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A multidimensional approach to measuring bank branch efficiency
Accepted Manuscript
A multidimensional approach to measuring bank branch efficiency Anna Grazia Quaranta , Anna Raffoni , Franco Visani PII: DOI: Reference:
S0377-2217(17)30903-7 10.1016/j.ejor.2017.10.009 EOR 14733
To appear in:
European Journal of Operational Research
Received date: Revised date: Accepted date:
10 November 2016 6 October 2017 9 October 2017
Please cite this article as: Anna Grazia Quaranta , Anna Raffoni , Franco Visani , A multidimensional approach to measuring bank branch efficiency, European Journal of Operational Research (2017), doi: 10.1016/j.ejor.2017.10.009
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ACCEPTED MANUSCRIPT Highlights The paper presents a 3 step approach to measuring bank branches efficiency The main aim is to represent the multidimensional nature of bank efficiency The approach is then applied to the 23 branches of a small-sized Italian bank The results confirm the potential effectiveness of the proposed approach
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A multidimensional approach to measuring bank branch efficiency
Anna Grazia Quaranta Assistant Professor
(MC), Italy
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Department of Economics and Law, Macerata University, Via Crescimbeni 20, 62100, Macerata
e-mail [email protected]
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Tel. +390733 258 3227
Anna Raffoni
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Senior Lecturer
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School of Business and Economics, Loughborough University – Loughborough, LE11 3TU, UK
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e-mail [email protected] Tel. +4401509 228232
Franco Visani (Corresponding author) Assistant Professor
Department of Management, Bologna University, Via Capo di Lucca 34, 40126, Bologna, Italy e-mail [email protected] Tel. +390543374636
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ACCEPTED MANUSCRIPT Abstract Bank branch efficiency measurements range from simple ratio and standard regression analyses to more complex frontier approaches, each with specific strengths and weaknesses. However, in isolation, the indexes that these approaches generate fail to capture the multidimensional nature of bank branch efficiency. This paper develops a three-step procedure that enables combining the strengths of the existing approaches. We begin by taking the widest number of efficiency indexes proposed in literature (step 1), reduce the redundant information through a collinearity analysis (step
test our approach on 23 branches of an Italian regional bank.
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2), and categorize bank branches into efficiency classes through a clustering procedure (step 3). We
The results show that this three-step approach is able to provide a multidimensional view of efficiency based on indexes employing a wide range of theoretical and methodological approaches with different ways of conceiving (intermediation vs. production) and measuring (stock, vs. flow, or physical
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measures) bank outputs and inputs, different definitions of efficiency (technical and cost efficiency), and different measurement approaches (ratios, standard regression analysis and frontier functions). The resulting efficiency ranking is consistent with those that univariate indexes generate and provides a balanced evaluation of branch efficiency when such indexes produce contradictory indications.
Keywords: OR in Banking, Bank Efficiency, Data Envelopment Analysis, Multidimensional
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Performance, Performance Measurement Systems.
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1. Introduction
Bank efficiency measurements have received increasing attention in recent years. The deregulation
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of the banking sector, the financial crisis, and low interest rates have had a negative impact on bank profitability, leading to the pursuit of new sources of income. In the field of bank efficiency
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measurements, the analysis of bank branches is particularly relevant to facilitate management control (Fethi & Pasiouras, 2010; Shyu & Chiang, 2012). Branches are still one of the main sources of costs for banks and contribute to a large part of the value provided to the final customer, even after the
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digitalization of many transactions (LaPlante & Paradi, 2015). Understanding the efficiency of different branches is therefore fundamental in a competitive environment where the need to reduce the number of branches to save costs requires safeguarding the customer experience (Reuters, 2016). Whilst there is no shortage of studies addressing branch efficiency (Avkiran, 2011), the way of representing and measuring its intrinsic multidimensionality still remains an issue. Due to their complex and varied nature, banking activity outputs and inputs can be conceived and measured in different ways, and efficiency itself can be defined and measured through different approaches. Various techniques have been used to address such issues: a) partial/total factor productivity or efficiency ratios; b) standard regressions analysing the impact of a number of inputs on a specific 3
ACCEPTED MANUSCRIPT output; and c) production or cost frontier functions obtained via parametric and non-parametric methods. However, each approach has specific strengths and weaknesses and in isolation fails to capture the multifaceted nature of bank branch efficiency (Paradi, Rouatt, & Zhu, 2011). In this context, our work devises a multivariate procedure that combines the strengths of the existing approaches to provide a multidimensional view of bank branch efficiency. While prior studies address efficiency measurement by either increasing the sophistication of existing methods (e.g., Holod & Lewis, 2011) or comparing the results of different models and discussing their merits and limitations
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in different contexts (e.g., Tsolas & Giokas, 2012), the innovation of our method lies in considering the widest possible set of theoretical and methodological approaches. Our choice is motivated by the idea that no single approach is able to globally represent branch efficiency and that the issue of subjectively selecting one interpretation over another could be removed by producing as many different representations of efficiency as possible. We do so by developing a three-step procedure that first includes all the possible ways to measure efficiency (first step). Through a statistical collinearity
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analysis, we then exclude the redundant indexes (second step). Finally, through cluster analysis (third step), we group branches into efficiency classes based on the values of the remaining efficiency indexes. We then apply this approach to the branches of an Italian regional bank. Our findings indicate that our three-step approach represents the multidimensional nature of
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branch efficiency, since it jointly considers: a) different bank output-input definitions (deriving from the intermediation and production approach); b) alternative ways of measuring outputs and inputs (stock, flow or physical measures); c) different concepts of efficiency (technical and cost efficiency);
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and d) different measurement approaches (ratios, standard regression analysis, and frontier functions). Furthermore, by grouping branches into classes showing common efficiency features rather than a
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single global dimension of efficiency, we provide an overall but still multidimensional indication of the efficiency of branches. This result is particularly relevant when univariate measures yield
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contradictory indications on branch efficiency, showing positive and negative performances on different aspects. In these cases, our proposed three-step procedure avoids radical distortions in the assessment of a branch and provides a balanced view of overall efficiency.
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Our research extends prior literature on the measurement of branch efficiency with the following
two key contributions. First, and to the best of our knowledge, this is the first study adopting an allencompassing interpretation of branch efficiency rather than focusing on one or two dimensions. Second, and accordingly, our work develops a new three-step multivariate procedure that addresses the call for advancing current methodologies by combining extant approaches (Paradi & Zhu, 2013). The remainder of the paper is organised as follows: Section 2 provides the theoretical foundations of the study; Section 3 explains the proposed approach; Section 4 presents the research methods and empirical analysis; the results are discussed in Section 5; and Section 6 sets out the conclusions and suggestions for future research. 4
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2. Theoretical background 2.1. The relevance of measuring bank branch efficiency Since the beginning of the 21st century, many different factors have increased the need for bank efficiency, particularly in the European Union. The deregulation of the banking sector and the introduction of the single currency in the early 2000s led to increased market competition. More recently, the financial crisis and low interest rates, partly generated by the Quantitative Easing (QE)
new sources of profitability (Beck, De Jonghe, & Schepens, 2013).
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promoted by the European Central Bank, have reduced interest income, thus increasing the need for
In this complex context, mainly influenced by external and non-manageable factors, efficiency improvements are often considered one of the few levers to act on to consistently increase bank profits (Chortareas, Girardone, & Ventouri, 2013). According to the European Central Bank (2015),
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the increase in competition and efficiency has led to a high reduction in the number of branches (from 230,505 in 2010 to 204,146 in 2014: -11.5%) and number of employees (from 3,144,191 in 2010 to 2,889,320 in 2014: -8.1%). Refocusing the banking sector on the most efficient activities has led to efficiency measurement becoming a key factor in guiding managerial decisions. This topic has received extensive attention in academic literature, although most studies focus on the institutional
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rather than the branch level (Fethi & Pasiouras, 2010). Investigating the use of Data Envelopment Analysis (DEA) to measure bank efficiency, Paradi and Zhu (2013) found 195 studies at the institutional level and only 80 at the branch level. The analyses at the two levels have different
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purposes. At the institutional level, they aim at showing the impact of external and internal factors (regulation, globalization, different governance systems, etc.) on the efficiency of the whole bank and
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to support benchmarking (Barth, Lin, Ma, Seade, & Song, 2013; Chortareas et al., 2013; Gaganis & Pasiouras, 2013). At the branch level, the evaluation concerns the factors affecting the efficiency of
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managerial activities in different branches. This is a very relevant topic: most of a bank‟s costs are generated at the branch level and even if recently affected by technological innovation, the relationship with a specific branch is still a relevant factor of customer satisfaction (Walsh, Forth,
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Thogmartin, Bickford, Desmangles, & Berz, 2010). Consequently, the efficiency analysis at the branch level can help in understanding the
performance drivers of the whole bank, supporting cost management initiatives, and controlling and improving managerial performance (Paradi & Zhu, 2013; Shyu & Chiang, 2012). It can lead to a series of managerial actions ranging from selecting those branches to keep open after a merger or acquisition to rewarding the performance of branch managers, from developing training programs to guiding investments in new technologies or job rotation in different branches. From a managerial perspective, such an analysis at the branch level can provide very useful decision-making support (LaPlante & Paradi, 2015). 5
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2.2. The multidimensional nature of bank branch efficiency Efficiency entails the ability to employ the lowest possible level of one or more inputs to generate the highest possible level of one or more outputs. When applying this concept to bank branches, the intrinsic multidimensionality of banking activities calls for defining and measuring the specific set of outputs and inputs (Kinsella, 1980). The literature defines the main activities of banks in different ways and hence the outputs and
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inputs considered most relevant (Bergendahl, 1998). The long-standing debate on this issue (Sealey & Lindley, 1977) has essentially led to two main approaches. According to the “intermediation” (or asset) approach, the main activity of banks is acting as intermediaries between liability holders and fund receivers. In this perspective, the role of a bank is evaluated from a macroeconomic point of view, namely, as an intermediary between those that have surplus funds and those that require funds.
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Thus, liabilities are considered the inputs of the production function and the different types of loans represent the outputs. For instance, Paradi et al. (2011) analyse the intermediation abilities of 816 branches of a Canadian bank, investigating the drivers of efficiency and the impact on profitability. The “production” approach instead considers commercial banks from a microeconomic perspective as service companies combining a series of production factors (labour and capital amongst others) as inputs to generate a series of transactions with their customers (mortgages, loans, money transfers,
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etc.), namely, the outputs (Benston, 1965). For examples of this second approach, we refer the reader to Camanho and Dyson (2005), Giokas (1991), Drake and Howcroft (2002).
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These two general approaches can be developed in various ways according to the specific class of outputs and inputs selected. In their classification, Berger and Humphrey (1992) highlight two further
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approaches to defining outputs and inputs. The “user cost” approach determines whether a financial product should be considered as an input or an output based on its net contribution to bank revenues. “If the financial return on an asset exceeds the opportunity cost of funds or if the financial costs of a
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liability are less than the opportunity cost, then the instrument is considered to be a financial output. Otherwise, it is considered to be a financial input” (Berger & Humphrey, 1992: 248). The first
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applications of this approach date back to the mid-80s (Hancock, 1985). The “value-added” approach defines as important outputs both assets and liabilities that generate high value-added for the bank. Less important outputs are intermediate products or inputs depending on their specific nature. The value that each category adds is calculated by allocating the operating cost to the different categories in a cost accounting approach (Berger & Humphrey, 1992). The boundaries between the production and intermediation approach are not as clear, and as such, are more subjective. Some studies consider the value-added and the user-cost approach as variations of the production approach (Kim & McKenzie, 2010: 377), while others include these in the intermediation approach (Camanho & Dyson, 2005: 486).
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activity. Analysed jointly, technical and allocative efficiency defines cost efficiency considering both technical abilities and prices (Farrell, 1957). Allocative efficiency is generally considered as a means of passing from technical to cost efficiency, and the efficiency measures usually adopted fall into the two technical and cost efficiency categories (Staub, Souza, & Tabak, 2010; Brissimis, Delis, & Tsionas, 2010). Most analyses reported in the literature focus on technical efficiency, since information on input and output costs/revenues tends to not be available or very difficult to obtain.
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According to the aforementioned premises, a single efficiency index is a combination of: a) the specific outputs-inputs definition (based on the intermediation or the production approach); b) the specific types of measures adopted to quantify outputs and inputs (stock, flow, or physical measures); and c) the way of measuring efficiency (technical or cost efficiency). Consequently, the concept of branch efficiency can be visualized as a three-dimensional space, as represented in Figure 1 below.
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Each point in the figure is a particular combination of the three dimensions indicated above and provides a specific (and therefore partial) view of the concept of efficiency. An effective approach to
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branch efficiency measurement should therefore consider multiple combinations of the three
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dimensions to adequately represent efficiency in its multidimensional perspective.
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Fig 1. The multidimensionality of bank branch efficiency
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The multidimensionality of bank branch efficiency is widely accepted in literature, but only partially translated into field studies. As Paradi et al. (2011) highlight, “most of the previous studies
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were limited to measuring one or two performance dimensions, which cannot fully reflect the overall branch functions” (p. 101). A number of studies attempt to represent the multidimensionality of bank branch activities to some degree. Oral and Yolalan (1990) analyse the relationship between operating
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efficiency and profitability using a non-parametric correlation of DEA efficiency scores. Schaffnit, Rosen, and Paradi (1997) focus on the effect of service quality and financial performance on
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operating efficiency. In a study of 68 branches of a Greek Bank, Athanassopoulos (1997) defines a DEA model including as outputs both tangible (operating efficiency) and intangible (service quality) components and embracing both the intermediation and the production approach. Manandhar and
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Tang (2002) propose a model including different aspects of bank branch efficiency: operating efficiency, service efficiency, and profitability. Similarly, Giokas (2008), in his analysis of 44 branches of a commercial bank, considers three different dimensions of efficiency: efficiency in managing the financial records of branches, efficiency in managing transactions with customers, and profit efficiency. Camaho and Dyson (2005) develop a DEA-based framework for the performance evaluation of bank branches based on both the intermediation and the production approach. Paradi et al. (2011) define a two-step DEA where production, profitability, and intermediation efficiency are evaluated in a first stage and then included as outputs in the second stage of the model.
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ACCEPTED MANUSCRIPT 2.3. The different approaches to bank branch efficiency measurement Bank efficiency, and specifically bank branch efficiency, can be measured in several different ways and academic literature offers a wide variety of approaches and applications (Fethi & Pasiouras, 2010). The first and most traditional approach is based on ratios (Schweser & Temte, 2002). Three broad categories of ratios proposed to measure bank branch efficiency are: Partial Factor Productivity Indexes (PFPIs), Efficiency Indexes (EIs), and Total Factor Productivity Indexes (TFPIs). PFPIs are
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defined by dividing a measure of value generated by the bank (for example, total loans, intermediation margin, value added, etc.) or a measure of total workload (number of transactions) by the amount of labour or capital employed (measured by number of employees, hours worked, computers, etc.), without considering the specific cost of the resources. Conversely, EIs generally compare the costs of inputs to either revenues or total assets or to other costs to quantify the value generated by the bank‟s
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activities. Finally, TFPIs jointly consider (at least) both labour and capital as inputs and weight them at the denominator of the ratio, usually employing a Cobb-Douglas production function (Coelli, Rao, O'Donnell, & Battese, 1998). Ratios are important measures of efficiency as they provide information on the performance of each branch that is easy to compute and read. This is one of the main reasons why practitioners and regulators still prefer ratios (KPMG, 2009; Thanassoulis, Boussofiane, & Dyson, 1996). On the other hand, they also have renowned limitations. First, PFPIs, by considering a
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single input at a time, provide an incomplete view of bank branch efficiency, inconsistent with the abovementioned multidimensional nature of branch efficiency. As Avkiran clearly explains, “focusing
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solely on individual key performance indicators can limit inferences that can be drawn, or it can bias the analysis because of a missing multi-dimensional perspective required to capture the complex
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operations of modern corporations” (Avkiran, 2011: 325). PFPIs can be compared only one at time, hypothesizing the other inputs as fixed (Yeh, 1996), and may provide inconsistent and misleading information when different PFPIs present dissimilar values (Coelli et al., 2005; Paradi et al., 2011). As
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for EIs (e.g., cost/income ratio), the values that different branches show could be generated by different output and input prices, and not only by the technical efficiency levels (Coelli et al., 2005).
