Analysing the Determinants of Bank Efficiency: The Case of ...
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Analysing the Determinants of Bank Efficiency: The Case of Italian Banks
Claudia Girardone, Philip Molyneux*, Edward P.M. GardenerSchool of Accounting, Banking and Economics, University of Wales, Bangor, Gwynedd, LL57 2DG, UK.
Abstract
This paper investigates the main determinants of Italian banks’ cost efficiency over the period 1993-96,
by employing a Fourier-flexible stochastic cost frontier in order to measure X-efficiencies and economies of
scale. Quality and riskiness of bank outputs are explicitly accounted for in the cost function and their impact on
cost efficiency levels are evaluated. The results show that mean X-inefficiencies range between 13 and 15 per
cent of total costs and they tend to decrease over time for all bank sizes. Economies of scale appear present and
significant, being especially high for popular and credit co-operative banks. Moreover, the inclusion of risk and
output quality variables in the cost function seems to reduce the significance of the scale economy estimates.
Following Spong et al. (1995) we undertake a profitability test that allows for the identification of banks that are
both cost and profit efficient. The results suggest that the most efficient and profitable institutions are more able
to control all aspects of costs, especially labour costs. Finally, we pool the data to carry out a logistic regression
model in order to examine bank- and market-specific factors that influence Italian banks’ inefficiency.
Confirming Mester (1993 and 1996), inefficiencies appear to be inversely correlated with capital strength and
positively related to the level of non-performing loans in the balance sheet. The analysis also shows that there is
no clear relationship between assets size and bank efficiency. Finally, it is possible to infer that quoted banks
seem to be on average more efficient than their non-quoted counterparts.
JEL classification: G21, D2.
Keywords: Italian banks; Cost function; Inefficiencies; Economies of scale.
* Corresponding author: School of Accounting, Banking and Economics, University of Wales Bangor, Gwynedd, Bangor
LL57 2DG (UK). E-mail: [email protected], Fax + 44 1248 364760, Tel. + 44 1248 382170.
Acknowledgements – Thanks to Professor G.B. Pittaluga from the Università degli Studi di Genova for his precious
comments and for providing the Bilbank database. We also wish to thank M. Brown, B. Casu and J. Williams from the
University of Wales, Bangor, for their valuable suggestions.
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1. Introduction
Banking has experienced dramatic changes over the last decade or so. Deregulation,
financial innovation and automation have been major forces impacting on the
performance of the banking sector. In such a context, banks have become
increasingly concerned about controlling and analysing their costs and revenues, as
well as measuring the risks taken to produce acceptable returns.
In line with these developments, an extensive literature has evolved examining
financial firm efficiency issues (see, for a comprehensive survey, Berger and
Humphrey, 1997), and different methodological approaches have been employed to
investigate financial firm efficiency (i.e. parametric and non-parametric techniques).
However, only a handful of studies have so far investigated how risk and output
quality factors influence bank efficiency levels (for example, Mester, 1996; Berger
and Mester, 1997; Altunbas, Liu, Molyneux and Seth, 1999).
This paper has two main objectives. First it aims to extend the established
literature by examining the determinants of Italian banks’ cost efficiency over the
period 1993-96, by employing a Fourier-flexible stochastic cost frontier to evaluate
X-efficiency and scale economies. Quality and riskiness of bank output are explicitly
accounted for in the cost function and their impact on efficiency levels are evaluated
and discussed. Secondly, the paper attempts to identify the main characteristics of
efficient banks. Following the approach suggested by Spong et al. (1995) our sample
of banks is subject to a profitability test that allows us to identify institutions that are
both cost and profit efficient. Following Mester (1993 and 1996) we also use a
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logistic regression model to examine bank- and market- specific factors which
influence banks’ inefficiency levels.
The paper is set out as follows. Section 2 provides a brief literature review on
recent developments in financial firm efficiency analysis placing particular emphasis
on various Italian studies. Section 3 outlines the methodology and section 4 reports
the results. Section 5 is the conclusion.
2. New views on bank efficiency
Over the last decade parametric studies of Italian bank cost efficiency (for example,
Baldini and Landi, 1990; Conigliani et al., 1991; Parigi et al., 1992; European
Commission, 1997; Resti, 1997; Inzerillo et al., 1999) have found evidence of
economies of scale across a wide range of bank sizes, and average X-inefficiency
levels are usually in line with those found in the international literature – typically
ranging between 15 and 20 percent. However, none of these studies have included
the level of capital and/or loan losses as arguments in the cost function to control for
risk of default and/or output quality, respectively. A relatively new approach (for
example, Hughes and Mester, 1993; McAllister and McManus, 1993; Clark, 1996;
Mester, 1996; Berger and Mester, 1997; Altunbas, Liu, Molyneux and Seth, 1999)
points to the importance of including measures of output quality and default risk on
the grounds that unless they are accounted for in the cost function, bank levels of X-
efficiencies and economies of scale may be miscalculated. In the case of Italian
banking the inclusion of these two variables could be crucial because recently credit
institutions have suffered from a dramatic increase in their level of non-performing
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loans (NPLs). For example, Italian banks based in the south of the country recorded
NPLs (as a percentage of total loans) of 24.2 per cent in 1996 and 21.8 percent in
1997, ratios that were more than twice the national average and high by any standard
(Bank of Italy, 1998). The achievement of more competitive conditions in the Italian
banking market during the 1990s has also brought about situations of crisis for
various banking firms. During the 1993-96 period the main banks in the south of
Italy experienced substantial reductions in their net interest income and were no
longer able to cover their relatively high operating expenses and loan losses. As a
consequence, these banks either reduced their size or were acquired by larger
(healthier) banks.
