The Pro T e Ciency of Small US

Journal of Banking & Finance 27 (2003) 307–325
www.elsevier.com/locate/econbase
The profit efficiency of small US

commercial banks
a,1 b,*
Aigbe Akhigbe , James E. McNulty
a
Moyer Chair in Finance, University of Akron, Akron, OH 44325, USA
b
Department of Finance, College of Business, Florida Atlantic University, Boca Raton, FL 33431, USA
Received 20 January 2000; accepted 1 August 2001
Abstract
This study investigates the profit efficiency (PROFEFF) of small banks (those under $500
million in total assets) for 1990–96. Assuming that small banks and large banks use the same
production technology, we find, consistent with Berger and Mester [J. Bank. Finance 21 (1997)
875], that small banks are more profit efficient than large banks. Small banks in non-metro-
politan statistical areas (non-MSA) areas are consistently more profit efficient than small
banks in MSAs. Cross-sectional analysis of the correlates of the PROFEFF estimates suggests
that structure–performance factors, relationship–development factors, and expense-preference
behavior play an important role in explaining the PROFEFF of small US commercial banks.
2002 Published by Elsevier Science B.V.
JEL classification: G2; D2; G21; G28; E58; E61; F33

Keywords: Profit efficiency; Commercial banking; Expense preference; Structure–performance; Loan
relationships
1. Introduction
Financial economists have long been interested in the financial performance of

small banks. This issue is especially important in the current era of bank consolida-
tion. As the industry consolidates, there are concerns that small commercial banks
*
Corresponding author. Tel.: +1-561-297-2708; fax: +1-561-297-3978.
E-mail address: mcnultyj@fau.edu (J.E. McNulty).
1
Tel.: +1-330-972-6883.
0378-4266/02/$ - see front matter 2002 Published by Elsevier Science B.V.

PII: S 0 3 7 8 - 4 2 6 6 ( 0 1 ) 0 0 2 5 0 - 3
308 A. Akhigbe, J.E. McNulty / Journal of Banking & Finance 27 (2003) 307–325
may not survive; these banks have traditionally performed the important function of
allocating credit to small businesses, an important source of job creation.
One difficulty in evaluating small bank performance relative to other banks is that
it is affected by inherent differences in asset composition, liability composition, ex-
penses, non-interest income, capital ratios, competition and access to credit informa-
tion. The profit efficiency (PROFEFF) analysis used in this paper produces a
sophisticated measure of financial performance which takes many of these differences
into account. The PROFEFF measure is estimated and then regressed on variables
which reflect differences in asset and liability composition, competition, location, or-
ganizational structure and other factors. This analysis provides a comprehensive pic-
ture of the differences between small banks and other banks for the period 1990–96. 2
We define small banks as those with less than $500 million in total assets.
In addition to the application of PROFEFF analysis, this approach is different be-
cause previous studies of small bank performance generally consider all small banks
as one group. Forty three percent of small banks are located in metropolitan statisti-
cal areas (MSAs) and 57% are located in non-MSA areas. 3 Since both types of small
banks are important parts of the banking community, it is important to understand
the differences in financial performance between the two sets of small banks.
Assuming that small banks and large banks use the same production frontier, we
find that small banks are more profit efficient than large banks, which is consistent
with Berger and Mester (1997). Small MSA banks are the least profit efficient of the
three types of banks considered. Our results suggest that small bank PROFEFF is
reduced by expense-preference (EP) behavior and increased by factors related to
market structure and lender–borrower relationship–development (RD).
2. Literature review and hypotheses
At least five theories have been advanced to explain why small bank financial per-
formance may differ from that of other banks. Empirical tests have found some sup-
port for most of these theories, but these tests have generally not been conducted
using a PROFEFF framework. 4 We do not attempt formal tests of the hypotheses,
but we use these hypotheses to characterize our results and to interpret these results.
The oldest theory, the structure–performance (SP) hypothesis (e.g., Gilbert, 1984;
Hannan, 1991a, b) suggests that, other things being equal, small banks in small com-
munities can charge higher rates on loans and pay lower rates on deposits than other
banks because there is less competition in small banking markets. This hypothesis is
consistent with higher PROFEFF at small non-MSA banks.
The EP hypothesis (e.g., Arnould, 1985; Berger and Hannan, 1998; Hannan and
Mavinga, 1980; Purroy and Salas, 2000; Rhoades, 1980) suggests that, ceteris pari-
2
DeYoung and Hasan (1998) also use a PROFEFF approach to evaluate small bank performance, but
their analysis deals exclusively with de novo banks.
3
MSAs generally have total population of 50,000 or above.
4
Berger and Hannan (1998) use a cost efficiency approach in evaluating the EP hypothesis.
A. Akhigbe, J.E. McNulty / Journal of Banking & Finance 27 (2003) 307–325 309
bus, managers of banks in less competitive markets may dissipate part of their ad-
vantages by enjoying perquisites such as higher salaries, more assistants, lavish office
quarters, etc. This hypothesis would suggest that PROFEFF at small, non-MSA
banks would be lower than under the pure SP hypothesis. A variant of the EP hy-
pothesis suggests that bank managers in smaller, less competitive markets may also
shift the bankÕs asset composition to less risky loans and securities out of a desire to
enjoy a ‘‘quiet life’’ (e.g., Rhoades and Rutz, 1982; Clark, 1986). Under the quiet life
(QL) hypothesis, ceteris paribus, these small banks limit their output of loans, and
earn less profits per dollar of assets and equity than under the SP hypothesis. In ef-
fect, these banks ‘‘cherry pick’’ potential loans and choose only those with clearly
superior risk–return characteristics. In this process, they reject loans that may gen-
erate additional profits and value for the bank. However, because PROFEFF is de-
fined as efficiency in producing a given level of output (see Eq. (1)), even if that level
of output is low, the QL hypothesis could be consistent with reasonably high PROF-
EFF for small banks in concentrated non-MSA markets. Nonetheless, QL managers
probably also engage in shirking behavior, which lowers PROFEFF. In summary,
PROFEFF would be expected to be lower at small banks under this theory than
under the pure SP hypothesis, because QL banks do not produce an optimal level
of output, and shirking increases the cost of producing that output. The direction
of the relationship between PROFEFF and QL behavior is thus ambiguous. But
whatever the empirical relationship, QL behavior should be more intense in less com-
petitive markets.
The fourth theory, the information advantage (IA) hypothesis (Nakamura, 1993a,
b; Mester et al., 1998) suggests that small banks have access to better credit informa-
tion than large banks (such as daily data on firm cash flows, which is available
through monitoring checking accounts). In addition, there is less of an agency prob-
lem between the bank and the loan officer at small banks because senior management
is closer to both the loan officer and the commercial loan customer. Other things
being equal, the IA hypothesis would suggest higher PROFEFF at small banks than
at large ones.
Fifth, Petersen and Rajan (1995) argue that there are less incentives to investing in
loan relationships in competitive markets because of the greater probability that the
loan customer may switch to a competing lender. This theory would suggest greater
PROFEFF at small banks in less competitive markets because RD is an important
way of reducing asymmetric information problems and increasing firm value (e.g.,
Diamond, 1984; Boot, 2000), and banks in these markets have a greater incentive
to invest in developing these relationships. We call this the RD hypothesis.
In summary, one of the five theories (IA) suggests that PROFEFF may be higher
at small banks on average than at large ones. At least two theories (SP and RD)
suggest that PROFEFF should be greater for small banks in non-MSA areas than
at small banks in MSAs. However, the QL and EP hypotheses suggest that small
banks with an SP advantage may dissipate some of this advantage with higher ex-
penses or shirking. While testing these theories is beyond the scope of this paper, a
given set of PROFEFF results would be more consistent with some theories than
others. For example, a finding of high PROFEFF at small banks in less competitive,
non-metropolitan markets relative to small banks in MSA markets would be more

