasury. The author thanks Tara Rice for excellent research
assistance and Kevin Jacques, Larry Mote, and two anonymous
referees for invaluable comments on earlier drafts.
themselves during bad times. Inefficient banks also
tend to make attractive merger targets, because they
can often be purchased for low price-to-book ratios
and then be made to run more efficiently.
Bank analysts generally measure “efficiency” in
terms of spending on overhead, such as physical plant
and bank personnel, relative to the amount of financial
services produced by the bank. Based on this notion
of efficiency, one would expect the banking industry
to be turning in some impressive efficiency gains,
because reducing overhead is a stated goal in many
bank mergers and bank holding company
reorganizations. However, a close look at the data
suggests otherwise. For example, the commercial
banking system currently spends more on labor than
it did a decade ago. Although total employment at
commercial banks has fallen by about 5% over the past
decade (and by about 13% per dollar of real assets),
this has been more than offset by a 19% increase in
real salaries and benefits per employee.
banks also operate more branch locations now than
they did a decade ago. The number of banks has
declined dramatically, but the number of branch offices
In 1985, the 14,373 commercial banks with insured deposits
held $3.646 billion of assets (in 1994 dollars), employed the
equivalent of 1,561,339 full-time employees, and paid them
an average of $34,200 in salaries and benefits (in 1994 dollars).
In 1994, the comparable figures were 10,444 banks, $4.012
billion of assets, 1,488,583 full-time employees, and $40,710
in salaries and benefits. Source: Reports of Condition and
Income, 1985, 1994.
per dollar of real assets has increased by about 4%,
and the number of automated teller machines (ATMs)
operated by banks has almost doubled.
(1994) reports that the number of bank locations (main
offices, branches, and ATMs) per person in the US
tripled between 1973 and 1992.
How can industry-wide expenditures on labor and
physical overhead be increasing at a time when the
most inefficient banks are exiting the industry?
Because efficiency and cost cutting are not always
one and the same. This article addresses some of the
misconceptions inherent in measuring the cost
efficiency of financial institutions. We illustrate
situations in which accounting-based cost ratios can
be misleading, and show that statistics-based efficient
cost frontier approaches, although far from flawless,
often provide more accurate estimates of cost
efficiency. Because these techniques require advanced
statistics training, we also demonstrate a simpler fix-
up procedure that allows the analyst to establish more
accurate benchmarks for accounting cost ratio
analysis. To put our empirical results in perspective,
we briefly review the bank cost literature, which
suggests that moving closer to the efficient cost
frontier yields larger potential cost savings for the
typical commercial bank than do scale economies,
scope economies, or technological change. Finally, we
recognize that neither statistics-based or accounting-
based measures of cost efficiency are complete gauges
of bank performance, and conclude that any
investigation of bank efficiency must consider
revenues as well as costs.
I. Accounting-Based Cost Ratios
Accounting-based cost ratios are a traditional
tool used by bank analysts to measure cost
efficiency. These easy-to-use bellwethers express
a bank’s annual noninterest expenditures (e.g.,
salaries, benefits, materials, physical capital,
outsourced services) as a percentage of its assets
or its annual revenue. All of the information needed
to construct these ratios can be read directly from a
bank’s basic financial statements.
Although cost ratios are easy to construct and use,
they can be difficult to interpret. Myopic analysis of
expenditures can be misleading—reduced spending
on labor, materials, or physical plant is no guarantee
that a bank is being run efficiently, and high levels of
spending on these items does not necessarily signal
inefficiency. Excessive cost cutting can damage
service quality, portfolio quality, and earnings. For
example, high expenditures on branches and/or ATMs
might provide greater convenience for customers, high
wages might result in the production of more financial
services per worker, and large employee rolls might
make a bank healthier if the additional workers are put
to work monitoring loans. Expense levels can also vary
significantly according to business strategy or
economic conditions. For instance, banks that produce
large amounts of fee-based services will incur large
amounts of labor expenses, banks located in fast-
growing markets will incur expansion-related expenses,
and banks in economically depressed regions will incur
large expenses related to administering problem loans.
An example of how cost ratio analysis can be
misleading is shown in Exhibit 1, which charts the
aggregate ratio of noninterest expenses to assets for
the US commercial banking system from 1985 through
The trend is unmistakably upward. The exhibit
suggests that the banking industry has become grossly
inefficient over time, spending over 20% more on labor,
materials, and physical plant now than a decade ago.