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Second, they are affected by accounting rules and policies. The drawbacks of TFPIs relate to the complexity of selecting all the inputs to consider and the need to specify a production function without any evidence of its reliability. Finally, all the ratios share some common limitations: a) they are by nature constant returns to scale and this is not always the case in bank branch efficiency; b) they do not support improvement initiatives (Paradi & Zhu, 2013). A second approach to efficiency measurement is based on standard regressions where a measure of output is defined as the dependent variable and a series of inputs are considered independent variables (Berger, Hancock, & Humphrey, 1993; Boufounou, 1995; Feldstein, 1967; Hensel, 2003; Murphy & Orgler, 1982). In the case of efficiency measurement, the value of a standard regression is in its
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ACCEPTED MANUSCRIPT potential forecasting support and the possibility to quantify the impact of each input on the output once the others are controlled for. However, this approach has some relevant limitations. First, it requires selecting a pre-defined (unknown) production or cost function. This problem is manageable by choosing a “general” function, such as the translog function. Second, a standard regression can only manage single output-multiple input relationships, while in a bank branch, different inputs (labour, machines, spaces, financial funds, etc.) are used to generate multiple outputs (transactions, mortgages, loans, customer satisfaction, etc.). Finally, a standard regression model is only able to
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indicate an average efficiency level, without providing a measure of inefficiency compared to the best in class (Soteriou, Karahanna, Papanastasiou, & Diakourakis, 1998). Although a useful forecasting tool to obtain the mean expected value of efficiency for a new branch, it does not evaluate the inefficiency of existing branches.
The third way to measure efficiency is based on identifying the production/cost frontier functions. Different approaches can be employed to obtain the frontier functions and can be classified according
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to the specification of the production/cost function (leading to the difference between parametric and non-parametric approaches) and the particular distribution of the error term (leading to the difference between deterministic and non-deterministic approaches). In the class of parametric deterministic approaches, the most well-known are the Deterministic Statistic Frontier (DSF) (Afriat, 1972) and the Deterministic Frontier Model (DFM) (Aigner & Chu, 1968). DSF starts from the weaknesses of
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standard regressions when applied to measuring efficiency and considers - still within the sphere of econometric approaches - a frontier where the distance between the observations and the estimated
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values of the production/cost function is unilaterally distributed with one-sided non-positive/nonnegative residuals. The main issue of this approach is the strong assumption that the entire distance between each observation and the frontier is due to inefficiency and not due to any other types of
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errors (measurement errors amongst others). Aigner and Chu‟s (1968) DFM is based on identifying via mathematical programming methods the function maximizing a single output given a series of
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inputs. The main issue of this approach is that, being based on mathematical programming, the parameters do not show any statistical properties (Forsund, Lovell, & Schmidt, 1985; Greene, 1980).
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Moving to the parametric stochastic approaches, the Stochastic (Statistic) Frontier Approach (SFA) (Aigner, Lovell, & Schmidt, 1977; Meeusen & Van Den Broeck, 1977) has garnered great attention in literature. SFA defines efficient frontiers as parametric functions where, contrary to the deterministic approaches, a series of potential random shocks are taken into consideration. Although this assumption is certainly more robust, it generates higher statistical complexity and further assumptions on the distribution of the two components of the total error (one related to efficiency, the other related to measurement errors and other random shocks) (Forsund et al., 1985). SFA is widely used in practice (Battese & Coelli, 1992, 1995; Coelli et al., 2005). Finally, the most frequently used non-parametric approaches are Data Envelopment Analysis (DEA) (Charnes, Cooper, & Rhodes, 1978, Banker, Charnes, & Cooper, 1984) and Free Disposal 10
ACCEPTED MANUSCRIPT Hull (FDH) (Deprins, Simar, & Tulkens, 1984), developed within the management science framework. DEA offers a wide family of non-parametric models providing an efficiency measure defined as the maximum value of the ratio of the weighted sum of outputs to the weighted sum of inputs. Its main aim is to identify, through mathematical (often linear) programming, a frontier of efficient Decision Making Units (DMUs) that “envelopes” the other units. DEA has received much attention from academics and is today the most commonly used approach for efficiency evaluations. In the banking sector alone, Paradi and Zhu (2013) find 275 DEA applications between 1985 and 2011. DEA models
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have many advantages: they can manage multiple inputs-multiple outputs; they do not require the specification of the production/cost function linking outputs and inputs; and they work well with small samples. However, DEA in its “basic” form also has limitations (Coelli et al., 2005; Fethi & Pasiouras, 2010): a) it assumes that the included inputs and outputs are measured without noise and without putting forward any axioms on the distributional structure of deviations from a best structure frontier (Banker, 1996); b) it is sensitive to outliers; c) it shows a large percentage of efficient DMUs
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when the number of observations is low compared to the number of inputs and outputs; and d) it treats inputs and outputs as homogeneous entities, thus giving rise to misleading results when these are heterogeneous. Finally, FDH is a more general version of DEA, not restricted to convex technologies. However, as for any other deterministic frontier, one of the main drawbacks of FDH is the presence of “super-efficient” outliers that can affect the frontier (Simar & Wilson, 2008).
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Several studies have been conducted to overcome the limits of the basic SFA and DEA models. As for the SFA, to avoid the need for a parametric functional form, Banker (1988), Banker and
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Maindiratta (1992), and Fan, Li, and Weersink (1996) developed different models to obtain a semiparametric approach to SFA, later developed further by other scholars (Kuosmanen, 2008; Kuosmanen & Johnson, 2010; Kuosmanen & Kortelainen, 2012; Kuosmanen, Johnson, &
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Saastamoinen, 2015). A different set of studies (Simar & Wilson, 2002; Simar, 2007) developed new approaches to SFA to obtain a non-parametric estimation of the expected inefficiency (for a recent
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study presenting semiparametric and non-parametric approaches to SFA, see Park, Simar, and Zelenyuk, 2015).
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On the other hand, a number of studies (which can be categorized under the “Stochastic DEA” umbrella) attempt to overcome the deterministic nature of the DEA frontier. These follow two different approaches (Olesen & Petersen, 2016). The first approach (Banker, 1993; Korostelev, Simar, & Tsybakov, 1995a, b; Simar & Wilson, 1998, 1999, 2007), through particular statistical axioms, develops an evolved DEA framework based on a statistical model and a sampling process. For instance, starting from Simar and Wilson (1998, 1999), several contributions use a bootstrapping technique with the aim of obtaining a statistical inference for DEA (Liu, Lu, & Lu, 2016). These modifications allow DEA to provide a consistent but biased estimator of the true frontier, although restrictive and unrealistic axioms need to be imposed (Olesen & Petersen, 2016). The second approach (Cooper, Huang, & Li, 1996; Land, Lovell, & Thore, 1993; Olesen & Petersen, 1995) 11
ACCEPTED MANUSCRIPT specifies a random reference technology and adopts specific DMU-distributions to replace the data on which the DEA analysis is based. These evolved interpretations of SFA and DEA have actually reduced the distance between the two approaches (Cooper & Lovell, 2011). Potentially, the hybrid models developed are almost free of the limitations of the original SFA and DEA methods. However, they are generally based on strong and often unrealistic assumptions that limit their use in real applications (Olesen & Petersen, 2016; Parmeter & Kumbhakar, 2014) and are thus rarely applied in the field of bank efficiency (see, for
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instance, Kao & Liu, 2009). Considering the methodological issues in measuring bank branch efficiency, extant contributions mainly follow two lines of enquiry. The first aims to develop more comprehensive versions of a specific approach. For instance, Cook, Hababou, and Tuenter (2000) develop a specific DEA approach to manage situations where inputs are shared by different activities. Camaho and Dyson (2005) define a DEA model to measure cost efficiency when price information is incomplete. Holod
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and Lewis (2011) propose a specific DEA model to solve traditional issues regarding the role of deposits as input or output. The second line of enquiry focuses on comparing the results of two different approaches to understand the reasons for dissimilarities and/or to derive managerial implications. For instance, Avkiran (2011) compares the results of a DEA application with financial ratios commonly used to evaluate and manage bank performance. Giokas (2008) and Tsolas and
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Giokas (2012) analyse DEA in comparison to a deterministic econometric approach to identify frontiers. Ruggiero (2007) compares the results of the stochastic frontier model and DEA using panel
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data. However, there is currently a lack of studies that combine the different approaches to efficiency measurement (ratios, efficiency indexes derived via standard regressions, and those obtained after identifying different types of frontiers) to leverage their respective strengths while containing their
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weaknesses. Paradi and Zhu (2013: 70) specifically call for these types of studies when concluding their review of DEA applications in bank branch efficiency measurement, “Another interesting future
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research area is to find new ways to apply DEA in conjunction with other advanced methodologies in order to extend such methodologies and to complement each other‟s strengths while eliminating their
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weaknesses”.
3. A multidimensional approach to efficiency measurement: Methodological aspects. Following the aforementioned considerations, we devise a multidimensional approach to the
measurement of bank branch efficiency. Our main aim is to provide a multifaceted interpretation of branch efficiency without focusing on a single specific dimension of the concept. From the methodological point of view, we do not intend to define the umpteenth development of existing approaches, potentially increasing their complexity and difficulty of understanding. Rather, we combine existing approaches in their simplest form to facilitate their practical implementation in the
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ACCEPTED MANUSCRIPT banking context. By considering the widest possible set of theoretical and methodological approaches, we aim to compensate for the natural weaknesses of each and reduce the subjectivity that usually characterises efficiency measurements. Our proposed approach, illustrated in Figure 2, can be described as a three-step method. The first step entails the application of all the methods to measure efficiency as previously discussed in Section 2. The selection of the specific indexes and the outputs-inputs measures is driven by two main criteria: a) the analysis of the literature and the indicators used by regulators to understand the entire set of
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potential indexes; b) the evaluation of the available data to understand which of the potential indexes are computable. The process therefore starts from computing the conventional ratios and then moving on to applying the standard regression models and frontier approaches (parametric and non-parametric, deterministic and stochastic). In other words, none of the existing theoretical and methodological positions would be favoured. This approach is intended to ensure the widest and most inclusive representation of the diverse nature of branch activities. Furthermore, it avoids privileging one
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approach over another, thus reducing subjectivity in: a) the selection of the method to measure efficiency (e.g., ratios vs. standard regressions vs. frontier approaches); b) the choice of the measurement of partial or total productivity; c) the decision on which outputs/inputs definition and measure to include; and d) the prioritization of one dimension of efficiency over another. Then (second step), we apply a multicollinearity analysis to the efficiency measures produced in
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the first step to remove redundant information. We define a specific Variance Inflation Factor (VIF) threshold and exclude from the analysis all the indexes with a VIF above the threshold. This therefore
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leaves the role of eliminating overlapping indexes to a more objective statistical approach and ensuring a multidimensional representation of branch efficiency. Finally, the third step entails a cluster analysis to group branches into efficiency classes for two
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reasons. First, as a multivariate procedure, it does not privilege any efficiency classification of branches provided by a specific approach, thus not favouring any theoretical or methodological
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position. This ensures considering a large number of factors that may influence the efficiency levels of the different branches. Second, this approach takes into consideration all the information provided
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by the different index values recorded in the branches and not only those related to homogeneous indexes, as occurs, for instance, when graphical analyses are applied. In other words, the aim is not to consider a single indicator globally representing bank efficiency, but to cluster the branches into groups with common efficiency features.
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Fig. 2. The proposed approach to bank branch efficiency measurement
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4. Empirical Analysis
The following sections present the development of the three steps of our proposed
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multidimensional approach to bank branch efficiency measurement and the main results obtained.
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4.1. Data set
We test the proposed approach on a bank operating in central Italy. To protect confidentiality, the bank‟s real name is not disclosed and we shall refer to it as „Alpha‟.
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Alpha is a regional bank (1.3 billion in total assets and 200 employees in 2014) operating through 23 branches with around 38,000 active customers. The branches are located in a single region and
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operate under the same technological, social, and economic conditions. The selection of the case is critical to our study, as the objective is to classify branches into
efficiency classes through a multivariate approach. We deemed Alpha appropriate for the following reasons:
a. The bank provides a wide range of services to both private and business customers, rendering branch comparison through multidimensional approaches a critical issue. b. The bank has an established information system capable of providing reliable and plentiful data for each branch. Such accessibility combined with the diversified activities ensures the computation of a considerable number of indicators representing different types of efficiency.
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ACCEPTED MANUSCRIPT c. The bank showed significant interest in the project and allowed us access to an ample and varied amount of data. Data collection took place in 2015. We held an initial focus group with the bank‟s senior management team and controller to discuss the existing approach to measuring branch efficiency, and examined any data disclosure and confidentiality issues. This led to the exclusion of some data considered sensitive, such as exact branch locations and other branch-specific contextual information (number of retail and business customers, personal information on employees working in each branch,
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etc.). The bank headquarters provided almost all the data required for the multivariate procedure. The bank‟s controller played a pivotal role throughout the project; his support was in fact critical to ensure a correct understanding of the information provided and to evaluate the reliability and consistency of the raw data.
The first step (computation of all the possible efficiency measures, given the available data) is the most time-intensive, requiring approximately 23 hours in our case and a combination of software
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(Excel, Stata and GAMS). Step 2, the multicollinearity analysis, took around 3 hours and reduced the number of indexes from 65 to 19. Finally, the cluster analysis (step 3) took approximately 10 hours to complete. We ran the step 2 and 3 analyses through IBM SPSS. Overall, the procedure required approximately 36 hours of work once the data were available.
Table 1 reports the main steps of the analysis, as well as information on timing and the software
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employed.
Details of the data analysis
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Table 1
Data Analysis
Time
Software
2 hours
Excel
(ii) Efficiency Indexes obtained after estimating the parameters of the standard regression models
3 hours
Stata
(iii) Efficiency Indexes derived from the frontier functions obtained according to Aigner and Chu (1968)
3 hours
GAMS
(iv) Efficiency Indexes derived from the Deterministic Statistic Frontier obtained via an econometric approach
5 hours
Stata
(v) Efficiency Indexes derived from the Stochastic Frontier Analysis obtained via an econometric approach
3 hours
Stata
(vi) Efficiency Indexes derived from the Non-Parametric Frontier obtained via DEA
3 hours
Excel
(vii) Efficiency Indexes derived from the Non-Parametric Frontier obtained via FDH
4 hours
Excel
Step 2. Collinearity analysis
3 hours
IBM SPSS
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Step 1. Indexes Computation
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(i) Efficiency Indexes in the form of ratios
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10 hours
Step 3. Cluster analysis
IBM SPSS
4.2. Step 1: Computing the widest possible set of efficiency measures suggested by literature The first task of the analysis is computing the widest possible set of efficiency measures developed in literature and feasible for the available data (ratios, efficiency indexes obtained after estimating the parameters of standard regression models, and those deriving from the frontier functions obtained in
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all the ways currently known). As a result, the efficiency measures expressed as ratios number 48: 32 Partial Labour Productivity Indexes (PLPIs); 1 Partial Capital Productivity Index (PCPI); 2 Total Factor Productivity Indexes (TFPIs); and 13 Efficiency Indexes (EIs) (see Table A.1 in the Appendix for the detailed list of the calculated ratios). Even if the correlation between many were intuitive, we included all for maximum objectivity of the analysis, leaving the selection of the most meaningful indicators to the subsequent multicollinearity analysis.
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Based on the available data, we implemented the following translog production function standard
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regressions:
where: -
represents the 23 branches analysed
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- NOP is the total annual number of transactions carried out by employees - EMP, HOURS, and COM respectively represent the number of employees, hours worked
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(measuring labour input), and computers in the information system (measuring capital input).
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As is evident, the only difference between the two models is the specific measure adopted for labour input: number of employees in the first, number of hours worked in the second. Both models are proposed in literature and even if we could have hypothesized a correlation between their results, we considered both, again leaving the role of reducing the set of efficiency indexes to the multicollinearity analysis. The estimated coefficients led to the definition of two vectors of regression residuals (
) with either positive or negative values. They measure the efficiency of each
branch comparing (as the difference of) the actual output of each with the (average) output estimated by the standard regressions at the same input level. The preliminary analysis highlighted the absence
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ACCEPTED MANUSCRIPT of clear outliers, a general distribution of the independent variables close to normal, and an acceptable level of collinearity among the regressors. Considering the different orders of magnitude of the regressors, we also carefully analysed the Beta coefficients and tested the further OLS assumptions for a multiple regression. All the parameters were statistically significant at the 95% probability level, with an R2 equal to 92% for model [1] and 90% for model [2]. Based on the same information used to generate the vectors
, we developed the
efficiency indexes based on frontiers. We considered and applied all the basic approaches to obtain a
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frontier function described in Section 2.3. For the parametric approaches (Deterministic Frontier Model, Deterministic Statistic Frontier, and Stochastic Frontier Analysis) we assumed the same production function defined in [1] and [2].