Another important recent issue in bank efficiency analysis concerns the choice of
the functional form for the cost function. Studies by leading researchers in the field
(see, for example, Mitchell and Onvural, 1996; Berger and DeYoung, 1997; Berger
et al., 1997; Berger and Mester, 1997; Altunbas, Liu, Molyneux and Seth, 1999) have
abandoned the typical U-shaped translog for the sinusoidal Fourier-flexible, which
combines the stability of the translog specification near the average of the sample
data with the flexibility of the Fourier specification for observations far from the
averages. The Fourier functional form is preferred to the translog because it better
approximates the underlying cost function across a broad range of outputs.
This paper advances the literature on bank efficiency by investigating the effects
of the inclusion of risk and output quality factors in the cost function. Moreover, we
adopt a stochastic Fourier-flexible cost function to calculate X-efficiency levels and
economies of scale for a sample of Italian banks between 1993 and 1996. The paper
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also uses a profitability test as suggested by Spong et al. (1995) to investigate the
characteristics of the most and least efficient banks in the Italian system.
3. Methodology
3.1. Input and Output Definition and Data Sample
Choosing the appropriate definition of bank output is an important issue for research
into banks’ cost efficiency. While the multiproduct nature of the banking firm is
widely recognised, there is still no agreement as to the explicit definition and
measurement of banks’ inputs and outputs. Generally, each definition of input and
output carries with it a particular set of banking concepts, which influence and limit
the analysis of the production characteristics of the industry.
The approach to output definition used in this study is a variation of the
intermediation approach, which was originally developed by Sealey and Lindley
(1977) and posits that total loans and securities are outputs, whereas deposits along
with labour and capital are inputs to the production process of banking firms. (Table
A.1 in the Appendix provides descriptive statistics on the outputs and input prices
included in our model).
The data used to construct the estimates for the cost function parameters are
derived from Bilbank, an Italian database of the Associazione Banche Private
Italiane. This database provides annual income and balance sheet data for credit
institutions belonging to different bank categories. The sample comprises an
unbalanced panel of 1,958 bank observations distributed in the following way: 545
banks in 1993, 523 in 1994, 466 in 1995 and 424 in 1996. The sample excludes: i)
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banks that are subsidiaries of foreign banks; ii) the central institutions for each
category of banks; and iii) special credit institutions (medium- and long- term
banks).1
Our sample constitutes nearly 50 per cent of the Italian banking market in
terms of number of banks. (As displayed in Table A.2, the difference in banks’ size
across the five classes is relatively high. The groups of very big banks have
approximately 400 times the average assets of the very small banks and 40 times the
average assets of small banks).2 We also investigate efficiency of banks across
geographical regions and therefore identify those institutions located in four major
regions: north-west, north-east, centre, south and islands.3
3.2. Stochastic Cost Frontier Model, X-Efficiencies and Economies of Scale
Researchers investigating bank cost efficiency postulate a relationship between costs,
input prices and output quantity. This relationship is based on the duality concept
between production and cost functions. The production function ( )XQQ =
summarises the technology of a firm, that is the existing relationship between inputs,
1 It should also be noted that in the empirical analysis most of the estimation is carried out using the FRONTIER
4.1 and TSP 4.0 packages. Since FRONTIER 4.1 does not tolerate missing values, banks with incomplete
accounting data could not be included in the data sample (Coelli, 1996 and Coelli et al., 1998).
2 The Bank of Italy categorises banks according to five size groups: very big; big; medium; small and very small.
3 These different regions are defined as follows: 1) North-West: Liguria, Lombardia, Piemonte, Valle d’Aosta; 2)
North-East: Emilia-Romagna, Friuli-Venezia Giulia, Trentino Alto Adige, Veneto; 3) Centre: Lazio, Marche,
Toscana, Umbria; 4) South and Islands: Abruzzo, Basilicata, Calabria, Campania, Molise, Puglia, Sardegna,
Sicilia. It should be noted that a bank was assigned to a given region if, over the period, it had its head office in
that area.
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X, and outputs, Q. The cost function ( )PQTCTC ,= shows the relationship between
total production costs, TC, and the prices of variable inputs. The duality condition
between the production and the cost function ensures that they contain the same
information about production possibilities and that there is a unique correspondence
between both functions. Moreover, observable production plans and cost levels
usually do not follow from perfectly rational and efficient decisions. On the contrary,
such factors as errors, lags between the choice of the plan and its implementation,
inertia in human behaviour and distorted communications and uncertainty are
amongst the factors that might cause X-inefficiencies to drive real data away from
the optimum (Resti, 1997).
This study employs the stochastic cost frontier approach to generate estimates of
X-efficiencies for each bank over the years 1993-96 along the lines first suggested by
Aigner et al. (1977) and Meeusen and van den Broeck (1977). For the i-th firm, the
single equation cost function model is represented by ( ) ijii TCTC ε+= BPQ ;,lnln ,
where TCi is the observed total cost of production for bank i, Qi is the vector of
banking output for bank i, Pj is the vector of input prices for bank j and B is a vector
of parameters. ( )BPQ ;,ln jiTC is the predicted log cost function of a cost minimising
bank operating at ( )BPQ ,, ji . Finally εi is a two-components error term that for the i-
th firm can be written as follows:
iii uv +=ε (1)
where vi is a two-sided error term representing statistical noise which is assumed to
be independently and identically distributed; and ui is a non-negative (or one-sided)
random variable representing inefficiency and assumed to be distributed
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independently of the vi. It is also assumed that the vi are normally distributed with
mean zero and variance σ v2 , and the ui are the absolute values of a variable that is
normally distributed with mean µ and variance 2uσ .
In the present study banks’ data over the period 1993-96 are organised in a panel.