consistent with the SP and RD hypotheses than with the others.
Both EP and QL behavior reflect agency problems between owners and managers.
DeYoung et al. (2001) find interesting evidence that PROFEFF at a sample of small
banks with hired managers improves when the interests of the outside manager are
aligned with those of the primary owners. Specifically, PROFEFF has an inverted U-
shaped relationship with the ownership share of the hired manager. PROFEFF is
low when managers have little or no ownership stake; it becomes much greater as
the outside managerÕs share increases; but it declines as the hired manager becomes
entrenched. The first and third outcomes reflect EP and/or QL behavior.
Most studies of bank performance report that small banks have higher returns on
assets (but not necessarily equity 5) than large ones. Most of these studies attribute
this effect at least partly to SP factors, although other factors, such as lower ex-
penses, are also noted. For example, Boyd and Runkle (1993) report an inverse re-
lationship between bank size and return on assets, which they attribute to monopoly
rents. However, they do not consider banks under $1 billion in assets. Since over 40%
of small banks are located in MSAs, where competition is generally strong, a pure SP
explanation of higher ROAs at small banks is inadequate. Yellin (1995) reports that
most Federal Reserve studies indicate that the performance of small banks compares
very favorably with that of other banks. Berger and Mester (1997) report greater
PROFEFF at small banks than at large ones. However, Elyasiani and Mehdian
(1995) suggest that, because of deregulation, the future survival of small banks is
in serious question. In a recent paper on the IA notion, McNulty et al. (2001) find
no consistent evidence of superior loan quality at small banks, but the analysis is re-
stricted to one large state (Florida).
3. Methodology
We examine the way in which bank PROFEFF may be affected by the aforemen-
tioned types of behavior by comparing the PROFEFF of three sets of banks––large
banks, small banks in MSAs, and small non-MSA banks––and by analyzing the cor-
relates of the PROFEFF measures. First we estimate the PROFEFF function for all
US banks for 1990, 1992, 1994 and 1996. This single-frontier approach is the one
most suited to address the issues noted in the introduction about the viability of
small banks.
The sample includes all banks in the report of condition and income database on
the Federal Reserve Bank of ChicagoÕs web page (www.frbchi.org) for which at least
one year of data are available, including newly chartered banks. We analyze the dif-
ferences between the two sets of PROFEFF estimates in Section 5 to evaluate our
5
Small banks generally have higher capital ratios, which, ceteris paribus, would give them lower interest
expense and higher returns on assets, but lower returns on equity because of the smaller amount of
leverage.
results relative to Berger and Mester (1997). We analyze the correlates of our PROF-
EFF measures in Section 6 to compare the performance of these two types of small
banks and to evaluate this performance in relation to the five theories outlined in the
previous section.
We also consider the possibility, noted by DeYoung and Hasan (1998), that small
banks may employ different production technologies and management strategies
than large banks. 6 We thus fit a separate PROFEFF function to data for small
banks and large banks to answer the following question: If the assumption of differ-
ent production technologies is warranted, do small banks or large banks operate
closer to their respective production frontiers?
PROFEFF measures how actual financial performance compares to the best-
practice frontier. It is measured as a percentage of the PROFEFF of the best-prac-
tice bank. For example, a PROFEFF measure of 0.75 means that a bank is 75% as
profit efficient as the best-practice bank. The frontier is estimated separately for each
year using a non-standard, Fourier-flexible form, as follows:
X
3
1X3 X
3 X
3
1X3 X
3
PREROA ¼ a0 þ bi Yi þ bij Yi Yj þ cm W m þ c Wm Wn
i
2 i j m
2 m n mn
X
3
1X3 X
3 3 X
X 3 3 X
X 3
þ /k Zk þ /kl Zk Zl þ qim Yi Wm þ /ik Yi Zk
k
2 k l i m i k
3 X
X 3 X
9
þ /mk Wm Zk þ ½di cos Xi þ hi sin Xi
m k i¼1
9 X
X 9
þ ½dij cosðXi þ Xj Þ þ /ij sinðXi þ Xj Þ
i¼1 j¼1
9 X
X 9 X
9
þ ½dijk cosðXi þ Xj þ Xk Þ þ /ijk sinðXi þ Xj þ Xk Þ
i¼1 j¼i k¼j
þ m þ l:
ð1Þ
PREROA is operating profits (earnings before taxes, extraordinary items, and loan
losses) as a percent of total assets. Y is a vector of three outputs which are defined at
the bank level: (1) total loans (commercial, industrial and real estate loans), (2) retail
deposits (demand deposits, time deposits and savings deposits), and (3) fee-based
financial services (non-interest income). W is a vector of three market prices for
6
Ninety five percent of our total observations are on banks under $500 million in assets. If small and
large banks use different production technologies, it may not be appropriate to use a PROFEFF function
estimated on a sample dominated by small banks to estimate large bank PROFEFF.
inputs, which we compute as county averages of bank level prices: (1) the wage rate
for labor; (2) the interest rate for borrowed funds; and (3) the price of physical
capital. 7 The Z vector is a set of three variables: (1) equity capital (defined at the
bank level) to control, in a very rough fashion, 8 for the potential increased cost of
funds due to financial risk. (2) a Hirschman–Herfindahl index (HHI; defined at the
county level) to control for differences in competitive conditions across markets), 9
and (3) the average non-performing loan ratio (defined at the county level) to control
for differences in economic conditions across markets. X is a set of nine variables that
transform the output (Y) variables so that they fall on the interval from 0 to 2p. 10
As Eq. (1) indicates, the non-standard Fourier is a hybrid form since it contains
both a quadratic profit function and a series of trigonometric (Fourier) terms. Like
DeYoung and Hasan, because of software limitations and limitations on the number
of observations, we estimate a modified version of this function. Our function con-
tains 18 trigonometric terms and 54 other terms for a total of 72 independent vari-
ables. This procedure of limiting the number of terms (especially the third-order
terms) has been applied in most other recent PROFEFF studies (e.g., DeYoung
and Hasan, 1998; Berger and Mester, 1997, 1999; DeYoung et al., 2001).
The Fourier function has been used in a number of recent efficiency studies (e.g.,
Berger and Mester, 1997, 1999; DeYoung and Hasan, 1998; DeYoung and Nolle,
