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DECOMPOSING THE TECHNICAL EFFICIENCY OF TRADING BANKS IN THE DEREGULATED PERIOD Dr Necmi K Avkiran AAIBF (Snr), ACIM, MASOR The University of Queensland Hospitality, Tourism, and Property Management Gatton, Qld 4345, Australia tel: 07 54601188 fax: 07 54601169 email: [email protected]

Abstract The purpose of this paper is to examine the productivity of Australian trading banks in the deregulated period 1986-1995. Data envelopment analysis and window analysis are used to follow the changes in pure technical efficiency, scale efficiency, and the nature of returns to scale. The main findings indicate declining average efficiency scores until 1991, followed by a steady rise thereafter. Interest expense emerges as an important source of inefficiency. There are some general trends regarding returns to scale. Most banks start the period at most productive scale size, switch to decreasing returns to scale, followed by increasing returns to scale in early 1990s, and show signs of most productive scale size again at the end of the study period. Overall, regional banks exhibit increasing returns to scale and major trading banks exhibit decreasing returns to scale. Also worthy of note is the mixed size of banks operating at most productive scale size. Only one regional bank and one major trading bank consistently operate at most productive scale size. The observed changes in productivity closely follow the events and prevailing conditions in the Australian banking industry.

Keywords: Pure technical and scale efficiency; returns to scale; data envelopment analysis; window analysis ________________________________________________ Announcement: The International DEA Symposium will be held in Australia in year 2000. Please visit the web site www.uq.edu.au/financesite/ for up-to-date information.

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DECOMPOSING THE TECHNICAL EFFICIENCY OF TRADING BANKS IN THE DEREGULATED PERIOD I. INTRODUCTION The purpose of this paper is to investigate the changes in the pure technical efficiency, scale efficiency and nature of returns to scale of Australian trading banks in the deregulated period. Productivity of a sample of ten banks is followed through 1986-1995 using the sensitivity analysis technique window analysis. The relative efficiency scores are generated using the nonparametric programming technique data envelopment analysis (DEA). Decomposing technical efficiency (TE) into pure technical efficiency (PTE) and scale efficiency (SE) allows an insight into the sources of inefficiencies. It also helps determine whether banks have been operating at most productive scale size (MPSS), increasing returns to scale (IRS) or decreasing returns to scale (DRS). The motivation for this study is to contribute to the debate about the productivity gains in the deregulated period and the most productive scale size, both of which have a direct impact on decisions to close branches and bank mergers. Deregulation of the Australian finance sector began in December 1983 when the dollar was floated and exchange controls lifted. Australia entered the deregulated period with 24 banks (excluding merchant banks and foreign banks). Deregulation continued to unfold with lifting of deposit controls, authorisation of savings banks to provide chequing facilities, invitation of foreign banks to operate in Australia, changes in ownership of authorised money market dealers, expansion of services by credit unions and building societies, and so on. These changes in the composition of the Australian finance sector make it difficult to set up a comparative prederegulation and post-deregulation study. 1 Furthermore, the deregulation literature from the rest of the world provides no conclusive findings (Berger and Humphrey, 1997) to lead Australian policy makers to expect a clear case of rising productivity as a result of deregulation. Therefore, it is imperative that research in this area continues. Currently, Australian banks are facing more competition from building societies, credit unions and mortgage originators. In the last few years, the lines separating the banks and other financial institutions have become blurred. Taking advantage of legislative and technological

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changes, state banks, regional banks and building societies are competing head-on with larger banks both across geographical boundaries and product range. Internet banking offered by nonbank entities is expected to pose a major competitive threat in the 21st century. The Australian banking sector can be argued to be experiencing a convergence. For instance, major trading banks that customarily depended on the bank's deposit base to make loans are increasingly financing their home loans through securitisation. This has come about as a direct result of mortgage originators successfully providing low-cost home loans. Similarly, non-bank institutions are increasingly packaging their services with products traditionally sold through banks. Banks are undergoing further restructuring with emphasis on generating revenue from fees rather than the interest spread. In a low-growth population, maturing markets are likely to lead to fiercer competition. Rationalisation or restructuring of the existing branch networks is part of the banks' response to competitive pressures in the deregulated period. For example, the Australia and New Zealand Banking Group (ANZ) has been implementing a major restructuring of its branch network to reduce operating costs and increase efficiency. Central to this exercise are staff redundancies, branch closures, and in some cases, re-engineering of the retail delivery channels aimed at improving efficiency and customer service. The study of pure technical and scale efficiencies provides an opportunity to assess the impact of deregulation on productivity of banks. It also provides an insight to the main sources of inefficiencies. While the Federal government is currently preoccupied with promoting the tax reforms planned for July 2000, it is highly likely to turn its attention to bank mergers and competition in the finance sector by 2001. Bank efficiency studies can contribute to the economic and political debates in this area. This paper examines the pure technical and scale efficiencies of four major trading banks and six regional trading banks for the period 1986-1995. The paper also investigates the nature of returns to scale and the main sources of inefficiencies over the same period. The principal findings for the deregulated period 1986-1995 indicate that average efficiency scores gradually declined until 1991, only to be followed by a steady rise thereafter. Banks appear to

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have come a full circle regarding the changes in returns to scale. Overall, regional banks tended to operate at increasing returns to scale. Section II of the paper provides the conceptual framework for measuring bank efficiency and DEA. Section III outlines the research design including DEA modelling options and window analysis. Section IV details the results of DEA and window analysis, as well as charting the changes in the nature of returns to scale. Finally, Section V discusses the key findings and outlines directions for further research in the area of Australian bank productivity.