Specifically, we employ the Battese and Coelli (1992) model of a stochastic frontier
function for panel data with firm effects which are assumed to be distributed as half-
normal random variables (that is, with µ=0)4 and are also permitted to vary
systematically with time. Therefore, it is possible to express this model as
itititit uvxTC ++= β , [with i = (1,2, ..., N) and t = (1,2, ..., T)], where TCit is (the
logarithm) of the total costs for the i-th firm in the t-th time period; xit is a k×1 vector
of (transformations of the) input and output quantities of the i-th firm in the t-th time
period; β is the vector of unknown parameters; and the vit and uit are defined as
above, with uit = {exp[η(t-T)]}, where η is an unknown scalar parameter to be
estimated that represents the hypothesis about the evolution or steadiness of
individual inefficiencies over the period under study.
Moreover, the parameterisation of Battese and Corra (1977) is employed, who
replaced σ v2 and σ u
2 with σ σ σ2 2 2= +v u and ( )γ σ σ σ= +u v u2 2 2 .5 As recently
emphasised by Coelli et al. (1998) the γ-parameterisation has an advantage in
4 There are many variations on this assumption in the literature (for details, see Greene, 1993 and Coelli et al.,
1998).
5 In the literature, the likelihood function has often been expressed in terms of the two variance parameters
222uv σσσ += and 22
vu σσλ ≡ (Aigner et al., 1977; Jondrow et al., 1982; Coelli, 1996). See also Battese and
Coelli (1993) and Coelli et al. (1998) for the log-likelihood function of the model used here given these
distributional assumptions.
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seeking to obtain the maximum likelihood estimates because the parameter space for
γ can be searched for a suitable starting value for the iterative maximisation
algorithm involved. In particular, a value of γ of zero indicates that the deviations
from the frontier are due entirely to noise, while a value of one would indicate that
all deviations are due to inefficiency.
As concerns the choice of the functional form for the cost function, this study
employs a Fourier-flexible form because it is a global approximation that has proved
to dominate the commonly specified translog form (see, for example, McAllister and
McManus, 1993; Mitchell and Onvural, 1996; Berger et al., 1997; Altunbas, Liu,
Molyneux and Seth, 1999). The resulting mixed cost function can be written as:
[ ] ( ) ( )[ ]
( ) ( )[ ] ii ij
ikjk
kjiijkjiij
i jjiijjiij
iiiii
ksjj
jsii
is
jj
jkii
iki j
jiij
sskki i j
jiijj
jiij
skj
jjii
i
zzzzzz
zzzzzz
SKSPSQ
KPKQPQ
SSKKPPQQ
skPQTC
εθλ
θλθλ
τβα
βαρ
ττγδ
ττβαα
+++++++
+++++++
++++
++++
+
+++
+++++=
∑∑∑
∑∑∑
∑∑
∑∑∑∑
∑ ∑∑∑
∑∑
= ≥≠≥
= ==
==
=== =
= = ==
==
2
1
2 2
2
1
2
1
4
1
3
1
2
1
3
1
2
1
2
1
3
1
2
1
3
1
3
1
2
1
3
1
2
10
sincos
sincossincos
lnlnlnlnlnln
lnlnlnlnlnln
lnlnlnlnlnlnlnln
21lnlnlnlnln
(2)
where TC is a measure of the normalised costs of production, comprising operating
costs and financial costs (interest paid on deposits); 1Q and 2Q are output quantities,
that is total loans and total securities, respectively; 1P is the normalised price of
labour; 2P is the normalised price of deposits; K is the level of financial capital; S is
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the ratio of NPLs to total loans; α β δ γ, , , ,ρ , λ, θ ,τ are parameters to be estimated;
and εi is the two-component error term as defined in (1). Moreover, the iz are
adjusted values of the natural log of output iQln so that they span the interval
[ ]ππ 29,.21. ∗∗ . In particular, the formula for iz used here is ( iQa ln2. ∗+∗− µµπ ),
where [ ]ba, is the range of iQln and ( ) ( )ab−∗−∗≡ ππµ 21.29. .
The Fourier-flexible form is a global approximation because the terms such as
izcos , izsin , iz2cos , iz2sin are mutually orthogonal over the [ ]π2,0 interval, so
that each additional term can make the approximating function closer to the true path
wherever it is most needed. As observed by Gallant (1981), by restricting the iz to
span the interval [ ]ππ 29,.21. ∗∗ , the approximation problems arising near the
endpoints are reduced.
In addition, standard symmetry has to be imposed on the translog portion of the
function: jiij δδ = and jiij γγ = , where )2,1( =i and )3,2,1( =j , and the following
linear restrictions on (2) are necessary and sufficient for linear homogeneity in factor
prices: ∑=
=3
1
1j
jβ ; ∑=
=3
1
0i
ijγ ; ∑=
=3
1
0j
ijρ ; ∑=
=3
1
0i
jkβ ; ∑=
=3
1
0i
jsβ . In accordance with
the assumed constraint of linear homogeneity in prices, TC, P1 and P2 are normalised
by the price of capital, 3P . It is also important to mention that consideration of input
share equations embodying Shephard’s Lemma restrictions is excluded in order to
allow for the possibility of allocative inefficiency (see, for example, Berger and
Mester, 1997). The Fourier terms are included only for the outputs, leaving the input
price effects to be described solely by the translog term (see, for example, Berger et
al., 1997 and Altunbas, Liu, Molyneux and Seth, 1999). The Fourier terms for the
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input prices are also excluded in order to conserve the limited number of Fourier
terms for the output quantities used to measure economies of scale. The input prices
also show very little variation, thereby providing greater justification for our
methodological approach.