1996; McAllister and McManus, 1993; Mitchell and Onvurall, 1996). The Fourier
form is generally considered to provide a better fit than other functions (e.g., the
translog) for banks with values of Y, W and Z that differ substantially from the sam-
ple mean. The non-standard Fourier form assumes that banks have some control
over output prices (e.g., DeYoung and Hasan, 1998; Humphrey and Pulley, 1997).
This is a reasonable assumption for loans, deposits and fee-based services. Because
output prices are not exogenous under these assumptions, profit is assumed to de-
pend on input prices and output quantities.
Eq. (1) is very similar to the function used by DeYoung and Hasan (1998). They
argue, and we agree, that this function is appropriate because: (1) it avoids the dif-
ficulty in measuring output prices and (2) output quantities (rather than output
prices) are allowed to explain a larger portion of the variation in profitability, which
is consistent with what we know about banking practice. We differ from DeYoung
and Hasan, 1998 in that we analyze the financial performance of all small banks,
rather than just de novos. In addition, our specification of input prices, output quan-
7
The wage rate equals total salaries and benefits divided by the number of full-time employees. The
price of capital equals expenses of premises and equipment divided by premises and fixed assets. The price
of deposits and purchased funds equals total interest expense divided by total deposits and purchased
funds.
8
Hughes et al. (2000) deal with the effect of risk in efficiency studies and provide a more detailed
discussion of the potential implications of incorporating risk considerations directly into the equations.
While the context of their discussion is cost efficiency, the same general considerations apply to PROFEFF
studies.
9
The HHI was calculated using the FDICÕs summary of deposits (branch office) data.
10
The methodology for performing these transformations is described in Berger and Mester (1997,
1999, p. 917n).
tities and other exogenous (Z) variables, described above, is different from theirs.
Some of the variables used to construct the PROFEFF function are also used later
as correlates. This procedure is justified because all theoretically important determi-
nants of profitability should be included in the PROFEFF function. Other PROF-
EFF studies follow a similar approach. 11
We employ the stochastic frontier approach proposed by Jondrow et al. (1982)
and used by DeYoung and Hasan (1998) to measure each bankÕs divergence from
the best-practice frontier. The stochastic frontier approach assumes that deviations
from the frontier include inefficiencies (profit inefficiencies in our case) and random
errors. Inefficiencies are assumed to follow an asymmetric, half normal distribution,
and the random errors follow a symmetric normal distribution. We estimate the in-
efficiency term as the expected value of the profit inefficiency conditional on the re-
siduals from each yearÕs profit function.
We estimate a separate PROFEFF function for each year––1990, 1992, 1994, and
1996. This approach allows the regression coefficients and the efficiency measures to
vary over time, thereby allowing maximum flexibility in the estimation procedure.
The technique produces up to four PROFEFF measures for each bank (the actual
number depends on the number of years of available data).
We define POTENTIAL PREROA as the estimated profitability of the bank if it
operated on the best-practice frontier. Since efficiency cannot be negative, we follow
other PROFEFF studies (e.g., DeYoung and Hasan, 1998) and define:
PROFEFF ¼ ðACTUAL PREROA=POTENTIAL PREROAÞ
if PREROA > 0;
PROFEFF ¼ 0 if PREROA < 0:
POTENTIAL PREROA thus equals actual PREROA plus inefficiency. PROFEFF
is an efficiency measure which ranges from zero for banks experiencing losses to one
for banks operating on the best-practice frontier.
4. Descriptive statistics
Table 1 presents the descriptive statistics for the banks in the sample. There are
35,807 observations (34,104 for small banks and 1703 for large banks) for the four
years. The first two columns of data indicate that, relative to large banks, the small
banks: (1) are slightly younger; (2) are operating in markets with slightly larger non-
performing loan ratios (MKTNPL); (3) are much less likely to belong to a MBHC;
(4) are much more likely to be state-chartered; (5) have non-performing loan ratios
(RELNPL) approximately equal to their market averages (by definition); (6) grow
about half as fast; (7) have fee income/total revenue ratios less than two-thirds as
high; (8) have lower demand deposits/assets; (9) have less large deposits; 12 (10)
11
See DeYoung and Hasan (1998, p. 580n) for an explanation of and justification for this procedure.
12
Federal funds purchased are excluded from this calculation.
Table 1
Descriptive statistics for the sample
Variable (1) Large (2) Small (3) Small MSA (4) Small non-MSA
Number of 1703 34104 14793 19311
observations
1 AGE 76.9880 61.2240 46.9860 72.1320
(39.9560) (36.8570) (38.4350) (31.5140)
2 MKTNPL 0.0092 0.0100 0.0098 0.0101
(0.0071) (0.0119) (0.0085) (0.0139)
3 MBHC 0.6794 0.2911 0.2931 0.2896
(0.4668) (0.4543) (0.4552) (0.4536)
4 NATIONAL 0.4844 0.2990 0.3272 0.2773
(0.4999) (0.4578) (0.4692) (0.4477)
5 RELNPL 0.0009 0.0001 0.0001 0.0001
(0.0102) (0.0143) (0.0139) (0.0146)
6 GROWTH 0.3148 0.1563 0.1947 0.1268
(1.3277) (0.3658) (0.4667) (0.2598)
7 FEEREV 0.1376 0.0910 0.1095 0.0768
(0.0743) (0.0596) (0.0726) (0.0421)
8 DEMDEP 0.1845 0.1504 0.1770 0.1301
(0.0750) (0.0655) (0.0758) (0.0470)
9 LARGEDEP 0.1052 0.0956 0.1025 0.0904
(0.0866) (0.0659) (0.0724) (0.0600)
10 ASSETS 1596.8000 86.9350 112.1400 67.6260
(1771.7000) (86.4090) (103.1800) (64.5850)
11 HHI 0.2327 0.3978 0.2494 0.5115
(0.1012) (0.2494) (0.1444) (0.2532)
12 NONMSA 0.0711 0.5662 – –
(0.2570) (0.4956)
13 1 TOTLOANS 0.3765 0.4505 0.4267 0.4686
(0.1349) (0.1422) (0.1406) (0.1408)
14 SALARY 0.0143 0.0161 0.0175 0.0151
(0.0052) (0.0056) (0.0066) (0.0044)
15 PREROA 0.0130 0.0131 0.0117 0.0142
(0.0094) (0.0087) (0.0111) (0.0059)
16 PREROE 0.1899 0.1226 0.0893 0.1480
(0.3870) (3.0889) (4.3760) (1.4764)
The variables are defined in Sections 6.2 and 6.3. There are two significance tests for each variable. The
first (columns (1) and (2)) tests differences between small and large banks (columns (1) and (2)). The second
(columns (3) and (4)) tests differences between small banks in MSAs and those outside MSAs (columns (3)
and (4)). The asterisks are placed at the larger variable when the difference is significant. The numbers in
parenthesis are standard deviations.

