Efficiency in Banking: Empirical Evidence from the Savings ... - Ivie

Efficiency in Banking: Empirical Evidence from the Savings
Banks Sector
S. Carbo a , E.P.M. Gardener b , and J. Williams b
a
Facultad de Ciencas Economicas y Empresariales, University of Granada, Spain
b Institute of European Finance, University of Wales, Bangor, Gwynedd LL57 2DG, UK.
Abstract
This study aims to contribute to the established literature by using the Fourier Flexible
functional form and stochastic cost frontier methodologies to estimate scale economies
and X-inefficiencies for a large sample of European savings banks between 1989 and
1996. In their extensive review of the bank efficiency literature, Berger and Humphrey
(1997) note that the volume of European studies has not matched that of the US and
there exists a paucity of cross-country studies. Whereas scale economies are widespread
and positively related to bank size, we find no evidence of a significant relationship
between size and X-efficiency. Generally, scale economies are found to range between
7 and 10 percent, while X-inefficiency measures appear to be much larger, around 22
percent. These results suggest that European savings banks can obtain cost reductions
through reducing managerial and other inefficiencies and also by increasing the scale of
production.
JEL Classification: G21
Keywords: Banking; Stochastic cost frontier; X-efficiency; Economies of scale.
Corresponding author: Jonathan Williams, Institute of European Finance, University of Wales, Bangor,
Gwynedd, LL57 2DG, United Kingdom. E-mail: jon.williams@bangor.ac.uk

1. Introduction
Savings banks are an important part of the European banking system accounting
for around 20% of banking system assets. In terms of customer deposits, savings banks
are even stronger with some national sectors holding over 30% and 40% market share
(European Savings Banks Group, 1997). Although their roots lie in retail banking,
savings banks have typically evolved to full-service banks that are virtually
indistinguishable from their commercial bank competitors (Gardener et al, 1997). As
such, savings banks are subject to those same competitive forces (and deregulatory
processes) that have and are shaping the EU banking system.
One feature that still differentiates the majority of savings banks from
commercial banks is their organisational form. Savings banks typically began as mutual
institutions and some operate with a significant level of state involvement. Competitive
pressures like the need to realise capital adequacy requirements have led to some
savings banks sectors being restructured 1 . In other sectors there is pressure to demutualise
and, indeed, convert into joint stock institutions 2 . Yet, there is no
requirement for savings banks to operate under any particular organisational structure,
providing EU competition law is not violated (Ehlermann, 1992) 3 .
The importance of evaluating the efficiency of savings banks is emphasised by
Köhler (1996, p. 7) who states that 'The savings banks of today are business concerns
1 The French savings banks sector, for example, was reconfigured in June 1991 with the result that the
number of savings banks reduced from over 180 to 35. The new number of French savings banks
corresponds to the 31 French regions and 4 overseas dependencies.
2 The conversion of four previously mutual UK building societies in 1997 provides such an example.
3 Post-1980, national policies and EU directives aimed to facilitate a more open and competitive
environment for banks. European law, however, considers the operations and functions of enterprises.
Providing that competition law is not violated, the law does not differentiate between or confer certain
advantages upon companies organised under private law as opposed to those belonging to the public,
cooperative, mutual and non-profit sectors (Ehlermann, 1992).
2

which have to stand up to competition through efficient business management and
sound earning capacity'. The Commission of the European Communities (1988) has
stressed in its 1992 single market programme that substantial benefits would accrue to
those sectors that can benefit from positive supply-side effects. In particular, 'price
reductions occasioned by competitive pressures will force firms to look actively for
reduction in costs through the elimination of areas of low productivity and/or by a
greater exploitation of scale economies' (European Economy, 1988, p.162).
In their extensive review of the bank efficiency literature, Berger and Humphrey
(1997) note that the volume of European studies has not matched that of the US and
there exists a paucity of cross-country studies. Despite the managerial objective to
improve efficiency, only a handful of studies have investigated the cost characteristics of
European banking markets. The present study aims to advance the established literature
by using the Fourier Flexible functional form and stochastic cost frontier approach in
order to evaluate evidence of scale and X-inefficiencies across the European savings
banks sector between 1989 and 1996.
We find that scale economies are widespread across different countries and they
increase with bank size. In general, scale economies are found to range between 7 and
10 percent, while X-inefficiency measures appear to be much larger, around 22 percent.
These results suggest that European savings banks can obtain cost reductions through
reducing managerial and other inefficiencies and also by increasing the scale of
production. Overall, large savings banks have scale economy advantages over their
smaller counterparts. However, size does not appear to confer advantages in terms of
X-efficiency. Given that larger banks realise greater scale economies this is likely to be
an important factor promoting consolidation in the European savings banks industry.
3

2. Efficiency in Banking - A Brief Literature Review
Over recent years the structure of European banking has been changing rapidly
and a primary motivation has been the drive for greater efficiency. A substantial US
literature has emerged (for example, see Berger et al. (1993), Karapakis et al. (1994),
Mester (1996), Mitchell and Onvural (1996)) which finds that X-efficiencies, brought
about by superior management, improved technologies and other factors, exceed those
efficiencies resulting from scale and scope economies. For instance, Berger et al. (1993)
note that scale and product-mix inefficiencies 'when accurately estimated', are usually
found to account for less than 5 percent of costs. Berger and Humphrey (1997) show
that out of 122 studies, the 60 that use parametric techniques find financial firm X-
inefficiencies averaging around 15% (compared with 28% for non-parametric
estimates). (Also Berger and Mester (1997) have found that average cost inefficiency in
US banks tended to decrease in the early 1990’s to around 13%.) Overall, however, the
general consensus from the literature is that banks will be more effective in reducing
their costs by emulating best cost practice (reducing X-inefficiencies) rather than
increasing size (scale economies) or diversifying (scope economies).
European research on cost efficiency in the banking sector has not matched the
volume of US studies and there have been only a few cross-country studies 4 . The
majority of European studies have focused on the issue of scale and scope economies in
individual countries and for particular types of banks. More recent literature has
attempted to evaluate X-inefficiencies in various European banking markets. The
earliest researchers used Cobb-Douglas and CES cost function methodologies to model
4 As identified by Berger and Humphrey (1997).
4

underlying cost functions, whereas from the mid-1980s onwards most studies have used
the translog functional form to estimate the cost characteristics of the banking industry.
For a comprehensive review of the European literature on scale and scope economies
and X-inefficiency see Molyneux et al. (1996, chapter 9). Overall, this literature tends
to find widespread evidence of scale economies in various European banking markets,
typically ranging between 5% and 10% whilst X-inefficiencies are around 20-25%.
Again, this general finding is confirmed in the EC (1997) study that found mixed
evidence on the level of scale economies while X-inefficiencies were estimated to be
around 25%.
In a recent paper Vennet (1998), uses the translog methodology to compare the
cost and profit efficiencies of European universal and specialist banks. Using a sample
of 2,375 EU banks from 17 countries for the years 1995 and 1996 he finds that financial
conglomerates are more revenue efficient than their specialised competitors and that
both cost and profit efficiency are higher in universal compared with non-universal
banks. Mean levels of inefficiency are 30% for estimates that use traditional
intermediation outputs (loans and securities) and 20% for estimates that include nontraditional
outputs (interest revenue and non-interest revenue). For diversified banks,
inefficiency appeared to be uncorrelated with size; however, small specialised banks
appeared to be relatively inefficient compared with their larger counterparts 5 .
While there is an emerging literature on the cost efficiency of banks in the
5 Vennet’s results on cost efficiency were found to be broadly in accordance with Allen and Rai’s (1996)
cross-country comparison of universal versus specialist banking systems. Scale economies were only
found for the smallest banks, those with assets under ECU 10 billion, with constant return thereafter and
diseconomies for the largest banks (assets exceeding ECU 100 billion). Vennet (1998) suggests that this
finding would suggest that the bank sizes for which no diseconomies are found are higher than in the
1980’s, a result that was also reported for US banks by Berger and Mester (1997).
5