In this research the parameters of the stochastic frontier cost function, defined by
eq. (2), are estimated using the Maximum-Likelihood (ML) approach. For instance,
the ML estimates of β and γ are obtained by finding the minimum of the log-
likelihood function as specified in Coelli et. al (1998). The nature of this log-
likelihood function given the distributional assumptions on v and u can also be found
in Battese and Coelli (1992).
Once the model is estimated, bank level measures of X-efficiencies are calculated
using the residuals and are usually given by the mean of the conditional distribution
of ui given iε . For the half-normal stochastic model the E(ui|εi) is considered as a
consistent estimator for individual X-efficiencies (Coelli et al., 1998). The resulting
cost efficiency ratio may be thought of as the proportion of costs or resource that are
used efficiently. For example, a bank with a cost efficiency of 0.80 is 80 per cent
efficient or equivalently wastes 20 per cent of its costs relative to a best practice firm
facing the same conditions.
A natural way to express the extent of scale economies is the proportional
increase in cost resulting from a small proportional increase in the level of output,
that is the elasticity of total cost with respect to output. The degree of economies of
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scale (SCALE) used here is given by ∑=
=m
i iQ
TCSCALE
1 ln
ln
∂∂
which represents the sum
of individual cost elasticities.6 This can be rewritten as:
( ) ( )
( ) ( )
( ) ( )∑∑∑
∑∑
∑∑∑
∑ ∑∑ ∑∑
= ≥≠≥
= =
===
= = = = =
++−+++
++−++
+−+++
+++=
2
1
2 2
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
3
1
cossin
cossin
cossinlnln
lnln
i ijikjk
kjiijkkjiijk
i jjiijjiij
iiiii
iis
iik
i i j i jjijjiji
zzzzzz
zzzz
zzSK
PQSCALE
θλ
θλ
θλαα
ρδα
(3)
where there are economies of scale if SCALE<1, constant returns to scale if
SCALE=1, and diseconomies of scale if SCALE>1. The degree of scale economies is
computed by using the mean values of output, input prices and risk and output
quality variables.
3.3. Profitability Test and Correlates with Inefficiency
Following Spong et al. (1995), we subject our cost efficiency measures derived from
the Fourier model to a profitability test. This is undertaken in order to identify banks
that are both cost – and profit – efficient. This approach is taken because the cost side
may provide inaccurate rankings of efficiency because a seemingly cost inefficient
bank might be offsetting higher expenses with higher revenues. Moreover, this test
6 Evanoff and Israilevich (1985) distinguish between scale elasticity and scale efficiency where the former is
measured as in equation (3) and the latter is measured as the change in output required to produce at minimum
efficient scale. Throughout this paper reference to economies and diseconomies of scale relates to scale
elasticities.
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provides an alternative to some of the consistency conditions recently suggested by
Bauer et al. (1997).
It follows that banks which do well on both cost efficiency and profitability tests
will comprise the “most efficient” bank category; banks that fare poorly on the two
tests are in the “least efficient” category. The two groups, comprising the most
efficient and least efficient banks were partitioned in the following way: 1) most
efficient group: banks that rank in the upper quartile of Italian banks on the cost
efficiency estimates and rank in the upper half in terms of ROA (return on assets),
and 2) least efficient group: banks that rank in the bottom quartile on the cost
efficiency estimates and rank in the bottom half in term of ROA. Subsequently, we
analyse the financial characteristics of efficient and inefficient banks by carrying out
a comparison between the major sources of income and expenses as well as several
other financial ratios for the year 1996.
Lastly, in order to investigate possible determinants of bank efficiency, firm-
specific measures of inefficiency derived exclusively from the model excluding risk
and output quality variables – that is, equation (2) without the variables K and S –,
are regressed on a set of independent variables relevant to the banking business. This
set of potential correlates with bank inefficiency is chosen in such a way that many
aspects of banking activities are considered: for instance, bank size, market
characteristics, geographic position, capital, performance and retail activities (see
also Mester, 1996; Berger and Mester, 1997; and Altunbas, Liu, Molyneux and Seth,
1999). A logistic functional form rather than a linear regression model is used
because the values of the inefficiency estimates, ( )iiuE εˆ , range between 0 and 1 (for
applications of this technique to the banking system, see Mester, 1993 and 1996).
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4. Results
4.1. Structural Tests
Structural tests are undertaken to see if the cost function that included the risk and
output quality variables differs significantly from the standard cost frontier
specification, the translog form, and the models including individual risk and quality
variables.
Table A.3 in the Appendix reports the likelihood ratio test statistics and shows
that the cost frontier including risk and quality variables provides the best fit to the
data. More specifically the cost function that includes the risk and quality variables
(RQCF) differs significantly from the standard model (CF) since the likelihood ratio
test rejects the hypothesis that the two models are not significantly different.
With particular regard to the choice of the functional form for the cost function,
the translog model is rejected at the 0.01 per cent level, thus supporting the choice of
the Fourier-flexible function. Similarly, the models excluding individual risk and
quality variables are all rejected against our model defined in (2) at the 0.01 per cent
level.
4.2. X-Efficiencies and Economies of Scale
Tables 1 and 2 report the average X-efficiency levels for banks grouped by size
classes, geographical areas (a bank is assigned to a given region if it has its head
office in that area) and bank types (the category “commercial banks” includes those
banks that are not savings, popular or credit co-operative banks). We distinguish
between different types of banks because mutual banks (savings and co-op banks)
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may have different managerial objectives compared with commercial banks and this
could be reflected in their cost efficiency. For instance, it could be the case that
mutual banks have objectives other than cost minimisation – such as serving the local
community and maximising returns to members.
Tables 1 & 2 here
Average inefficiency levels range between approximately 13 and 15 per cent.