Significant at the 10% level.


average $86.9 million in total assets vs. $1.6 billion for large banks; (11) operate in
markets with HHIs averaging 0.3979 (vs. 0.2327 for large banks); (12) are much
more likely to be in a non-metropolitan area; (13) have a higher proportion of their
assets in securities and other non-loan assets; (14) have higher ratios of salaries to
total assets. In addition, relative to the large banks, the small banks have similar
ratios of PREROA to assets but lower ratios of PREROA to equity.
The last two columns of Table 1 indicate that 43.3% (14,793 out of 34,104) of the
small bank observations are on banks in MSAs. Relative to their counterparts in
MSAs, non-MSA banks: (1) are older; (2) operate in markets with higher non-per-
forming loan ratios; (3) are equally likely to belong to a MBHC; (4) are less likely
to be national banks; (5) have non-performing loan ratios (RELNPL) approximately
equal to their market averages (by definition); (6) grow about two thirds as fast; (7)
have non-performing loan ratios (RELNPL) approximately equal to their market
averages (by definition, as above); (8) have lower demand deposits/assets ratios;
(9) have lower large deposits; (10) are smaller; (11) have much higher HHIÕs; (12)
not applicable; (13) have higher ratios of non-loan assets/total assets (14) have lower
ratios of salaries/assets; (15) have higher PREROA and PREROE.
5. Profit efficiency measures
Table 2 shows our PROFEFF estimates for various classes of banks for each year.
Panel A shows the results when a single frontier is used. As noted, this is the ap-
proach most suited for answering questions about the viability of small banks.
For the period as a whole, for all small banks, estimated PROFEFF is 74.74% (Panel
A). Put differently, the average small bank in the sample is 74.74% as efficient as the
best-practice bank in the sample for the period 1990–96. This is within the general
range of the estimates produced in other PROFEFF studies.
The single-frontier results in Panel A show that small banks are more profit effi-
cient than large banks for the period as a whole. However, this is entirely due to the
first two years, when large bank profitability was especially weak because of macro-
economic conditions. Small and large bank profitability is not significantly different
for 1994 and 1996. This finding of significantly greater PROFEFF for small banks
based on a single frontier is consistent with Berger and Mester (1997). They also re-
port, using two different PROFEFF methodologies, that small banks are more profit
efficient. The result in Panel A that small bank PROFEFF is greater than large when
a single frontier is used is consistent with the IA hypothesis. The PROFEFF results
for small and large banks are in contrast to the PREROA statistics in Table 1 which
show no significant difference between small and large banks. As discussed earlier,
PROFEFF is a much more sophisticated performance measure than return on
assets.
Reflecting the very low level of large bank PROFEFF in 1990 (only 55.85%),
PROFEFF based on the single-frontier approach improved more over the period
for large banks than for small ones, by approximately 25 percentage points (from
0.5585 to 0.8093) for large banks vs. 14 (from 0.6626 to 0.8024) for small ones. This
is consistent with the observation that many large banks experienced major restruc-
turing and cost cutting in the mid 1990s, which apparently improved their PROF-
EFF. In addition, in 1990 many banks, particularly large ones, were experiencing
major loan losses and loan quality problems. (Large banks have higher ratios of
Table 2
Summary statistics for profit efficiency
Year Small banks Large banks Difference
N Mean Std N Mean Std Mean t-stat
Panel A: Small versus large banks using a single frontier for all banks
1990 9757 0.6626 0.2882 401 0.5585 0.3355 0.1041 6.13
1992 8934 0.7566 0.2204 407 0.7241 0.2488 0.0325 2.59
1994 8153 0.7898 0.1692 427 0.7903 0.1733 0.0005 0.06
1996 7260 0.8024 0.1588 468 0.8093 0.153 0.0069 0.94
1990–96 34104 0.7474 0.2277 1703 0.7251 0.2544 0.0223 3.55
Panel B: Small versus large banks using separate frontiers