The data are misleading, however, because this cost
ratio does not control for increases in fee-based
activities, which have significantly altered the
relationship between noninterest expenses and assets
at banks. Fee-based activities (e.g., mutual fund sales,
data processing, letters of credit, financial advice,
mortgage servicing) only generate noninterest
expense and add next to nothing to a bank’s asset
base. The bias is confirmed in Exhibit 1 by adding
the aggregate ratio of noninterest income to assets,
which increases in sympathy with the cost ratio.
Thus, expense ratios can be misleading in trend
analysis if product mix changes over time and in
cross-sectional analysis if the banks being
compared have dissimilar product mixes.
A more frequently used cost ratio expresses
noninterest expense as a percentage of net revenue—
bank analysts often refer to this ratio as the efficiency
ratio, and we will simply call it EFFRAT.
Because it
uses revenues rather than assets as a base, EFFRAT
relates overhead spending to the entire range of bank
activities, both on and off the balance sheet. Exhibit 2
displays aggregate EFFRAT for the commercial
banking system from 1985 through 1994. Note that the
upward expense trend from Exhibit 1 has disappeared.
In 1985, commercial banks held $3.646 billion of assets
(in 1994 dollars) and operated 49,478 banking offices and
48,118 ATMs. In 1994, the comparative figures were $4.012
billion of assets, 56,397 bank offices, and 109,080 ATMs.
Sources: Rhoades (1995), Reports of Condition and Income,
1985, 1994.
Unless otherwise indicated, all data used in this article are
taken from the Reports of Condition and Income (a.k.a., the
call reports) between 1985 and 1994.
Net revenue equals net interest income (interest income minus
interest expense) plus noninterest income. Some analysts use
variants of EFFRAT, but the form defined here is the most
common. See Toevs and Sitka (1994).
EFFRAT bounces up and down across time, but if the
bad bank performance years of 1990 and 1991 are
ignored the trend in EFFRAT is consistent with the
expected post-deregulation improvements in industry-
wide cost efficiency.
But EFFRAT is not a flawless measure of bank cost
efficiency, either. Because it has net revenue in its
denominator, EFFRAT is sensitive to changes in the
term structure of interest rates. For example, for liability-
sensitive banks (banks that lend long and borrow
short), a steepening of the yield curve enhances
interest margins and drives up net revenue. Evidence
of this phenomenon can be seen in Exhibit 2. Aggregate
EFFRAT tends to move in the opposite direction of
the aggregate ratio of interest margin to assets, which
implies that changes in the yield curve can create
misleading movements in EFFRAT over time.
Unless the analyst is careful, EFFRAT can also be
misleading when used to compare the performance of
an individual bank to the performance of a group of
peer institutions having similar characteristics. Asset
size is the characteristic used most often to identify a
peer group of banks. However, EFFRAT can vary even
among equally efficient banks of similar size. Exhibit 3
plots EFFRAT values for 330 commercial banks in 1994,
each of which held between $90 and $100 million in
assets. The banks are divided into four groups
according to the percentage of net revenue derived
from noninterest income. Note that average EFFRAT
increases markedly across the four groups, climbing
from 0.57 in the first group (for which noninterest
income averaged just 7% of net revenue) to 0.72 in the
fourth group (for which noninterest income averaged
26% of net revenue).
II. Cost Frontier Analysis
Cost frontier analysis provides an alternative to
accounting-based efficiency ratios. In cost frontier
analysis, the analyst attempts to estimate the maximum
amount that a bank could reduce its costs while still
producing the same amount and combination of
financial services. We refer to these potential cost
savings simply as cost inefficiencies, or sometimes as
X-inefficiencies. Note that eliminating cost
inefficiencies is separate and distinct from achieving
scale economies, which requires a bank to increase
the amount of output it produces. Similarly, shedding
cost inefficiencies differs from capturing increased
scope economies, which requires a bank to alter the
combination of outputs it produces.
Perhaps the biggest advantage of cost frontier
analysis is the luxury of not having to construct peer
groups of banks with similar characteristics. Instead,
cost frontier analysis uses statistical techniques to
simulate a hypothetical best practice bank similar to
the real bank that is under evaluation. The hypothetical
Exhibit 1. Overhead Costs-to-Assets—Annual Aggregate Data for US Commercial Banks from
1985 to 1994
Nonperforming loans comprised about 3.7% of total loans
for commercial banks in both 1990 and 1991, substantially
above the normal levels of between 2 and 3%. Deteriorating
loan quality causes reductions in interest income (reducing
the denominator of EFFRAT) and increases in labor
intensive activities such as monitoring loans, renegotiating
terms, and working out defaulted loans (increasing the
numerator of EFFRAT).