Similar figures can be found in various recent studies of Italian banks (see, for
example, Allen and Rai, 1996; European Commission, 1997) and, although
differences are not large, the most efficient banks seem to be the big, medium and
very small banks. Moreover, X-inefficiency levels seem to decrease over time and
for all sizes of banks.
When the X-efficiency results are grouped according to banks operating in
different geographical areas, it appears that the lowest efficiency levels are generally
found for banks having their head office in the centre and south of the country, thus
confirming the apparent existence of significant disparities among geographical
regions. Finally, according to the different bank types, it is possible to observe that
on average the better performing banks seem to be the credit co-operatives together
with popular banks, possibly reflecting a greater homogeneity of the co-operative
banking sector. Altunbas, Evans and Molyneux (1999) found similar results for
German banks and they argue that mutual banks tend to have a lower cost of funds
than other bank types due, for example, to their (possible) local monopolies.
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Table 3 provides the pooled efficiency scores from the estimation of our model in
relation to each asset-based quartile in order to check whether size can effectively be
considered as a determinant of potential cost reductions. From the table it appears
that both the mean and the median of firm-specific X-efficiency estimates tend to
decrease from Quartile 1 to Quartile 4 [Quartile 1 (4) contains the smallest (largest)
firms]. This suggests that, on average, larger banks deviate more from their
respective cost-efficient frontier than do smaller banks. Relatively speaking, the
smallest banks appear to be less inefficient than their larger counterparts
Table 3 here
The same data (assets in logarithms) are reported in Figure 1. The scatter diagram
suggests that the dispersion of the efficiency scores is quite high, thus implying that
in many cases similar-sized banks have different efficiency levels and, supposedly,
different costs. From a general viewpoint, a slight inverse trend between total assets
and X-efficiencies seems to prevail.
Figure 1: Bank Size and Efficiency Scores
0.60
0.70
0.80
0.90
1.00
1 3 5 7 9 11 13TOTAL ASSETS (values in logs)
X-E
FF
.
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Table 4 reports economies of scale estimates for each year together with their
significance levels. The results seem to confirm that big and medium banks show
high and significant scale economies in the majority of cases, and very small banks
also appear to enjoy substantial economies. Very big banks do not appear to
experience potentially realisable scale economies in the years under study and mainly
exhibit constant returns to scale.
Table 4 here
Table 5 shows scale economy estimates according to different bank types and
geographic areas. The table reveals several interesting patterns: i) commercial banks
show high and significant economies of scale especially in the northern part of the
country; ii) savings banks appear on average the less likely to gain from potential
scale economies; and iii) popular and credit co-operative banks appear best able to
exploit cost reductions in terms of economies of scale.
Table 5 here
Finally, if we compare the results on the X-efficiencies (Table 1) and economies
of scale (Table 4) derived from the cost function including risk and output quality
factors (RQCF) with those obtained from the standard cost function (CF) we find that
X-efficiency results are similar. However, it does appear to be the case that the extent
of scale economies seems to be overstated if risk and quality factors are not included
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in the cost function specification. This result is broadly in accordance with the recent
findings of Berger and Mester (1997) and Altunbas, Liu, Molyneux and Seth (1999).
4.3. Profitability Test and Correlates with Inefficiency
So far our analysis has only focused on cost efficiency. Spong et al. (1995),
however, note that it is important to combine both cost efficiency estimates with a
profitability test so as to evaluate financial firm efficiency. This is because one needs
to evaluate banks’ ability to use resources effectively in producing products and
services (cost efficiency), and their skill at generating income from these services
(profitability). Following Spong et al. (1995) we partition our sample of banks into
two categories – the most and least efficient – in terms of their cost efficiency and
profits performance. The most (least) efficient banks are those that rank in the upper
(lower) quartile according to the cost efficiency estimates and in the upper (lower)
half in terms of return on assets. Table 6 shows the number of banks and their
efficiency and profitability characteristics according to the aforementioned
partitioning.
Table 6 here
For the four years under study, an average of 75 banks satisfy the selection criteria
for the most efficient group and 84 banks are classified in the least efficient group.
The mean bank in the least efficient group has a cost efficiency of only 0.77, which
indicates that the bank with the highest efficiency in the sample could have produced
the same amount of output as the least efficient bank at only 77 per cent of their cost.
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In contrast, the average cost efficiency level for the most efficient banks is
approximately 0.95, thus indicating less disparity with the “best” bank in the sample.
Moreover, as an average for the four years, the ROA for the most efficient banks is
equal to 1.66% compared with 0.09% for the poorest performers.
In order to analyse the financial characteristics of efficient and inefficient banks
Table 7 shows a comparison between the major sources of income and expenses as
well as several other financial ratios for these banks. The table reveals how efficient
and inefficient banks differ. The table also shows financial characteristics for the
sample “all banks” and also for a sub-sample of “large banks only”. This latter group
includes the following bank sizes: very big, big, medium and small (see Table A.2
for their assets size range). The choice of creating such a sub-sample is motivated by
the fact that the relatively large number of very small banks found in the least and
most efficient bank categories could bias our interpretation of the results.
Table 7 here
On the earnings side, the advantages held by the most efficient banks seems to
relate to their income generating capacity and, as expected, expenses control.
Focusing on the sample “all banks” the most efficient group has, for instance, an
advantage over inefficient banks in terms of higher interest received on assets. On
the other hand, the most inefficient banks have relatively high non-interest revenues
compared with the most efficient banks, thus suggesting that there might be some
differences in the way the two groups generate income. However, these results
20
change if the very small banks are excluded from the sample, which shows a greater
importance of non-interest income for the most efficient group.