More specifically, the different approaches adopted to obtain a frontier function led to the following vectors: 1)
and
, i.e., the vectors of the distances between the empirical output value
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and the frontier value identified with the parametric deterministic approach of Aigner and Chu (1968) (Deterministic Frontier Model: DFM) based on mathematical programming 2)
and
, i.e., the vectors of the distances between the empirical output
value and the frontier value identified with a parametric deterministic econometric approach (Deterministic Statistic Frontier: DSF) and thus imposing non-positive regression residuals and
, i.e., the vectors of the distances between the empirical output
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3)
value and the frontier value identified with a parametric stochastic econometric approach
4)
and
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(Stochastic Frontier Analysis: SFA)1
, i.e., the vectors of the ratios between the empirical output value
approach)2 5)
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and the frontier value identified via Data Envelopment Analysis (non-parametric deterministic
and
, i.e., the vectors of the ratios between the empirical output value
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and the frontier value identified via Free Disposal Hull (again, a non-parametric deterministic approach)
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A first analysis of the ten vectors generated by the five different frontier definition approaches shows that the order of the branches in relation to the level of efficiency is entirely coincidental. We then applied the same five approaches to a different set of outputs and inputs. We defined total
financial assets as output and number of employees, and operating costs as inputs. For the parametric 1
We followed the common assumption that , representing the symmetric component of the error due to random factors and measurement errors, follows a normal distribution and that the component due to inefficiency is non-negative and follows a one-side normal distribution. A second assumption is that the two components of are independent (covariance equal to 0 for every observation). For all the regressions, all the parameters were statistically significant at the 95% probability level, with an R 2 at least equal to 91% and 90% respectively for the frontier function in the form of [1] and [2]. 2 The DEA model used is an output-oriented CCR model.
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ACCEPTED MANUSCRIPT approaches (DFM, DSF, and SFA), we again hypothesized a translog function. As a consequence, we defined five other vectors measuring the difference of the empirical values of the output from the frontier values, i.e., approach),
(DFM approach), (DEA approach) and
(DSF approach),
(SFA
(FDH approach). Again, the efficiency
order of the 23 branches generated by the five different approaches was exactly the same. In summary, at the end of this first part of the analysis, we calculated 65 efficiency measures for each branch: 48 ratios, 2 indexes deriving from the standard regressions, and 15 obtained from the
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different basic frontier identification approaches. We used all the approaches defined in literature to measure efficiency, representing all the different views of efficiency, considering different outputs and inputs (based on the production and the intermediation approaches), and adopting all their different measurement options (stock, flow, and physical values). As a consequence, we measured the efficiency of branches with the maximum possible level of multidimensionality.
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4.3. Step 2: The multicollinearity analysis to reduce the number of efficiency indicators
In line with the designed approach and to remove redundant information, we ran a multicollinearity analysis where a conservative level of 5 for the VIF was used as the threshold to retain an index in the analysis. At the end of this evaluation, 19 out of 65 efficiency indexes were retained: 9 Partial Labour Productivity Indexes (PLPI1, PLPI31, PLPI30, PLPI4, PLPI6, PLPI7, PLPI8,
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PLPI17, PLPI19), 1 Partial Capital Productivity Index (PCPI1), 1 Total Factor Productivity Index (TFPI1), 5 Efficiency Indexes expressed as ratios (EI1,EI2, EI5, EI9, EI11), 1 vector of standard
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regression residuals (PFEI2), and two vectors of efficiency values (PFFEI2_AC and PFFEI3_AC) derived from the frontier functions obtained according to the DFM approach.
23 branches.
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Table A.2 in the Appendix reports the values of the 19 residual efficiency measures for each of the
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4.4. Step 3: The cluster analysis
We developed the cluster analysis through the following steps:
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- A preliminary analysis aimed at identifying potential outliers that may adversely affect the
construction of the cluster. The negative outcome of this assessment enabled us to process all the available values for the efficiency indexes. - Since the 19 variables have different units of measure and/or orders of magnitude, we transformed their values so as not to alter the actual weight of the individual information provided by the various efficiency indexes during the subsequent processing. This methodological choice definitively ruled out any over- or under-dimensioning of the actual importance of the variables used for grouping. To transform the values, we derived the z scores via the normal standardization process. 18
ACCEPTED MANUSCRIPT - As mentioned in the previous section, the information in the 15 efficiency measure vectors generated by the five frontier approaches substantially coincides. As a consequence, the multicollinearity analysis left only two of the 15 obtained vectors, i.e.,
.
Considering the relevance of these types of indicators, we attempted to use all 15 vectors in the cluster analysis in all the different combinations of two vectors at a time to check for any substantial change in branch allocation to the different groups. The composition of the clusters remained substantially unchanged.
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- As all the variables are quantitative, we used different hierarchical and a non-hierarchical (kmeans) approaches to cluster analysis to compare the results and to test the robustness of the groups obtained.
- With regard to the hierarchical methods, as it was possible to use all the algorithms and all the similarity measures through the software (SPSS), we carried out a number of tests combining their
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variants in almost every possible way. The clusters did not substantially change.
All the variables included as inputs for the clustering procedure were statistically significant in the grouping process. The k-means approach and the various hierarchical approaches implemented provided clusters substantially composed of the same branches3.
Table 2 reports the three clusters of branches obtained with the k-means clustering procedure and
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the Ward procedure (similarity measure = simple Euclidean distance) 4 , while Table 3 reports the average value of each efficiency index within each of the three resulting clusters.
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We then analysed the composition of the branches within each cluster. All the large-sized branches belong to Cluster 1, except for branch O, included in the second cluster. Only one medium-sized branch (H) belongs to the cluster of the most efficient branches, while B, E, J, M and T are members of
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the second cluster and K, N and P of the third cluster. The small branches Q, U and W belong to the
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second group, while D, F, L, R, S and V to the third group.
Table 2. The clusters obtained through the k-means and Ward clustering methods Cluster 2
Cluster 3
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Cluster 1
3
To verify the stability of the solutions obtained, we implemented the different procedures (hierarchical and nonhierarchical) several times using the aggregation data arranged in different random order. The results obtained within the same procedure were very similar. As for the k-means approach, given that the ordering of the initial cluster centres may affect the final solution, we ran various permutations of the values of the initial centres and the final results remained substantially unchanged. 4 We report these particular results as the Ward method is generally considered preferable in application contexts such as this. The preference in showing the results obtained from the Ward method in relation to the use of the simple Euclidean distance as a measure of similarity instead simply derived from the fact that the simple Euclidean distance is the default measure SPSS uses in a non-hierarchical cluster analysis via a k-means procedure.
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ACCEPTED MANUSCRIPT Branches showing the highest values for the measures
Branches showing average values for all the indicators
Branches showing lowest values for the measures
, highest values for the measures
and closest to zero for
and further away from zero (negative) for
Branches A, C, G, H, I
Branches B, E, J, M, O, Q, T, U, W
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lowest values for the measures
Branches D, F, K, L, N, P, R, S, V
As external analysts with no other information on the branches, we could not further investigate the efficiency drivers. However, an internal analyst or an external consultant with all the necessary
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information on the location of the branches, the bank‟s strategies, and the contextual factors affecting performance could run a more thorough analysis to understand the efficiency drivers and define the most appropriate actions to improve this.
Table 3. Average values of the 19 clustering variables within each cluster Cluster 1 25.505.466 386 122 26.357.609 7.207.922 143.769 686.511 58.786 254.478 4.427 6.263.909 0.4953 0.0020 55.255 0.0046 0.0964 0.1613 0.0000 0.0000
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Measure
Cluster 2 9.816.415 299 99 10.492.073 5.134.279 115.426 432.334 29.108 110.002 3.155 3.233.688 0.3596 0.0055 92.413 0.0095 0.2310 0.0247 -0.0235 -0.0192
Cluster 3 5.076.926 201 64 6.164.203 2.238.880 78.325 201.057 8.449 38.260 2.103 1.077.100 0.2352 0.0129 177.116 0.0190 0.4464 -0.1151 -0.2059 -0.2942
4.5. Validation of the proposed three-step procedure We validated the proposed approach by comparing the results of the three-step procedure with those produced by each of the 19 indexes used in the cluster analysis. This validation process involved two stages: (1) a quantitative assessment of the similarity of the rankings, and (2) a detailed 20
ACCEPTED MANUSCRIPT qualitative analysis of their divergences. We deemed this approach appropriate given the nonobservable nature of the problem entity („true‟ efficiency performance of the bank branch), which limited the possibility of employing statistical procedures and artificial data (Sargent, 2013). Each of the 19 univariate indexes describes a specific (and partial) view of the overall efficiency of a branch and none could therefore be considered as a gold standard. Since the non-observability of the problem entity calls for the most thorough investigation possible (Sargent, 2013), we employed a combination of objective (quantitative) and subjective (qualitative) approaches in the validation process. To do so,
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we first partitioned the efficiency values of each individual index into three classes taking into account the symmetric or asymmetric distribution of the related values5. For each individual index, we then allocated the branches to one of the three classes based on their specific efficiency value (Table 4). We assessed the degree of similarity between the efficiency classes obtained through the clustering procedure and those produced by each of the univariate indexes by computing the percentage of coincidence of the two classifications and Spearman‟s rho correlation index (Spearman, 1904; Gosset,
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1921). The results show that on average the percentage of coincidence between the classifications generated by the multivariate approach and that of each univariate index separately is 74% (ranging from 65% with PLPI_4 to 96% with PLPI_8), while Spearman‟s rho is 0.83 (ranging from 0.76 with PLPI_31 to 0.96 with PLPI_8). Furthermore, when classified differently, branches are always allocated in adjacent classes. In other words, only one-class changes were observed. None of the
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reported differences show branches included in Cluster 1 ending up in Cluster 3 (and vice-versa) under a different approach.
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At this stage, we undertook a detailed examination of the branches classified in different classes by the univariate indexes compared to the clustering procedure to investigate our proposed multivariate procedure‟s ability to provide a multifaceted representation of branch efficiency compared to
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univariate measures of efficiency. The qualitative analysis shows that the multivariate approach appears to better balance positive and negative performances on different dimensions of efficiency
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(Table 4). Branches performing well or badly on all dimensions are consistently classified in the first class (high-efficiency) or in the third class (low-efficiency), regardless of the approach taken. For
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example, both the cluster analysis and each univariate index rank branches D, L and S in class 3. However, when branch performance is not as clear-cut on all aspects, discrepancies emerge. 5
For indexes with a symmetric distribution of values, we identified the low-efficiency class by considering the minimum efficiency value as the lower class limit and the mean of the efficiency value less their standard deviation as the upper class limit. The medium-efficiency class included values between the mean of the efficiency values less their standard deviation and the mean of the efficiency values plus their standard deviation. Finally, the high-efficiency class comprised values between the mean of the efficiency values plus their standard deviation and the maximum efficiency value recorded by the index. Where the index presented a certain degree of asymmetry in the value distribution, we divided the efficiency values into three same-sized classes. We obtained these by deducting the lowest efficiency value from the highest efficiency value and then dividing by three. The low-efficiency class boundaries were therefore represented by the lowest efficiency value and the lowest efficiency value plus the class width respectively. The medium-efficiency class included values between the lowest efficiency value plus the class width and the maximum efficiency value less the class width. Finally, the highefficiency class comprised values between the maximum efficiency value less the class width and the maximum efficiency value.
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Table 4. Comparison of the cluster analysis and univariate efficiency indexes rankings PL PI _ 8 1 2 1 3 2 3 1 1 1 2 3 3 2 3 2 3 2 3 3 2 2 3 3
PL PI _1 7 1 3 1 3 3 3 1 1 1 2 3 3 2 3 2 3 2 3 3 3 2 3 3
PL PI _1 9 1 3 1 3 3 3 1 1 1 3 3 3 2 3 2 3 3 3 3 3 2 3 3
P C PI _1 1 2 1 3 2 3 1 2 2 2 3 3 2 3 2 3 2 3 3 2 2 3 2
TF PI _ 1 1 3 1 3 3 3 1 1 1 2 3 3 2 3 2 3 2 3 3 3 2 3 3
E I _ 1 2 3 2 3 3 3 2 2 2 2 3 3 2 3 2 3 2 3 3 3 2 3 3
E I _ 2 1 2 1 3 2 3 1 1 1 2 2 3 2 2 2 3 2 3 3 2 2 3 2
E I _ 5 1 1 1 3 1 2 1 1 1 1 2 3 1 2 1 2 1 2 3 1 1 2 2
E I _ 9 1 1 1 3 2 2 1 1 1 1 2 3 1 2 1 2 1 3 3 2 1 2 2
EI _ 1 1 1 2 1 3 2 2 1 1 1 2 2 3 2 2 2 3 2 3 3 2 2 2 2
P FE I_ 2 1 2 2 3 3 3 2 2 2 2 3 3 2 3 2 3 2 3 3 3 2 3 3
PFF EI_ 2_A C 1 2 1 3 2 2 1 1 1 2 2 3 1 2 2 3 2 3 3 2 2 3 2
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PL PI _ 7 1 2 1 3 2 2 1 1 2 2 2 3 2 2 2 2 2 2 3 2 2 2 2
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PL PI _ 6 1 2 1 3 2 2 1 1 1 2 2 3 1 2 2 3 2 3 3 2 2 2 2
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PL PI _ 4 1 3 1 3 3 3 1 1 1 3 3 3 2 3 3 3 3 3 3 3 3 3 3
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PL PI _3 0 1 2 1 3 2 2 1 1 2 2 2 3 2 2 2 3 2 3 3 2 2 2 2
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PL PI _3 1 1 3 2 3 3 3 2 2 2 3 3 3 2 3 2 3 3 3 3 3 2 3 3
PFF EI_ 3_A C 1 2 1 3 2 2 1 1 1 2 2 3 1 2 2 3 2 3 3 2 2 3 2
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PL Br PI an _ ch 1 A 1 B 3 C 1 D 3 E 3 F 3 G 1 H 1 I 1 J 3 K 3 L 3 M 2 N 3 O 2 P 3 Q 3 R 3 S 3 T 3 U 2 V 3 W 3
The analysis of branches B, E, J, O, Q, T and U shows that depending on the univariate index
selected, their performance can be interpreted as manifesting high-, medium- or low-efficiency. For instance, branch B records high-efficiency in 2 indexes (Class 1), medium-efficiency in 11 indexes (Class 2), and low-efficiency in 7 indexes (Class 3). In all cases, the proposed multivariate approach consistently classifies B, E, J, O, Q, T and U in the medium-efficiency category (Cluster 2). All in all, the multivariate nature of the proposed approach would seem to better account for divergent performances on different aspects of efficiency compared to the univariate approaches. In other words, 22
ACCEPTED MANUSCRIPT our proposed procedure does not penalise or reward branches on single dimensions based on good or bad performances. Rather, it jointly considers the outcomes of all the univariate indexes and balances positive and negative performances as measured by the different approaches. The analysis of branches P and W further support this point. For instance, EI_2 includes both branches in the mediumefficiency group. However, the two branches appear to be quite different. P falls into the lowest efficiency group in 16 out of 19 indexes, whilst W in 9 out of 19. By balancing different dimensions, our proposed multivariate approach appears to provide a better description of the overall efficiency
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level of the two branches: P, which performs negatively in most efficiency indexes, is included in the “low-efficiency” group; W, which tends to perform better than P in a number of other efficiency aspects, is included in the “medium-efficiency” class. Univariate approaches tend to over- or underestimate efficiency when a single measure (single view) of efficiency is used to rank branches.
In sum, both the quantitative and qualitative assessments confirm that the efficiency view that our proposed approach provides is consistent with those generated by the univariate indexes. Furthermore,
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when they yield contradictory results, our three-step procedure offers a balanced description of branch efficiency.
5. Discussion
Banking efficiency is difficult to compute due to the complex and varied nature of the outputs and
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inputs involved (Kinsella, 1980). Extant research addresses the issue either by increasing the level of sophistication of existing approaches (Cook et al., 2000; Holod & Lewis, 2011) or by comparing
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different methods and discussing their limitations and merits in different contexts (Giokas, 2008, 2012; Avkiran, 2011). Conversely, the three-step procedure here proposed is based on the notion that no single approach is able to provide a multidimensional view of banking efficiency and addresses this
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issue by combining the widest possible range of theoretical and methodological approaches. First, the ability to ensure a multifaceted representation of efficiency emerges from the analysis of
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the type of indexes used. From a theoretical perspective, the 19 indexes identified in the collinearity analysis represent different ways of conceiving bank outputs-inputs (intermediation and production
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approach), alternative ways of measuring outputs and inputs (stock, flow, or physical measures), and different concepts of efficiency (technical and cost efficiency). For instance,
(net revenues on
services/number of employees) derives from the production-view of banking activity, using both flow (for the output) and physical (for the input) measures, providing a measure of technical efficiency. Conversely,
(operating cost/total financial assets) and
(operating costs/total assets) originate
from the intermediation view of banking activity, adopting a stock-type measure (for the output) and a flow-type measure (for the input), providing an indication of cost efficiency. Table 5 summarises the different dimensions of efficiency as explained by the residual indexes.