II. CONCEPTUAL FRAMEWORK There is little reliable empirical research on bank efficiency in Australia. Existing studies deal mostly with economies of scale and are inconclusive (Edgar et al., 1971; Hatch and Lewis, 1973; Burgess and Walker, 1978; Valentine and Williamson, 1982; Swan and Harper, 1982; Swan and Simmonds, 1989). The small number of Australian banks and the often unavailable banking data make it difficult to undertake econometric analysis. The US-based studies dominate the literature on bank efficiency where the larger marketplace facilitates data collection. Most of the efficiency literature focus on cost effects of economies of scale (size) and scope (product mix) (Hunter and Timme, 1986; Berger et al., 1987; Elyasiani and Mehdian, 1990; Ferrier and Lovell, 1990; Noulas et al., 1990; Hunter and Timme, 1991; Berger and Humphrey, 1991; Fields et al., 1993; McAllister and McManus, 1993; Rhoades, 1993). The conventional studies on scale and scope economies suffer from a number of difficulties. For example, the translog cost function generates a poor approximation when banks of assorted sizes are used. Another potential problem is that scope economies can be confounded with x-efficiency differences when applied to banks off the efficient frontier. In response to these problems, alternative research designs have emerged. For instance, in some studies the translog cost function has been replaced by non-parametric estimation procedures such as the kernel regression technique (McAllister and McManus, 1993). Yet other researchers have moved away from the cost function, focusing on the profit function instead in an effort to estimate optimal scope economies (Berger et al., 1993a). The theoretical appeal of working with

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the profit function is that it accounts for the revenue effects as well as the cost effects of operating at incorrect levels or mixes of inputs and outputs (Akhavein et al., 1997). More recently, the focus has shifted to x-efficiencies, that is, the ability of management to control costs and generate revenues (Elyasiani and Mehdian, 1990; Ferrier and Lovell, 1990; English et al., 1993; Allen and Rai, 1996; Mester, 1996). X-efficiency comprises allocative and technical efficiencies of banks, where allocative inefficiency is defined as a decline in performance from selecting an ineffective production plan, and technical inefficiency is defined as the poor implementation of this production plan (Berger et al., 1993a). Existing studies indicate that x-inefficiencies constitute 20% or more of costs, while economies of scale and scope inefficiencies account for less than 5% of costs in banking (Berger et al., 1993b). While there is no consensus amongst researchers about the inputs and outputs of a bank, there are two principal schools of thought on bank behaviour. One of these is the intermediation approach to modelling bank behaviour in which deposits are regarded as being converted into loans (Mester, 1987). The intermediation approach is preferable since it normally includes interest expense, a large proportion of any bank’s total costs (Elyasiani and Mehdian, 1990; Berger and Humphrey, 1991). The alternative is the production approach where banks are regarded as using labour and capital to generate deposits and loans (outputs are usually measured in number of accounts rather than dollars). A third approach to modelling bank behaviour is that of value-added (Berger and Humphrey, 1992). Under this approach high value creating activities such as making loans and taking deposits are classified as outputs and measured in dollar terms, whereas labour, physical capital and purchased funds are classified as inputs (Wheelock and Wilson, 1995). A fourth approach is known as user-cost. The user-cost approach assigns an asset as an output if the financial returns are greater than the opportunity cost of funds. Similarly, a liability item is regarded as an output if the financial costs are less than the opportunity cost. If neither of these conditions is satisfied, the asset or the liability is classified as input (Berger and Humphrey, 1992). The user-cost approach is usually attributed to Hancock (1986). According to Hancock, user costs can be calculated for all the assets and liabilities on the balance sheet. It is

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also worth noting that the assignment of assets and liability items as inputs or outputs may change with movements in interest rates and service charges. Similarly, there is no consensus on the best procedure for measuring x-efficiencies. The principal measurement problem is distinguishing variations in x-efficiency from random error. Examples of different procedures are the econometric frontier approach, the thick frontier approach, the distribution-free approach, and DEA. Each of these approaches makes different assumptions about the distribution of x-efficiency differences and random error (Berger et al., 1993b). DEA, the technique adopted in this study, usually assumes no random error, thus implying that all deviations from the estimated efficient frontier actually constitute xinefficiencies. Other researchers who have recently used DEA in measuring relative bank efficiency include Berg et al. (1992), Berg et al. (1993), Drake and Howcroft (1994), Elyasiani and Mehdian (1995), Favero and Papi (1995), Fukuyama (1995), Haag and Jaska (1995), Sherman and Ladino (1995), Wheelock and Wilson (1995), Zaim (1995), Grifell-Tatje and Lovell (1996), Miller and Noulas (1996), Bhattacharyya et al. (1997), and Resti (1997). For brevity, only those studies that used DEA to examine bank efficiency in a deregulated period are reviewed following a theoretical discussion of DEA, which appears next. A more comprehensive survey of efficiency analysis of financial institutions can be found in Berger and Humphrey (1997). DEA is a non-parametric linear programming technique that computes a comparative ratio of outputs to inputs for each unit, which is reported as the relative efficiency score. The efficiency score is usually expressed as either a number between 0-1 or 0-100%. A decision making unit with a score less than 1 is deemed inefficient relative to other units. Traditional DEA measures the technical efficiency of decision making units (DMUs) as opposed to their allocative efficiency. In the context of DEA, allocative efficiency is defined as the effective choice of inputs vis. à vis. prices with the objective of minimising production costs (ie. selection of an effective production plan), whereas technical efficiency investigates how well the production process converts inputs into outputs (i.e. effective implementation of the production plan).