mutual sector in various European countries (see, for example, Lang and Welzel 1996,
and Grifell-Tatje and Lovell 1996), the most comprehensive studies appear to be on the
UK building societies sector (see, for example, Drake and Weyman-Jones 1996,
McKillop and Glass 1994 and Glass and McKillop 1999) 6 . The aforementioned UK
studies use both parametric and non-parametric methods. McKillop and Glass (1994)
use a hybrid translog cost function to obtain estimates of overall and augmented
economies of scale, input-specific economies of scale, product-specific economies of
scale and economies of scope. They found evidence of significant augmented
economies of scale both for national and local building societies, but only constant
returns to scale for regional building societies. In terms of augmented input-specific
economies of scale, unit cost savings associated with the increased use of physical
capital were found for national societies but not for regional societies. Cost
inefficiencies were found to exist for local and regional building societies in mortgage
and non-mortgage product areas. There was apparently no evidence of economies of
scope.
Using data from 1988, Drake and Weyman-Jones (1996) use both parametric
and non-parametric techniques, and found that inefficiency in the building society sector
was in the region of 12%-13%. Glass and McKillop (1999) use linear programming
techniques and Malmquist productivity indices to estimate total productivity change in
the building society sector between 1989 and 1993. Total productivity change is
decomposed into efficiency change and technical change: the former being further
6 We have included efficiency studies of the UK building societies sector in the literature review because
of the building societies’ mutual characteristics, which are common to other (although not all) European
savings banks. The UK building societies, however, are not included in the estimations contained in
section 4 of this paper, because they are not legally defined as savings banks and their activities are
6

decomposed into changes in pure technical efficiency, changes in scale efficiency and
changes in input congestion. Glass and McKillop (1999) found evidence of substantial
productivity growth being caused in the main by progressive shifts in technology.
Although improvements in efficiency were found, these changes were small and due to
improvements in scale efficiency. A third major finding was that there has been a large
increase in the attainment of size efficiency. The technical efficiency estimates of Glass
and McKillop confirmed the earlier findings of Drake and Weyman-Jones.
The above literature review draws attention to the limited number of crosscountry
efficiency studies. It also highlights the main techniques, both parametric and
non-parametric, used to model these relationships. While the debate continues as to the
most appropriate methodology, there appears to be a preference in recent US studies for
the parametric approach, (for example see Kaparakis et al. (1994), Mester (1996),
Mitchell and Onvural (1996) and Mester and Berger (1997)). Resti (1997), in his study
of the Italian banking market, has also shown that both linear programming and
stochastic cost frontier approaches tend to provide similar cost efficiency results. (A
finding also confirmed by Drake and Weyman-Jones, 1996.) This study, therefore, aims
to use a parametric approach - the stochastic cost frontier and Fourier Flexible (FF)
functional form - to approximate the underlying cost characteristics of the European
savings bank industry from which estimates of X-efficiency and scale economies will be
obtained.
heavily dependent on mortgage finance, whereas other European savings banks are more diversified in
terms of their assets.
7

3. Methodology
While there continues to be debate about the definition of outputs used in cost
efficiency studies, we follow (like many other empirical researchers) along the lines of the
traditional intermediation approach as suggested by Sealey and Lindley (1977), where the
inputs, labour, physical capital and deposits are used to produce earning assets. Two of
our outputs, total loans and total securities are earning assets and we also include total
off-balance sheet items (measured in nominal terms) as a third output. Although the
latter are technically not earning assets, this type of business constitutes an increasing
source of income for banks and therefore should be included when modeling banks' cost
characteristics, otherwise, total output would tend to be understated (Jagtiani and
Khanthavit, 1996) 7 .
Inefficiency measures are estimated using the stochastic cost frontier approach.
This approach labels a bank as inefficient if its costs are higher than those predicted for
an efficient bank producing the same input/output combination and the difference
cannot be explained by statistical noise. The cost frontier is obtained by estimating a
cost function with a composite error term, the sum of a two-sided error representing
random fluctuations in cost and a one-sided positive error term representing
inefficiency.
Ferrier and Lovell (1990) have shown that inefficiency measures for individual
firms can be estimated using the stochastic frontier approach as introduced by Aigner et al.
7 Mester (1996) has suggested that risk should be controlled for in the cost function, but because
standardised data on such items as loan-loss provisions and BIS capital ratios were unavailable for many
banks in the sample, the authors could not include risk terms in the cost function specification.
8

(1977) and Meeusen and van den Broeck (1977). The single-equation stochastic cost
function model can be given as:
TC = TC(Q
i
, P i ) + ε i
(1)
where TC is observed total cost, Q i is a vector of outputs, and P i is an input-price vector.
Following Aigner et al. (1977), we assume that the error of the cost function is:
ε = u + v (2)
where u and v are independently distributed; u is assumed to be distributed as half-normal,
2
~ N( 0,
u
)
u σ , that is, a positive disturbance capturing the effects of inefficiency, and v is
assumed to be distributed as two-sided normal with zero mean and variance, σ 2 v, capturing
the effects of the statistical noise.
Observation-specific estimates of the inefficiencies, u, can be estimated by using
the conditional mean of the inefficiency term, given the composed error term, as proposed
by Jondrow et al. (1982). The mean of this conditional distribution for the half-normal
model is shown as:
σλ ⎡ f( εi
λ / σ )
E(u | ) = 1+ 1- F( / ) +
i εi 2 ⎢
λ ⎣ εi
λ σ
⎛
⎜
⎝
εi
λ
σ
⎞ ⎤
⎟
⎠ ⎥
⎦
(3)
where λ = σ u /σ v and total variance, σ 2 = σ 2 u + σ 2 v; F(.) and f(.) are the standard normal
distribution and density functions, respectively. E(u⏐ε) is an unbiased but inconsistent
estimator of u i , since regardless of N, the variance of the estimator remains non-zero (see
Greene, 1993; pp.80-82). Jondrow et al. (1982) have shown that the ratio of the variability
for u and v can be used to measure a banks' relative inefficiency, where λ = σ u /σ v , is a
9

measure of the amount of variation stemming from inefficiency relative to noise for the
sample. The X-inefficiency term, u, is assumed to remain constant over time for each
bank. Estimates of this model can be computed by maximising the likelihood function
directly (see Olson, Schmidt and Waldman, 1980).
Previous studies modelling international bank inefficiencies such as, Allen and Rai
(1996) and Vennet (1998) and those which examine US banks, such as Kaparakis et al.
(1994), and Mester (1996), all use the half-normal specification to test for inefficiency
differences between banking institutions 8 .
The next step, given the choice of the half-normal inefficiency stochastic frontier
approach, relates to choosing the underlying cost function specification. In this study, we
use the Fourier Flexible (FF) form to examine the specification, which best fits the
underlying cost structure of EU banking systems. Gallant (1981, 1982), Mitchell and
Onvural (1996) and Berger et al. (1997) have stated that the FF is the global
approximation which can be shown to dominate the conventional translog functional
form 9 . Berger et al. (1997) report that local approximations such as the translog may
8 See Bauer (1990) for a detailed review of the frontier literature and how different stochastic assumptions
can be made. Cebenoyan et al. (1993), for example, uses the truncated normal model. Mester (1993) in
common with many studies uses the half-normal distribution. Stevenson (1980) and Greene (1990) have
used the normal and gamma model, respectively. Altunba and Molyneux (1994) find that efficiency
estimates are relatively insensitive to different distributional assumptions when testing the half normal,
truncated normal, exponential and gamma efficiency distributions, as all distributions yield similar
inefficiency levels for the German banking market. Vennet (1998) uses both the half-normal and
exponential distributions to derive the efficiencies, but notes that there was little difference between the
two and so reports the half-normal estimates.
9 The translog functional form for a cost function represents a second-order Taylor series approximation of
any arbitrary, twice-differentiable cost function at a given (local) point. This restrictive property of the
translog forms part of White’s (1980) critique, which led Gallant (1981) to propose the Fourier flexible
functional form. Ivaldi et al. (1996) argue that a second-order approximation is insufficient and at least a
third-order approximation is required to generate a flexible cost function. The translog, however, is nested in
a third-order approximation for the Fourier. Gallant (1981) highlights White’s criticism of the translog when
he states that Taylor’s theorem leads to misunderstanding of parameter estimates and test statistics. This is
because statistical methods ‘essentially expand the true function in a (general) Fourier series – not in a
Taylor’s series’ (Gallant, 1981, p. 212). Ivaldi et al. (1996) state that fixing the order of approximation in the
expansion allows the estimation of the Fourier flexible form via parametric estimation methods.
10