As concerns the expense side, the most efficient and least efficient banks show
similar interest expenses. This means that the most efficient banks do not have
important advantages in funding costs, and therefore they are achieving their
performance by other means, other factors being equal. Furthermore, it seems
apparent that efficient banks are more effective in controlling operating costs, and
particularly staff expenses.
With regard to their balance sheet structures, in 1996 the most efficient banks hold
more securities and have higher levels of equity than their inefficient counterparts,
thus providing a high level of protection to their customers. Moreover, the most
efficient banks appear to have better asset quality, thereby implying that they are
assigning more attention and resources to loan origination, monitoring and other
credit judgement activities.
Finally, in order to investigate the possible determinants of bank efficiency, firm-
specific X-inefficiencies are regressed on a set of independent variables relevant to
the banking business. As stressed by Mester (1996), the findings are intended mainly
to indicate where banks might look for clues toward increasing their efficiency. As
shown in Table 8 the estimates indicate that different variables significantly correlate
with inefficiencies in the Italian banking sector. Again our sample banks are divided
into large banks (very big, big, medium and small banks), and very small banks.
Table 8 here
21
In accordance with Mester’s findings (1993 and 1996), inefficiencies are always
inversely correlated with financial capital. On the one hand, this is quite predictable
since banks with low inefficiency will tend to have more profits as they will be able
(holding dividends constant) to retain more earnings as capital. However, this result
should not be interpreted as saying that if a bank increases its capital/assets ratio then
its inefficiency will decrease. As Mester (1996) points out, this could also be
explained as an indication that higher capital ratios may prevent moral hazard both
for the bank and its managers. Moreover, inefficiencies are usually inversely
correlated with bank performance variables, although this relationship is
insignificantly different from zero.
With regard to the coefficient for the level of NPLs, it is always positively related
to bank inefficiency. In fact, higher efficiency is expected to be correlated with better
credit risk evaluation (see also Mester, 1993; Berger and DeYoung, 1997; Altunbas,
Liu, Molyneux and Seth, 1999). Over the period 1993-96, inefficient banks also
tended to have a higher intensity of retail banking business, a higher number of
branches than efficient banks, and a higher interest margin to assets ratio. These
factors appear to be important in determining variations in efficiency among size
classes.
The results concerning the relationship between total assets size and bank
efficiency are mixed. The coefficient is not significantly different from zero for both
the ‘all’ and ‘large bank’ categories. These findings show that there is no statistical
evidence that larger banks are more or less X-efficient than their smaller
counterparts. In fact, from the results it is possible to see that an inverse relationship
between assets size and inefficiency appears only to hold within a specific bank size
22
group (i.e. very small banks). The results also indicate that quoted banks are, on
average, more efficient than their non-quoted counterparts. Finally, the significance
and negative sign of the dummy variable for private banks suggests that, at least
large private banks tend to have lower levels of inefficiency.
5. Conclusions
During the 1990s the Italian banking system has experienced a decline in
profitability brought about by the fall in interest margins and persistently high levels
of staffing costs. In addition, adverse macroeconomic conditions have lead to a
substantial increase in non-performing loans especially for banks located in specific
geographical areas of the country.
The response of the banking system to these pressures has been to undertake a
substantial consolidation movement resulting in an increase in the number of banking
groups and promoting the privatisation process. Evidence on efficiency and
profitability gains following M&A activities in Italy are mixed (see for example
Resti, 1998; Focarelli et al., 1999). As to the privatisation process, by the end of
1993 over 90 per cent of those banks previously acting as public foundations had
become joint-stock companies. Despite this only some 30 banks are publicly listed
and more than 50 per cent of the banking system is still in public hands (Resti, 1998).
The aim of this paper was to provide an empirical analysis of the cost efficiency
of the Italian banking sector over the period 1993-96 taking into account the risks
associated with banks’ operations. We found that mean X-inefficiency levels range
between 13 and 15 per cent of their total costs and they tend to decrease over time
23
and for all sizes of banks. Similarly, economies of scale appear present and
significant in the Italian banking system when considered as a whole. These are quite
important results if we consider that during 1993-96 the process of consolidation and
restructuring of the system has aimed at gradually increasing banks’ size.
The most cost efficient banks, both in terms of X-efficiency and economies of
scale, are big and medium sized banks generally located in the northern part of the
country. Furthermore, the results for credit co-operative banks confirm other studies
that economies of scale can be particularly high at a local level and for very small
banks because of possible local monopolies.
We also compare the results on X-efficiencies and economies of scale derived
from the cost function including risk and output quality factor and the standard cost
function. In line with recent findings by Berger and Mester (1997) and Altunbas, Liu,
Molyneux and Seth (1999), the X-efficiency estimates are similar across the two
different cost function specifications. In contrast, the level and significance of scale
economy estimates appears lower as a result of the inclusion of risk and output
quality factors in the cost function.
Following the profitability test as suggested by Spong et al. (1995), the main
differences between the “most efficient” and “least efficient” bank seem to be mainly
related to staff expenses. In the context of important technological improvements in
banks’ productive processes, this suggests an urgent need for greater labour market
flexibility and the consequent substitution of labour for capital. Moreover, inefficient
banks always appear to have lower levels of equity/assets and higher levels of non-
performing loans.
24
Finally, we pooled the data to carry out a logistic regression model in order to
examine bank- and market-specific factors that influence banks’ efficiency.
Confirming Mester (1993 and 1996), inefficiencies appear to be inversely correlated
with capital and positively related to the level of non-performing loans. This latter
finding suggests that efficient banks are assigning more attention and resources to
loan origination, monitoring and other credit judgement activities. Interestingly, over
the period 1993-96 inefficient banks also tended to have (on average) a greater retail
banking orientation, higher interest margins and more branches compared with their
efficient counterparts.