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In order to discriminate effectively between efficient and inefficient banks, there is a need for a sample size larger than the product of number of inputs and outputs (Dyson et al., 1998). However, DEA can be used with small sample sizes (Evanoff and Israilevich, 1991) and many such examples can be found in literature (e.g. Sherman and Gold, 1985; Parkan, 1987; Oral and Yolalan, 1990; Haag and Jaska, 1995). Another rule of thumb for selecting an appropriate sample size is to ensure that the sample size is at least three times larger than the sum of number of inputs and outputs (Stern et al., 1994). An advantage of DEA is that there is no preconceived structure imposed on the data in determining the efficient units (Banker, 1984; Al-Faraj et al., 1993; Burley, 1995; Mester, 1996). That is, DEA does not assume a particular production technology or correspondence. The importance of this feature of DEA is that a bank's efficiency can be assessed based on other observed performance. As an efficient frontier technique, DEA identifies the inefficiency in a particular DMU by comparing it to similar DMUs regarded as efficient, rather than trying to associate a DMU's performance with statistical averages that may not be applicable to that DMU. Figure 1 shows a simple DEA model to highlight this principle. The solid line going through efficient DMUs L, M and N depicts the efficient frontier that represents achieved efficiency. For example, DMU K is classified as inefficient in this sample of ten units and it needs to travel to K' along the ray joining the origin with the efficient frontier before it can also be deemed efficient. DMU K would be directly compared to units M and N (a facet) on the efficient frontier in calculating its efficiency score (ie. reference set or peer group). In this case, DMU M would make a greater contribution to DMU K's score. Clearly, the efficient frontier envelopes all other data points, thus giving rise to the name data envelopment analysis.

[Insert Figure 1]

The principal disadvantage of DEA is that it assumes data to be free of measurement error (Mester, 1996). When the integrity of data has been violated, DEA results cannot be interpreted with confidence. While the need for reliable data is the same for all statistical

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analysis, DEA is particularly sensitive to unreliable data because the units deemed efficient determine the efficient frontier and thus, the efficiency scores of those units under this frontier. For example, an unintended reclassification of the efficient units could lead to recalculation of efficiency scores of the inefficient units (Berger and Humphrey, 1997). This potential problem with DEA is addressed through stochastic DEA designed to account for random disturbances. Two recent examples in this area are Li (1998) and Sengupta (1998). Another caveat of DEA is that those DMUs indicated as efficient are only efficient in relation to others in the sample. It may be possible for a unit outside the sample to achieve a higher efficiency than the best practice DMU in the sample. Another way of expressing this is to say that an efficient unit does not necessarily produce the maximum output feasible for a given level of input (Miller and Noulas, 1996). It has already been stated that DEA generates efficiency scores, thus helping to distinguish the efficient from the inefficient units. Nevertheless, a list of units sorted on efficiency scores cannot always be considered as truly rank ordered (Sherman, 1988). DEA identifies a unit as either efficient or inefficient compared to other units in its reference set, where the reference set is comprised of efficient units most similar to that unit in their configuration of inputs and outputs. Knowing which efficient banks are most comparable to the inefficient bank enables the analyst to develop an understanding of the nature of inefficiencies and re-allocate scarce resources to improve productivity. The nature of technical inefficiencies can be due to the ineffective implementation of the production plan in converting inputs to outputs (pure technical inefficiency) and due to the divergence of the DMU from the most productive scale size (scale inefficiency). MPSS, as per Banker (1984), is that size of operations where a DMU's production of outputs is maximised per unit of inputs. This study details a sensitivity analysis of panel data on Australian trading banks where the technical efficiency is decomposed into pure technical efficiency and scale efficiency. In this context, scale inefficiency does not refer to diseconomies of scale which depends on prices but to that component of technical inefficiency that can be attributed to the DMU operating at a scale other than MPSS. It should be noted that amongst banks, technical inefficiency is more

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prevalent than allocative inefficiency (Berger et al., 1993a). Allocative efficiency is not addressed in this paper. Review of the DEA literature that investigates bank productivity in a deregulated period begins here. Berg et al. (1992) study the productivity of Norwegian banks before and after deregulation. They follow the value-added approach to bank behaviour. Analysis reveals productivity regress in the pre-deregulation years mainly due to the banks raising their inputs and creating idle capacity in anticipation of increased competition with the introduction of deregulation. The advent of Norwegian banking deregulation was in 1984. The authors report a rapid growth in productivity from 1987 onwards. A stable set of frontier banks are identified for 1980-1989 where productivity growth is observed principally among the least efficient banks. By the end of the study period, productivity levels become similar, implying increased competition during the deregulated era. Elyasiani and Mehdian (1995) investigate the movements in decomposed technical efficiency and technological change for two sets of commercial banks grouped on asset size. Data collected for 1979 and 1986 represent the pre- and post-deregulation periods in the USA. DEA modelled on the intermediation approach to bank behaviour indicates that small and large banks have different efficient frontiers. Small banks emerge as more efficient in the prederegulation year but this gap closes in the post-deregulation year. Market conditions appear to have impacted on the small banks differently compared to the large banks, where most small banks struggled to keep up with the changing conditions. Overall, the average efficiency measures decline from 1979 to 1986. Zaim (1995) studies the effects of liberalisation policies on the economic efficiency of Turkish commercial banks. Using the intermediation approach to modelling bank behaviour, data are collected for the years 1981 and 1990, representing the pre- and post-deregulation periods. Findings indicate that technical efficiency increased on average by 10%, while the difference between banks on technical efficiency decreased. On scale efficiency, most banks were able to shift to MPSS. In both pre- and post-deregulation periods, most of the inefficiency appears to be sourced in pure technical inefficiency. A rather unexpected finding indicates that