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Table 5 Number of efficiency indexes by efficiency concept, outputs/inputs definition, and measures of output Outputs/Inputs Definition
Intermediation Approach
Output Measure
Stock
Flow
Technical
2
3
Cost
3
2
Physical Quantities
Stock
Flow
Physical Quantities
1
2
4
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Efficiency Concept
Production Approach
1
1
The two ways of considering bank activities are equally represented (10 outputs/inputs definitions from the intermediation approach and 9 outputs/inputs definitions from the production approach) as are the different concepts of efficiency (12 indexes of technical efficiency and 7 indexes of cost
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efficiency), and type of output measure (6 are stock measures, 8 are flow measures, and 5 are physical measures). As for type of measure, the indicators are categorised according to the output rather than the input measure, although worth highlighting is that most of the indexes include different types of measures for outputs and inputs. For example,
incorporates a flow measure of output (net
interest margin) and a physical measure of input (number of employees). Similarly,
includes a
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flow measure of input (operating costs) and a stock measure of output (total financial assets). Evident from classifying the type of measure in the output perspective is that all the measures considered for
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the intermediation approach cannot be physical quantities, representing the stock or flow of intermediated resources. Conversely, several indexes represent the intermediation approach where the input is physical quantities (number of employees, number of hours worked, etc.). In general, some
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measures are not as clear-cut from a theoretical point of view (Camaho & Dyson, 2005; Kim & Mackenzie, 2010) and all the classifications include some subjective judgements. Table 5 is therefore
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descriptive and has no normative intent. Figure 3 shows a selection of residual indexes plotted against the three-dimensional illustration of efficiency reported in Figure 1. As is clear from the graphic representation, the residual indexes are
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able to provide a rich and varied description of efficiency.
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Fig. 3. 3D Plot of selected residual indexes
From a methodological point of view, we computed the residual indexes using a number of
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different methodologies providing a full account of those available. After performing the collinearity analysis, several types of ratios, an efficiency index obtained after estimating the parameters of a
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standard regression model, and two indexes derived from two different production frontier functions remained. In detail, the 19 remaining indexes include: 9 Partial Labour Productivity Indexes (PLPI1, PLPI4, PLPI6, PLPI7, PLPI8, PLPI17, PLPI19, PLPI30, PLPI31), 1 Partial Capital Productivity Index
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(PCPI1), 1 Total Factor Productivity Index (TFPI1) and 5 Efficiency Indexes represented through ratios (EI1, EI2, EI5, EI9, EI11), 1 vector of standard regression residuals (
and 2 vectors of
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distances between the empirical output value and the production frontier identified through the parametric deterministic approach of Aigner and Chu (1968) (
and
).
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Second, the clustering procedure enabled an overall but multidimensional indication of branch efficiency. Three clear-cut clusters, representing high, medium, and low efficiency branches, emerged from the analysis. This outcome is of particular relevance, since a comprehensive approach prompts issues of readability and interpretation of the resulting information. We grouped the branches with common efficiency features into classes (as described by each of the 19 univariate residual indexes) rather than a ranking based on a single indicator globally representing branch efficiency. By jointly considering the outcomes of all the univariate indexes, the cluster analysis provides a ranking that is consistent with those generated by each of the univariate indexes when a branch either performs positively or negatively across all dimensions of efficiency. However, when discrepancies emerge, it is able to balance positive and negative performances as measured by the different univariate 25
ACCEPTED MANUSCRIPT approaches. As the results of the validation process show, the use of a multivariate procedure avoids radical distortions in the assessment of a branch and provides a more accurate description of efficiency.
6. Conclusions This paper presents a three-step approach providing a multidimensional view of bank branch efficiency. The first step includes the widest number of efficiency indexes generated by all existing
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theoretical and methodological approaches with the aim of embracing the multidimensional nature of efficiency. Thereafter, we reduced the redundant indexes through a collinearity analysis, and finally, clustered the branches based on the remaining values of the indexes.
The analysis of the 23 branches of an Italian regional bank shows that our proposed three-step approach generates a multivariate efficiency ranking that: a) is based on indexes representing different
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output-input definitions and proxies (intermediation vs. production approach; stock vs. flow or physical measures), different views of efficiency (cost vs. technical efficiency), and different measurement approaches (ratios, standard regression analysis, and frontier functions); b) is consistent with those obtained through existing univariate approaches; and c) provides balanced solutions when different univariate approaches yield inconsistent rankings for the same branch. Furthermore, our proposed approach enables removing the initial “subjective” and potentially
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biased choice of which output/input definition and measure, and which efficiency definition and measurement approach to include in the analysis. The application also shows the practical feasibility
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of the approach. Excluding the dataset preparation, a prerequisite regardless of the procedure, the overall analysis required approximately 36 hours, an acceptable amount of time considering the
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relevance of the information generated.
We conclude with some remarks on the limitations of our work and indications for future research. First, we conducted the research on the branches of a single bank located in the same region,
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consistently with our main research objective (studying the ability of our three-step approach to provide a multidimensional view of branch efficiency) and the specific case analysed. However,
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efficiency could be affected by external factors related to geographic/institutional and managerial aspects that are beyond the control of managers and employees. Future research could analyse which approach is able to take into consideration these environmental factors in the three-step approach. A second development consists in investigating the possibility of applying our proposed approach not only to compare bank branches but also whole banks, to address the increasing demand from regulators to analyse efficiency. From a theoretical point of view, no obstacles impede using the three-step approach in different contexts, but further studies could investigate the issues and the contributions to literature that this approach could generate. Finally, while this paper is largely “technical”, future research could also investigate the organisational and managerial implications of
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ACCEPTED MANUSCRIPT adopting our proposed approach. This is consistent with the growing interest in understanding the application of OR approaches in practice (Franco & Hämäläinen, 2016).
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High-Powered Branch Network in Retail Banking. The Boston Consulting Group.
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ACCEPTED MANUSCRIPT Appendix
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Table A1. Efficiency indexes in the ratio form
)
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(
(
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(
33
(
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= cost income ratio
= tangible assets = tangible assets net of real estate
2,7 7,8 3,4 50
B
M ed iu m
90, 93, 24 0
C
L ar ge
2,7 1,8 9,3 10
42, 34, 57 0
E
M ed iu m
85, 41, 11 0
S m all
60, 12, 45 0
AC D
S m all
F
54 5
29 6
35 9
12 9
2,9 1,9 3,2 15
97
92, 14, 47 2
19 6
28 4
20 7
P L PI _7
P L PI _8
P L PI _1 7
P L PI _1 9
P C P I_ 1
1, 51 ,0 91
7, 79 ,3 45
69 ,8 32
2, 91 ,4 20
5, 0 4 6
1, 12 ,1 45
3, 89 ,1 23
23 ,4 51
89 ,8 91
3, 0 3 8
1, 48 ,4 56
7, 45 ,3 67
63 ,8 81
2, 86 ,7 31
4, 7 6 3
64 ,3 67
1, 53 ,2 14
6, 65 1
27 ,8 35
2, 0 5 6
1, 09 ,2 95
3, 77 ,7 42
19 ,1 55
74 ,7 24
90 ,2 34
2, 45 ,3 89
49 ,3 41
M
A
L ar ge
PL PI _4
P L PI _6 79 ,8 2, 34 1 46 ,2 7, 98 1 73 ,4 1, 56 2
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PL PI _1
P L PI _3 0
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SI Z E
P L PI _3 1
12 7
2,8 1,4 3,2 85
56
52, 65, 69 6
94
91, 55, 10 2
17 ,4 2, 65 8 41 ,8 4, 77 5
71
71, 13, 72 3
26 ,7 3, 41 9
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B ra n c h
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Table A2. The values of the 19 remaining indicators for each of the 23 branches.
9, 78 3
34
T F PI _1 71 ,6 1, 23 0 27 ,4 5, 63 1 68 ,9 9, 91 2
E I _ 1 0. 5 1 2 1 0. 3 2 6 0 0. 5 0 4 3
E I _ 2 0. 0 0 1 6 0. 0 0 5 6 0. 0 0 1 6
2, 9 5 4
7, 83 ,4 56 22 ,9 7, 75 3
0. 1 0 9 8 0. 3 0 5 5
0. 0 1 3 8 0. 0 0 6 3
2, 2 6 7
12 ,9 8, 73 4
0. 1 6 3 3
0. 0 1 2 3
E I _ 9 0. 0 0 3 9 0. 0 1 0 7 0. 0 0 4 0
E I _ 1 1 0. 0 7 3 8 0. 2 6 5 2 0. 0 8 2 3
1, 11 ,4 99
0. 0 2 2 3 0. 0 1 1 9
0. 4 9 8 7 0. 2 9 5 2
1, 40 ,2 19
0. 0 1 5 0
0. 3 8 7 4
E I_ 5
49 ,7 83
98 ,3 42
52 ,8 95
1, 98 ,2 56
P F E I_ 2 0. 3 9 2 4 0. 0 0 7 6 0. 1 3 0 8 0. 1 6 3 5 0. 0 0 6 5 0. 0 6 5 4
PF FEI _2_ AC
PF FEI _3_ AC
0.0 000
0.0 000
0.0 164
0.0 198
0.0 000
0.0 000
0.2 289
0.3 715
0.0 229
0.0 202
0.1 635
0.2 437
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95, 23, 24 0
K
M ed iu m
65, 78, 91 0
L
S m all
36, 52, 31 0
M
M ed iu m
1,1 8,9 6,7 10
N
M ed iu m
70, 43, 29 0
29 8
21 1
18 8
32 9
22 1
11 3
99
96, 27, 77 5
75
76, 70, 57 6
29 ,9 6, 32 1
52
48, 29, 65 8
10 9
1,5 0,5 1,7 75
1,1 3,8 3,4 56
81
10 3
1,1 4,4 8,2 38
64
60, 72, 57 5
20 ,3 5, 16 7 53 ,4 9, 14 3 18
P
M ed iu m
52, 13, 56 0
Q
S m all
1,0 6,3 2,4 50
29 9
10 2
1,0 5,7 3,4 21
R
S
47,
19
61
54,
AC O
19 9
33 ,2 5, 68 1 59 ,8 2, 31 5
81, 17, 49 1
L ar ge
32 5
15 ,3 2, 98 1 66 ,9 8, 43 5
4, 7 4 1
1, 39 ,8 72
6, 26 ,7 68
52 ,3 13
2, 24 ,5 61
3, 8 3 9
1, 34 ,2 13
5, 87 ,9 34
48 ,5 61
2, 13 ,4 48
3, 7 4 8
1, 15 ,6 12
4, 23 ,7 45
27 ,8 43
94 ,2 35
3, 2 2 9
94 ,2 18
2, 63 ,4 52
58 ,7 62
1, 40 ,1 34 5, 56 ,3 89
1, 30 ,1 25
63 ,4 4, 56 7 56 ,7 8, 91 9 52 ,3 4, 91 9 32 ,4 5, 71 8
0. 5 0 2 3 0. 4 9 2 3 0. 4 6 5 6 0. 3 6 7 8
0. 0 0 1 8 0. 0 0 2 1 0. 0 0 2 7 0. 0 0 5 0
15 ,6 7, 21 3
0. 1 9 4 6
6, 96 ,9 19 48 ,7 2, 34 1
0. 9 3 2 4 0. 4 5 3 8
0. 0 1 4 2 0. 0 0 3 2
16 ,4 4, 78 1 40 ,2 3, 18 9
0. 2 0 3 4 0. 4 1 1 9
0. 0 1 1 0 0. 0 0 4 1
0. 1 4 5 6 0. 3 8 4 4
0. 0 1 3 0 0. 0 0 4 5
0.
0.
0. 0 0 4 3 0. 0 0 5 3 0. 0 0 5 6 0. 0 0 9 4
0. 0 9 8 2 0. 1 0 4 5 0. 1 2 3 4 0. 2 1 9 9
0. 0 1 4 7
0. 3 7 1 1
0. 0 2 4 9 0. 0 0 6 0
0. 5 2 9 1 0. 1 4 7 6
0. 0 1 3 5 0. 0 0 7 6
0. 3 4 5 6 0. 1 6 5 3
79 ,8 34
0. 0 1 7 3 0. 0 0 8 4
0. 4 5 6 7 0. 1 9 2 3
0. 1 1 9 9 0. 0 8 7 2 0. 0 7 6 3 0. 0 1 0 9 0. 0 5 4 5 0. 1 7 4 4 0. 0 7 6 3 0. 0 3 2 7 0. 0 4 3 6 0. 1 0 9 0 0. 0 2 1 8
1,
0.
0.
-
56 ,1 23
0.0 000
0.0 000
0.0 000
0.0 000
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J
M ed iu m
33 6
2,2 1,1 7,2 13
59 ,3 42
2, 56 ,2 31
0.0 000
0.0 000
0.0 142
0.0 036
0.1 308
0.1 753
0.2 616
0.3 815
0.0 000
0.0 000
0.1 090
0.1 426
0.0 087
0.0 012
0.2 289
0.3 188
0.0 098
0.0 021
-
-
0. 0 1 1 4
57 ,3 49
60 ,1 23
84 ,3 52
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2,2 1,3 2,4 50
11 9
6, 93 ,1 43
50 ,8 32
2, 5 8 0
5, 73 4
22 ,3 67
1, 5 8 9
44 ,5 67
1, 90 ,9 32
3, 7 3 9
10 ,9 94
M
I
L ar ge
34 3
2,5 3,8 7,1 28
1, 45 ,2 13
ED
2,4 3,8 7,3 40
12 4
71 ,3 2, 56 1 67 ,9 9, 89 9 67 ,8 3, 24 5 49 ,4 2, 36 1
PT
H
M ed iu m
34 7
2,6 9,4 7,2 03
CE
G
L ar ge
2,6 0,3 4,7 80
98 ,3 21
2, 87 ,3 45
13 ,6 73
59 ,7 32
2, 6 1 9
1, 20 ,7 24
4, 72 ,3 49
38 ,9 91
1, 29 ,9 81
3, 2 4 8
83 ,2 56
1, 98 ,3 42
8, 02 3
39 ,8 31
2, 0 9 3
1, 19 ,8 32
4, 67 ,8 21
34 ,5 67
1, 09 ,3 49
3, 2 3 1
10 ,3 2, 49 9 37 ,3 4, 98 9
79
1,
7,
30
2,
9,
35
1, 38 ,4 45
2, 23 ,9 81
65 ,8 71
1, 32 ,4 51
76 ,3 45
1, 67 ,2 34
S
S m all
27, 43, 23 0
T
M ed iu m
80, 37, 12 0
U
S m all
1,1 6,4 5,7 80
S m all
54, 32, 17 0
S m all
75, 94, 63 0
V
18 8
27 4
32 7
20 1
25 5
86, 49 2
,9 3, 45 2
,4 46
74 ,5 29
47
42, 76, 91 6
92
88, 81, 17 2
10 6
1,1 8,5 0,1 77
14 ,9 8, 35 1 40 ,9 2, 13 4 63 ,5 9, 23 1
68
66, 44, 69 9
24 ,5 1, 89 2
86 ,3 24
2, 13 ,8 89
86
86, 26, 52 1
39 ,7 2, 13 7
1, 01 ,2 37
3, 28 ,7 61
54 3
,2 34
0 8 5
87 ,3 49
5, 73 ,2 19 19 ,8 3, 42 9 43 ,2 6, 71 9
49 ,9 98
1, 33 ,2 19
4, 70 8
19 ,6 43
1, 4 9 0
1, 04 ,2 31
3, 56 ,4 39
17 ,8 32
71 ,2 31
2, 8 3 0
1, 25 ,6 32
5, 18 ,6 34
40 ,1 28
1, 64 ,3 24
3, 4 4 5
1 3 4 6
0 1 3 2
0. 0 7 6 4 0. 2 9 3 2 0. 4 2 5 6
0. 0 1 4 5 0. 0 0 7 9 0. 0 0 3 7
71 ,4 45
0.2 289
0.3 279
0.2 943
0.3 843
0.0 229
0.0 213
0.0 076
0.0 011
0.2 071
0.3 021
0.1 090
0.1 031
2, 65 ,7 78 1, 19 ,3 45
69 ,3 48
8, 93 4
15 ,4 37
0 1 9 9
4 6 7 8
0. 0 2 7 4 0. 0 1 2 0 0. 0 0 6 3
0. 5 6 1 1 0. 3 1 9 8 0. 1 5 0 2
44 ,5 26
2, 1 5 1
11 ,0 9, 73 2
0. 1 5 6 3
0. 0 1 2 8
1, 56 ,2 39
0. 0 1 6 0
0. 4 0 0 2
65 ,3 48
2, 6 7 7
18 ,7 3, 42 1
0. 2 6 7 9
0. 0 0 9 1
1, 26 ,7 81
0. 0 1 2 8
0. 3 2 3 2
AC
CE
PT
ED
W
7
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81, 84 0
M
m all
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0. 1 6 3 5 0. 1 8 5 3 0. 0 0 1 1 0. 0 7 6 3 0. 0 8 7 2 0. 0 2 1 8
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Graphical Abstract
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A multidimensional approach to measuring bank branch efficiency Anna Grazia Quaranta , Anna Raffoni , Franco Visani PII: DOI: Reference:
S0377-2217(17)30903-7 10.1016/j.ejor.2017.10.009 EOR 14733
To appear in:
European Journal of Operational Research
Received date: Revised date: Accepted date:
10 November 2016 6 October 2017 9 October 2017
Please cite this article as: Anna Grazia Quaranta , Anna Raffoni , Franco Visani , A multidimensional approach to measuring bank branch efficiency, European Journal of Operational Research (2017), doi: 10.1016/j.ejor.2017.10.009
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Highlights The paper presents a 3 step approach to measuring bank branches efficiency The main aim is to represent the multidimensional nature of bank efficiency The approach is then applied to the 23 branches of a small-sized Italian bank The results confirm the potential effectiveness of the proposed approach
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A multidimensional approach to measuring bank branch efficiency
Anna Grazia Quaranta Assistant Professor
(MC), Italy
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Department of Economics and Law, Macerata University, Via Crescimbeni 20, 62100, Macerata
e-mail [email protected]
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Tel. +390733 258 3227
Anna Raffoni
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Senior Lecturer
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School of Business and Economics, Loughborough University – Loughborough, LE11 3TU, UK
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e-mail [email protected] Tel. +4401509 228232
Franco Visani (Corresponding author) Assistant Professor
Department of Management, Bologna University, Via Capo di Lucca 34, 40126, Bologna, Italy e-mail [email protected] Tel. +390543374636
2
ACCEPTED MANUSCRIPT Abstract Bank branch efficiency measurements range from simple ratio and standard regression analyses to more complex frontier approaches, each with specific strengths and weaknesses. However, in isolation, the indexes that these approaches generate fail to capture the multidimensional nature of bank branch efficiency. This paper develops a three-step procedure that enables combining the strengths of the existing approaches. We begin by taking the widest number of efficiency indexes proposed in literature (step 1), reduce the redundant information through a collinearity analysis (step
test our approach on 23 branches of an Italian regional bank.