In Exhibit 3, all of the inter-group comparisons of EFFRAT
are significantly different from zero at the 0.05 level. DeYoung
(1994) finds a pattern similar to that shown in Exhibit 3 for
banks of all sizes in 1992.
bank produces the same level and combination of
financial services, under the same market conditions,
as does the real bank, but does so at the lowest cost
possible. Cost inefficiency is estimated by comparing
the expenses actually incurred by the real bank to the
simulated expenses for the best practice bank, i.e., the
expenses that the bank in question would have incurred
had it been operating on the efficient cost frontier.
Exhibit 4 shows a simplified picture of an efficient
total cost frontier. The points suspended in the center
of the graph represent the annual total expenses
incurred by banks of different asset sizes. The efficient
cost frontier curves through the lower portion of this
expense cloud, representing the total expenses incurred
by best practice banks. For each bank, cost
inefficiency is measured by the vertical distance
between its actual expenses and its potential low cost
position on the frontier. This vertical gap is the total
cost savings a bank could potentially capture by
achieving best practice cost levels. Although no bank
can consistently incur less than best practice costs,
notice that some of the banks in Exhibit 4 are located
slightly below the efficient cost frontier. These
deviations reflect random, one-time fluctuations in
Exhibit 2. Overhead Costs-to-Net Revenues (EFFRAT)—Annual Aggregate Data for All US
Commercial Banks from 1985 to 1994
Exhibit 3. Overhead Costs-to-Net Revenue (EFFRAT) for 330 US Commercial Banks with Assets
Between $90 and $100 million in 1994
reported expenses due to measurement error or luck.
As described below, the chief goal of cost frontier
techniques is to disentangle these random vertical cost
fluctuations from the vertical cost inefficiency gaps.
Cost inefficiency will be overstated if positive random
errors are mistaken for excess costs and understated if
negative random errors are allowed to cancel out some
or all of a bank’s excess expenditures.
Note that Exhibit 4 is only a stylized representation
of an actual cost frontier. For one thing, Exhibit 4 has
only one attribute (asset size) over which to compare
the expense levels of banks. An actual cost frontier
contains multiple attributes that drive bank expenses,
such as portfolio mix, input prices, state branching
laws, and regional economic conditions. Including
multiple cost drivers allows the analyst to simulate the
expense levels for hypothetical best practice banks
that have attributes more closely resembling those of
the banks under investigation. Hence, by estimating a
single cost frontier, the analyst can evaluate the cost
efficiency of dozens, hundreds, or even thousands of
banks with very different attributes, largely eliminating
the need to construct peer groups.
Regardless of it simplicity, Exhibit 4 illustrates two
of the fundamental cost inefficiency patterns found in
the banking industry. First, the very smallest banks
tend to exhibit the highest levels of cost inefficiency.
Some of these banks operate in rural markets where a
lack of competitive rivalry creates less pressure to
operate efficiently, while others are newly chartered
banks still traveling down a learning curve. Second,
with the exception of the very small banks, cost
inefficiency is not necessarily related to asset size.
Large and moderate-sized banks are equally likely to
operate near the cost frontier or far above it. Although
large banks should be able to attract more highly skilled
managers who are better able to control costs, the
complexity of large banks makes them more difficult to
operate efficiently, and these two phenomena may tend
to cancel each other out.
Depending on the methodology used, the time
period examined, and the set of banks being evaluated,
cost frontier studies generally conclude that the typical
bank could reduce its total expenses by 15 to 25% by
operating on the efficient cost frontier. Berger, Hunter,
and Timme (1993) provide a review of this literature.
However, the application of cost frontier analysis to
commercial banks is constantly being refined, and
several more recent studies have found substantially
smaller levels of cost inefficiency. Berger and DeYoung
(1995) estimated that operating cost inefficiencies
averaged between 5 and 10% across the entire US
banking industry, Mester (1996) concluded that total
accounting cost inefficiencies averaged about 8% for
banks in three east coast states, and Clark (1996) found
total economic cost inefficiencies of less than 5% for
large US banks.