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state banks are more efficient than privately owned banks. On the other hand, state banks emerge as more prone to allocative inefficiency. Grifell-Tatje and Lovell (1996) investigate the productive efficiency of Spanish savings banks. The data cover the post-deregulation period 1986-1991 and the authors follow the valueadded approach to modelling bank behaviour. Findings show a rapid decline in measured productivity mainly due to the worsening performance of best-practice savings banks. At the same time, the standard practice banks tend to catch up with the benchmark banks by declining at a slower pace. The authors also test two interesting hypotheses, namely, the impact of branching and consolidations on performance. Results indicate that productivity decline in fastbranching banks has been less severe, and that mergers and acquisitions had a neutral effect on productive efficiency. Bhattacharyya et al. (1997) investigate the impact of liberalisation on commercial banks in the early years of deregulation of the Indian banking industry. Data examined cover the period 1986-1991 and bank behaviour is modelled on the value-added approach. The authors combine DEA with stochastic frontier analysis. Overall, the results indicate that publicly owned banks are the most efficient banks. However, foreign banks appear to catch up with the public banks by the end of the study period. This is attributed to the more efficient branching of foreign banks where they concentrate in metropolitan areas and their better adaptation to the competitive environment. Shyu (1998) reports a study of operating efficiency in Taiwan’s banking industry for pre- and post-deregulation periods. Data cover the periods 1986-1989 and 1992-1995, and bank behaviour is modelled on the user-cost approach. The findings indicate improvement in overall efficiency and most banks close to being scale efficient. Principal source of inefficiency is identified as allocative rather than technical, in particular during the pre-deregulation period. In conclusion, Shyu comments on the importance of increasing size and diversifying output in the effort to raise bank efficiency in the deregulated period. The above review of DEA literature investigating the impact of deregulation on bank productivity leads to only one conclusion. That is, the findings vary depending on the prevailing market and regulatory conditions as well as research design.

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III. RESEARCH DESIGN Ten Australian trading banks in the deregulated period comprise the study sample. Foreign banks were omitted because between 1986-1995, most operated as subsidiary banks with restrictive capital adequacy requirements and dealt mainly in wholesale banking. Four of the banks are major trading banks and six are regional banks as shown in Table 1 (others could not be included due to inconsistent availability of data between 1986-1995). The research design calls for identification of the main sources of technical inefficiencies, window analysis of the pure technical efficiency and scale efficiency scores across 1986-1995, and determination of the nature of returns to scale.

[insert Table 1]

It was possible to collect data on 4 inputs (staff numbers, deposits, interest expense, and non-interest expense) and 3 outputs (net loans, net interest income, and non-interest income) through the reserve bank of Australia.2 In the spirit of directly measuring management’s success in controlling costs and generating revenues in a discriminating model, net loans, deposits, and staff numbers were dropped from the data envelopment analysis, leaving two input and two output variables. Modelling input minimisation, the DEA analysis was run with interest expense and non-interest expense as controllable inputs, and net interest income and non-interest income as outputs. The selected variables can be argued to fall under the intermediation approach to modelling bank behaviour where interest expense is a proxy for deposits, and net interest income is a proxy for loans. Non-interest expense represents the resources expended in converting deposits to loans, and non-interest income represents the fees charged for services other than interest income. Examples of other studies where these variables were used include Charnes et al. (1990), Yue (1992), Miller and Noulas (1996), Bhattacharyya et al. (1997), and Brockett et al. (1997). The dollar entries were deflated back to the base year 1986.

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Input minimisation (also known as input orientation or contraction) instructs DEA to reduce the inputs as much as possible without dropping the output levels. For instance, the analyst could opt for input minimisation in an exercise to save costs. Alternatively, when the management's focus is on raising productivity without increasing the resource base, output maximisation (also known as output orientation or expansion) could be specified. Under output maximisation, outputs are raised without increasing the inputs. It is worth noting that when none of the inputs are controllable by management, one can only specify the output maximisation model. It is also possible to find slacks in inputs or outputs. For example, under input minimisation, potential improvements indicated by DEA may suggest increasing one or more of the outputs while lowering the inputs. Such output slacks depict outputs that are underproduced. Similarly, under output maximisation, the results may suggest raising outputs as well as reducing inputs (ie. an input slack). In such a case, input reduction implies over-utilised inputs. Another model specification in DEA is a choice between constant returns to scale (CRS) and variable returns to scale (VRS). Constant returns to scale assumes that there is no significant relationship between the scale of operations and efficiency. That is, large banks are just as efficient as small banks in converting inputs to outputs. Under constant returns to scale, input minimisation and output maximisation produce the same relative efficiency scores, provided all the inputs are controllable. On the other hand, variable returns to scale means a rise in inputs is expected to result in a disproportionate rise in outputs (Drake and Howcroft, 1994). A sensible approach is to run the DEA model under CRS and VRS and compare the efficiency scores. If the majority of the DMUs emerge with different scores under the two assumptions, then it is safe to assume VRS. Put another way, if the majority of DMUs are assessed as having the same efficiency, one can work with CRS without being concerned about scale inefficiency confounding the measure of technical efficiency. In this study, examination of efficiency scores warrants use of VRS. The CRS efficiency score represents technical efficiency, which measures inefficiencies due to the input/output configuration and as well as the size of operations. On the other hand,