distort scale economy measurements since it imposes a symmetric U-shaped average cost
curve. This feature of the translog might not fit very well data that are far from the mean
in terms of output size or mix (Berger and Mester, 1997). The FF alleviates this problem
since it can approximate any continuous function and any of its derivatives (up to a fixed
order). Any inferences that are drawn from estimates of the FF are unaffected by
specification errors (Ivaldi et al., 1996). Since the FF is a combination of polynomial and
trigonometric expansions, the order of approximation can increase with the size of the
sample size. This is due to the mathematical behaviour of the sine and cosine functions
which are mutually orthogonal over the [0, 2π] interval and function space-spanning.
Berger and Mester (1997) note that goodness of fit for the estimated efficient frontier is
important in estimating efficiency, since inefficiencies are measured as deviations from the
frontier. The global property is important in banking where scale, product mix and other
inefficiencies are often heterogeneous, therefore, local approximations (such as those
generated by the translog) may be relatively poor approximation to the underlying true cost
function.
Ivaldi et al. (1996) state the Fourier can represent a broader range of cost structures
than other functional forms. Those authors determine differences in the description of a
technology by fitting Fourier and translog cost functions. They concur that the Fourier is
suitable for estimating cost functions on panel data sets that are characterised by variables
with large variances. For this reason, the local point estimate produced by the translog
functional form is inappropriate to approximate the true technology. The results of the
tests performed by Ivaldi et al. (1996) find the global approximation of the Fourier better
captures the heterogeneity of their sample, whilst the translog only revealed average
properties.
11

Hence, the FF is a semi-nonparametric approach used to tackle the problem arising
when the true functional form of the relationship is unknown. As noted above, the
methodology was first proposed by Gallant (1981, 1982), and later discussed by Elbadawi,
Gallant and Souza (1983), Chalfant and Gallant (1985), Eastwood and Gallant (1991),
Gallant and Souza (1991). It has been applied to the analysis of bank cost efficiency by
Spong et al. (1995), Mitchell and Onvural (1996) and Berger et al. (1997). Vennet (1998)
estimates both the translog and FF cost function in his study of European universal and
specialist banks but reports only the translog estimates because the results are similar.
To calculate the inefficiency measures, the FF form, including a standard translog
and all first, second and third-order trigonometric terms, as well as a two-component error
structure is estimated using a maximum likelihood procedure. This is shown as:
3
∑[
a
i= 1
i
∑
1 ⎡
⎢
2 ⎣
cos (
3
i= 1
3
∑
j= 1
3
∑
i= 1
3
∑
i= 1
z
) +
i
ln
3
∑
j= 1
3
∑
m= 1
b
δ
ρ
3
∑[
a
k≥
j,
k≠i
sin (
i
TC
ij
= α0+
im
lnQ
lnQ
z
ijk
i
)
i
3
∑
lnQ +
i
3
] +∑
cos (
i= 1
i= 1
z
αilnQ+
j
lnPm+
i
+
3
∑
l= 1
3
∑
i= 1
∑
3
∑[
a
j=
1
z
j
+
i
∑
3
3
l= 1
m= 1
γ
β
ψ T lnQ +
z
i
k
ij
) +
lm
l
cos (
b
lnPl+
t1T
+
lnP
i
ijk
z
l
∑
+
sin (
lnP
3
l= 1
i
θ lT
lnP l+
z
z
i
) +
j
m
+
+ t11T
z
b
j
ij
+
2
⎤
⎥+
⎦
sin (
z
k
)
z
i
+
] +
(4)
where
lnTC = the natural logarithm of total costs (Operating and Financial cost);
lnQ i = the natural logarithm of bank outputs (i.e. loans, securities, off-balance sheet
items);
ε
z
j
)
] +
12

lnP l = the natural logarithm of ith input prices (i.e. wage rate, interest rate and physical
capital price);
T = time trend;
Z i = the adjusted values of the log output lnQ i such that they span the interval [0, 2π];
α, β, δ i , γ, Ψ, θ, ρ, a, b and t are coefficients to be estimated.
Following Berger et al. (1997), the study applies Fourier terms only for the
outputs, leaving the input price effects to be defined entirely by the translog terms. The
primary aim is to maintain the limited number of Fourier terms for describing the scale
and inefficiency measures associated with differences in bank size. Moreover, the usual
input price homogeneity restrictions can be imposed on logarithmic price terms, whereas
they cannot be easily imposed on the trigonometric terms 10 .
In addition, the scaled log-output quantities, z i , are calculated as z i = µ i (lnQ i +
w i ), lnQ i are unscaled log-output quantities; µ i and w i are scaled factors, writing the
periodic sine and cosine trigonometric functions within one period of length 2π before
applying the FF methodology (see Gallant 1981). The µ i s are chosen to make the largest
observations for each scaled log-output variable close to 2π; w i s are restricted to assume
the smallest values close to zero. In this study, we restricted the z i to span between 0.001
10 Mitchell and Onvural (1996; p.181) did not impose restrictions on the trigonometric input price
coefficients for computational reasons. Gallant (1982), however, has shown that this should not prevent
an estimated FF cost equation from closely approximating the true cost function.
13

and 6 to reduce approximation problems near the endpoints as discussed by Gallant
(1981) and applied by Mitchell and Onvural (1996) 11 .
Since the duality theorem requires that the cost function is linearly homogeneous
in input prices and continuity requires that the second order parameters are symmetric, the
following restrictions apply to the parameters of the cost function in equation (4):
3
∑
l= 1
β
l
=
1;
3
∑
l= 1
δ
γ
ij
lm
=
= 0
δ
ji
;
3
∑
l= 1
θ
and γ
l
lm
= 0 ;
= γ
ml
3
∑
m = 1
ρ
im
=
0;
(5)
The cost frontiers are estimated using the random effects panel data approach (as
in Lang and Welzel, 1996). We use the panel data approach because technical efficiency
is better studied and modelled with panels (see Baltagi and Griffin, 1988; Cornwell,
Schmidt and Sickles, 1990; Kumbhakar, 1993). The random effects model is preferred
over the fixed effects model because fixed effects is considered to be the more
appropriate specification if we are focusing on a specific set of N firms. Moreover, and
if N is large, a fixed effects model would also lead to a substantial loss of degrees of
freedom (see, for example, Baltagi, 1995). Thus, the unbalanced nature of our dataset
determines the use of the random effects model.
11 Berger et al. (1997) restricted z i to span [.1; 2, .9; 2], however, the use of this interval provided
inconsistent results in the present study. While Mitchell and Onvural (1996) adopted a second
trigonometric order in their study, we preferred to use a third trigonometric order following Berger et al.
(1997). According to Gallant (1982), increasing the number of trigonometric orders, relative to sample
size, reduces approximation errors. Eastwood and Gallant (1991) show that the FF cost function produces
consistent and asymptotically normal parameter estimates when the number of parameters estimated is set
to the number of effective observations raised to the two thirds power. However, Gallant (1981) advocates
that even a limited number of trigonometric orders is sufficient to obtain global approximations. The
choice of the range used by different researchers is, however, subjective and relative to the size of data set
analysed.
14