Finally, the analysis also shows that there is no clear relationship between assets
size and bank efficiency. However, from the results it is possible to infer that quoted
banks, on average, appear to be more efficient than their non-quoted counterparts.
25
Appendix
Table A.1: Variable DescriptionVariables Symbol Description
Total Costs TC Staff expenses + other non-interest expenses + interest paid
Output 1 Q1 Total customer loans
Output 2 Q2 Other earning assets
Input Price 1 P1 Staff expenses / average number of personnel
Input Price 2 P2 Interest expenses / total customer deposits
Input Price 3 P3 Other non-interest expenses / total fixed assets
Financial Capital K Total equity
Asset Quality S Non-performing loans / total loans
Table A.2: Distribution of Sample Banks by Average Assetsa,b,c
Bank size 1993 1994 1995 1996 Mean
Very Big 141,816.2 (8) 140,645.1 (8) 142,232.2 (8) 136,131.1 (8) 140,206.2 (8)
Big 35,360.8 (12) 34,875.7 (12) 37,597.1 (12) 37,755.9 (12) 36,397.4 (12)
Medium 11,717.8 (25) 12,000.9 (25) 12,770.4 (22) 13,844.6 (21) 12,583.4 (23)
Small 3,849.2 (67) 3,528.9 (62) 3,708.9 (60) 3,853.0 (58) 3,735.0 (62)
Very Small 364.1 (433) 342.4 (416) 365.0 (364) 392.2 (325) 365.9 (385)
a Billions of Italian Lire.
b In brackets the number of banks.
c All monetary aggregates are expressed at 1996 prices.
Table A.3: Structural Testsa,b
Test Performed
[versus RQCF] Test Statistics
Degrees
of Freedom
Critical
Value 201.χ
Outcome
CF = Standard cost frontier 98.4 k = 13 27.69 Rejected
Translog formc 120 k = 14 29.14 Rejected
Npls/Total loans only (S only) 23 k = 7 18.48 Rejected
Equity only (K only) 83.4 k = 7 18.48 Rejected
a The likelihood ratio statistics is calculated as ( )[ ] ( )[ ]{ }10 lnln2 HLHL −− were ( )0HL and ( )1HL are the values of the
likelihood function under the null and the alternative hypotheses, 0H and
1H , respectively.
b RQCF = cost function estimates with risk and output quality variables. The CF (standard cost frontier) is like the model specified
in eq. (2) excluding K and S (risk and output quality variables, respectively).
c The translog form tested here includes K and S.
26
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Table 1: Average Values of X-Efficiency Grouped by Size Classesa
1993 1994 1995 1996 1993 1994 1995 1996
RQCF RQCF RQCF RQCF CF CF CF CF
Very big 83.2% 84.0% 84.7% 85.4% 81.2% 81.8% 82.3% 82.8%
Big 85.1% 85.8% 86.4% 87.1% 85.2% 85.6% 86.1% 86.5%
Medium 85.6% 86.2% 87.2% 87.5% 85.9% 86.3% 87.0% 87.0%
Small 81.1% 82.0% 82.8% 83.5% 81.6% 82.3% 82.8% 83.3%
Very small 85.2% 86.2% 87.0% 87.6% 85.4% 86.1% 86.7% 87.1%
a RQCF= cost function estimates with risk and output quality variables; CF = standard cost function estimates.
30
Table 2: Average Values of X-efficiency Grouped by Bank Types and Geographical Areasa
1993 1994 1995 1996
By region North-west 86.4% 87.6% 88.0% 88.4%
North-east 84.9% 85.8% 87.0% 87.4%
Centre 83.6% 84.5% 85.0% 85.3%
South and islands 83.5% 84.4% 85.2% 86.1%
By bank type Commercial 80.5% 81.8% 82.6% 83.2%
Savings 82.3% 83.2% 84.1% 85.0%
Popular 84.1% 85.6% 86.6% 87.1%
Credit co-op. 86.4% 87.1% 87.7% 88.2%
a Unless otherwise stated, results refer to RQCF, that is the cost function estimates with risk and output quality variables.
31
Table 3: Bank Size and Efficiency Levelsa
Assets rangeb,c Mean Median Stdev Min Max
Quartile 1 12.7-106.8 (58.8) 87.7% 87.7% 0.065 65.5% 99.2%
Quartile 2 106.9-290 (188.9) 85.7% 85.6% 0.069 65.2% 99.5%
Quartile 3 290.1-1,410.2 (653.9) 86.2% 86.5% 0.073 65.2% 99.6%
Quartile 4 1410.3-254,043.9 (17,226.5) 83.7% 83.0% 0.066 69.7% 99.6%
a Unless otherwise stated, results refer to RQCF, that is the cost function estimates with risk and output quality variables.
b Mean values in brackets.
c Values in billions of Italian Lire.
32
Table 4: Economies of Scale (by Size of Banks)a,b,c
1993 1994 1995 1996 1993 1994 1995 1996
RQCF RQCF RQCF RQCF CF CF CF CF
Very big 1.078 1.078 1.057 1.062 1.039 1.049 1.011 1.029
Big 0.823* 0.849* 0.805** 0.874 0.756** 0.785** 0.745** 0.814*
Medium 0.821** 0.806** 0.818** 0.800** 0.762** 0.751** 0.767** 0.744**
Small 0.980 0.967 1.002 0.913 0.925 0.917 0.951 0.866**
Very small 0.767*** 0.771*** 0.784*** 0.847*** 0.754*** 0.761*** 0.779*** 0.844***
All banks 0.801*** 0.802*** 0.819*** 0.859*** 0.779*** 0.784*** 0.803*** 0.844***
*, **, *** means statistically significant at the 10%, 5% and .1% respectively.
a If SCALE >, < or = 1 then there are diseconomies, economies of scale or constant returns to scale
respectively.
b In this case the standard error refers to the hypothesis H0=1.
c RQCF= cost function estimates with risk and output quality variables; CF = standard cost function estimates.