1990 9757 0.6567 0.2929 401 0.6412 0.3426 0.0155 0.9
1992 8934 0.7514 0.2257 407 0.7587 0.2615 0.0073 0.56
1994 8153 0.7853 0.1769 427 0.8439 0.1575 0.0586 7.58
1996 7260 0.7877 0.1861 468 0.8546 0.1355 0.0669 10.24
1990–96 34104 0.7404 0.2358 1703 0.7795 0.2489 0.0391 6.42
Panel C: Small MSA versus small non-MSA banks using a single frontier for all banks
1990 4218 0.5818 0.328 5539 0.7242 0.2358 0.1424 23.88
1992 3981 0.7014 0.2636 4953 0.801 0.1653 0.0996 20.78
1994 3547 0.7579 0.1994 4606 0.8143 0.1366 0.0564 14.43
1996 3047 0.7785 0.1801 4213 0.8198 0.1389 0.0413 10.59
1990–96 14793 0.6967 0.2677 19311 0.7862 0.1822 0.0895 34.95
This table presents our PROFEFF estimates for three classes of banks for the period 1990–96. PROFEFF
is a sophisticated performance measure which takes differences in asset composition, liability composition,
competition and other factors into consideration. PROFEFF ranges from zero for the least efficient banks
to one for banks which are operating on the best-practice frontier. Panel A presents the results when a
single PROFEFF frontier is estimated for small banks and large banks. Panel B presents the results when
separate PROFEFF frontiers are estimated for small banks and large banks. Panel C presents the results
when the small bank estimates are dis-aggregated by geographic area.

loans to assets and would thus be expected to do worse in a recession.) In contrast,

by the mid 1990s, loan quality and provisions for loan losses were at extremely low
levels. 13 Since not all banks were experiencing these problems in 1990, the standard
deviation of PROFEFF also dropped considerably (especially for large banks) be-
tween 1990 and 1996, as the economy strengthened.
Panel B shows the results when the PROFEFF function is estimated separately
for small banks and large banks. We present these results because of the possibility
that small and large banks may use different production technologies. According to
these estimates, PROFEFF is significantly greater on average for large banks for the
13
A convenient statistical summary of these dramatic differences is shown in Madura (2001, p. 525).
period as a whole––0.7795 vs. 0.7404, and two of the differences are statistically sig-
nificant at the 1% level. This result suggests that, if small and large banks do use dif-
ferent production technologies, the average large bank operates closer to its efficient
frontier than the average small bank. The separate-frontier results in panel B show
the same pattern as in Panel A––large bank PROFEFF improves relative to that of
small banks from 1990 to 1996.
Panel C reports the small bank estimates (based on the single frontier approach)
separately for MSA and non-MSA banks. These results indicate that small banks in
non-MSA areas are consistently more profit efficient than small banks in MSAs. The
difference was as great as 14.2 percentage points in 1990 (0.7242 vs. 0.5818), but it
shrinks gradually to 4.1 percentage points in 1996. Importantly, the PROFEFF ad-
vantages of the small non-MSA banks in each year are significant at the 1% level. We
attribute this difference to SP and RD factors. Finally, small banks in MSAs are the
least profit efficient (0.6967 for the period as a whole) of the three types of banks con-
sidered.
6. Correlates of the profit efficiency measures
As discussed in the literature review, small bank PROFEFF is affected by a num-

ber of factors related to competition and location, as well as the bankÕs asset and li-
ability composition. We explore some of these relationships in detail here. As
discussed in more detail in Section 7, we construct five models to consider the factors
discussed in this section.
6.1. Factors related to structure–performance, relationship––development and infor-

mation advantage
As noted, the SP and RD hypotheses both suggest that, ceteris paribus, PROF-
EFF should be greater in more concentrated markets. The RD hypothesis is rela-
tively new (Petersen and Rajan, 1995) so it was not considered in earlier studies of
bank performance. Many studies include the HHI in a regression equation to esti-
mate the SP effect, and we do this as well. However, since most concentrated markets
are located outside of MSAs, the HHI by itself will pick up location factors (e.g., dif-
ferences in market characteristics, such as income levels) as well as competitive and
RD factors. Thus we also use the interaction term NONMSA HHI. NONMSA
equals one for non-MSA markets (counties) and zero otherwise.
The IA and RD hypotheses stress the importance of lender–borrower relation-
ships to small bank success in increasing shareholder value. To the extent that smal-
ler banks rely more on developing and maintaining these relationships than banks
that are larger (but are still under $500 million in total assets), these hypotheses sug-
gest that PROFEFF may decline as size increases. We include a size variable, LNAS-
SETS, the natural log of total assets, to test for this effect. LNASSETS is also an
important control variable used in other studies.
6.2. Quiet-life and expense-preference behavior
As noted, banks in non-competitive markets may dissipate this advantage