Within sample scale economies are calculated as in Mester (1996) and are
evaluated at the mean output and input price levels for the respective size quartiles. A
measure of economies of scale (SE) is given by the following cost elasticity by
differentiating the cost function in equation (4) with respect to output. This gives us:
3
3
3 3
3 3
3
SE = = i+ ij Q j
∑ ∑α
∑∑δ
ln + ∑∑ ρ im
ln Pm+
∑
i=1 ∂ ln Qi
i=1 i=1 j=1
i=1 m=1
i=1
3
∑
i=
1
[ ]
3 3
[ a sin( Z ) − b cos( Z )] + a sin( Z + Z ) − b cos( Z + Z )
i
3
∑
i=
1
∂ lnTC
i
3
∑
j=
1
i
3
∑
k≥
j,
k ≠i
[ a sin( Z + Z + Z ) − b cos( Z + Z + Z )]
ijk
i
∑
i=
1
i
∑
j=
1
j
ij
k
i
ijk
j
i
ij
j
i
k
ψ T +
i
j
+
(6)
If SE < 1 then increasing returns to scale, implying economies of scale;
If SE = 1 then constant returns to scale;
If SE > 1 then decreasing returns to scale, implying diseconomies of scale.
4. Data and Results
This study uses banks' balance sheet and income statement data for a sample of
European savings banks between 1989 and 1996, obtained from the London-based
International Bank Credit Analysis Ltd's 'BankScope' database. Table 1 reports the
definition, mean and standard deviation of the input and output variables in real terms
used in the cost frontier estimations, all data are in real 1996 terms and they have been
converted using individual country GDP deflators. (Parameter estimates of the cost
frontier are shown in Table A1 in the Appendix.)
Table 1 here.
15

Table 2 shows the composition of the European savings banks sample. It should
be noted that a small number of savings banks are represented in Finland, Luxembourg,
the Netherlands, Portugal and Sweden. This is due partly to the fact that there are a
number of very small savings banks in Finland and Sweden for which data are difficult
to obtain, and because the savings bank sectors in Luxembourg, the Netherlands, and
Portugal are dominated by a relatively large single savings bank. In contrast, the German
savings banks sector is most heavily represented followed by Italy, Spain, Denmark,
Austria and Belgium. The large number of German savings banks from 1993 onwards
are due to limited data availability prior to that date. The table also shows that the most
comprehensive data were available for 1994-1996 and that savings banks with assets
size ranging between ECU 500 million and ECU 2,500 million accounted for over half
the sample.
Table 2 here.
Tables 3 and 4 show the scale economy estimates and mean inefficiencies of
national savings banks sectors for different sizes of banks over the years 1989 to 1996.
Generally, scale economies are prevalent across the sector and typically vary between 7
and 10 percent. Thus, a 100 percent increase in the level of all outputs would lead to
about a 93 to 90 percent increase in total costs, respectively. The bottom part of Table 3
shows that larger savings banks, across all European countries, realise greater scale
economies compared with their smaller counterparts. Overall, banks under ECU 200
million in assets experience constant returns to scale, thereafter, economies increase
systematically with size. In other words, scale economies become larger with size and
16

optimal bank size appears to be inexhausted 12 . The magnitude of these scale economy
estimates accord with the findings of previous studies of the US banking market (for
example, see Berger et al. 1993), although only a handful of studies find evidence of
inexhaustable scale economies (see, for example, McAllister and McManus, 1993;
Hughes et al., 1995; and Lang and Welzel, 1996).
Table 3 here.
Mean inefficiencies are shown in Table 4 by national savings banks sectors. The
general finding is that industry inefficiency rose between 1989 and 1991 (from 22.3% to
22.7%), thereafter falling to a level of 21.6% in 1996. This suggests that the same level
of output could be produced with approximately 78% of current inputs if savings banks
were operating on the efficient frontier. This is in the same range as those found in the
US literature as well as the studies undertaken by Resti (1997) on Italian banks and
Grifell-Tatje and Lovell (1996) on Spanish savings banks.
Table 4 here.
The lower panel of Table 4 shows the distribution of mean X-inefficiencies by
bank asset size. As noted above, smaller savings banks are found to be more cost X-
efficient than larger savings banks. Savings banks with assets less than ECU 99.9
million and between ECU 100-199.9 million, have mean X-inefficiency of 20.8% and
21.2%, respectively, compared with larger savings banks, with assets between ECU
2,500-4999.9 and greater than ECU 5,000 million, and mean X-inefficiencies of 22.2%
and 22.1%, respectively. Yet, the two smallest classes of savings banks realise
12 Our finding of inexhausted optimal bank size might be due to the relatively small size of most savings
banks. Similar findings appear elsewhere in the banking literature, for example, Lang and Welzel (1996),
who in a study of German co-operative banks, attribute a finding of scale economies in all size classes to
the relatively small size of banks in their sample.
17

diseconomies of scale in all countries (except Austria and Italy). This finding suggests
there are unrealised benefits that could be achieved through increased size for small
savings banks, or through consolidation. The fact that scale economies increase with
size and that optimal bank size is inexhausted supports an argument for further
consolidation.
Considering that the years 1993 to 1996 contain the most data, Table 4 shows
that the smallest size group is the most mean cost X-efficient between 1993 and 1996,
despite mean X-inefficiency deteriorating over this period. At 1996, however, the most
cost-efficient savings banks had assets between ECU 200-299.9 million, followed by
size classes ECU 100-199.9 (21.3%), ECU 1-99.9 million (21.4%) and ECU 1,000–
2,499.9 million (21.5%). The least X-efficient size class in 1996 was the largest class
(above ECU 5,000 million) with a mean X-inefficiency of 22%. The data for 1996,
however, show first, that smaller savings banks are losing their apparent cost efficiency
advantage, second, slightly larger savings banks are becoming more X-efficient (ECU
200-299.9 million), which could reflect policy makers earlier decision to create savings
banks of greater mass. Finally, the range of X-inefficiencies across savings banks of
different size class has narrowed suggesting that previously visible cost efficiency
advantages pertaining to asset size may be dissipating over time (see Table 4).
There are four organisational and economic models that are commonly being
followed by European savings banks 13 . These models are not entirely heterogeneous
with several common elements, including commitment to social and economic activities
within localities and the sharing of technology. Generally, the models reflect a spectrum
of different ownership types, ranging from state to private ownership and non-profit
18

orientation to profit. The first model is the ‘state’ model in which savings banks,
generally, are non-profit institutions owned by mutual authorities and subject to some
operational and geographic boundaries (for example, Germany). The second ‘mixed’
model has a more diverse ownership structure than the ‘state’ model, including
municipal authorities, depositors and employees (for example, Spain). Under the ‘state’
and ‘mixed’ models savings banks have limited means of raising equity capital due to
their ownership. This is not the case in the two remaining models, the ‘in-transition’
model and the ‘marketised model’ (for example, Italy and the UK, respectively). In the
former model, savings banks are in the process of converting their organisational form
to joint stock company status, first to reduce public fiscal responsibility to savings
banks, and second to allow savings banks to raise private equity capital through the
issue of shares. The latter ‘marketised’ model is the final outcome of the ‘in-transition’
model. It is characterised by the demutualisation of a large proportion of the savings
banks sector with increasing competitive pressures on remaining mutuals.
There is no strong evidence to suggest that one model dominates the others in
terms of either X-efficiency or economies of scale. In cases where the average size 14 of
savings banks has increased (for example, as a result of restructuring in France and
through consolidation in Spain), evidence that larger average size conveys translates into
greater X-efficiencies is ambiguous. Interestingly, the least X-efficient savings banks
are in sectors that can be classified as ‘in-transition’ and ‘marketised’ (for example, the
restructured Finnish and demutualised Belgian sectors, respectively). Nevertheless, this
13 See Gardener et al. (1997).
14 The average assets size of savings banks as classified by the five models is as follows. French, ECU
5,699 m; German, ECU 1,427 m; Italian, ECU 3,779 m; Spanish, ECU 5,372 m; UK building societies,
ECU 2,486 m. The data are at 1997 (Gardener et al. 1999).
19

finding should be treated with caution since the relative importance of savings banks is
much reduced in such countries, and the future prospects for the remaining savings
banks are unclear.
Overall, the results suggest that for the sector as a whole, that greater cost
savings are to be obtained if savings banks focus their attentions on reducing
managerial, technological and other inefficiencies, compared with increasing size.
Nevertheless, there are still cost reductions of between 7 and 10 percent that can be
realised through increasing output size.
To further investigate the determinants of European savings banks X-
inefficiency we use a logistic regression model as suggested in Mester (1993 and 1996).
Since the values of estimated inefficiencies range between zero and one the logistic
functional form is preferred over the linear regression model. We model the X-
inefficiency values against various firm-specific characteristics. The independent
variables used include TASSET = bank total assets size measured in millions of ECU,
CRATIO = equity/total assets, ROAA = return on average assets, NL/TASSET = net
loans/total assets, OBS/TASSET = off-balance sheet items (nominal value)/total assets
and finally, LA/C&SF= liquid assets / customer and short-term funding. TASSET
controls for the overall size of the bank. CRATIO is the financial capital ratio and this
should be inversely related to inefficiency on the grounds that banks with low
inefficiency will have higher profits and hence will be able to (holding dividends
constant) retain more earnings as capital. ROAA is a performance measure and this
should be inversely related to inefficiency. NL/TASSET, OBS/TASSET, and LA/C&SF
are proxies for business mix. The logistic parameter estimates are shown in Table 5.
Table 5 here.
20