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the VRS efficiency score represents pure technical efficiency, that is, a measure of efficiency without scale efficiency. It is thus possible to decompose TE into PTE and SE. Scale efficiency can be calculated by dividing PTE into TE. The graphical derivation of this relationship can be found in Coelli et al. (1998). Providing an example of technical efficiency score would help interpret the bank scores reported in the next section. For instance, if technical efficiency of Advance was calculated to be 89%, it is possible to interpret this number from two different perspectives if VRS is accepted. Assuming output maximisation, it means that Advance is under-producing by 11%. Assuming input minimisation (the modelling option adopted in this study), TE of 89% indicates that inputs can be reduced by 12.36% [(1/0.89)-1] (Drake and Howcroft, 1994). Once the VRS is established and SE scores computed, the analysis can be taken a step further. This involves determining whether a particular DMU is experiencing IRS, DRS, or operating at MPSS. To make this assessment, DEA is repeated with non-increasing returns to scale (NIRS) and efficiency scores compared. It should be noted that, by definition, NIRS implies CRS or DRS. So, if the score for a particular DMU under VRS equals the NIRS score, then that DMU must be operating under DRS. Alternatively, if the score under VRS is not equal to the NIRS score, this implies a DMU operating under IRS (Coelli et al., 1998). When the VRS score equals the CRS score, then the DMU is said to be operating at most productive scale size. It is also possible to impose weight restrictions on inputs and outputs to reflect their perceived relative importance. For example, if bank policy-makers regard non-interest income as more desirable than net interest income, then appropriate constraints can be set up in the linear program. However, before imposing weight restrictions on the optimisation program the analyst should look for evidence of a variable being either over- or under-represented in computation of efficiency scores. Furthermore, there is a caveat for using weight restrictions even in the presence of such evidence. That is, too many restricted variables will disrupt optimisation. Those interested in reading about weight restrictions are referred to Dyson and Thanassoulis (1988), Beasley (1990), Boussofiane et al. (1991), Allen et al. (1997), Schaffnit et al. (1997), and Thanassoulis and Allen (1998). In this study, no weight restrictions are imposed.

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Window analysis is a commonly used sensitivity analysis technique in DEA. It allows for an assessment of the stability of relative efficiency scores over time. The sensitivity in question is to that of external factors that may distort figures for a particular year and a varying group of reference units. The so-called 'window' is usually three years. In a panel data set over ten years, a three-year window produces eight windows (see Table 2).

[Insert Table 2]

In window analysis, data on a bank in different years are treated as separate DMUs. Thus, 10 banks and a window size of 3 is equivalent to 30 DMUs, providing a better degrees of freedom then anticipated at first glance of the number of banks. In examining efficiency scores in window analysis, a bank that is efficient in one year regardless of the windows is said to be stable in its efficiency rating relative to other banks. Yue (1992) and Charnes et al. (1985) provide examples of window analysis in DEA.

IV. RESULTS AND ANALYSIS Table 3 introduces examples of potential improvements that can be observed through DEA. For instance, Westpac is rated as 90% efficient in converting its inputs into outputs relative to the peer banks in its reference set. Potential improvements indicated by DEA suggest a decrease of 10% in both inputs. Bearing in mind that DEA was set up for input minimisation, the 4% potential increase in non-interest income should be interpreted as an output slack. That is, Westpac can simultaneously reduce its inputs and increase one of its outputs. In implementing such a benchmarking exercise, the analyst looks at the banks in the corresponding peer group to develop a better understanding of efficient operations. In the case of Westpac, NAB is the efficient bank with the highest peer weight at .483 and is placed at the top of the list of banks to be emulated. 3

[Insert Table 3]

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Table 4 reports the findings from CRS analysis (ie. technical efficiency) of the bank data. The purpose of Table 4 is to summarise the main sources of inefficiencies (as observed amongst inputs and outputs) for each bank over the ten-year period. For instance, in 1987 Advance could have reduced its interest expenses by 26% and increased its non-interest income by 8%. Macquarie (regional trading bank) and NAB (major trading bank) are technically efficient throughout the study period. This observation indicates that a bank can be productive at very different sizes. Overall, interest expense emerges as the dominant source of inefficiency across the sample. This is a reflection of the banks competing on interest rates offered on deposits following lifting of the restrictions.

[Insert Table 4]

Technical efficiency can be further examined by decomposing it into pure technical efficiency and scale efficiency. Table 5 provides an example of one such decomposition using 1995 data. Decomposition indicates that half the banks were scale inefficient. However, the means and standard deviations show that most of the technical inefficiency is in the form of pure technical inefficiency.

[Insert Table 5]

Table 6 provides an overview of decomposed technical efficiency over the study period. TE and PTE exhibit a gradual decline between 1986 and 1991, only to experience a steady rise between 1992 and 1995. The same trend can be observed for SE where the switch from decline to rise happens a year later (in 1993). This is a manifestation of the banks becoming more adept in controlling expenses and striving towards MPSS through branch closures and staff redundancies, and the impact of technology. Another study of the Australian banks for the period of 1986-1995 reports a steady rise in employee productivity (operating income per employee) (Avkiran, 1999).