33
Table 5: Economies of Scale (by Bank Types and Geographical Areas)a,b,c
1993 1994 1995 1996
Commercial North-west 0.859*** 0.864*** 0.872** 0.878**
North-east 0.891** 0.889** 0.922* 0.906**
Centre 0.944 0.952 0.925* 0.962
South and islands 0.940 0.941 0.955 0.944
Savings North-west 0.970 0.972 0.980 0.983
North-east 0.943 0.943 0.966 0.914
Centre 0.979 0.985 0.997 0.964
South and islands 0.966 0.957 0.981 0.933
Popular North-west 0.890* 0.882* 0.897* 0.856**
North-east 0.928* 0.917* 0.926* 0.937
Centre 0.928* 0.870** 0.865** 0.882**
South and islands 0.914** 0.910** 0.905** 0.920*
Credit co-op. North-west 0.828*** 0.765*** 0.783*** 0.882**
North-east 0.712*** 0.736*** 0.752*** 0.844**
Centre 0.676*** 0.677*** 0.706*** 0.775***
South and islands 0.700*** 0.686*** 0.716*** 0.740***
*, **, *** means statistically significant at the 10%, 5% and .1% respectively.
a If SCALE >, < or = 1 then there are diseconomies, economies of scale or constant returns to scale
respectively.
b In this case the standard error refers to the hypothesis H0=1.
c Unless otherwise stated, results refer to RQCF, that is the cost function estimates with risk and output quality variables.
34
Table 6: Profitability Test (1993-96)a
Banks Number of banks Cost eff. (averages) % Roa (averages) %
1993 Most efficient 79 94.4 1.65
Least efficient 79 74.4 -0.05
1994 Most efficient 82 94.6 1.35
Least efficient 96 76.1 -0.02
1995 Most efficient 72 94.9 1.85
Least efficient 84 77.3 0.12
1996 Most efficient 68 94.8 1.79
Least efficient 75 78.5 0.33
a The two groups, comprising the most efficient and least efficient banks were partitioned in the following way: 1) most efficient
group: banks that rank in the upper quartile of Italian banks on the cost efficiency estimates and rank in the upper half in term of
ROA (Return On Assets), and 2) least efficient group: banks that rank in the bottom quartile on the cost efficiency estimates and
rank in the bottom half in term of ROA.
35
Table 7: Sample Bank Information (Group Averages – 1996 data)a
All banks Large banks only b
1996 Most
efficient
Least
efficient
Most
efficient
Least
efficient
Number of banks 68 75 31 29
Cost efficiency index % 94.8 78.5 93.1 76.9
ROA 1.79 0.33 0.72 0.18
Interest received 9.63 9.11 8.90 9.01
Non-interest income 0.19 3.71 0.78 0.76
Interest paid 5.26 5.04 4.94 5.02
Operating costs 2.98 4.0 2.98 4.1
Staff expenses/operating costs 56.7 61.9 61.45 62.51
Staff expenses 1.69 2.46 1.84 2.54
Other non-interest expenses 1.13 0.81 1.14 1.53
Loans 40.7 43.6 46.29 41.0
Deposits 54.7 54.2 44.48 52.3
Securities 13.4 11.8 14.5 13.5
Equity 11.3 8.50 11.0 8.16
Fixed assets 1.44 2.62 2.32 2.51
Interest margin 4.40 4.10 3.99 4.01
Npls/total loans 4.42 6.70 4.41 7.98
a Unless otherwise stated, values are expressed as percentage of total assets.
b The group of large banks includes the previously defined very big, big, medium, and small banks.
36
Table 8: Logistic regressions (all banks, large banks and very small banks)a,b
Parameter All banks Large banks Very small banks
Intercept -3.002*** -2.9196*** -2.9505***
Assets 0.0004 0.0019 -0.2884***
Margin 7.6265*** 12.6647** 5.1413**
Branches 0.0446* 0.0319 2.0613***
Retail 0.9974*** 1.5393*** 0.7914***
Owners° -0.0721 -0.1558** 0.0855
Non-perf 0.0093*** 0.0011 0.0132***
Perform -0.0072 -0.0193 -0.0206
Capital -1.5664** -1.6798* -1.2127**
Quoted° -0.1835** -0.2691*** –
Northwe° -0.2158*** -0.1027* -0.2430***
Northea° -0.1568*** -0.2887*** -0.0709*
Cent° -0.0041 -0.0476 0.0467
Com° 0.4331*** -0.2029 0.3662***
Sav° 0.2832*** -0.3682** 0.1728*
Popul° 0.2128*** -0.4417** 0.1431**
a Assets = total assets; Margin = interest margin / total assets; Branches = number of branches; Retail = (customer loans + customer
deposits) / total assets; Owners = 1 for private bank and 0 for public; Non-perf = non-performing loans / total loans; Perform = net
income / equity; Capital = equity / total assets; Quoted = 1 for quoted banks and 0 for not quoted; Northwe = dummy for north-
western banks; Northea = dummy for north-eastern banks; Cent = dummy for banks located in the centre; Com = commercial banks;
Sav = saving banks; Popul = popular banks. ° indicates dummy variable.
b All banks: number of obs. 1,958 – log-likelihood function 2606.08. Large banks: number of obs. 420 – log-likelihood function
627.16.Very small banks: number of obs. 1,538 – log-likelihood function 2057.24.