In accordance with Mester's (1996) findings, inefficiencies are inversely
correlated with the financial capital variable (CRATIO) and bank performance (ROAA).
This is, of course, to be expected given that banks with low inefficiency will have more
profits as they will be able to (holding dividends constant) retain more earnings as
capital. The estimates also reveal that there is an inverse relationship between asset size
(TASSET) and efficiency. Efficient banks also appear to have lower loan-to-assets ratios
and higher liquidity ratios. The level of savings banks off-balance sheet business is not
statistically related to X-efficiency.
5. Conclusion
This paper advances the established literature on modelling the cost
characteristics of banking markets by applying the Fourier Flexible functional form and
stochastic cost frontier methodologies to estimate scale economies and X-inefficiencies
for a large sample of European savings banks between 1989 and 1996. As far as we are
aware this is the only cross-country study that compares X-efficiencies and scale
economies in the sector. The results reveal that scale economies are widespread across
different countries and they increase with bank size. In general, scale economies are
found to range between 7 and 10 percent, while X-inefficiency measures appear to be
much larger, around 22 percent. These results are similar to those found in earlier US
and European studies, and they suggest that European savings banks can obtain cost
reductions through reducing managerial and other inefficiencies and also by increasing
the scale of production. Overall, large savings banks have scale economy advantages
over their smaller counterparts. Size, however, does not appear to confer advantages in
terms of X-efficiency. Given that larger banks realise greater scale economies this may
be an important factor promoting consolidation in the European savings banks industry.
21

Several important and interesting findings are reported in this study. It appears
that the different organisational models followed by European savings banks do not
convey any obvious difference in the level of X-inefficiency and economies of scale. In
some sectors that are ‘in-transition’ and/or are ‘marketised’, savings banks are less X-
efficient than those organised under other models. It is unclear whether this relates to
the authority’s diminishing commitment to a viable savings banks sector, or to one
organisational model being superior to another. These results, however, are important
in terms of the demutualisation debate that surrounds the industry.
Our results indicate that smaller savings banks are more X-efficient than larger
banks. Whilst this finding implies relative managerial quality in small savings banks,
we generally find that savings banks with less than ECU 199.9 million worth of assets
do not achieve economies of scale. Hence, there is a tension between the X-efficiency
and economies of scale results for small savings banks with the latter finding suggesting
that smaller savings banks could benefit from increased consolidation. Indeed, the
results indicate that the differential in X-efficiency across different sized banks is
narrowing over time. Hence, the mean smaller savings banks are becoming less costefficient
whilst the average larger savings banks have become more X-efficient. There
are various possible explanations for this finding. A more competitive environment
may exert relatively greater pressure on smaller savings banks, whereas larger savings
banks may be able to take advantage of their size whilst simultaneously targeting
reducing cost inefficiencies. Savings banks participate in many sharing arrangements,
for example, in payments systems both at national and pan-European levels. It is
possible that this feature of the industry might convey benefits in terms of economies of
scale but have little or no impact on X-efficiency.
22

References
Aigner, D., C. Lovell and P. Schmidt, (1977), ‘Formulation and estimation of stochastic
frontier production models’, Journal of Econometrics, 6, 21-37.
Allen, L. and A. Rai, (1996), ‘Operational efficiency in banking: an international
comparison’, Journal of Banking and Finance, 20 (4), 655-672.
Altunba , Y. and P. Molyneux, (1994), ‘Sensitivity of stochastic frontier estimation to
distributional assumptions: the case of the German banks’, Institute of European
Finance Paper (preliminary version, unpublished in 1994).
Altunba , Y. and P. Molyneux, (1996), ‘Economies of scale and scope in European
banking’, Applied Financial Economics 6, 367-375.
Altunba , Y. and P. Molyneux, (1996a), ‘Cost economies in EU Banking systems’,
Journal of Economics and Business 48, 217-230.
Andersen, Arthur, (1993), European Banking and Capital Markets - a Strategic Forecast,
Research Report, (London: The Economist Intelligence Unit).
Baltagi, B.H., (1995), Econometric analysis of panel data, (Chichester, UK: John Wiley &
Sons Ltd).
Baltagi, B.H., and J.M. Griffin, (1988), ‘A general index of technical change’, Journal of
Political Economy, vol. 96, no. 1, 20-41.
Battese, G.E. and T.J. Coelli (1992), ‘Frontier production functions, technical efficiency
and panel data: with application to paddy farmers in India’, Journal of Productivity
Analysis, 3, pp. 153-169.
Bauer, P., (1990), ‘Recent developments in the econometric estimations of frontiers’,
Journal of Econometrics, 46, 39-56.
Berger, A.N., J.H. Leusner, and J.J. Mingo, (1997), ‘The efficiency of bank branches’,
Journal of Monetary Economics, 40, pp. 141-162.
Berger, A.N., W.C. Hunter and S.G. Timme, (1993), ‘The efficiency of financial
institutions: A review and preview of research past, present, and future’, Journal of
Banking and Finance, 17, 221-249.
Berger, A.N and D.B. Humphrey, (1997), ‘Efficiency of financial institutions:
International survey and directions for future research’, European Journal of
Operational Research, 98, 175-212
Berger, A.N and L.J. Mester (1997), ‘Inside the black box: What explains differences in
the efficiencies of financial institutions’, Journal of Banking and Finance, 21, 7,
895-947
Carbo, S. and J. Williams (1999), ‘Stakeholder Value in European Savings Banks’, in L.
Schuster (ed.) Shareholder Value Management in Banking, Macmillan.
Cebenoyan, A.S., E.S. Cooperman, C.A Register and S.C. Hudgins, (1993), ‘The relative
efficiency of stock versus mutual S&Ls: A stochastic cost frontier approach’,
Journal of Financial Services Research, 7, 151-170.
Cecchini, P., (1988), The European Challenge in 1992: The Benefits of a Single Market,
(Aldershot: Gower)
Chalfant, J. A. and A.R. Gallant, (1985), ‘Estimating substitution elasticities with the
Fourier cost function’, Journal of Econometrics 28, 205-222.
Commission of the European Communities, (1988), European Economy: The Economics
of 1992, No. 35, March, (Brussels: EU).
Cornwell, C., P. Schmidt and R.C. Sickles, (1990), ‘Production frontiers with crosssectional
and time-series variation in efficiency levels’, Journal of Econometrics,
46, 185-200.
23