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2), and categorize bank branches into efficiency classes through a clustering procedure (step 3). We
The results show that this three-step approach is able to provide a multidimensional view of efficiency based on indexes employing a wide range of theoretical and methodological approaches with different ways of conceiving (intermediation vs. production) and measuring (stock, vs. flow, or physical
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measures) bank outputs and inputs, different definitions of efficiency (technical and cost efficiency), and different measurement approaches (ratios, standard regression analysis and frontier functions). The resulting efficiency ranking is consistent with those that univariate indexes generate and provides a balanced evaluation of branch efficiency when such indexes produce contradictory indications.
Keywords: OR in Banking, Bank Efficiency, Data Envelopment Analysis, Multidimensional
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Performance, Performance Measurement Systems.
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1. Introduction
Bank efficiency measurements have received increasing attention in recent years. The deregulation
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of the banking sector, the financial crisis, and low interest rates have had a negative impact on bank profitability, leading to the pursuit of new sources of income. In the field of bank efficiency
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measurements, the analysis of bank branches is particularly relevant to facilitate management control (Fethi & Pasiouras, 2010; Shyu & Chiang, 2012). Branches are still one of the main sources of costs for banks and contribute to a large part of the value provided to the final customer, even after the
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digitalization of many transactions (LaPlante & Paradi, 2015). Understanding the efficiency of different branches is therefore fundamental in a competitive environment where the need to reduce the number of branches to save costs requires safeguarding the customer experience (Reuters, 2016). Whilst there is no shortage of studies addressing branch efficiency (Avkiran, 2011), the way of representing and measuring its intrinsic multidimensionality still remains an issue. Due to their complex and varied nature, banking activity outputs and inputs can be conceived and measured in different ways, and efficiency itself can be defined and measured through different approaches. Various techniques have been used to address such issues: a) partial/total factor productivity or efficiency ratios; b) standard regressions analysing the impact of a number of inputs on a specific 3
ACCEPTED MANUSCRIPT output; and c) production or cost frontier functions obtained via parametric and non-parametric methods. However, each approach has specific strengths and weaknesses and in isolation fails to capture the multifaceted nature of bank branch efficiency (Paradi, Rouatt, & Zhu, 2011). In this context, our work devises a multivariate procedure that combines the strengths of the existing approaches to provide a multidimensional view of bank branch efficiency. While prior studies address efficiency measurement by either increasing the sophistication of existing methods (e.g., Holod & Lewis, 2011) or comparing the results of different models and discussing their merits and limitations
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in different contexts (e.g., Tsolas & Giokas, 2012), the innovation of our method lies in considering the widest possible set of theoretical and methodological approaches. Our choice is motivated by the idea that no single approach is able to globally represent branch efficiency and that the issue of subjectively selecting one interpretation over another could be removed by producing as many different representations of efficiency as possible. We do so by developing a three-step procedure that first includes all the possible ways to measure efficiency (first step). Through a statistical collinearity
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analysis, we then exclude the redundant indexes (second step). Finally, through cluster analysis (third step), we group branches into efficiency classes based on the values of the remaining efficiency indexes. We then apply this approach to the branches of an Italian regional bank. Our findings indicate that our three-step approach represents the multidimensional nature of
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branch efficiency, since it jointly considers: a) different bank output-input definitions (deriving from the intermediation and production approach); b) alternative ways of measuring outputs and inputs (stock, flow or physical measures); c) different concepts of efficiency (technical and cost efficiency);
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and d) different measurement approaches (ratios, standard regression analysis, and frontier functions). Furthermore, by grouping branches into classes showing common efficiency features rather than a
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single global dimension of efficiency, we provide an overall but still multidimensional indication of the efficiency of branches. This result is particularly relevant when univariate measures yield
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contradictory indications on branch efficiency, showing positive and negative performances on different aspects. In these cases, our proposed three-step procedure avoids radical distortions in the assessment of a branch and provides a balanced view of overall efficiency.
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Our research extends prior literature on the measurement of branch efficiency with the following
two key contributions. First, and to the best of our knowledge, this is the first study adopting an allencompassing interpretation of branch efficiency rather than focusing on one or two dimensions. Second, and accordingly, our work develops a new three-step multivariate procedure that addresses the call for advancing current methodologies by combining extant approaches (Paradi & Zhu, 2013). The remainder of the paper is organised as follows: Section 2 provides the theoretical foundations of the study; Section 3 explains the proposed approach; Section 4 presents the research methods and empirical analysis; the results are discussed in Section 5; and Section 6 sets out the conclusions and suggestions for future research. 4
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2. Theoretical background 2.1. The relevance of measuring bank branch efficiency Since the beginning of the 21st century, many different factors have increased the need for bank efficiency, particularly in the European Union. The deregulation of the banking sector and the introduction of the single currency in the early 2000s led to increased market competition. More recently, the financial crisis and low interest rates, partly generated by the Quantitative Easing (QE)
new sources of profitability (Beck, De Jonghe, & Schepens, 2013).
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promoted by the European Central Bank, have reduced interest income, thus increasing the need for
In this complex context, mainly influenced by external and non-manageable factors, efficiency improvements are often considered one of the few levers to act on to consistently increase bank profits (Chortareas, Girardone, & Ventouri, 2013). According to the European Central Bank (2015),
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the increase in competition and efficiency has led to a high reduction in the number of branches (from 230,505 in 2010 to 204,146 in 2014: -11.5%) and number of employees (from 3,144,191 in 2010 to 2,889,320 in 2014: -8.1%). Refocusing the banking sector on the most efficient activities has led to efficiency measurement becoming a key factor in guiding managerial decisions. This topic has received extensive attention in academic literature, although most studies focus on the institutional
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rather than the branch level (Fethi & Pasiouras, 2010). Investigating the use of Data Envelopment Analysis (DEA) to measure bank efficiency, Paradi and Zhu (2013) found 195 studies at the institutional level and only 80 at the branch level. The analyses at the two levels have different
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purposes. At the institutional level, they aim at showing the impact of external and internal factors (regulation, globalization, different governance systems, etc.) on the efficiency of the whole bank and
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to support benchmarking (Barth, Lin, Ma, Seade, & Song, 2013; Chortareas et al., 2013; Gaganis & Pasiouras, 2013). At the branch level, the evaluation concerns the factors affecting the efficiency of
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managerial activities in different branches. This is a very relevant topic: most of a bank‟s costs are generated at the branch level and even if recently affected by technological innovation, the relationship with a specific branch is still a relevant factor of customer satisfaction (Walsh, Forth,
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Thogmartin, Bickford, Desmangles, & Berz, 2010). Consequently, the efficiency analysis at the branch level can help in understanding the
performance drivers of the whole bank, supporting cost management initiatives, and controlling and improving managerial performance (Paradi & Zhu, 2013; Shyu & Chiang, 2012). It can lead to a series of managerial actions ranging from selecting those branches to keep open after a merger or acquisition to rewarding the performance of branch managers, from developing training programs to guiding investments in new technologies or job rotation in different branches. From a managerial perspective, such an analysis at the branch level can provide very useful decision-making support (LaPlante & Paradi, 2015). 5
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2.2. The multidimensional nature of bank branch efficiency Efficiency entails the ability to employ the lowest possible level of one or more inputs to generate the highest possible level of one or more outputs. When applying this concept to bank branches, the intrinsic multidimensionality of banking activities calls for defining and measuring the specific set of outputs and inputs (Kinsella, 1980). The literature defines the main activities of banks in different ways and hence the outputs and
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inputs considered most relevant (Bergendahl, 1998). The long-standing debate on this issue (Sealey & Lindley, 1977) has essentially led to two main approaches. According to the “intermediation” (or asset) approach, the main activity of banks is acting as intermediaries between liability holders and fund receivers. In this perspective, the role of a bank is evaluated from a macroeconomic point of view, namely, as an intermediary between those that have surplus funds and those that require funds.
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Thus, liabilities are considered the inputs of the production function and the different types of loans represent the outputs. For instance, Paradi et al. (2011) analyse the intermediation abilities of 816 branches of a Canadian bank, investigating the drivers of efficiency and the impact on profitability. The “production” approach instead considers commercial banks from a microeconomic perspective as service companies combining a series of production factors (labour and capital amongst others) as inputs to generate a series of transactions with their customers (mortgages, loans, money transfers,
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etc.), namely, the outputs (Benston, 1965). For examples of this second approach, we refer the reader to Camanho and Dyson (2005), Giokas (1991), Drake and Howcroft (2002).
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These two general approaches can be developed in various ways according to the specific class of outputs and inputs selected. In their classification, Berger and Humphrey (1992) highlight two further
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approaches to defining outputs and inputs. The “user cost” approach determines whether a financial product should be considered as an input or an output based on its net contribution to bank revenues. “If the financial return on an asset exceeds the opportunity cost of funds or if the financial costs of a
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liability are less than the opportunity cost, then the instrument is considered to be a financial output. Otherwise, it is considered to be a financial input” (Berger & Humphrey, 1992: 248). The first
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applications of this approach date back to the mid-80s (Hancock, 1985). The “value-added” approach defines as important outputs both assets and liabilities that generate high value-added for the bank. Less important outputs are intermediate products or inputs depending on their specific nature. The value that each category adds is calculated by allocating the operating cost to the different categories in a cost accounting approach (Berger & Humphrey, 1992). The boundaries between the production and intermediation approach are not as clear, and as such, are more subjective. Some studies consider the value-added and the user-cost approach as variations of the production approach (Kim & McKenzie, 2010: 377), while others include these in the intermediation approach (Camanho & Dyson, 2005: 486).
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ACCEPTED MANUSCRIPT Once outputs and inputs are defined, they can be inferred through different types of measures including financial stock or flow values, or a specific amount of physical resources not expressed in financial terms. The final issue relates to the way in which efficiency can be measured. Some studies focus on technical efficiency or the amount of one or more production factors needed to generate a certain amount of one or more outputs, without considering the cost of inputs and outputs. A second approach measures allocative efficiency or the ability to select the less costly resource able to manage a defined
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activity. Analysed jointly, technical and allocative efficiency defines cost efficiency considering both technical abilities and prices (Farrell, 1957). Allocative efficiency is generally considered as a means of passing from technical to cost efficiency, and the efficiency measures usually adopted fall into the two technical and cost efficiency categories (Staub, Souza, & Tabak, 2010; Brissimis, Delis, & Tsionas, 2010). Most analyses reported in the literature focus on technical efficiency, since information on input and output costs/revenues tends to not be available or very difficult to obtain.
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According to the aforementioned premises, a single efficiency index is a combination of: a) the specific outputs-inputs definition (based on the intermediation or the production approach); b) the specific types of measures adopted to quantify outputs and inputs (stock, flow, or physical measures); and c) the way of measuring efficiency (technical or cost efficiency). Consequently, the concept of branch efficiency can be visualized as a three-dimensional space, as represented in Figure 1 below.
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Each point in the figure is a particular combination of the three dimensions indicated above and provides a specific (and therefore partial) view of the concept of efficiency. An effective approach to
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branch efficiency measurement should therefore consider multiple combinations of the three
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dimensions to adequately represent efficiency in its multidimensional perspective.
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Fig 1. The multidimensionality of bank branch efficiency
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The multidimensionality of bank branch efficiency is widely accepted in literature, but only partially translated into field studies. As Paradi et al. (2011) highlight, “most of the previous studies
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were limited to measuring one or two performance dimensions, which cannot fully reflect the overall branch functions” (p. 101). A number of studies attempt to represent the multidimensionality of bank branch activities to some degree. Oral and Yolalan (1990) analyse the relationship between operating
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efficiency and profitability using a non-parametric correlation of DEA efficiency scores. Schaffnit, Rosen, and Paradi (1997) focus on the effect of service quality and financial performance on
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operating efficiency. In a study of 68 branches of a Greek Bank, Athanassopoulos (1997) defines a DEA model including as outputs both tangible (operating efficiency) and intangible (service quality) components and embracing both the intermediation and the production approach. Manandhar and
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Tang (2002) propose a model including different aspects of bank branch efficiency: operating efficiency, service efficiency, and profitability. Similarly, Giokas (2008), in his analysis of 44 branches of a commercial bank, considers three different dimensions of efficiency: efficiency in managing the financial records of branches, efficiency in managing transactions with customers, and profit efficiency. Camaho and Dyson (2005) develop a DEA-based framework for the performance evaluation of bank branches based on both the intermediation and the production approach. Paradi et al. (2011) define a two-step DEA where production, profitability, and intermediation efficiency are evaluated in a first stage and then included as outputs in the second stage of the model.
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ACCEPTED MANUSCRIPT 2.3. The different approaches to bank branch efficiency measurement Bank efficiency, and specifically bank branch efficiency, can be measured in several different ways and academic literature offers a wide variety of approaches and applications (Fethi & Pasiouras, 2010). The first and most traditional approach is based on ratios (Schweser & Temte, 2002). Three broad categories of ratios proposed to measure bank branch efficiency are: Partial Factor Productivity Indexes (PFPIs), Efficiency Indexes (EIs), and Total Factor Productivity Indexes (TFPIs). PFPIs are
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defined by dividing a measure of value generated by the bank (for example, total loans, intermediation margin, value added, etc.) or a measure of total workload (number of transactions) by the amount of labour or capital employed (measured by number of employees, hours worked, computers, etc.), without considering the specific cost of the resources. Conversely, EIs generally compare the costs of inputs to either revenues or total assets or to other costs to quantify the value generated by the bank‟s
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activities. Finally, TFPIs jointly consider (at least) both labour and capital as inputs and weight them at the denominator of the ratio, usually employing a Cobb-Douglas production function (Coelli, Rao, O'Donnell, & Battese, 1998). Ratios are important measures of efficiency as they provide information on the performance of each branch that is easy to compute and read. This is one of the main reasons why practitioners and regulators still prefer ratios (KPMG, 2009; Thanassoulis, Boussofiane, & Dyson, 1996). On the other hand, they also have renowned limitations. First, PFPIs, by considering a
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single input at a time, provide an incomplete view of bank branch efficiency, inconsistent with the abovementioned multidimensional nature of branch efficiency. As Avkiran clearly explains, “focusing
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solely on individual key performance indicators can limit inferences that can be drawn, or it can bias the analysis because of a missing multi-dimensional perspective required to capture the complex
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operations of modern corporations” (Avkiran, 2011: 325). PFPIs can be compared only one at time, hypothesizing the other inputs as fixed (Yeh, 1996), and may provide inconsistent and misleading information when different PFPIs present dissimilar values (Coelli et al., 2005; Paradi et al., 2011). As
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for EIs (e.g., cost/income ratio), the values that different branches show could be generated by different output and input prices, and not only by the technical efficiency levels (Coelli et al., 2005).