Still, since even these smaller
Berger and Humphrey (1991) showed that, although accounting
costs vary widely for banks of all sizes, cost dispersion is
markedly larger for banks with less than $50 million in
assets (1984 dollars).
There is no definitive evidence on the relationship between
bank size and cost efficiency. Some studies have found a
positive relationship, while others have found a negative
or no relationship. DeYoung (1997) includes a brief
discussion of this literature.
Operating cost includes only noninterest expenses, total
accounting cost adds interest expenses to this, and total
economic cost adds the opportunity cost of capital to this.
Exhibit 4. An Example of an Efficient Cost Frontier
estimates of cost inefficiencies are found for banks of
all sizes, they represent the potential for cost
reductions more widespread than those available from
scale economies.
Banking economists have used three different
statistics-based methods to disentangle cost
inefficiencies from random cost fluctuations. The thick
cost frontier approach, introduced by Berger and
Humphrey (1991), uses accounting cost ratios to
separate banks into high cost and low cost groups,
isolates random error by estimating a separate cost
function for each group, and measures cost inefficiency
as the vertical distance between the two cost functions.
This approach is impractical for our purposes because
it estimates cost inefficiency for the banking industry
in general but not for individual banks. The
distribution-free approach, developed by Berger (1993)
based on earlier work by Schmidt and Sickles (1984),
estimates a cost function using a time series-cross
section data set, then measures cost inefficiency by
averaging together the annual residuals for each bank.
The annual random errors tend to cancel each other
out in the averaging process, leaving only cost
inefficiency—which is assumed to be constant over
time—in the averaged residuals. This technique is also
inappropriate for our purposes because it generates
long-run average estimates of cost inefficiency that
are not directly comparable to annual accounting-
based cost ratios. The stochastic cost frontier
approach, which was made tractable by Jondrow,
Lovell, Materov, and Schmidt (1982), estimates a cost
function with a two-part error structure in which
random error and cost inefficiencies are separate,
independent elements. Cost inefficiency is assumed
to follow a one-sided positive (usually half-normal)
distribution. Although this approach has been
criticized for imposing a specific distribution on the
unknown patterns of cost inefficiencies, we use it here
because it generates annual estimates of cost
inefficiency for individual banks. A more in-depth
discussion of these three approaches is beyond the
scope of this article—the interested reader can refer
to the above citations for technical details.
A. Example: A Stochastic Cost Frontier
The stochastic cost frontier (SCF) approach is based
on a cost equation that relates a bank’s expenses to
the conditions that drive those expenses, such as
output levels, input prices, and regional economic or
regulatory conditions. As described above, the SCF
cost equation also contains a two-part, or composite,
error structure that distinguishes random cost
fluctuations from cost inefficiencies. The following
equation is a simplified example:
Costs = f (output, input, other ) + U + V (1)
Including a wide variety of expense drivers (output
levels, input prices, and other conditions) in the cost
equation ensures that the resulting efficient cost
frontier can be used to simulate a best practice bank
that closely matches the characteristics of the banks
that the analyst wishes to evaluate. The composite
error structure U+V separates the two vertical
components of costs that are unrelated to the
expense drivers. When Equation (1) is estimated
properly, V isolates and absorbs any random
disturbances and prevents them from affecting the
estimate of cost inefficiency U.
In this study, we include only noninterest expenses
on the left-hand side of Equation (1). This makes the
resulting estimates of cost frontier inefficiency more
comparable to accounting-based cost ratios like
EFFRAT, which include only noninterest expenses.
On the right-hand-side of Equation (1) we include five
types of output (C&I loans, real estate loans, consumer
loans, noninterest income, and transactions services),
two input prices (the wage rate and the price of
physical capital), and dummy variables that control
for state-level branching laws. We assume a Fourier-
flexible functional form for Equation (1) and impose a
truncated normal distribution on the inefficiency term
The resulting efficient cost frontier was estimated
using 1994 data for 9,622 commercial banks.
Exhibit 5 compares estimated cost inefficiency from
our SCF model to the accounting cost ratio EFFRAT,
using the same 330 banks shown in Exhibit 3. Recall
that EFFRAT overstated inefficiency for banks that
generated large portions of their income from fee-based
activities. In contrast, the SCF estimates of frontier
cost inefficiency (expressed as the percentage by
which a bank could reduce its noninterest costs by
moving to the efficient frontier) do not contain this
bias. Frontier cost inefficiency averages between 5 and
6%, and none of the differences between the four
groups of banks are significantly different from zero.