Drake, L. and T.G. Weyman-Jones (1996), ‘Productive and allocative inefficiencies in UK
Building societies: A comparison of non-parametric and stochastic frontier
techniques’, The Manchester School of Economics and Social Studies, 60, 1, March,
pp. 22-37.
Eastwood, B.J. and A.R. Gallant, (1991), ‘Adaptive rules for semi-nonparametric
estimators that achieve asymptotic normality’ Economic Theory 7, 307-340.
Elbadawi, I., A.R. Gallant and G. Souza, (1983), ‘An elasticity can be estimated
consistently without a priori knowledge of functional form’, Econometrica 51,
1731-1753.
Ehlermann, C.D. (1992), ‘European Community Competition Policy, Public Enterprise
and the Cooperative, Mutual and Nonprofit Sector’, Annals of Public and
Cooperative Economics, Vol. 63, 4, pp.555-571.
European Commission (1997), Credit Institutions and Banking, Volume 3, Subseries II:
Impact on Services, The Single Market Review (London: Kogan Page).
European Economy, (1988), Creation of A European Financial Area, Commission of the
European Communities, no.36, May, (Brussels: EU).
European Savings Banks Group (1997), Annual Report.
Ferrier, G.D., and C.A.K. Lovell (1990), ‘Measuring cost efficiency in banking:
econometric and linear programming evidence’ Journal of Econometrics 46, 229-
245.
Gallant, A.R. and G. Souza, (1991), ‘On the asymptotic normality of Fourier Flexible
form estimates’, Journal of Econometrics 50, 329-353.
Gallant, A.R., (1981), ‘On the bias in Flexible Functional forms and essentially
unbiased form: The Fourier Flexible form’, Journal of Econometrics 15, 211-245.
Gallant, A.R., (1982), ‘Unbiased determination of production technologies’, Journal of
Econometrics 20, 285-324.
Gardener, E.P.M., P. Molyneux, J. Williams & S. Carbo (1997), ‘European Savings
Banks: Facing Up To The New Environment’, International Journal of Bank
Marketing, Vol. 15, no.7, pp. 243-254.
Gardener, E., P. Molyneux & J. Williams (1999), European Savings Banks: Coming of
Age? (Lafferty Publications)
Glass, J.C. and D.G. McKillop (1999), ‘A post deregulation analysis of the sources of
productivity growth in UK building societies’, Working Paper, Queen’s University,
Belfast.
Greene, W.M., (1990), ‘A gamma-distributed stochastic frontier model’, Journal of
Econometrics, 46, 141-163.
Greene, W.M., (1993), ‘The econometric approach to efficiency analysis’, in Fried, H.O.,
C.A. Lovell and P. Schmidt (eds.) The Measurement of Productive Efficiency:
Techniques and Applications, (Oxford: Oxford University Press).
Griffell-Tatje, E. and C.A.K. Lovell (1996), ‘Deregulation and productivity decline: the
case of Spanish savings banks’, European Economic Review, 40, pp. 1281-1303.
Hughes, J.P., W. Lang, L.J. Mester and C.G. Moon (1995), ‘Recovering banking
technologies when managers are not risk-neutral’, Conference on Bank Structure
and Competition, Federal Reserve Board of Chicago, May, pp. 349-368.
Hunter, W.C. and S.G. Timme, (1991), ‘Technological change in large US commercial
banks’, Journal of Business, 64, 339-362.
Humphrey, D.B., (1993), ‘Cost and technical change: effects from bank deregulation’,
Journal of Productivity Analysis, 4, 9-34.
24

Institute of European Finance, Challenges and the Future of Savings Banks in the Single
Financial Market of the EU, (Institute of European Finance: Bangor), 1998.
Ivaldi, M., N. Ladoux, H. Ossard and M. Simioni (1996), ‘Comparing Fourier and
Translog specifications of multiproduct technology: evidence from an incomplete
panel of French farmers’, Journal of Applied Economics, vol. 11, pp. 649-667.
Jagtiani, J. and A. Khanthavit, (1996), ‘Scale and scope economies at large banks:
Including off-balance sheet products and regulatory effects (1984-1991)’, Journal of
Banking and Finance, 20 (7), 1271-1287.
Jondrow, J., C.A. Lovell, I.S. Materov and P. Schmidt, (1982), ‘On estimation of technical
inefficiency in the stochastic frontier production function model’, Journal of
Econometrics, 19 (July), 233-238.
Kaparakis, E.I., S.M. Miller and A.G. Noulas, (1994), ‘Short-run cost inefficiencies of
commercial banks’, Journal of Money, Credit and Banking, 26, no.4 (November),
875-893.
Köhler, H. (1996), in Mura, J. (ed), History of European Savings Banks, Deutscher
Sparkassenverlag GmbH, Stuttgart.
Kumbhakar, S.C., (1993), ‘Production risk, technical efficiency and panel data’,
Economics Letters, 41, 11-26.
Lang, G. and P. Welzel, (1996), ‘Efficiency and technical progress in banking: empirical
results for a panel of German cooperative banks’, Journal of Banking and Finance,
20, 1003-1023.
Maudos, J., J.M. Pastor and J. Quesada, (1996), ‘Technical progress in Spanish banking:
1985-1994’, University of Valencia and IVIE Discussion Paper, WP-EC 96-06.
McAllister, P.H. and D. McManus (1993), ‘Resolving the scale efficiency puzzle in
banking’, Journal of Banking and Finance, 17, pp. 389-405.
McKillop, D.G., J. C. Glass and Y. Morikawa, (1996), ‘The composite cost function and
efficiency in giant Japanese banks’, Journal of Banking and Finance, 20, 1651-
1671.
McKillop, D.G. and J.C. Glass (1994), ‘A cost model of building societies as producers of
mortgages and other financial products’, Journal of Business, Finance and
Accounting, 21(7), pp. 1031-1046.
Meeusen, W. and J. van den Broeck, (1977), ‘Efficiency estimation from Cobb-Douglas
production functions with composed error, International Economic Review, 18, 435-
444.
Mester, L.J., (1993), ‘Efficiency in the savings and loan industry’, Journal of Banking and
Finance, 17, 267-286.
Mester, L.J., (1996), ‘A study of bank efficiency taking into account risk-preferences’,
Journal of Banking and Finance, 20, 1025-1045.
Mitchell, K. and N.M. Onvural, (1996), ‘Economies of scale and scope at large
comercial banks: Evidence from the Fourier Flexible functional form’, Journal of
Money, Credit and Banking, Vol. 28, No. 2, 178-199.
Molyneux, P., Y. Altunba and E.P.M. Gardener, (1996), Efficiency in European
Banking, (Chichester, UK: John Wiley & Sons).
Nelson, R.A., (1984), ‘Regulation, capital vintage, and technical change in the electric
utility industry’, Review of Economics and Statistics, 66, (February), 59-69.
Olson, R.E., P. Schmidt and D.M. Waldman, (1980), ‘A monte carlo study of estimators
of stochastic frontier production functions’, Journal of Econometrics, 13, 67-82.
25

Resti, A., (1997), ‘Evaluating the cost-efficiency of the Italian Banking system: What
can be learned from the joint application of parametric and non-parametric
techniques’, Journal of Banking and Finance, Vol. 21, 221-250.
Revell, J. (1989), The Future of Savings Banks: A Study of Spain and the Rest of
Europe, Institute of European Finance, Research Monographs in Banking and
Finance no. 8, (University of Wales, Bangor, UK: Institute of European Finance)
Sealey, C. and J.T. Lindley, (1977), ‘Inputs, outputs and a theory of production and cost at
depository financial institution’, Journal of Finance 32, 1251-1266.
Spong, K., R.J. Sullivan and R. DeYoung, (1995), ‘What makes a bank efficient? - A
look at financial characteristics and bank management and ownership structure’,
FRB of Kansas City Review, December, 1-19.
Stevenson, R.E., (1980), ‘Likelihood functions for generalised stochastic frontier
estimation’, Journal of Econometrics, 13, 57-66.
Tolstov, G.P. (1962), Fourier Series, (London: Prentice-Hall Int.).
Vennet, R.V., (1998), ‘Cost and profit dynamics in financial conglomerates and universal
banks in Europe’, paper presented at the SUERF/CFS Colloquim, Franfurt, 15-17
October
White, H, (1980), ‘Using least squares to approximate unknown regression functions’,
International Economic Review, vol. 21, pp. 149-170.
26