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Second, they are affected by accounting rules and policies. The drawbacks of TFPIs relate to the complexity of selecting all the inputs to consider and the need to specify a production function without any evidence of its reliability. Finally, all the ratios share some common limitations: a) they are by nature constant returns to scale and this is not always the case in bank branch efficiency; b) they do not support improvement initiatives (Paradi & Zhu, 2013). A second approach to efficiency measurement is based on standard regressions where a measure of output is defined as the dependent variable and a series of inputs are considered independent variables (Berger, Hancock, & Humphrey, 1993; Boufounou, 1995; Feldstein, 1967; Hensel, 2003; Murphy & Orgler, 1982). In the case of efficiency measurement, the value of a standard regression is in its
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ACCEPTED MANUSCRIPT potential forecasting support and the possibility to quantify the impact of each input on the output once the others are controlled for. However, this approach has some relevant limitations. First, it requires selecting a pre-defined (unknown) production or cost function. This problem is manageable by choosing a “general” function, such as the translog function. Second, a standard regression can only manage single output-multiple input relationships, while in a bank branch, different inputs (labour, machines, spaces, financial funds, etc.) are used to generate multiple outputs (transactions, mortgages, loans, customer satisfaction, etc.). Finally, a standard regression model is only able to
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indicate an average efficiency level, without providing a measure of inefficiency compared to the best in class (Soteriou, Karahanna, Papanastasiou, & Diakourakis, 1998). Although a useful forecasting tool to obtain the mean expected value of efficiency for a new branch, it does not evaluate the inefficiency of existing branches.
The third way to measure efficiency is based on identifying the production/cost frontier functions. Different approaches can be employed to obtain the frontier functions and can be classified according
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to the specification of the production/cost function (leading to the difference between parametric and non-parametric approaches) and the particular distribution of the error term (leading to the difference between deterministic and non-deterministic approaches). In the class of parametric deterministic approaches, the most well-known are the Deterministic Statistic Frontier (DSF) (Afriat, 1972) and the Deterministic Frontier Model (DFM) (Aigner & Chu, 1968). DSF starts from the weaknesses of
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standard regressions when applied to measuring efficiency and considers - still within the sphere of econometric approaches - a frontier where the distance between the observations and the estimated
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values of the production/cost function is unilaterally distributed with one-sided non-positive/nonnegative residuals. The main issue of this approach is the strong assumption that the entire distance between each observation and the frontier is due to inefficiency and not due to any other types of
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errors (measurement errors amongst others). Aigner and Chu‟s (1968) DFM is based on identifying via mathematical programming methods the function maximizing a single output given a series of
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inputs. The main issue of this approach is that, being based on mathematical programming, the parameters do not show any statistical properties (Forsund, Lovell, & Schmidt, 1985; Greene, 1980).
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Moving to the parametric stochastic approaches, the Stochastic (Statistic) Frontier Approach (SFA) (Aigner, Lovell, & Schmidt, 1977; Meeusen & Van Den Broeck, 1977) has garnered great attention in literature. SFA defines efficient frontiers as parametric functions where, contrary to the deterministic approaches, a series of potential random shocks are taken into consideration. Although this assumption is certainly more robust, it generates higher statistical complexity and further assumptions on the distribution of the two components of the total error (one related to efficiency, the other related to measurement errors and other random shocks) (Forsund et al., 1985). SFA is widely used in practice (Battese & Coelli, 1992, 1995; Coelli et al., 2005). Finally, the most frequently used non-parametric approaches are Data Envelopment Analysis (DEA) (Charnes, Cooper, & Rhodes, 1978, Banker, Charnes, & Cooper, 1984) and Free Disposal 10
ACCEPTED MANUSCRIPT Hull (FDH) (Deprins, Simar, & Tulkens, 1984), developed within the management science framework. DEA offers a wide family of non-parametric models providing an efficiency measure defined as the maximum value of the ratio of the weighted sum of outputs to the weighted sum of inputs. Its main aim is to identify, through mathematical (often linear) programming, a frontier of efficient Decision Making Units (DMUs) that “envelopes” the other units. DEA has received much attention from academics and is today the most commonly used approach for efficiency evaluations. In the banking sector alone, Paradi and Zhu (2013) find 275 DEA applications between 1985 and 2011. DEA models
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have many advantages: they can manage multiple inputs-multiple outputs; they do not require the specification of the production/cost function linking outputs and inputs; and they work well with small samples. However, DEA in its “basic” form also has limitations (Coelli et al., 2005; Fethi & Pasiouras, 2010): a) it assumes that the included inputs and outputs are measured without noise and without putting forward any axioms on the distributional structure of deviations from a best structure frontier (Banker, 1996); b) it is sensitive to outliers; c) it shows a large percentage of efficient DMUs
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when the number of observations is low compared to the number of inputs and outputs; and d) it treats inputs and outputs as homogeneous entities, thus giving rise to misleading results when these are heterogeneous. Finally, FDH is a more general version of DEA, not restricted to convex technologies. However, as for any other deterministic frontier, one of the main drawbacks of FDH is the presence of “super-efficient” outliers that can affect the frontier (Simar & Wilson, 2008).
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Several studies have been conducted to overcome the limits of the basic SFA and DEA models. As for the SFA, to avoid the need for a parametric functional form, Banker (1988), Banker and
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Maindiratta (1992), and Fan, Li, and Weersink (1996) developed different models to obtain a semiparametric approach to SFA, later developed further by other scholars (Kuosmanen, 2008; Kuosmanen & Johnson, 2010; Kuosmanen & Kortelainen, 2012; Kuosmanen, Johnson, &
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Saastamoinen, 2015). A different set of studies (Simar & Wilson, 2002; Simar, 2007) developed new approaches to SFA to obtain a non-parametric estimation of the expected inefficiency (for a recent
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study presenting semiparametric and non-parametric approaches to SFA, see Park, Simar, and Zelenyuk, 2015).
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On the other hand, a number of studies (which can be categorized under the “Stochastic DEA” umbrella) attempt to overcome the deterministic nature of the DEA frontier. These follow two different approaches (Olesen & Petersen, 2016). The first approach (Banker, 1993; Korostelev, Simar, & Tsybakov, 1995a, b; Simar & Wilson, 1998, 1999, 2007), through particular statistical axioms, develops an evolved DEA framework based on a statistical model and a sampling process. For instance, starting from Simar and Wilson (1998, 1999), several contributions use a bootstrapping technique with the aim of obtaining a statistical inference for DEA (Liu, Lu, & Lu, 2016). These modifications allow DEA to provide a consistent but biased estimator of the true frontier, although restrictive and unrealistic axioms need to be imposed (Olesen & Petersen, 2016). The second approach (Cooper, Huang, & Li, 1996; Land, Lovell, & Thore, 1993; Olesen & Petersen, 1995) 11
ACCEPTED MANUSCRIPT specifies a random reference technology and adopts specific DMU-distributions to replace the data on which the DEA analysis is based. These evolved interpretations of SFA and DEA have actually reduced the distance between the two approaches (Cooper & Lovell, 2011). Potentially, the hybrid models developed are almost free of the limitations of the original SFA and DEA methods. However, they are generally based on strong and often unrealistic assumptions that limit their use in real applications (Olesen & Petersen, 2016; Parmeter & Kumbhakar, 2014) and are thus rarely applied in the field of bank efficiency (see, for
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instance, Kao & Liu, 2009). Considering the methodological issues in measuring bank branch efficiency, extant contributions mainly follow two lines of enquiry. The first aims to develop more comprehensive versions of a specific approach. For instance, Cook, Hababou, and Tuenter (2000) develop a specific DEA approach to manage situations where inputs are shared by different activities. Camaho and Dyson (2005) define a DEA model to measure cost efficiency when price information is incomplete. Holod
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and Lewis (2011) propose a specific DEA model to solve traditional issues regarding the role of deposits as input or output. The second line of enquiry focuses on comparing the results of two different approaches to understand the reasons for dissimilarities and/or to derive managerial implications. For instance, Avkiran (2011) compares the results of a DEA application with financial ratios commonly used to evaluate and manage bank performance. Giokas (2008) and Tsolas and
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Giokas (2012) analyse DEA in comparison to a deterministic econometric approach to identify frontiers. Ruggiero (2007) compares the results of the stochastic frontier model and DEA using panel
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data. However, there is currently a lack of studies that combine the different approaches to efficiency measurement (ratios, efficiency indexes derived via standard regressions, and those obtained after identifying different types of frontiers) to leverage their respective strengths while containing their
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weaknesses. Paradi and Zhu (2013: 70) specifically call for these types of studies when concluding their review of DEA applications in bank branch efficiency measurement, “Another interesting future
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research area is to find new ways to apply DEA in conjunction with other advanced methodologies in order to extend such methodologies and to complement each other‟s strengths while eliminating their
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weaknesses”.
3. A multidimensional approach to efficiency measurement: Methodological aspects. Following the aforementioned considerations, we devise a multidimensional approach to the
measurement of bank branch efficiency. Our main aim is to provide a multifaceted interpretation of branch efficiency without focusing on a single specific dimension of the concept. From the methodological point of view, we do not intend to define the umpteenth development of existing approaches, potentially increasing their complexity and difficulty of understanding. Rather, we combine existing approaches in their simplest form to facilitate their practical implementation in the
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ACCEPTED MANUSCRIPT banking context. By considering the widest possible set of theoretical and methodological approaches, we aim to compensate for the natural weaknesses of each and reduce the subjectivity that usually characterises efficiency measurements. Our proposed approach, illustrated in Figure 2, can be described as a three-step method. The first step entails the application of all the methods to measure efficiency as previously discussed in Section 2. The selection of the specific indexes and the outputs-inputs measures is driven by two main criteria: a) the analysis of the literature and the indicators used by regulators to understand the entire set of
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potential indexes; b) the evaluation of the available data to understand which of the potential indexes are computable. The process therefore starts from computing the conventional ratios and then moving on to applying the standard regression models and frontier approaches (parametric and non-parametric, deterministic and stochastic). In other words, none of the existing theoretical and methodological positions would be favoured. This approach is intended to ensure the widest and most inclusive representation of the diverse nature of branch activities. Furthermore, it avoids privileging one
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approach over another, thus reducing subjectivity in: a) the selection of the method to measure efficiency (e.g., ratios vs. standard regressions vs. frontier approaches); b) the choice of the measurement of partial or total productivity; c) the decision on which outputs/inputs definition and measure to include; and d) the prioritization of one dimension of efficiency over another. Then (second step), we apply a multicollinearity analysis to the efficiency measures produced in
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the first step to remove redundant information. We define a specific Variance Inflation Factor (VIF) threshold and exclude from the analysis all the indexes with a VIF above the threshold. This therefore
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leaves the role of eliminating overlapping indexes to a more objective statistical approach and ensuring a multidimensional representation of branch efficiency. Finally, the third step entails a cluster analysis to group branches into efficiency classes for two
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reasons. First, as a multivariate procedure, it does not privilege any efficiency classification of branches provided by a specific approach, thus not favouring any theoretical or methodological
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position. This ensures considering a large number of factors that may influence the efficiency levels of the different branches. Second, this approach takes into consideration all the information provided
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by the different index values recorded in the branches and not only those related to homogeneous indexes, as occurs, for instance, when graphical analyses are applied. In other words, the aim is not to consider a single indicator globally representing bank efficiency, but to cluster the branches into groups with common efficiency features.
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Fig. 2. The proposed approach to bank branch efficiency measurement
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4. Empirical Analysis
The following sections present the development of the three steps of our proposed
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multidimensional approach to bank branch efficiency measurement and the main results obtained.
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4.1. Data set
We test the proposed approach on a bank operating in central Italy. To protect confidentiality, the bank‟s real name is not disclosed and we shall refer to it as „Alpha‟.
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Alpha is a regional bank (1.3 billion in total assets and 200 employees in 2014) operating through 23 branches with around 38,000 active customers. The branches are located in a single region and
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operate under the same technological, social, and economic conditions. The selection of the case is critical to our study, as the objective is to classify branches into
efficiency classes through a multivariate approach. We deemed Alpha appropriate for the following reasons:
a. The bank provides a wide range of services to both private and business customers, rendering branch comparison through multidimensional approaches a critical issue. b. The bank has an established information system capable of providing reliable and plentiful data for each branch. Such accessibility combined with the diversified activities ensures the computation of a considerable number of indicators representing different types of efficiency.
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ACCEPTED MANUSCRIPT c. The bank showed significant interest in the project and allowed us access to an ample and varied amount of data. Data collection took place in 2015. We held an initial focus group with the bank‟s senior management team and controller to discuss the existing approach to measuring branch efficiency, and examined any data disclosure and confidentiality issues. This led to the exclusion of some data considered sensitive, such as exact branch locations and other branch-specific contextual information (number of retail and business customers, personal information on employees working in each branch,
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etc.). The bank headquarters provided almost all the data required for the multivariate procedure. The bank‟s controller played a pivotal role throughout the project; his support was in fact critical to ensure a correct understanding of the information provided and to evaluate the reliability and consistency of the raw data.
The first step (computation of all the possible efficiency measures, given the available data) is the most time-intensive, requiring approximately 23 hours in our case and a combination of software
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(Excel, Stata and GAMS). Step 2, the multicollinearity analysis, took around 3 hours and reduced the number of indexes from 65 to 19. Finally, the cluster analysis (step 3) took approximately 10 hours to complete. We ran the step 2 and 3 analyses through IBM SPSS. Overall, the procedure required approximately 36 hours of work once the data were available.
Table 1 reports the main steps of the analysis, as well as information on timing and the software
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employed.
Details of the data analysis
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Table 1
Data Analysis
Time
Software
2 hours
Excel
(ii) Efficiency Indexes obtained after estimating the parameters of the standard regression models
3 hours
Stata
(iii) Efficiency Indexes derived from the frontier functions obtained according to Aigner and Chu (1968)
3 hours
GAMS
(iv) Efficiency Indexes derived from the Deterministic Statistic Frontier obtained via an econometric approach
5 hours
Stata
(v) Efficiency Indexes derived from the Stochastic Frontier Analysis obtained via an econometric approach
3 hours
Stata
(vi) Efficiency Indexes derived from the Non-Parametric Frontier obtained via DEA
3 hours
Excel
(vii) Efficiency Indexes derived from the Non-Parametric Frontier obtained via FDH
4 hours
Excel
Step 2. Collinearity analysis
3 hours
IBM SPSS
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Step 1. Indexes Computation
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(i) Efficiency Indexes in the form of ratios
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10 hours
Step 3. Cluster analysis
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4.2. Step 1: Computing the widest possible set of efficiency measures suggested by literature The first task of the analysis is computing the widest possible set of efficiency measures developed in literature and feasible for the available data (ratios, efficiency indexes obtained after estimating the parameters of standard regression models, and those deriving from the frontier functions obtained in
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all the ways currently known). As a result, the efficiency measures expressed as ratios number 48: 32 Partial Labour Productivity Indexes (PLPIs); 1 Partial Capital Productivity Index (PCPI); 2 Total Factor Productivity Indexes (TFPIs); and 13 Efficiency Indexes (EIs) (see Table A.1 in the Appendix for the detailed list of the calculated ratios). Even if the correlation between many were intuitive, we included all for maximum objectivity of the analysis, leaving the selection of the most meaningful indicators to the subsequent multicollinearity analysis.
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Based on the available data, we implemented the following translog production function standard
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regressions:
where: -
represents the 23 branches analysed
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- NOP is the total annual number of transactions carried out by employees - EMP, HOURS, and COM respectively represent the number of employees, hours worked
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(measuring labour input), and computers in the information system (measuring capital input).
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As is evident, the only difference between the two models is the specific measure adopted for labour input: number of employees in the first, number of hours worked in the second. Both models are proposed in literature and even if we could have hypothesized a correlation between their results, we considered both, again leaving the role of reducing the set of efficiency indexes to the multicollinearity analysis. The estimated coefficients led to the definition of two vectors of regression residuals (
) with either positive or negative values. They measure the efficiency of each
branch comparing (as the difference of) the actual output of each with the (average) output estimated by the standard regressions at the same input level. The preliminary analysis highlighted the absence
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ACCEPTED MANUSCRIPT of clear outliers, a general distribution of the independent variables close to normal, and an acceptable level of collinearity among the regressors. Considering the different orders of magnitude of the regressors, we also carefully analysed the Beta coefficients and tested the further OLS assumptions for a multiple regression. All the parameters were statistically significant at the 95% probability level, with an R2 equal to 92% for model [1] and 90% for model [2]. Based on the same information used to generate the vectors
, we developed the
efficiency indexes based on frontiers. We considered and applied all the basic approaches to obtain a
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frontier function described in Section 2.3. For the parametric approaches (Deterministic Frontier Model, Deterministic Statistic Frontier, and Stochastic Frontier Analysis) we assumed the same production function defined in [1] and [2].