Hence, because the SCF cost equation controls for
the effects of noninterest income on operating costs,
our estimates of frontier cost inefficiency do not suffer
from the bias found in EFFRAT.
B. Example: A Middle Ground
Although the SCF method—or either of the other
frontier efficiency approaches discussed above—can
In application, cost inefficiency is estimated as the expected
value of U conditional on the residual U+V.
Most studies conclude that inefficiencies due to excess interest
expenses are small relative to inefficiencies due to excess
noninterest expenses. See Berger, Hunter, and Timme (1993).
This specification is more general than the usual translog,
half normal specification most often found in the literature.
See Berger and DeYoung (1995) for further details of this
cost model.
be used to correct for such biases, implementing these
methods require a great deal of time and statistical
expertise. Instead, the analyst might use a more
rudimentary statistical procedure to fix-up the simple
EFFRAT ratio. One possible approach is to regress
EFFRAT on a set of variables including the variable
thought to be causing the bias. In the following
equation, A represents assets, NI = noninterest
income, and NR = net revenue. The equation is a simple
ordinary least squares regression example for the 330
banks shown in Exhibit 5:
EFFRAT = 0.1834 + (0.0038)A + 0.6033 (NI/NR)
(0.2056) (0.0022) (0.0636) (2)
where assets are in millions of dollars, adjusted R
equals 0.1978, and the coefficient standard errors
appear in parentheses. Once estimated, Equation (2)
becomes a formula for determining a corrected-EFFRAT
benchmark to which any of the 330 banks can be
compared. For example, for a bank with assets of $95
million and noninterest income-to-net revenue of 15%,
we generate the appropriate benchmark by substituting
these values into the right-hand-side of the formula.
This yields a corrected-EFFRAT benchmark of 63.5%—
if the actual EFFRAT of this bank is above (below)
63.5%, then the bank is operating more (less)
inefficiently than the average bank. In contrast, for a
$95 million bank that generates 20% of its net revenues
from noninterest income, the appropriate corrected-
EFFRAT benchmark is a higher 66.5%.
By using adjustments like this, the analyst can add
some flexibility to accounting-based cost ratio analysis
without going through the complicated process of
estimating an efficient cost frontier. Of course,
Equation (2) is only one example. Quadratic and
double-log specifications yielded slightly better
statistical fits than did this simple linear model, but
made similar predictions. By adding additional right-
hand-side variables to the fix-up equation, the analyst
might be able to control for other inter-bank biases in
EFFRAT, such as organizational form (banks that are
affiliates of holding companies might incur fewer
overhead expenses) or local economic conditions
(banks in low growth regions might incur higher
expenditures to administer problem loans). The analyst
should not, however, add variables that are directly
influenced by bank management. For example,
including the nonperforming loan ratio in the formula
will likely set too high a corrected-EFFRAT benchmark,
because nonperforming loans are often caused by poor
(i.e., inefficient) loan portfolio management.
III. Scale, Scope, and Technological
For most commercial banks, cost inefficiencies are a
potential source for large cost savings. But moving
closer to the best practice cost frontier is not the only
way a bank can improve its cost structure. Some banks
could reduce per unit costs simply by growing larger,
others by changing the mix of financial services they
produce. For the vast majority of banks, however, the
savings available from changing the scale or scope of
their operations are small relative to the potential
savings from eliminating cost inefficiencies.
Exhibit 5. Overhead Costs-to-Net Revenue (EFFRAT) and Estimated Frontier Cost Inefficiency for
330 US Commercial Banks with Assets Between $90 and $100 Million in 1994
Furthermore, as time passes and new production
methods cause the cost frontier to shift down, the
efficiency gains from becoming a best practice bank
can become larger.
A. Technological Change
Technological change can shift the cost frontier in a
number of ways. New low-cost technologies such as
ATMs can be substituted for existing high-cost
technology such as brick-and-mortar branch locations.
Computer systems, high-speed check readers, and
check imaging systems can allow banks to reduce costs
by substituting physical capital for labor. Deregulation
can also provide an opportunity to reorganize inputs
in a lower-cost fashion. As federal and state laws
restricting branch banking eroded, banks were able
to reduce overhead costs by abandoning some of
the Byzantine multibank holding company
arrangements previously necessary to circumvent
these restrictions. Expanded powers can allow
banks to provide new financial services (e.g.,
securities underwriting, mutual fund sales, mortgage
servicing) using overhead originally put in place to
service depositors and loan customers. Increases
in market competition can produce pressure to more
quickly adopt cost-reducing technologies.