Table 1 Descriptive statistics of the outputs and input variables used in the model,
1989-1996 *
Variables Description Mean StDev Min Max
TC Total cost (operating and financial cost) 138.2 437.1 0.6 9407.5
(ECU m)
P 1 Price of labour (%) (total personnel 0.015 0.005 0.001 0.049
expenses/total assets)
P 2 Price of funds (%) (total interest 0.051 0.016 0.019 0.246
expenses/total funds (demand, saving,
time inter-bank deposits, long-term debt,
subordinated debt and other))
P 3 Price of physical capital (total 0.472 0.166 0.062 0.992
depreciation and other capital
expenses/total fixed assets)
Q 1 The ECU value of total aggregate loans 1007.0 2648.9 3.6 45481.0
(all types of loans) (ECU m)
Q 2 The ECU value of total aggregate 790.2 3144.9 2.1 88368.6
securities (short term investment, equity
and other investments and public sector
securities) (ECU m)
Q 3 The ECU value of the off-balance sheet 261.0 3714.0 0.0 159290.0
activities (nominal values) (ECU m)
Number of observations: 4,083
* The figures have been deflated using country specific GDP deflators with 1996 as a base year.
27

Table 2 European savings banks sample: Number and size distribution across
countries 1989-1996
1989 1990 1991 1992 1993 1994 1995 1996 All
Austria 4 4 4 6 6 9 16 16 65
Belgium 1 1 1 5 13 14 15 14 64
Denmark 3 3 5 14 24 29 36 34 148
Finland 0 0 0 0 1 1 1 1 4
France 0 0 1 8 17 20 18 18 82
Germany 51 53 68 224 605 655 627 584 2867
Italy 36 38 40 46 61 62 64 62 409
Luxembourg 1 1 1 2 4 4 3 3 19
Netherlands 0 0 0 1 1 2 3 3 10
Portugal 1 1 2 3 3 2 3 3 18
Spain 43 45 47 50 52 52 51 51 391
Sweden 0 0 1 1 1 1 1 1 6
All 140 146 170 360 789 852 840 791 4083
Asset size ECU m 1989 1990 1991 1992 1993 1994 1995 1996 All
1 - 99.9 2 2 3 12 26 25 27 23 120
100 - 199.9 4 3 4 22 69 76 61 50 289
200 - 299.9 4 5 7 23 89 88 77 61 354
300 - 499.9 11 12 13 38 132 135 124 108 573
500 - 999.9 32 31 34 84 215 244 240 232 1112
1,000 - 2,499.9 45 48 57 113 169 181 190 194 997
2,500 - 4,999.9 24 25 28 38 52 61 72 72 372
5,000 + 18 20 24 30 36 41 47 50 266
All 140 146 170 360 789 852 840 791 4083
28

Table 3 Scale economies for European savings banks, 1989-1996
1989 1990 1991 1992 1993 1994 1995 1996 All
Austria 0.931* 0.929* 0.932* 0.931* 0.921* 0.932* 0.918* 0.912* 0.922*
Belgium 0.882* 0.882* 0.881* 0.914* 0.944* 0.946* 0.939* 0.923* 0.933*
Denmark 0.980* 0.990* 0.981* 1.029* 1.030* 1.030* 1.034* 1.033* 1.028*
Finland -- -- -- -- 0.915* 0.908* 0.904* 0.890* 0.904*
France -- -- 0.885* 0.896* 0.886* 0.881* 0.872* 0.871* 0.879*
Germany 0.909* 0.907* 0.907* 0.926* 0.931* 0.929* 0.927* 0.924* 0.926*
Italy 0.902* 0.901* 0.902* 0.908* 0.912* 0.913* 0.908* 0.904* 0.907*
Luxembourg 0.842* 0.828* 0.827* 0.906* 0.977* 0.969* 0.928* 0.924* 0.929*
Netherlands -- -- -- 0.924* 0.905* 0.999* 0.990* 0.997* 0.979*
Portugal 0.943* 0.953* 1.002 0.922* 0.913* 0.883* 0.910* 0.907* 0.923*
Spain 0.915* 0.913* 0.913* 0.912* 0.906* 0.902* 0.900* 0.899* 0.907*
Sweden -- -- 0.878* 0.891* 0.881* 0.875* 0.895* 0.878* 0.883*
All 0.911* 0.909* 0.910* 0.924* 0.930* 0.929* 0.927* 0.924* 0.925*
Assets Size (ECU million)
1 - 99.9 100 - 199.9 200 - 299.9 300 – 499.9 500 - 999.9 1,000 - 2,499.9 2,500 - 4,999.9 5,000 + All
Austria -- 0.994 0.992 0.929* 0.890* 0.949* 0.913* 0.830* 0.922*
Belgium 1.096* -- 0.939* 0.922* 0.880* 0.883* 0.869* 0.848* 0.933*
Denmark 1.082* 1.020* 0.972* 0.961* 0.903* 0.891* -- -- 1.028*
Finland -- -- -- -- -- 0.904* -- -- 0.904*
France -- -- 0.956* -- 0.929* 0.909* 0.876* 0.846* 0.879*
Germany 1.079* 1.027* 0.985* 0.943* 0.905* 0.898* 0.899* 0.886* 0.926*
Italy 1.103* 0.997* 0.963* 0.934* 0.901* 0.893* 0.897* 0.868* 0.907*
Luxembourg 1.079* 1.001 0.978* 0.961* -- -- -- 0.818* 0.929*
Netherlands -- 1.088* -- -- 0.937* -- -- 0.919* 0.979*
Portugal 1.089* 1.001 -- 0.959* 0.938* 0.936* -- 0.842* 0.923*
Spain 1.097* 1.035* 1.004 0.961* 0.910* 0.895* 0.890* 0.861* 0.907*
Sweden -- -- -- -- -- -- -- 0.883* 0.883*
All 1.086* 1.026* 0.981* 0.943* 0.905* 0.898* 0.895* 0.866* 0.925*
Assets Size (ECU m) 1989 1990 1991 1992 1993 1994 1995 1996 All
1 – 99.9 1.104* 1.103* 1.096* 1.085* 1.086* 1.087* 1.083* 1.084* 1.086*
100 – 199.9 1.024* 1.028* 1.026* 1.031* 1.021* 1.023* 1.031* 1.032* 1.026*
200 – 299.9 0.977* 0.987 0.993 0.992 0.979* 0.976* 0.981* 0.986 0.981*
300 – 499.9 0.960* 0.954* 0.951* 0.953* 0.939* 0.938* 0.942* 0.945* 0.943*
500 – 999.9 0.907* 0.904* 0.907* 0.911* 0.904* 0.903* 0.904* 0.905* 0.905*
1,000 – 2,499.9 0.901* 0.900* 0.898* 0.897* 0.896* 0.899* 0.898* 0.898* 0.898*
2,500 – 4,999.9 0.893* 0.895* 0.895* 0.898* 0.893* 0.894* 0.896* 0.894* 0.895*
5,000 + 0.872* 0.872* 0.873* 0.870* 0.865* 0.862* 0.863* 0.862* 0.866*
All 0.911* 0.909* 0.910* 0.924* 0.930* 0.929* 0.927* 0.924* 0.925*
Note: *denotes statistically significantly different from 1.0 at the 5% level
29