through QL behavior (e.g., a less than optimal asset composition (less loans and
more securities) and shirking) and through EP behavior. To determine if PROFEFF
is negatively affected by QL behavior, we include the variable (1 TOTLOANS).
We also interact this variable with the HHI to produce the variable (1
TOTLOANS) HHI. Banks with higher levels of non-loan assets operating in mar-
kets with higher HHIs might be expected to have lower PROFEFF if the QL theory
accurately reflects small bank behavior. Thus, we expect the coefficient of this term
to be negative.
To determine if the results reflect EP behavior, we include the variable SAL-
ARY HHI, where SALARY is the ratio of salaries to total assets. EP behavior
lowers PROFEFF. Thus, we expect the coefficient of this interaction term to be neg-
ative since other studies (e.g., Berger and Hannan, 1998) have found major evidence of
EP behavior at commercial banks. We also include SALARY as a separate variable.
6.3. Regression analysis of the correlates of the PROFEFF function
Table 3 presents the results of estimating five equations based on the general
model shown below:
PROFEFF ¼ f ðAGE; MKTNPL; MBHC; NATIONAL; RELNPL;
GROWTH; FEEREV; DEMDEP; LARGEDEP; LNASSETS;
YEAR92; YEAR94; YEAR96; HHI; NONMSA;
ð1 TOTLOANSÞ; SALARY; NONMSA HHI;
ð1 TOTLOANSÞ HHI; SALARY HHIÞ ð2Þ
where
• PROFEFF ¼ our single-frontier estimate of profit efficiency;

• AGE ¼ bank age (in years);
• MKTNPL ¼ the non-performing loan ratio for all banks in the market (i.e.,
county), a measure of aggregate credit risk;
• MBHC ¼ 1 for banks affiliated with a multibank holding company (otherwise
zero);
• NATIONAL ¼ 1 for national banks (otherwise zero);
• RELNPL ¼ the relative non-performing loan ratio, i.e., the difference between
the non-performing loan ratio for the bank and that for the county as a whole
(MKTNPL), a measure of firm-specific credit risk;
• GROWTH ¼ asset growth over the previous year;
• FEEREV ¼ total non-interest income/total revenue;
• DEMDEP ¼ demand deposits/total deposits;
• LARGEDEP ¼ large (over $100,000) deposits/total deposits;
• LNASSETS ¼ the natural logarithm of total assets;
Table 3
Tobit regression results for small banks
Variable Model 1a Model 2b Model 3c Model 4d Model 5e
Coefficient Chi-sq Coeff. Chi-sq Coefficient Chi-sq Coefficient Chi-sq Coefficient Chi-sq
A. Akhigbe, J.E. McNulty / Journal of Banking & Finance 27 (2003) 307–325

INTERCEPT 0.3348 1275.95 0.3452 1230.06 0.3515 1094.94 0.3444 1109.46 0.3776 940.97
AGE 0.0151 174.03 0.0149 166.64 0.0149 169.95 0.0152 175.13 0.0147 164.27
MKTNPL 0.5833 238.65 0.5823 235.54 0.5794 233.28 0.5819 238.26 0.5759 229.33
MBHC 0.0175 70.93 0.0177 72.51 0.0177 72.42 0.0175 70.29 0.0178 73.13
NATIONAL 0.0086 17.95 0.0083 16.92 0.0085 17.81 0.0086 18.03 0.0083 16.93
RELNPL 0.0254 0.48 0.0255 0.48 0.0258 0.49 0.0225 0.38 0.0218 0.35
GROWTH 0.0007 0.06 0.0009 0.09 0.0008 0.06 0.0006 0.04 0.0008 0.07
FEEREV 0.0287 1.70 0.0271 1.51 0.0260 1.39 0.0233 1.11 0.0160 0.52
DEMDEP 0.0422 5.66 0.0507 8.01 0.0417 5.54 0.0427 5.77 0.0505 7.92
LARGEDEP 0.1239 67.48 0.1203 63.34 0.1225 66.04 0.1249 68.49 0.1205 63.52
LNASSETS 0.0144 144.15 0.0146 147.98 0.0147 148.57 0.0143 140.85 0.0147 148.27
YEAR92 0.0249 97.19 0.0249 97.12 0.0247 95.68 0.0251 98.80 0.0250 97.93
YEAR94 0.0236 107.26 0.0273 106.89 0.0270 104.60 0.0276 109.25 0.0273 107.06
YEAR96 0.0356 175.03 0.0355 174.26 0.0350 171.05 0.0359 177.45 0.0355 173.77
HHI 0.0479 119.82 0.0783 62.78 0.0899 45.65 0.0767 31.30 0.1669 54.78
NONMSA 0.0130 31.97 0.0252 36.02 0.0129 31.30 0.0132 32.67 0.0248 34.33
1 TOTLOANS 0.0363 25.67 0.0377 27.62 0.0721 31.37 0.0353 24.10 0.0760 34.22
SALARY 0.3595 1.95 0.3357 1.70 0.3429 1.78 0.3087 0.60 0.6742 2.79
NONMSA HHI – – 0.0378 11.93 – – – – 0.0363 10.80
(1 TOTLOANS) HHI – – – – 0.0881 11.25 – – 0.0986 13.32
SALARY HHI – – – – – – 1.8522 4.94 2.7511 10.40
319
Table 3 (continued)
320
Variable Model 1a Model 2b Model 3c Model 4d Model 5e
Coefficient Chi-sq Coeff. Chi-sq Coefficient Chi-sq Coefficient Chi-sq Coefficient Chi-sq
Sample size 34104 34104 34104 34104 34104
A. Akhigbe, J.E. McNulty / Journal of Banking & Finance 27 (2003) 307–325

No. of observations 32607 32607 32607 32607 32607
Missing values 1497 1497 1497 1497 1497
Log likelihood 5337.18 5343.23 5342.79 5339.64 5353.95
This table presents the results of the five models. The variables are as defined in Section 6. The equations are estimated using a Tobit regression because
PROFEFF is bounded so that all observations fall in the interval (0,1).