It is important to distinguish between shifts in the
efficient cost frontier and the position of banks relative
to the cost frontier. For example, say that a bank’s
distance from the cost frontier increased from 10% of
costs to 12% of costs, but the cost frontier itself fell
by 5% of costs due to technological progress over the
same time period. Then the bank’s expenses would
have decreased by roughly 3% (5% minus 2%) despite
having fallen further behind the best practice banks.
Exhibit 6 characterizes in rough fashion how our SCF
operating cost frontier changed position between 1985
and 1994. Exhibit 7 reports three sets of results, by
asset size, that correspond to the moving cost frontier
in Exhibit 6: shifts in the cost frontier, changes in the
average bank’s position relative to the frontier, and
the combined effect of these two changes.
Our results suggest that the cost frontier pivoted
somewhere around $100 million in assets between 1985
and 1994. For the average bank smaller than $100
million, the cost frontier fell by roughly 1.5%. This
small reduction enhances the best practice potential
for thousands of banks (about 80% of the industry)
and is a relatively impressive decline when compared
to the increases in the cost frontier for larger banks.
The frontier rose by about 7% for banks with between
$100 and $300 million in assets and by between 10 and
11% for banks larger than $300 million. On average,
banks of all sizes moved closer to the cost frontier
over the course of the decade, which suggests that
the banks that survived the structural upheaval of the
1980s and 1990s either were more cost efficient to
start out or stayed alive (i.e., did not fail or were
not acquired) by becoming more cost efficient.
Hence, the cost efficiency gap between average
banks and best practice banks shrank over time,
but not by enough to offset the upward movement
in the cost frontier for large banks.
Although our results do not correspond with the
conventional notion of technology marching
inexorably ahead over time, they are consistent with
other studies. Bauer, Berger, and Humphrey (1993)
found that the cost frontier for all commercial banks
moved up at an annual rate of about 1 or 2% from 1977
through 1988, and Grabowski, Rangan, and Rezvanian
(1994) concluded that the cost frontier for a random
sample of 669 commercial banks moved up by about
4% between 1983 and 1987. None of these results,
however, necessarily indicate technological regress,
because technological advancements do not always
reduce costs once they are applied. For example, a
new technology might enhance service quality while
leaving costs unchanged or higher. ATMs improve
service quality for depositors by making banking more
convenient, but because depositors are likely to use
this convenient service more frequently than they used
the branch, adoption of the new technology doesn’t
necessarily reduce the costs of servicing depositors.
This may be one reason why the cost frontier moved
up for large banks, which own and operate ATM
networks more intensively than do small banks.
Furthermore, the disparate movements in the cost
frontier for small and large banks may not be related
at all to technological change. Large banks were
more likely to incur transitional expenses related to
acquisitions made during the post-deregulation
period, and bank regulators eased some of the
costly regulatory reporting requirements for small
banks during the 1990s.
B. Scale Economies
Following industry deregulation, commercial banks
1 3
To make these inter-temporal comparisons, we used a
technique similar to that used by Elyasiani and Mehdian (1990)
in a bank production model. First, we calculated 1985 cost
inefficiency by comparing banks’ actual 1985 costs to the
1985 cost frontier. Second, we calculated how 1985 banks
would have fared relative to 1994 best practice banks by
comparing banks’ actual 1985 costs (converted to 1994
dollars) to the 1994 cost frontier. This resulted in two sets of
inefficiency estimates for each bank, which we then averaged
by size class and compared to each other to determine whether,
and in which direction, the cost frontier moved over time.
The years 1985 and 1994 make good points of comparison,
because in each year the economy was expanding and few
banks were experiencing serious credit quality problems. Both
cost frontiers are expressed in 1985 dollars.
grew larger by acquiring other banks, by absorbing
their fellow bank holding company affiliates, and by
exploiting the chance to enter new geographic and
product markets. By growing larger, a bank might be
able to reduce its per unit costs by capturing scale
economies, i.e., cost savings from spreading fixed costs
over larger amounts of output and from making better
use of specialized labor and capital inputs.