Table 4 Mean inefficiency levels for European savings banks, 1989-1996
1989 1990 1991 1992 1993 1994 1995 1996 All
Austria 0.212 0.207 0.228 0.229 0.201 0.200 0.193 0.190 0.202
Belgium 0.402 0.391 0.440 0.274 0.256 0.249 0.256 0.250 0.262
Denmark 0.199 0.222 0.253 0.216 0.205 0.220 0.215 0.227 0.219
Finland -- -- -- -- 0.292 0.337 0.329 0.318 0.319
France -- -- 0.275 0.221 0.225 0.234 0.234 0.233 0.231
Germany 0.216 0.214 0.215 0.216 0.217 0.209 0.212 0.212 0.213
Italy 0.222 0.226 0.221 0.221 0.220 0.231 0.232 0.222 0.225
Luxembourg 0.209 0.219 0.230 0.259 0.239 0.244 0.316 0.272 0.256
Netherlands -- -- -- 0.212 0.223 0.253 0.269 0.268 0.255
Portugal 0.349 0.372 0.255 0.303 0.311 0.251 0.285 0.275 0.292
Spain 0.230 0.231 0.240 0.235 0.232 0.230 0.228 0.232 0.232
Sweden -- -- 0.171 0.176 0.165 0.178 0.179 0.165 0.172
All 0.223 0.225 0.227 0.221 0.219 0.214 0.216 0.216 0.218
Assets Size (ECU million)
1 - 99.9 100 - 199.9 200 - 299.9 300 – 499.9 500 – 999.9 1,000 - 2,499.9 2,500 - 4,999.9 5,000 + All
Austria -- 0.200 0.204 0.196 0.166 0.226 0.183 0.204 0.202
Belgium 0.200 -- 0.230 0.219 0.264 0.250 0.389 0.256 0.262
Denmark 0.209 0.223 0.233 0.231 0.225 0.208 -- -- 0.219
Finland -- -- -- -- -- 0.319 -- -- 0.319
France -- -- 0.221 -- 0.228 0.224 0.233 0.236 0.231
Germany 0.195 0.207 0.210 0.219 0.215 0.211 0.208 0.210 0.213
Italy 0.211 0.212 0.220 0.229 0.231 0.219 0.219 0.222 0.225
Luxembourg 0.169 0.248 0.477 0.394 -- -- -- 0.240 0.256
Netherlands -- 0.297 -- -- 0.231 -- -- 0.254 0.255
Portugal 0.169 0.203 -- 0.251 0.284 0.347 -- 0.257 0.292
Spain 0.230 0.232 0.240 0.221 0.218 0.235 0.251 0.226 0.232
Sweden -- -- -- -- -- -- -- 0.172 0.172
All 0.208 0.212 0.215 0.220 0.218 0.218 0.222 0.221 0.218
Assets Size (ECU m) 1989 1990 1991 1992 1993 1994 1995 1996 All
1 - 99.9 0.210 0.233 0.199 0.194 0.203 0.210 0.211 0.214 0.208
100 - 199.9 0.215 0.215 0.226 0.212 0.213 0.212 0.208 0.213 0.212
200 - 299.9 0.214 0.215 0.248 0.223 0.217 0.211 0.217 0.209 0.215
300 - 499.9 0.228 0.236 0.229 0.223 0.223 0.214 0.220 0.219 0.220
500 - 999.9 0.217 0.221 0.220 0.220 0.218 0.215 0.218 0.218 0.218
1,000 - 2,499.9 0.227 0.226 0.230 0.223 0.222 0.213 0.214 0.215 0.218
2,500 - 4,999.9 0.231 0.229 0.228 0.224 0.220 0.225 0.215 0.217 0.222
5,000 + 0.218 0.217 0.223 0.231 0.221 0.215 0.224 0.220 0.221
All 0.223 0.225 0.227 0.221 0.219 0.214 0.216 0.216 0.218
30

Table 5 Logistic parameter estimates: determinants of savings banks inefficiency
Variable Coefficient Standard Error T-ratio
Constant 0.2841 0.00340 83.463
TASSET 0.0012 0.00042 2.774
CRATIO -0.0307 0.01406 -2.185
ROAA -0.3267 0.11105 -2.942
NL/TASSET -0.0936 0.00374 -24.999
OBS/TASSET -0.0052 0.00479 -1.089
LA/C&SF 0.0507 0.00404 12.570
Number of observations 4088.0
Log likelihood function 8338.5
31

APPENDIX
Table A1 Maximum likelihood parameter estimates for European savings banks using FF stochastic
cost frontier
Variable
Para
mete
r
Coefficie
nt
Standard
Error
T-
Value
Variable
Para
mete
r
Coefficie
nt
Standard
Error
T-
Value
Constant α0 1.66480 0.05306 31.373 cos (z1) a1 0.01275 0.00439 2.901
lnQ1 α1 0.51787 0.01682 30.783 sin (z1) b1 -0.01828 0.00367 -4.987
lnQ2 α2 0.49463 0.01522 32.497 cos (z2) a2 0.00703 0.00431 1.632
lnQ3 α3 0.01489 0.01039 1.433 sin (z2) b2 0.02513 0.00391 6.424
lnP1 β1 0.36888 0.02361 15.622 cos (z3) a3 -0.01959 0.00498 -3.935
lnP2 β2 0.58789 0.02225 26.417 sin (z3) b3 0.01207 0.00419 2.884
lnQ1 lnQ1 /2 δ11 -0.01899 0.00347 -5.480 cos (z1+z1) a11 0.00794 0.00358 2.219
lnQ1 lnQ2 δ12 -0.01995 0.00217 -9.213 sin (z1+z1) b11 -0.01347 0.00342 -3.942
lnQ1 lnQ3 δ13 0.00201 0.00193 1.040 cos (z1+z2) a12 -0.02179 0.00504 -4.327
lnQ2 lnQ2 /2 δ22 -0.01991 0.00311 -6.407 sin (z +z2) b12 0.00598 0.00418 1.429
lnQ2 lnQ3 δ23 -0.01570 0.00161 -9.726 cos (z1+z3) a13 0.01757 0.00385 4.563
lnQ3 lnQ3 /2 δ33 0.00573 0.00168 3.407 sin (z1+z3) b13 0.02723 0.00429 6.345
lnP1 lnP1 /2 γ11 0.01158 0.00539 2.150 cos (z2+z2) a22 0.00272 0.00351 0.775
lnP1 lnP2 γ12 -0.01017 0.00372 -2.736 sin (z2+z2) b22 0.00235 0.00338 0.696
lnP2 lnP2 /2 γ22 0.00493 0.00129 3.822 cos (z2+z3) a23 -0.01345 0.00429 -3.134
lnP1 lnQ1 ρ11 0.04127 0.00394 10.476 sin (z2+z3) b23 -0.03347 0.00410 -8.163
lnP1 lnQ2 ρ12 -0.02049 0.00398 -5.150 cos (z3+z3) a33 0.00440 0.00264 1.666
lnP1 lnQ3 ρ13 -0.01913 0.00279 -6.850 sin (z3+z3) b33 0.00264 0.00322 0.820
lnP2 lnQ1 ρ21 -0.03700 0.00359 -10.292 cos (z+z1+z2) a112 0.00504 0.00316 1.595
lnP2 lnQ2 ρ22 0.04554 0.00336 13.539 sin (z1+z1+z2) b112 -0.00027 0.00350 -0.077
lnP2 lnQ3 ρ23 0.01519 0.00302 5.023 cos (z1+z1+z3) a113 -0.00830 0.00376 -2.207
T τ -0.00419 0.00554 -0.756 sin (z1+z1+z3) b113 0.01632 0.00369 4.426
T*T τ11 -0.00156 0.00028 -5.503 cos (z1+z2+z2) a122 -0.00876 0.00345 -2.543
lnQ1T ψ1τ -0.00247 0.00097 -2.545 sin (z1+z2+z2) b122 -0.00731 0.00342 -2.136
lnQ2T ψ2τ 0.00232 0.00083 2.790 cos (z1+z2+z3) a123 0.01670 0.00456 3.663
lnQ3T ψ3τ -0.00062 0.00074 -0.838 sin (z1+z2+z3) b123 -0.00449 0.00479 -0.937
lnP1T θ1τ 0.01230 0.00124 9.881 cos (z1+z3+z3) a133 -0.00881 0.00344 -2.559
lnP2T θ2τ -0.01514 0.00131 -11.555 sin (z1+z3+z3) b133 0.00232 0.00359 0.647
lnP3 β3 0.04323 0.01224 3.532 cos (z2+z2+z3) a223 0.00645 0.00348 1.851
lnP1lnP3 γ13 -0.00140 0.00187 -0.749 sin (z2+z2+z3) b223 0.00246 0.00402 0.611
lnP2lnP3 γ23 0.00524 0.00212 2.472 cos (z2+z3+z3) a233 -0.01323 0.00330 -4.006
lnP3lnP3 γ33 -0.00384 0.00254 -1.512 sin (z2+z3+z3) b233 -0.00095 0.00389 -0.244
lnP3lnQ1 ρ31 -0.00427 0.00356 -1.199 σ²u/ 2.94580 0.10190 28.909
σ²v
lnP3lnQ2 ρ32 -0.02506 0.00668 -3.751 σ²v 0.11419 0.00089 127.80
lnP3lnQ3 ρ33 0.00394 0.00345 1.142
lnP3T θ3τ 0.00284 0.00120 2.367
32