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[Insert Table 6]

The observations based on Table 6 can be further dissected through window analysis. Window analysis of the pure technical efficiency scores is presented in Table 7. There is no clear trend for the change in productivity in the period 1986-1995 that is shared by all the banks. For example, while Advance and BankWA show generally rising pure technical efficiency scores in the 1990s, others exhibit a mixed performance. These two banks are the main driving force behind the steady rise in mean PTE scores reported in Table 6. The top performers of the period identified in Table 4, namely, Macquarie, NAB, and to a lesser extent BankQLD, maintain their position with stable efficiency scores over time. These consistent performers are characterised by high means and low standard deviations. Similarly, such banks exhibit low differences in their scores within the same year or across the study period. On the opposite end of the spectrum, the worst performer on pure technical efficiency is BankSA. This bank is characterised by a lower mean and a higher standard deviation of efficiency scores. BankSA scores drop considerably in 1991. This can be explained by the particularly large non-accruals in 1991 that lead to the state government indemnifying $2.2 billion of state bank capital (KPMG 1992).

[Insert Table 7]

Window analysis of the scale efficiency scores of the same trading banks paints a different picture (see Table 8). Overall, top performers on scale efficiency over time are BankSA, Macquarie, and SBankNSW. BankSA was identified as the worst overall performer on pure technical efficiency (see Table 7). This finding indicates that the main sources of inefficiencies for BankSA and SBankNSW depicted in Table 4 were not due to operating under or over most productive scale size. Once again, there is no clear common trend in change of scale efficiency except Advance, ANZ and Westpac showing a steady improvement after 1991.

[Insert Table 8]

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What is the evidence on returns to scale? In 1986 most of the trading banks in the sample were operating at MPSS, with three banks displaying increasing returns to scale (see Figure 2). By 1988, the number of banks at MPSS was halved and the number of banks at DRS had increased five-fold. This indicates an overall growth in the scale of operations beyond MPSS. That is, at DRS, an increase in inputs is accompanied by a less than proportionate rise in outputs. Years 1989-91 is a period of relative stability in scale of operations when most trading banks would have been taking stock of the lending excesses of the late 1980s. The period of 1992-95 is characterised by more banks experiencing increasing returns to scale as branch closures and staff redundancies took effect. At IRS, an increase in inputs leads to a more than proportionate rise in outputs. In the final year of the study period (ie. 1995), the inclination is for IRS and DRS banks to begin operating at MPSS. It appears that between 1986-1995 the banks have come almost a full circle in the nature of their returns to scale.

[Insert Figure 2]

Table 9 provides further information on returns to scale detailed at the individual bank level. For example, two banks that were technically efficient throughout the ten-year period (ie. NAB and Macquarie; see Table 4) were operating at MPSS as expected. It should be noted that a bank can be inefficient (in pure technical sense) but still be rated as operating at MPSS as long as it is scale efficient. Another interesting observation from Table 9 concerns the nature of returns to scale between 1986-1995. In general, the major trading banks have operated at DRS (indicating above optimal sizes) and regional trading banks have operated at IRS (indicating below optimal sizes).

[Insert Table 9]

The data in Table 10 provides further support that those banks operating at decreasing returns to scale are well above the average bank size (measured by staff numbers)4 . That is, the

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DRS banks across 1993-95, which happen to be the three major trading banks, could raise their productivity by downsizing. Similarly, the IRS banks (with one exception) are substantially below the corresponding average size. This observation suggests that the IRS banks could enjoy proportionately higher outputs for every additional unit of inputs. The implication for IRS banks (dominated by the regional banks) is to enlarge the scale of their operations in striving for MPSS.

[Insert Table 10]

On the other hand, those banks experiencing MPSS are maximising their outputs for the inputs expended. Across 1993-95, Advance, Macquarie and NAB are the permanent members of the MPSS group, with the most noticeable newcomers being CBA and Westpac in 1995. It is worth noting that the MPSS banks do not share a common size. That is, it is quite feasible for different banks to reach MPSS at different sizes depending on the configuration of their inputs and outputs.

V. DISCUSSION The principal findings for the deregulated period 1986-1995 indicate that average efficiency scores gradually declined until 1991, followed by a steady rise thereafter. This can be explained by a number of developments in the period. The unprofitable lending decisions in the 1980s following deregulation would have impacted the interest income (output) of most banks but particularly the big four ie. ANZ, CBA, NAB and Westpac. On the input side of the equation, interest expense emerges as a significant source of inefficiency as banks were allowed to compete with each other on deposit rates and types of interest paying products. This was particularly noticeable because banks had been slow in setting up a trade-off between offering competitive deposit rates and raising fees (a politically sensitive exercise). Once the banks recovered from the consequences of their poor decisions and the market rules of competitive engagement became clearer, the average efficiency scores exhibited a steady rise in 1990s. More specifically, Advance and BankWA provided the main driving force behind the steady