a
Model 1: PROFEFF ¼ f(AGE, MKTNPL, MBHC, NATIONAL, RELNPL, GROWTH, FEEREV, DEMDEP, LARGEDEP, LNASSETS, YEAR92,
YEAR94, YEAR96, HHI, NONMSA, (1 TOTLOANS), SALARY).
b
YEAR94, YEAR96, HHI, NONMSA, (1 TOTLOANS), SALARY, NONMSA HHI).
c
YEAR94, YEAR96, HHI, NONMSA, (1 TOTLOANS), SALARY, (1 TOTLOANS) HHI).
d
YEAR94, YEAR96, HHI NONMSA, (1 TOTLOANS), SALARY, SALARY HHI).
e
YEAR94, YEAR96, HHI, NONMSA, (1 TOTLOANS), SALARY, NONMSA HHI, (1 TOTLOANS) HHI, SALARY HHI).
Table 4
Derivatives of the profit efficiency equations
Model 1a Model 2b Model 3c Model 4d Model 5e

d PROFEFF/d HHI 0.0479 0.0569 0.0502 0.0469 0.0576
d PROFEFF/d NONMSA 0.0130 0.0102 0.0129 0.0132 0.0104
d PROFEFF/d TOTLOANS 0.0363 0.0377 0.0371 0.0353 0.0368
d PROFEFF/d SALARY 0.3595 0.3357 0.3429 0.4281 0.4202

a
Model 1: PROFEFF ¼ f(AGE, MKTNPL, MBHC, NATIONAL, RELNPL, GROWTH, FEEREV,
DEMDEP, LARGEDEP, LNASSETS, YEAR92, YEAR94, YEAR96, HHI, NONMSA, (1
TOTLOANS), SALARY).
b
TOTLOANS), SALARY, NONMSA HHI).
c
TOTLOANS), SALARY, (1 TOTLOANS) HHI).
d
DEMDEP, LARGEDEP, LNASSETS, YEAR92, YEAR94, YEAR96, HHI NONMSA, (1
TOTLOANS), SALARY, SALARY HHI).
e
TOTLOANS), SALARY, NONMSA HHI, (1 TOTLOANS) HHI, SALARY HHI).
14
• HHI ¼ the Hirshman–Herfindahl index of market concentration for the county;
• NONMSA ¼ 1 for banks headquartered in non-metropolitan counties;
• 1 TOTLOANS ¼ 1 total loans/total assets;
• SALARY ¼ total salaries/total assets;
We also include indicator variables for each year (YEAR92, YEAR94 and
YEAR96) to control for differences in the condition of the banking industry. 15
Eq. (2) is estimated using a Tobit regression because PROFEFF is bounded so that
all observations fall in the interval (0,1).
We first estimate the equation without the interaction terms to allow the full effect
of each variable to be captured by one coefficient, thus minimizing any collinearity
problems. This approach allows us to test the significance of one coefficient repre-
senting each of the three effects. We then add each interaction term separately; finally
we include all the interaction terms in one equation. This produces five separate sets
of estimates. To compare the estimates and test the robustness of the results, we pre-
sent the derivatives of the PROFEFF equation with respect to HHI, NONMSA,
(1 TOTLOANS) and SALARY in Table 4.
14
The HHI was computed using the FDICÕs branch office survey.
15
Only YEAR92, YEAR94 and YEAR96 are included in the regression equation. If we were to use all
four indicator variables for the four years, as well as an intercept term, there would be perfect
multicollinearity. To avoid this problem, we exclude the YEAR90 variable.
We first consider the control variables (all variables except the following (since
they are considered in connection with the hypotheses): HHI, NONMSA, (1
TOTLOANS) and SALARY. As Table 3 indicates, the results for most of the control
variables are consistent across the five equations. PROFEFF is (significantly) posi-
tively related to bank age, and demand deposits/total deposits. The positive relation-
ship to AGE is as expected since DeYoung and Hasan (1998) find that the PROFEFF
of recently chartered banks is substantially below average. The positive relationship to
DEMDEP is also as expected since demand deposits are a low cost source of funds
which also generate fee income. Small bank PROFEFF is (significantly) negatively re-
lated to the market non-performing loan ratio, the existence of a multibank holding
company relationship, the presence of a national bank charter, and large deposits/total
deposits. These results are also as expected––non-performing loans reduce profits and
PROFEFF; large deposits are more expensive than retail deposits. The reasons for the
negative signs on the coefficients of MBHC and NATIONAL are not apparent.
The positive coefficient of LNASSETS indicates that as bank size increases, but
remains under $500 million in total assets, PROFEFF increases. This result is incon-
sistent with the IA and RD hypotheses. As discussed in Section 6, these hypotheses
stress the importance of lender–borrower relationships to small bank profitability.
These hypotheses would thus suggest that PROFEFF might be largest for the smal-
lest banks.
We now consider the other three coefficients in model 1. (As noted, model 1 has
no interaction terms.) The coefficient of the HHI is positive and significant in model
1, indicating that, as expected, PROFEFF is greater for banks in more concentrated
markets. Ceteris paribus, an increase in the HHI from the median (0.3206) to the
75th percentile (0.5078) raises PROFEFF by 0.90 percentage points.
The coefficient of NONMSA is positive and significant, and it indicates that
PROFEFF is approximately 1.3 percentage points higher for banks in non-metro-
politan counties. Since the HHI may not fully capture all the complex effects of
competition on bank performance, it is possible that this is a residual SP effect.
The coefficient of (1 TOTLOAN) is also positive and significant. This result indi-
cates that banks with higher levels of non-loan assets actually have higher levels of
PROFEFF. The QL hypothesis predicts that these banks would have lower profits
and hence lower PROFEFF. There are two reasonable explanations for the positive
coefficient, which, it should be noted, is small. First, it reflects the effects of conser-
vative lending strategies, which would be expected to raise PROFEFF. Second, as
also noted earlier, PROFEFF is defined as efficiency in producing a given level of
output, even if that level of output (loans 16) is low.
Focusing on the derivatives in Table 4 shows the range of estimates for the effect on
PROFEFF of the four variables under consideration. (Most of the derivatives are sig-
nificant at the 1% level.) The most important finding from Table 4 is that the results
are extremely robust. The effect of an increase in the HHI from zero to one would be
to raise PROFEFF by between 4.69 and 5.76 percentage points. Thus a more normal
16
There are three outputs, but for most banks loans generate the most revenue.
change in the HHI, say from 0.40 to 0.50, would be one-tenths of the above amounts,
or between 47 and 58 basis points. This may reflect a combination of SP and RD fac-
tors. The effect of non-metropolitan location is an increase of between 1.02 and 1.30
percentage points, which probably reflects these same factors. The effect of an in-