More specifically, the different approaches adopted to obtain a frontier function led to the following vectors: 1)
and
, i.e., the vectors of the distances between the empirical output value
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and the frontier value identified with the parametric deterministic approach of Aigner and Chu (1968) (Deterministic Frontier Model: DFM) based on mathematical programming 2)
and
, i.e., the vectors of the distances between the empirical output
value and the frontier value identified with a parametric deterministic econometric approach (Deterministic Statistic Frontier: DSF) and thus imposing non-positive regression residuals and
, i.e., the vectors of the distances between the empirical output
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3)
value and the frontier value identified with a parametric stochastic econometric approach
4)
and
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(Stochastic Frontier Analysis: SFA)1
, i.e., the vectors of the ratios between the empirical output value
approach)2 5)
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and the frontier value identified via Data Envelopment Analysis (non-parametric deterministic
and
, i.e., the vectors of the ratios between the empirical output value
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and the frontier value identified via Free Disposal Hull (again, a non-parametric deterministic approach)
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A first analysis of the ten vectors generated by the five different frontier definition approaches shows that the order of the branches in relation to the level of efficiency is entirely coincidental. We then applied the same five approaches to a different set of outputs and inputs. We defined total
financial assets as output and number of employees, and operating costs as inputs. For the parametric 1
We followed the common assumption that , representing the symmetric component of the error due to random factors and measurement errors, follows a normal distribution and that the component due to inefficiency is non-negative and follows a one-side normal distribution. A second assumption is that the two components of are independent (covariance equal to 0 for every observation). For all the regressions, all the parameters were statistically significant at the 95% probability level, with an R 2 at least equal to 91% and 90% respectively for the frontier function in the form of [1] and [2]. 2 The DEA model used is an output-oriented CCR model.
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ACCEPTED MANUSCRIPT approaches (DFM, DSF, and SFA), we again hypothesized a translog function. As a consequence, we defined five other vectors measuring the difference of the empirical values of the output from the frontier values, i.e., approach),
(DFM approach), (DEA approach) and
(DSF approach),
(SFA
(FDH approach). Again, the efficiency
order of the 23 branches generated by the five different approaches was exactly the same. In summary, at the end of this first part of the analysis, we calculated 65 efficiency measures for each branch: 48 ratios, 2 indexes deriving from the standard regressions, and 15 obtained from the
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different basic frontier identification approaches. We used all the approaches defined in literature to measure efficiency, representing all the different views of efficiency, considering different outputs and inputs (based on the production and the intermediation approaches), and adopting all their different measurement options (stock, flow, and physical values). As a consequence, we measured the efficiency of branches with the maximum possible level of multidimensionality.
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4.3. Step 2: The multicollinearity analysis to reduce the number of efficiency indicators
In line with the designed approach and to remove redundant information, we ran a multicollinearity analysis where a conservative level of 5 for the VIF was used as the threshold to retain an index in the analysis. At the end of this evaluation, 19 out of 65 efficiency indexes were retained: 9 Partial Labour Productivity Indexes (PLPI1, PLPI31, PLPI30, PLPI4, PLPI6, PLPI7, PLPI8,
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PLPI17, PLPI19), 1 Partial Capital Productivity Index (PCPI1), 1 Total Factor Productivity Index (TFPI1), 5 Efficiency Indexes expressed as ratios (EI1,EI2, EI5, EI9, EI11), 1 vector of standard
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regression residuals (PFEI2), and two vectors of efficiency values (PFFEI2_AC and PFFEI3_AC) derived from the frontier functions obtained according to the DFM approach.
23 branches.
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Table A.2 in the Appendix reports the values of the 19 residual efficiency measures for each of the
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4.4. Step 3: The cluster analysis
We developed the cluster analysis through the following steps:
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- A preliminary analysis aimed at identifying potential outliers that may adversely affect the
construction of the cluster. The negative outcome of this assessment enabled us to process all the available values for the efficiency indexes. - Since the 19 variables have different units of measure and/or orders of magnitude, we transformed their values so as not to alter the actual weight of the individual information provided by the various efficiency indexes during the subsequent processing. This methodological choice definitively ruled out any over- or under-dimensioning of the actual importance of the variables used for grouping. To transform the values, we derived the z scores via the normal standardization process. 18
ACCEPTED MANUSCRIPT - As mentioned in the previous section, the information in the 15 efficiency measure vectors generated by the five frontier approaches substantially coincides. As a consequence, the multicollinearity analysis left only two of the 15 obtained vectors, i.e.,
.
Considering the relevance of these types of indicators, we attempted to use all 15 vectors in the cluster analysis in all the different combinations of two vectors at a time to check for any substantial change in branch allocation to the different groups. The composition of the clusters remained substantially unchanged.
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- As all the variables are quantitative, we used different hierarchical and a non-hierarchical (kmeans) approaches to cluster analysis to compare the results and to test the robustness of the groups obtained.
- With regard to the hierarchical methods, as it was possible to use all the algorithms and all the similarity measures through the software (SPSS), we carried out a number of tests combining their
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variants in almost every possible way. The clusters did not substantially change.
All the variables included as inputs for the clustering procedure were statistically significant in the grouping process. The k-means approach and the various hierarchical approaches implemented provided clusters substantially composed of the same branches3.
Table 2 reports the three clusters of branches obtained with the k-means clustering procedure and
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the Ward procedure (similarity measure = simple Euclidean distance) 4 , while Table 3 reports the average value of each efficiency index within each of the three resulting clusters.
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We then analysed the composition of the branches within each cluster. All the large-sized branches belong to Cluster 1, except for branch O, included in the second cluster. Only one medium-sized branch (H) belongs to the cluster of the most efficient branches, while B, E, J, M and T are members of
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the second cluster and K, N and P of the third cluster. The small branches Q, U and W belong to the
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second group, while D, F, L, R, S and V to the third group.
Table 2. The clusters obtained through the k-means and Ward clustering methods Cluster 2
Cluster 3
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Cluster 1
3
To verify the stability of the solutions obtained, we implemented the different procedures (hierarchical and nonhierarchical) several times using the aggregation data arranged in different random order. The results obtained within the same procedure were very similar. As for the k-means approach, given that the ordering of the initial cluster centres may affect the final solution, we ran various permutations of the values of the initial centres and the final results remained substantially unchanged. 4 We report these particular results as the Ward method is generally considered preferable in application contexts such as this. The preference in showing the results obtained from the Ward method in relation to the use of the simple Euclidean distance as a measure of similarity instead simply derived from the fact that the simple Euclidean distance is the default measure SPSS uses in a non-hierarchical cluster analysis via a k-means procedure.
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ACCEPTED MANUSCRIPT Branches showing the highest values for the measures
Branches showing average values for all the indicators
Branches showing lowest values for the measures
, highest values for the measures
and closest to zero for
and further away from zero (negative) for
Branches A, C, G, H, I
Branches B, E, J, M, O, Q, T, U, W
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lowest values for the measures
Branches D, F, K, L, N, P, R, S, V
As external analysts with no other information on the branches, we could not further investigate the efficiency drivers. However, an internal analyst or an external consultant with all the necessary
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information on the location of the branches, the bank‟s strategies, and the contextual factors affecting performance could run a more thorough analysis to understand the efficiency drivers and define the most appropriate actions to improve this.
Table 3. Average values of the 19 clustering variables within each cluster Cluster 1 25.505.466 386 122 26.357.609 7.207.922 143.769 686.511 58.786 254.478 4.427 6.263.909 0.4953 0.0020 55.255 0.0046 0.0964 0.1613 0.0000 0.0000
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CE
PT
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Measure
Cluster 2 9.816.415 299 99 10.492.073 5.134.279 115.426 432.334 29.108 110.002 3.155 3.233.688 0.3596 0.0055 92.413 0.0095 0.2310 0.0247 -0.0235 -0.0192
Cluster 3 5.076.926 201 64 6.164.203 2.238.880 78.325 201.057 8.449 38.260 2.103 1.077.100 0.2352 0.0129 177.116 0.0190 0.4464 -0.1151 -0.2059 -0.2942
4.5. Validation of the proposed three-step procedure We validated the proposed approach by comparing the results of the three-step procedure with those produced by each of the 19 indexes used in the cluster analysis. This validation process involved two stages: (1) a quantitative assessment of the similarity of the rankings, and (2) a detailed 20
ACCEPTED MANUSCRIPT qualitative analysis of their divergences. We deemed this approach appropriate given the nonobservable nature of the problem entity („true‟ efficiency performance of the bank branch), which limited the possibility of employing statistical procedures and artificial data (Sargent, 2013). Each of the 19 univariate indexes describes a specific (and partial) view of the overall efficiency of a branch and none could therefore be considered as a gold standard. Since the non-observability of the problem entity calls for the most thorough investigation possible (Sargent, 2013), we employed a combination of objective (quantitative) and subjective (qualitative) approaches in the validation process. To do so,
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we first partitioned the efficiency values of each individual index into three classes taking into account the symmetric or asymmetric distribution of the related values5. For each individual index, we then allocated the branches to one of the three classes based on their specific efficiency value (Table 4). We assessed the degree of similarity between the efficiency classes obtained through the clustering procedure and those produced by each of the univariate indexes by computing the percentage of coincidence of the two classifications and Spearman‟s rho correlation index (Spearman, 1904; Gosset,
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1921). The results show that on average the percentage of coincidence between the classifications generated by the multivariate approach and that of each univariate index separately is 74% (ranging from 65% with PLPI_4 to 96% with PLPI_8), while Spearman‟s rho is 0.83 (ranging from 0.76 with PLPI_31 to 0.96 with PLPI_8). Furthermore, when classified differently, branches are always allocated in adjacent classes. In other words, only one-class changes were observed. None of the
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reported differences show branches included in Cluster 1 ending up in Cluster 3 (and vice-versa) under a different approach.
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At this stage, we undertook a detailed examination of the branches classified in different classes by the univariate indexes compared to the clustering procedure to investigate our proposed multivariate procedure‟s ability to provide a multifaceted representation of branch efficiency compared to
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univariate measures of efficiency. The qualitative analysis shows that the multivariate approach appears to better balance positive and negative performances on different dimensions of efficiency
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(Table 4). Branches performing well or badly on all dimensions are consistently classified in the first class (high-efficiency) or in the third class (low-efficiency), regardless of the approach taken. For
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example, both the cluster analysis and each univariate index rank branches D, L and S in class 3. However, when branch performance is not as clear-cut on all aspects, discrepancies emerge. 5
For indexes with a symmetric distribution of values, we identified the low-efficiency class by considering the minimum efficiency value as the lower class limit and the mean of the efficiency value less their standard deviation as the upper class limit. The medium-efficiency class included values between the mean of the efficiency values less their standard deviation and the mean of the efficiency values plus their standard deviation. Finally, the high-efficiency class comprised values between the mean of the efficiency values plus their standard deviation and the maximum efficiency value recorded by the index. Where the index presented a certain degree of asymmetry in the value distribution, we divided the efficiency values into three same-sized classes. We obtained these by deducting the lowest efficiency value from the highest efficiency value and then dividing by three. The low-efficiency class boundaries were therefore represented by the lowest efficiency value and the lowest efficiency value plus the class width respectively. The medium-efficiency class included values between the lowest efficiency value plus the class width and the maximum efficiency value less the class width. Finally, the highefficiency class comprised values between the maximum efficiency value less the class width and the maximum efficiency value.
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Table 4. Comparison of the cluster analysis and univariate efficiency indexes rankings PL PI _ 8 1 2 1 3 2 3 1 1 1 2 3 3 2 3 2 3 2 3 3 2 2 3 3
PL PI _1 7 1 3 1 3 3 3 1 1 1 2 3 3 2 3 2 3 2 3 3 3 2 3 3
PL PI _1 9 1 3 1 3 3 3 1 1 1 3 3 3 2 3 2 3 3 3 3 3 2 3 3
P C PI _1 1 2 1 3 2 3 1 2 2 2 3 3 2 3 2 3 2 3 3 2 2 3 2
TF PI _ 1 1 3 1 3 3 3 1 1 1 2 3 3 2 3 2 3 2 3 3 3 2 3 3
E I _ 1 2 3 2 3 3 3 2 2 2 2 3 3 2 3 2 3 2 3 3 3 2 3 3
E I _ 2 1 2 1 3 2 3 1 1 1 2 2 3 2 2 2 3 2 3 3 2 2 3 2
E I _ 5 1 1 1 3 1 2 1 1 1 1 2 3 1 2 1 2 1 2 3 1 1 2 2
E I _ 9 1 1 1 3 2 2 1 1 1 1 2 3 1 2 1 2 1 3 3 2 1 2 2
EI _ 1 1 1 2 1 3 2 2 1 1 1 2 2 3 2 2 2 3 2 3 3 2 2 2 2
P FE I_ 2 1 2 2 3 3 3 2 2 2 2 3 3 2 3 2 3 2 3 3 3 2 3 3
PFF EI_ 2_A C 1 2 1 3 2 2 1 1 1 2 2 3 1 2 2 3 2 3 3 2 2 3 2
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PL PI _ 7 1 2 1 3 2 2 1 1 2 2 2 3 2 2 2 2 2 2 3 2 2 2 2
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PL PI _ 6 1 2 1 3 2 2 1 1 1 2 2 3 1 2 2 3 2 3 3 2 2 2 2
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PL PI _ 4 1 3 1 3 3 3 1 1 1 3 3 3 2 3 3 3 3 3 3 3 3 3 3
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PL PI _3 0 1 2 1 3 2 2 1 1 2 2 2 3 2 2 2 3 2 3 3 2 2 2 2
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PL PI _3 1 1 3 2 3 3 3 2 2 2 3 3 3 2 3 2 3 3 3 3 3 2 3 3
PFF EI_ 3_A C 1 2 1 3 2 2 1 1 1 2 2 3 1 2 2 3 2 3 3 2 2 3 2
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PL Br PI an _ ch 1 A 1 B 3 C 1 D 3 E 3 F 3 G 1 H 1 I 1 J 3 K 3 L 3 M 2 N 3 O 2 P 3 Q 3 R 3 S 3 T 3 U 2 V 3 W 3
The analysis of branches B, E, J, O, Q, T and U shows that depending on the univariate index
selected, their performance can be interpreted as manifesting high-, medium- or low-efficiency. For instance, branch B records high-efficiency in 2 indexes (Class 1), medium-efficiency in 11 indexes (Class 2), and low-efficiency in 7 indexes (Class 3). In all cases, the proposed multivariate approach consistently classifies B, E, J, O, Q, T and U in the medium-efficiency category (Cluster 2). All in all, the multivariate nature of the proposed approach would seem to better account for divergent performances on different aspects of efficiency compared to the univariate approaches. In other words, 22
ACCEPTED MANUSCRIPT our proposed procedure does not penalise or reward branches on single dimensions based on good or bad performances. Rather, it jointly considers the outcomes of all the univariate indexes and balances positive and negative performances as measured by the different approaches. The analysis of branches P and W further support this point. For instance, EI_2 includes both branches in the mediumefficiency group. However, the two branches appear to be quite different. P falls into the lowest efficiency group in 16 out of 19 indexes, whilst W in 9 out of 19. By balancing different dimensions, our proposed multivariate approach appears to provide a better description of the overall efficiency
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level of the two branches: P, which performs negatively in most efficiency indexes, is included in the “low-efficiency” group; W, which tends to perform better than P in a number of other efficiency aspects, is included in the “medium-efficiency” class. Univariate approaches tend to over- or underestimate efficiency when a single measure (single view) of efficiency is used to rank branches.
In sum, both the quantitative and qualitative assessments confirm that the efficiency view that our proposed approach provides is consistent with those generated by the univariate indexes. Furthermore,
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when they yield contradictory results, our three-step procedure offers a balanced description of branch efficiency.
5. Discussion
Banking efficiency is difficult to compute due to the complex and varied nature of the outputs and
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inputs involved (Kinsella, 1980). Extant research addresses the issue either by increasing the level of sophistication of existing approaches (Cook et al., 2000; Holod & Lewis, 2011) or by comparing
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different methods and discussing their limitations and merits in different contexts (Giokas, 2008, 2012; Avkiran, 2011). Conversely, the three-step procedure here proposed is based on the notion that no single approach is able to provide a multidimensional view of banking efficiency and addresses this
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issue by combining the widest possible range of theoretical and methodological approaches. First, the ability to ensure a multifaceted representation of efficiency emerges from the analysis of
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the type of indexes used. From a theoretical perspective, the 19 indexes identified in the collinearity analysis represent different ways of conceiving bank outputs-inputs (intermediation and production
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approach), alternative ways of measuring outputs and inputs (stock, flow, or physical measures), and different concepts of efficiency (technical and cost efficiency). For instance,
(net revenues on
services/number of employees) derives from the production-view of banking activity, using both flow (for the output) and physical (for the input) measures, providing a measure of technical efficiency. Conversely,
(operating cost/total financial assets) and
(operating costs/total assets) originate
from the intermediation view of banking activity, adopting a stock-type measure (for the output) and a flow-type measure (for the input), providing an indication of cost efficiency. Table 5 summarises the different dimensions of efficiency as explained by the residual indexes.