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rise in pure technical efficiency from 1992 onwards. Similarly, Advance, ANZ and Westpac contributed to the steady rise in scale efficiency from 1991 onwards. A few years into the deregulated period most banks were operating at MPSS. Towards the end of 1980s banks shifted towards decreasing returns to scale. On the other hand, early 1990s were characterised by more banks operating at increasing returns to scale. In 1995 once again the banks started to experience MPSS, appearing to have come a full circle. Macquarie and NAB emerge as the only two banks consistently operating at MPSS throughout 1986-1995. Did the regional banks and the major banks significantly differ in their nature of returns to scale? Regional banks almost invariably tended to operate at increasing returns to scale between 1986-1995, whereas the big four operated mostly at decreasing returns to scale but sometimes at MPSS. This suggests that regional banks can raise their productivity by becoming larger. However, MPSS banks do not share a common size so it would be a mistake for regional banks to automatically target one of the big four banks’ size in their quest for optimal size. A DEA study of U.S. banks similarly reports that larger banks are more likely to operate at decreasing returns to scale (Miller and Noulas, 1996). Decomposing technical efficiency scores into pure technical efficiency and scale efficiency indicates what can be realised in the short-term and in the long-term. For instance, if the inefficiency is mainly due to the sub-optimal size of operations, say, a bank is running under a regime of increasing returns to scale, then the bank needs to plan for expansion. While this exercise can be accelerated through in-market mergers or business collaboration, it is still a time consuming exercise. However, pure technical inefficiency can usually be addressed in the shortterm by experimenting with new combinations of inputs and outputs observed from the operations of efficient peers. DEA identifies the efficient peers for the inefficient banks and objectively determines the productivity improvements. As such, it is a valuable benchmarking tool for management that can become part of a continuos improvement program. A less tangible benefit of using DEA is the management having to identify the key inputs/outputs of the organisation who may not have explicitly followed such a line of investigation in the past. DEA can also be a natural extension

19

of the balanced scorecard system of integrating financial measures with non-financial operational measures. The DEA process outlined in this study can help bank executives and public policymakers allocate scarce resources and seek direction for productivity improvement. In an environment of increasing competition in the deregulated era, banks need to increasingly use tried and tested methods of analysing productivity. DEA provides such a method. Measures of relative efficiency can be indicators of the likelihood of bank failure or takeover (Wheelock and Wilson, 1995). Nevertheless, like other techniques, DEA has its limitations. While DEA can be used to set targets for improvement of desired outputs or reduction of inputs, the technique does not instruct the analyst on how to reach those targets. It would be essential to investigate what sort of organisational or environmental factors may be obstructing the manifestation of inputs as outputs. DEA's main application as a managerial decision-making tool should be one of testing the established knowledge and initiating an investigation when a significant contradiction arises. The major limitation of this study is the absence of an attempt to analyse the potential frontier shift from one year to the next. Inefficiency is not necessarily limited to technical inefficiency, which measures the distance of a bank from the efficient frontier. Changes in productivity over time may also be a result of technical change or progress. The so-called Malmquist total factor productivity index can capture the overall change in sector productivity and is the product of technical efficiency and technical change. The analysis of frontier shift and probing of dynamic efficiency of trading banks are planned as a separate study.

20

Appendix: Introduction to Mathematics of DEA Relative efficiency of a DMU is defined as the ratio of weighted sum of outputs to weighted sum of inputs. This can be written as follows: Equation 1 s

ho =

∑u

y ro

r

r =1 m

∑v x i =1

i

io

where s = number of outputs u r = weight of output r y ro = amount of output r produced by the DMU m = number of inputs vi = weight of input i x io = amount of input i used by the DMU

Equation 1 assumes constant returns to scale and controllable inputs. While outputs and inputs can be measured and entered in this equation without standardisation, determining a common set of weights can be difficult. DMUs might value outputs and inputs quite differently. The CCR model addresses this concern.

CCR Model Charnes et al. (1978) addressed the above problem by permitting a DMU to adopt a set of weights that will maximise its relative efficiency ratio without the same ratio for other DMUs exceeding 1. Thus, Equation 1 is re-written in the form of a fractional programming problem.

Equation 2 s

max ho =

∑u r =1 m

r

y ro

∑v x i =1

i

io

21

subject to s

∑u y r =1 m

r

rj

≤ 1 for each DMU in the sample, where j = 1,..., n (number of DMUs).

∑v x

i ij

i =1

To measure efficiency, Equation 2 is converted into the more familiar components of a linear programming problem. In equation 3, the denominator is set to a constant and the numerator is maximised. Equation 3

max ho =

s

∑u y r

ro

r =1

subject to m

∑v x i =1

i io

=1

s

m

r =1

i =1

∑ ur y rj − ∑ vi xij ≤ 0 ur , vi ≥ ε To prevent the mathematical omission of an output or an input in the iterative calculation of efficiency, weights u and v are not allowed to fall below small positive numbers (ε). Equation 3 uses controllable inputs and constant returns to scale. It is a primal linear programming problem that models input minimisation.

BCC Model Banker et al. (1984) addressed variable returns to scale. They introduced a new variable in the CCR model that separated scale efficiency from technical efficiency. The BCC primal linear programming problem that measures pure technical efficiency is depicted in Equation 4.