crease in the ratio of non-loan assets to total assets from zero to one is an increase
in PROFEFF of between 3.53 and 3.77 percentage points. A more normal increase
of, say, 10 percentage points would thus produce an increase in PROFEFF of 35
to 38 basis points. As noted, this is probably the result of conservative lending strat-
egies, particularly since the equations were estimated using data for two years when
bank profits were below normal because of loan quality problems (1990 and, to a les-
ser extent, 1992) at some banks. There is more variability with respect to the estimates
of the fourth derivative, the ratio of salaries to total assets. Nonetheless, there is evi-
dence from models 4 and 5 that EP behavior lowers PROFEFF.
In summary, PROFEFF is increased by SP and RD factors (which cannot be sep-
arated empirically). It is difficult to quantify the effect of QL factors because these are
confounded by the effects of conservative lending strategies. Likewise, while there is
evidence in the literature of substantial EP behavior, the effects of this behavior on
PROFEFF are not apparent from the detailed analysis of the correlates of the
PROFEFF function conducted here.
We test the possibility that the results may be influenced by different input prices.
The input prices used to estimate the PROFEFF function (the WÕs in Eq. (1)) could be
influenced by EP and/or QL behavior because they are estimated from bank call re-
ports. 7 For example, bank managers following an EP style may dissipate profits in
excess expenditures on both salaries and premises, which would distort the wage rate.
In addition, QL managers may not bid aggressively for deposits and purchased funds,
even in rapid growth areas, which would distort the price of deposits and purchased
funds. To deal with these possibilities, we estimate a separate PROFEFF function
with three external input price variables: (a) the price of labor is the county wage rate
estimated from the Census BureauÕs County Business Patterns by dividing total pay-
rolls by the number of employees; (b) a proxy for the price of capital, per-capita in-
come, used because rents and prices of commercial property would be expected to be
highly correlated with per-capita income and (c) a proxy for the price of deposits and
purchased funds. This last variable is equal to the growth in total personal income
(the broadest measure of local economic activity) for the period 1980–92. The reason-
ing is that the demand for funds would be greater in rapid growth areas. While the
connection is loose, this is the best proxy variable available. 17 Importantly, both
the PROFEFF estimates and the regression analysis of the correlates (not shown
here) are substantially unaffected by this procedure. In fact, the average PROFEFF
estimates for each bank group are precisely the same. Thus, the results presented here
are extremely robust with respect to the specification of input prices.
17
This procedure of evaluating the robustness of the results by using external input prices was
suggested by the comments of an anonymous reviewer who called attention to these potential limitations
of ‘‘internal’’ input prices.
7. Summary and conclusions
We apply separate PROFEFF functions to data for small banks (those under
$500 million in assets) and large banks for 1990, 1992, 1994 and 1996. Assuming that
small and large banks use the same production technology, we find, consistent with
Berger and Mester (1997) results for an earlier period, that small banks are more
profit efficient than large banks for the period as a whole.
Over 40% of small banks are located in MSAs, where competition is generally
strong, so a pure SP explanation of small bank profitability (e.g., Boyd and Runkle,
1993) is inadequate. Small banks in MSAs are the least profit efficient of the three
categories of banks considered. Based on the single-frontier approach, we find the
PROFEFF of small non-MSA banks to be 0.7862 vs. only 0.6967 for small banks
in MSAs for this period as a whole. The difference is significant at the 1% level;
we attribute it to both SP and RD factors (Petersen and Rajan, 1995).
Regression analysis of the correlates of the PROFEFF estimates for small banks
indicates that PROFEFF increases as bank size increases, for banks under $500 mil-
lion in total assets. In addition, PROFEFF is negatively related to conditions asso-
ciated with EP behavior. We find that, ceteris paribus, when the HHI increases from
the median to the 75th percentile, PROFEFF increases by 0.90 percentage points.
We attribute this increase to a combination of SP and RD factors. In general, we
conclude that EP, SP and RD factors each play an important role in explaining
the PROFEFF of small US commercial banks.
Acknowledgements
We thank Aruna Srinivasan for suggesting the approach used in this paper, and
Ken Cyree, Elyas Elyasiani, Iftekhar Hasan, Bill Jackson and two anonymous refer-
ees for very helpful comments and/or discussion on an earlier draft. We especially
thank Bob DeYoung for his comments. We also thank Bobie Taylor for statistical
assistance. The usual caveats apply.
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Journal of Banking & Finance 27 (2003) 307–325

The proﬁt eﬃciency of small US

JEL classiﬁcation: G2; D2; G21; G28; E58; E61; F33

Financial economists have long been interested in the ﬁnancial performance of

0378-4266/02/$ - see front matter 2002 Published by Elsevier Science B.V.

2. Literature review and hypotheses

non-metropolitan markets relative to small banks in MSA markets would be more

5. Proﬁt eﬃciency measures

Panel B: Small versus large banks using separate frontiers

loans to assets and would thus be expected to do worse in a recession.) In contrast,

6. Correlates of the proﬁt eﬃciency measures

As discussed in the literature review, small bank PROFEFF is aﬀected by a num-

6.1. Factors related to structure–performance, relationship––development and infor-

6.2. Quiet-life and expense-preference behavior

As noted, banks in non-competitive markets may dissipate this advantage

6.3. Regression analysis of the correlates of the PROFEFF function

• PROFEFF ¼ our single-frontier estimate of proﬁt eﬃciency;

A. Akhigbe, J.E. McNulty / Journal of Banking & Finance 27 (2003) 307–325

A. Akhigbe, J.E. McNulty / Journal of Banking & Finance 27 (2003) 307–325

7. Summary and conclusions

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