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Table 5 Number of efficiency indexes by efficiency concept, outputs/inputs definition, and measures of output Outputs/Inputs Definition
Intermediation Approach
Output Measure
Stock
Flow
Technical
2
3
Cost
3
2
Physical Quantities
Stock
Flow
Physical Quantities
1
2
4
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Efficiency Concept
Production Approach
1
1
The two ways of considering bank activities are equally represented (10 outputs/inputs definitions from the intermediation approach and 9 outputs/inputs definitions from the production approach) as are the different concepts of efficiency (12 indexes of technical efficiency and 7 indexes of cost
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efficiency), and type of output measure (6 are stock measures, 8 are flow measures, and 5 are physical measures). As for type of measure, the indicators are categorised according to the output rather than the input measure, although worth highlighting is that most of the indexes include different types of measures for outputs and inputs. For example,
incorporates a flow measure of output (net
interest margin) and a physical measure of input (number of employees). Similarly,
includes a
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flow measure of input (operating costs) and a stock measure of output (total financial assets). Evident from classifying the type of measure in the output perspective is that all the measures considered for
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the intermediation approach cannot be physical quantities, representing the stock or flow of intermediated resources. Conversely, several indexes represent the intermediation approach where the input is physical quantities (number of employees, number of hours worked, etc.). In general, some
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measures are not as clear-cut from a theoretical point of view (Camaho & Dyson, 2005; Kim & Mackenzie, 2010) and all the classifications include some subjective judgements. Table 5 is therefore
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descriptive and has no normative intent. Figure 3 shows a selection of residual indexes plotted against the three-dimensional illustration of efficiency reported in Figure 1. As is clear from the graphic representation, the residual indexes are
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able to provide a rich and varied description of efficiency.
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Fig. 3. 3D Plot of selected residual indexes
From a methodological point of view, we computed the residual indexes using a number of
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different methodologies providing a full account of those available. After performing the collinearity analysis, several types of ratios, an efficiency index obtained after estimating the parameters of a
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standard regression model, and two indexes derived from two different production frontier functions remained. In detail, the 19 remaining indexes include: 9 Partial Labour Productivity Indexes (PLPI1, PLPI4, PLPI6, PLPI7, PLPI8, PLPI17, PLPI19, PLPI30, PLPI31), 1 Partial Capital Productivity Index
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(PCPI1), 1 Total Factor Productivity Index (TFPI1) and 5 Efficiency Indexes represented through ratios (EI1, EI2, EI5, EI9, EI11), 1 vector of standard regression residuals (
and 2 vectors of
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distances between the empirical output value and the production frontier identified through the parametric deterministic approach of Aigner and Chu (1968) (
and
).
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Second, the clustering procedure enabled an overall but multidimensional indication of branch efficiency. Three clear-cut clusters, representing high, medium, and low efficiency branches, emerged from the analysis. This outcome is of particular relevance, since a comprehensive approach prompts issues of readability and interpretation of the resulting information. We grouped the branches with common efficiency features into classes (as described by each of the 19 univariate residual indexes) rather than a ranking based on a single indicator globally representing branch efficiency. By jointly considering the outcomes of all the univariate indexes, the cluster analysis provides a ranking that is consistent with those generated by each of the univariate indexes when a branch either performs positively or negatively across all dimensions of efficiency. However, when discrepancies emerge, it is able to balance positive and negative performances as measured by the different univariate 25
ACCEPTED MANUSCRIPT approaches. As the results of the validation process show, the use of a multivariate procedure avoids radical distortions in the assessment of a branch and provides a more accurate description of efficiency.
6. Conclusions This paper presents a three-step approach providing a multidimensional view of bank branch efficiency. The first step includes the widest number of efficiency indexes generated by all existing
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theoretical and methodological approaches with the aim of embracing the multidimensional nature of efficiency. Thereafter, we reduced the redundant indexes through a collinearity analysis, and finally, clustered the branches based on the remaining values of the indexes.
The analysis of the 23 branches of an Italian regional bank shows that our proposed three-step approach generates a multivariate efficiency ranking that: a) is based on indexes representing different
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output-input definitions and proxies (intermediation vs. production approach; stock vs. flow or physical measures), different views of efficiency (cost vs. technical efficiency), and different measurement approaches (ratios, standard regression analysis, and frontier functions); b) is consistent with those obtained through existing univariate approaches; and c) provides balanced solutions when different univariate approaches yield inconsistent rankings for the same branch. Furthermore, our proposed approach enables removing the initial “subjective” and potentially
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biased choice of which output/input definition and measure, and which efficiency definition and measurement approach to include in the analysis. The application also shows the practical feasibility
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of the approach. Excluding the dataset preparation, a prerequisite regardless of the procedure, the overall analysis required approximately 36 hours, an acceptable amount of time considering the
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relevance of the information generated.
We conclude with some remarks on the limitations of our work and indications for future research. First, we conducted the research on the branches of a single bank located in the same region,
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consistently with our main research objective (studying the ability of our three-step approach to provide a multidimensional view of branch efficiency) and the specific case analysed. However,
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efficiency could be affected by external factors related to geographic/institutional and managerial aspects that are beyond the control of managers and employees. Future research could analyse which approach is able to take into consideration these environmental factors in the three-step approach. A second development consists in investigating the possibility of applying our proposed approach not only to compare bank branches but also whole banks, to address the increasing demand from regulators to analyse efficiency. From a theoretical point of view, no obstacles impede using the three-step approach in different contexts, but further studies could investigate the issues and the contributions to literature that this approach could generate. Finally, while this paper is largely “technical”, future research could also investigate the organisational and managerial implications of
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ACCEPTED MANUSCRIPT adopting our proposed approach. This is consistent with the growing interest in understanding the application of OR approaches in practice (Franco & Hämäläinen, 2016).
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High-Powered Branch Network in Retail Banking. The Boston Consulting Group.
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ACCEPTED MANUSCRIPT Appendix
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Table A1. Efficiency indexes in the ratio form
)
AC
CE
(
(
PT
(
33
(
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= cost income ratio
= tangible assets = tangible assets net of real estate
2,7 7,8 3,4 50
B
M ed iu m
90, 93, 24 0
C
L ar ge
2,7 1,8 9,3 10
42, 34, 57 0
E
M ed iu m
85, 41, 11 0
S m all
60, 12, 45 0
AC D
S m all
F
54 5
29 6
35 9
12 9
2,9 1,9 3,2 15
97
92, 14, 47 2
19 6
28 4
20 7
P L PI _7
P L PI _8
P L PI _1 7
P L PI _1 9
P C P I_ 1
1, 51 ,0 91
7, 79 ,3 45
69 ,8 32
2, 91 ,4 20
5, 0 4 6
1, 12 ,1 45
3, 89 ,1 23
23 ,4 51
89 ,8 91
3, 0 3 8
1, 48 ,4 56
7, 45 ,3 67
63 ,8 81
2, 86 ,7 31
4, 7 6 3
64 ,3 67
1, 53 ,2 14
6, 65 1
27 ,8 35
2, 0 5 6
1, 09 ,2 95
3, 77 ,7 42
19 ,1 55
74 ,7 24
90 ,2 34
2, 45 ,3 89
49 ,3 41
M
A
L ar ge
PL PI _4
P L PI _6 79 ,8 2, 34 1 46 ,2 7, 98 1 73 ,4 1, 56 2
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PL PI _1
P L PI _3 0
PT
SI Z E
P L PI _3 1
12 7
2,8 1,4 3,2 85
56
52, 65, 69 6
94
91, 55, 10 2
17 ,4 2, 65 8 41 ,8 4, 77 5
71
71, 13, 72 3
26 ,7 3, 41 9
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B ra n c h
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Table A2. The values of the 19 remaining indicators for each of the 23 branches.
9, 78 3
34
T F PI _1 71 ,6 1, 23 0 27 ,4 5, 63 1 68 ,9 9, 91 2
E I _ 1 0. 5 1 2 1 0. 3 2 6 0 0. 5 0 4 3
E I _ 2 0. 0 0 1 6 0. 0 0 5 6 0. 0 0 1 6
2, 9 5 4
7, 83 ,4 56 22 ,9 7, 75 3
0. 1 0 9 8 0. 3 0 5 5
0. 0 1 3 8 0. 0 0 6 3
2, 2 6 7
12 ,9 8, 73 4
0. 1 6 3 3
0. 0 1 2 3
E I _ 9 0. 0 0 3 9 0. 0 1 0 7 0. 0 0 4 0
E I _ 1 1 0. 0 7 3 8 0. 2 6 5 2 0. 0 8 2 3
1, 11 ,4 99
0. 0 2 2 3 0. 0 1 1 9
0. 4 9 8 7 0. 2 9 5 2
1, 40 ,2 19
0. 0 1 5 0
0. 3 8 7 4
E I_ 5
49 ,7 83
98 ,3 42
52 ,8 95
1, 98 ,2 56
P F E I_ 2 0. 3 9 2 4 0. 0 0 7 6 0. 1 3 0 8 0. 1 6 3 5 0. 0 0 6 5 0. 0 6 5 4
PF FEI _2_ AC
PF FEI _3_ AC
0.0 000
0.0 000
0.0 164
0.0 198
0.0 000
0.0 000
0.2 289
0.3 715
0.0 229
0.0 202
0.1 635
0.2 437
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95, 23, 24 0
K
M ed iu m
65, 78, 91 0
L
S m all
36, 52, 31 0
M
M ed iu m
1,1 8,9 6,7 10
N
M ed iu m
70, 43, 29 0
29 8
21 1
18 8
32 9
22 1
11 3
99
96, 27, 77 5
75
76, 70, 57 6
29 ,9 6, 32 1
52
48, 29, 65 8
10 9
1,5 0,5 1,7 75
1,1 3,8 3,4 56
81
10 3
1,1 4,4 8,2 38
64
60, 72, 57 5
20 ,3 5, 16 7 53 ,4 9, 14 3 18
P
M ed iu m
52, 13, 56 0
Q
S m all
1,0 6,3 2,4 50
29 9
10 2
1,0 5,7 3,4 21
R
S
47,
19
61
54,
AC O
19 9
33 ,2 5, 68 1 59 ,8 2, 31 5
81, 17, 49 1
L ar ge
32 5
15 ,3 2, 98 1 66 ,9 8, 43 5
4, 7 4 1
1, 39 ,8 72
6, 26 ,7 68
52 ,3 13
2, 24 ,5 61
3, 8 3 9
1, 34 ,2 13
5, 87 ,9 34
48 ,5 61
2, 13 ,4 48
3, 7 4 8
1, 15 ,6 12
4, 23 ,7 45
27 ,8 43
94 ,2 35
3, 2 2 9
94 ,2 18
2, 63 ,4 52
58 ,7 62
1, 40 ,1 34 5, 56 ,3 89
1, 30 ,1 25
63 ,4 4, 56 7 56 ,7 8, 91 9 52 ,3 4, 91 9 32 ,4 5, 71 8
0. 5 0 2 3 0. 4 9 2 3 0. 4 6 5 6 0. 3 6 7 8
0. 0 0 1 8 0. 0 0 2 1 0. 0 0 2 7 0. 0 0 5 0
15 ,6 7, 21 3
0. 1 9 4 6
6, 96 ,9 19 48 ,7 2, 34 1
0. 9 3 2 4 0. 4 5 3 8
0. 0 1 4 2 0. 0 0 3 2
16 ,4 4, 78 1 40 ,2 3, 18 9
0. 2 0 3 4 0. 4 1 1 9
0. 0 1 1 0 0. 0 0 4 1
0. 1 4 5 6 0. 3 8 4 4
0. 0 1 3 0 0. 0 0 4 5
0.
0.
0. 0 0 4 3 0. 0 0 5 3 0. 0 0 5 6 0. 0 0 9 4
0. 0 9 8 2 0. 1 0 4 5 0. 1 2 3 4 0. 2 1 9 9
0. 0 1 4 7
0. 3 7 1 1
0. 0 2 4 9 0. 0 0 6 0
0. 5 2 9 1 0. 1 4 7 6
0. 0 1 3 5 0. 0 0 7 6
0. 3 4 5 6 0. 1 6 5 3
79 ,8 34
0. 0 1 7 3 0. 0 0 8 4
0. 4 5 6 7 0. 1 9 2 3
0. 1 1 9 9 0. 0 8 7 2 0. 0 7 6 3 0. 0 1 0 9 0. 0 5 4 5 0. 1 7 4 4 0. 0 7 6 3 0. 0 3 2 7 0. 0 4 3 6 0. 1 0 9 0 0. 0 2 1 8
1,
0.
0.
-
56 ,1 23
0.0 000
0.0 000
0.0 000
0.0 000
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J
M ed iu m
33 6
2,2 1,1 7,2 13
59 ,3 42
2, 56 ,2 31
0.0 000
0.0 000
0.0 142
0.0 036
0.1 308
0.1 753
0.2 616
0.3 815
0.0 000
0.0 000
0.1 090
0.1 426
0.0 087
0.0 012
0.2 289
0.3 188
0.0 098
0.0 021
-
-
0. 0 1 1 4
57 ,3 49
60 ,1 23
84 ,3 52
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2,2 1,3 2,4 50
11 9
6, 93 ,1 43
50 ,8 32
2, 5 8 0
5, 73 4
22 ,3 67
1, 5 8 9
44 ,5 67
1, 90 ,9 32
3, 7 3 9
10 ,9 94
M
I
L ar ge
34 3
2,5 3,8 7,1 28
1, 45 ,2 13
ED
2,4 3,8 7,3 40
12 4
71 ,3 2, 56 1 67 ,9 9, 89 9 67 ,8 3, 24 5 49 ,4 2, 36 1
PT
H
M ed iu m
34 7
2,6 9,4 7,2 03
CE
G
L ar ge
2,6 0,3 4,7 80
98 ,3 21
2, 87 ,3 45
13 ,6 73
59 ,7 32
2, 6 1 9
1, 20 ,7 24
4, 72 ,3 49
38 ,9 91
1, 29 ,9 81
3, 2 4 8
83 ,2 56
1, 98 ,3 42
8, 02 3
39 ,8 31
2, 0 9 3
1, 19 ,8 32
4, 67 ,8 21
34 ,5 67
1, 09 ,3 49
3, 2 3 1
10 ,3 2, 49 9 37 ,3 4, 98 9
79
1,
7,
30
2,
9,
35
1, 38 ,4 45
2, 23 ,9 81
65 ,8 71
1, 32 ,4 51
76 ,3 45
1, 67 ,2 34
S
S m all
27, 43, 23 0
T
M ed iu m
80, 37, 12 0
U
S m all
1,1 6,4 5,7 80
S m all
54, 32, 17 0
S m all
75, 94, 63 0
V
18 8
27 4
32 7
20 1
25 5
86, 49 2
,9 3, 45 2
,4 46
74 ,5 29
47
42, 76, 91 6
92
88, 81, 17 2
10 6
1,1 8,5 0,1 77
14 ,9 8, 35 1 40 ,9 2, 13 4 63 ,5 9, 23 1
68
66, 44, 69 9
24 ,5 1, 89 2
86 ,3 24
2, 13 ,8 89
86
86, 26, 52 1
39 ,7 2, 13 7
1, 01 ,2 37
3, 28 ,7 61
54 3
,2 34
0 8 5
87 ,3 49
5, 73 ,2 19 19 ,8 3, 42 9 43 ,2 6, 71 9
49 ,9 98
1, 33 ,2 19
4, 70 8
19 ,6 43
1, 4 9 0
1, 04 ,2 31
3, 56 ,4 39
17 ,8 32
71 ,2 31
2, 8 3 0
1, 25 ,6 32
5, 18 ,6 34
40 ,1 28
1, 64 ,3 24
3, 4 4 5
1 3 4 6
0 1 3 2
0. 0 7 6 4 0. 2 9 3 2 0. 4 2 5 6
0. 0 1 4 5 0. 0 0 7 9 0. 0 0 3 7
71 ,4 45
0.2 289
0.3 279
0.2 943
0.3 843
0.0 229
0.0 213
0.0 076
0.0 011
0.2 071
0.3 021
0.1 090
0.1 031
2, 65 ,7 78 1, 19 ,3 45
69 ,3 48
8, 93 4
15 ,4 37
0 1 9 9
4 6 7 8
0. 0 2 7 4 0. 0 1 2 0 0. 0 0 6 3
0. 5 6 1 1 0. 3 1 9 8 0. 1 5 0 2
44 ,5 26
2, 1 5 1
11 ,0 9, 73 2
0. 1 5 6 3
0. 0 1 2 8
1, 56 ,2 39
0. 0 1 6 0
0. 4 0 0 2
65 ,3 48
2, 6 7 7
18 ,7 3, 42 1
0. 2 6 7 9
0. 0 0 9 1
1, 26 ,7 81
0. 0 1 2 8
0. 3 2 3 2
AC
CE
PT
ED
W
7
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81, 84 0
M
m all
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0. 1 6 3 5 0. 1 8 5 3 0. 0 0 1 1 0. 0 7 6 3 0. 0 8 7 2 0. 0 2 1 8
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AC
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Graphical Abstract
37