To evaluate a bank’s potential for scale economies,
we must consider two components of expenses. Exhibit
8 illustrates these two components in terms of costs
per dollar of assets, or per unit cost. First, consider
the point at which the cost advantages of growing
larger are exhausted—this is generally referred to as
minimum efficient scale, or simply MES. The
conventional view among banking economists is that
MES in banking is somewhere between $100 to $300
million of assets, which implies that banks larger than
this pursue growth for reasons other than cost savings.
This view is based on scores of studies that include
banks of all sizes—naturally, studies that include only
large banks (over $1 billion of assets) find higher
estimates of MES. Evanoff and Israilevich (1991) and
Berger, Hunter, and Timme (1993) provide reviews of
this literature. However, recent studies that explicitly
account for the costs associated with risk conclude
that MES might be substantially higher than $300
million. McAllister and McManus (1993) note that
larger banks follow business strategies that expose
them to higher risk, which necessitates extra
expenditures on labor to monitor riskier loans and
higher interest rates to compensate the bank’s creditors
for default risk. They perform a crude correction for
this and find scale economies up to $500 million. Clark
(1996) estimates the economic cost of bank production
(i.e., including the opportunity cost of capital) and
finds scale economies up to $3 billion in assets. Hughes
and Mester (1994) suggest that bank managers might
Exhibit 6. Estimated Total Operating Cost Frontiers—All US Commercial Banks in 1985 and 1994
Exhibit 7. Estimated Changes in Cost Inefficiency at US Commercial Banks Between 1985 and
Ave rag e A sset S ize
(1985 Dollars)
Nu mber of
Banks in 1985
Change in Position
of Cost Front ier
Change in C ost
In effi ci en cy fo r
Av erage Bank
App ro xi mate Ne t
Change in
O perating Costs
< $100 million
fell by 1.5%
fell 2.9%
fell 4.4%
$100 - $300 million
rose by 6.6%
fell 2.5%
increased 4.1%
$300 million - $1 billion 458
rose by 11.0%
fell 3.0%
increased 8.0%
$1- $10 bill ion
rose by 10.5%
fell 2.3%
increased 8.2%
> $10 billion
rose by 10.2%
fell 3.2%
increased 7.0%
actually prefer to employ high levels of labor and equity
capital to reduce risk but can economize on these inputs
as their banks grow larger and become more diversified.
These authors allow for risk-averse managerial
preferences in their cost model, and conclude that scale
economies are available to even the largest banks.
The second important component is the amount by
which a bank’s costs decline as it grows from its
present size to MES size. Evanoff and Israilevich (1995)
call this scale inefficiency, and it is illustrated in Exhibit
8 by the vertical distance YZ. Using results from a
number of existing bank cost studies to make their
point, the authors show that scale inefficiencies can
be as much as 25% of costs for banks that are initially
very far below MES. However, their estimates suggest
that the bulk of these scale inefficiencies are eliminated
by the time banks reach even one-tenth to one-quarter
of MES (roughly $30 to $75 million in assets by
conventional estimates) after which scale
inefficiencies amount to only around 5% of costs.
Savings of this magnitude are substantially smaller
than the potential savings available to the average
bank by moving closer to the best practice frontier
and are limited to small banks.
C. Scope Economies
After financial markets were deregulated in the early
1980s, banks’ largest commercial loan customers began
to go directly to financial markets for credit, and banks
found themselves competing for deposit customers
with thrift institutions, credit unions, and mutual funds.
Commercial banks responded by offering a broader
array of deposit and investment products (e.g.,
interest-bearing checking, money market accounts,
mutual funds), by further diversifying their portfolios
into consumer and real estate loans, and by generating
more noninterest income (e.g., insurance sales,
mortgage servicing, credit enhancements). By
producing a more heterogenous output mix, a bank
might be able to capture scope economies, i.e., cost
savings from using the same inputs to produce several
different types of output.
The production costs of a multiproduct bank that
produces deposit services, loans, and fee-based
financial services might be less than the aggregate
costs of three single-product banks that collectively
produce the same output mix. For example, in the
course of providing financial services for a checking
account customer, a bank generates a great deal of
information about that customer ’s income, purchasing
habits, and other cash flows. This information might
be recycled to evaluate the depositor’s credit-
worthiness should she apply for a loan, or to identify
the most likely set of investment or insurance products
to cross-sell to the customer. Strong evidence of
cost synergies at multiproduct banks would
strengthen arguments for expanding banks’ powers
Clark (1996) points out that these results may be artificially
amplified by the relatively narrow definition of output used by
Hughes and Mester.
Evanoff and Israilevich’s estimates of scale inefficiencies
could be overestimates, because they base their estimates
predominantly on the results of conventional cost functions,
rather than on frontier cost functions. Conventional cost
functions tend to confound scale inefficiency and cost
inefficiency for the very smallest banks.
Exhibit 8. An Example of Scale Efficiencies and Scale Economies
to offer more non-traditional financial services (e.g.,
investment banking services, insurance
underwriting), and would weaken proposals to
protect the deposit insurance fund by separating
“narrow” banks (insured depositories that take
deposits and invest them only in risk-free Treasury
securities) from other intermediaries (institutions
that make risky loans but fund themselves with
uninsured deposits and commercial paper).
Until recently, banking cost studies have generated
little reliable evidence of scope economies at
commercial banks. Conclusions of scope diseconomies
were not unusual, and point estimates of scope
economies often exceeded economically reasonable
magnitudes. Mester (1987) and Clark (1988) provide
reviews of this literature. Measuring scope economies
presents a number of technical problems, however, and
recent studies that employ innovative statistical
methods produce more economically reasonable
estimates. Berger and Humphrey (1991), Pulley and
Braunstein (1992), and Pulley and Humphrey (1993)
have found that multiproduct banks, defined as
producing various loan and deposit outputs, have
between a 10 and 40% cost advantage over single
product producers. However, even these estimates
greatly overstate the cost savings available to the
typical commercial bank from scope economies,
because most banks already produce deposit services
and several types of loan products.
IV. Conclusions
Accounting-based cost ratios are popular tools for
analyzing the efficiency of banks because they are
simple to construct and easy to use. However, bank
efficiency is a complex phenomenon for which simple
analysis can yield misleading conclusions. Comparing
the cost ratios of two different banks is inappropriate
unless both banks are nearly identical in terms of
product mix, bank size, market conditions, and other
characteristics that can affect the banks’ expenses.
Alternatively, a bank’s cost ratio might be compared
to the average of the cost ratios across a peer group of
the bank’s rivals, but the effort required to construct
an appropriate peer group can overwhelm the simplicity
that made cost ratio analysis attractive in the first place.
Cost frontier analysis is rapidly becoming a standard
analytical tool for financial economists studying
commercial bank performance, and it solves some of
the problems associated with cost ratio analysis.
Given adequate data, a cost frontier allows the analyst
to estimate the cost inefficiencies of hundreds or even
thousands of banks at a time. Cost frontier analysis
solves the peer group problem, because each individual
bank is compared with a hypothetical best practice
benchmark that corresponds exactly to that bank’s
individual characteristics. However, performing cost
frontier analysis can require the analyst to invest a
great deal of time and statistical expertise. With this in
mind, we have proposed a modified hybrid approach
that combines the simplicity of cost ratios with the
flexibility of cost frontiers.
In closing, note that both cost frontier analysis and
accounting-based cost ratio analysis are incomplete
measures of bank efficiency. A bank that offers better-
than-average service quality generally must incur
additional expenses, which will make the bank appear
to be cost inefficient—however, the bank’s earnings
need not fall, and may even increase, because the
marketplace is usually willing to pay higher prices for
higher quality. Similarly, two banks might be operating
at equal distances above the cost frontier, and hence
be equally cost efficient—however, one of these two
banks might be earning higher revenues by pricing its
assets more aggressively than the other. Finally, a bank
that spends large amounts on underwriting and
monitoring its loan portfolio will appear to be relatively
cost inefficient in the short run—however, the bank
will probably be more cost efficient in the long run
due to lower nonperforming loan expenses. Hence,
bank analysts should be careful to supplement cost
efficiency analysis with an analysis of bank earnings.
Although high cost ratios and/or high frontier cost
inefficiency estimates are generally good indicators
of inefficient operations, the analyst can draw a stronger
conclusion if earnings ratios are also subpar.
Recent papers by Berger, Hancock, and Humphrey (1993),
Akhavein, Berger, and Humphrey (1996), and DeYoung and
Nolle (1996) have estimated efficient profit frontiers, which
consider both the revenue efficiency and the cost efficiency
of commercial banks. Such efforts are still in their exploratory
stages, and numerous empirical and theoretical questions have
yet to be answered. Like cost frontier analysis, these techniques
are accessible only to analysts well-versed in statistics who
have access to data from a large number of banks. Because
profit frontier analysis assumes that the firm seeks to maximize
profits, it should not be applied to credit union data.
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