22

Equation 4 s

max ho = ∑ u r y ro + c o r =1

subject to m

∑v x i =1

i

io

=1

s

m

r =1

i =1

∑ u r y rj − ∑ v i x ij − c o ≤ 0 ur , vi ≥ ε

BCC Model with Uncontrollable Inputs The variable returns to scale model that incorporates the effect of non-discretionary inputs can be read in Banker and Morey (1986). It is probably the most useful model for evaluating the relative efficiency of organisational units in the business world. It acknowledges that DMUs may not be operating at MPSS and that some of the inputs may well be outside the control of the manager. Under such circumstances, it does not make sense to talk about reducing all the inputs. Potential improvements should be calculated only for the controllable or discretionary inputs. Equation 5 shows a general model that assumes input contraction. Equation 5 p

s

max h0 =

∑ u r y ro − ∑ w j z j0 + c 0 r =1

j =1

m

∑v x i =1

i

i0

subject to s

p

∑ u r y rq − ∑ w j z jq + c0 r =1

j =1

m

∑v x i =1

i

≤1 ; q = 1,..., n

iq

u r ≥ 0 ; r =1,..., s v i ≥ 0 ; i = 1,..., m w j ≥ 0 ; j = 1,..., p 23

where s = number of outputs u r = weight of output r yro = amount of output r produced by the DMU under evaluation m = number of controllab le inputs vi = weight of controllab le input i xio = amount of controllab le input i used by the DMU p = number of uncontroll able inputs w j = weight of uncontroll able input j z jo = amount of uncontroll able input j used by the DMU

24

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28

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29

L M

Output y per unit of input z

πQ

πP

¡ K'

πT πR

πO

πK

N πS

Output x per unit of input z Figure 1. A Two-Output, One-Input DEA Model Showing the Efficient Frontier

30

7 Number of Banks

6 5 ORS IRS DRS

4 3 2 1 0 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 Year

Figure 2. Summary of Changes in Nature of Returns to Scale for Trading Banks, 19861995

31

Table 1. Trading Banks in the Study Sample Unit

Name of Trading Bank

Abbreviation Used

1

Advance Bank Australia

Advance

2

ANZ Banking Group (major)

ANZ

3

Bank of Queensland

BankQLD

4

Bank of South Australia

BankSA

5

Bank of Western Australia

BankWA

6

Commonwealth Bank of Australia (major)

CBA

7

Macquarie Bank

Macquarie

8

National Australia Bank (major)

NAB

9

State Bank of NSW

SBankNSW

10

Westpac Banking Corporation (major)

Westpac

32

Table 2. Periods Corresponding to Each Window on Bank Panel Data Window 1 Window 2 Window 3 Window 4 Window 5 Window 6 Window 7 Window 8

1986

1987

1988

1987

1988

1989

1988

1989

1990

1989

1990

1991

1990

1991

1992

1991

1992

1993

1992

1993

1994

1993

1994

1995

33

Table 3. Examples of Potential Improvements under Variable Returns to Scale (1995 Data)

Inputs

Outputs

ANZ

Interest expense

↓6%

Net interest income

↑22% (slack)

(.979)

Non-interest expense

↓2%

Non-interest income

-----

Peer Group: NAB (.821), Macquarie (.179) SbankNSW

Interest expense

↓52%

Net interest income

-----

(.815)

Non-interest expense

↓18%

Non-interest income

-----

Peer Group: BankQLD (.756), Advance (.183), NAB (.061) Westpac

Interest expense

↓10%

Net interest income

-----

(.900)

Non-interest expense

↓10%

Non-interest income

↑4% (slack)

Peer Group: NAB (.483), Advance (.309), CBA (.208)

34

Table 4. Summary of the Sources of Highest Technical Inefficiencies (CRS) Amongst Inputs and Outputs for Individual Trading Banks, 1986-1995

Advance

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

Inex(-33)

Inex(-26)

Inex(-31)

Inex(-42)

Inex(-43)

Inex(-47)

Inex(-56)

Effnt

Effnt

Effnt

Inex(-13)

Inex(-18)

Inex &

Inex(-29)

Inex(-19)

Inex(-22)

Inex(-24)

Inex(-18)

Ninin(8) ANZ

Inex &

Effnt

Ninex(-3)

Ninex(-15)

BankQLD

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Ninin(55)

Ninin(30)

BankSA

Inex(-32)

Inex(-20)

Inex(-43)

Inex(-54)

Inex(-41)

Inex(-72)

Inex(-74)

Inex(-63)

Inex(-54)

Inex(-21)

Ninin(44)

Ninin(23)

BankWA

Inex(-38)

Inex(-51)

Inex(-59)

Inex(-44)

Inex(-33)

Inex(-57)

Inex(-49)

Inex(-30)

Inex(-30)

Inex(-19)

CBA

Effnt

Ninin(46)

Ninin(31)

Effnt

Inex(-12)

Effnt

Inex(-13)

Ninex(-16)

Inex(-14)

Effnt

Ninin(7)

Ninin(5)

Macquarie

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

NAB

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

Effnt

SbankNSW

Inex(-28)

Inex(-40)

Inex(-47)

Inex(-41)

Inex(-30)

Inex(-48)

Inex(-52)

Inex(-51)

Inex(-61)

Inex(-50)

Westpac

Effnt

Inex &

Inex(-14)

Inex(-29)

Effnt

Inex(-23)

Inex &

Inex(-23)

Inex(-23)

Inex &

Ninex(-2)

Ninex(-23)

Ninex(-10)

Ninin(10) Notes:

'Inex' denotes interest expense (number in brackets represent percentage potential improvement; -ve for input contraction and +ve for output expansion). 'Ninex' denotes non-interest expense. 'Netinin' denotes net interest income. 'Ninin' denotes non-interest income. 'Effnt' denotes fully efficient banks.

35

Table 5. An Example of Decomposing Technical Efficiency Scores (1995 Data) Bank

Technical Efficiency (CRS scores)

Pure Technical Efficiency (VRS scores)

Scale Efficiency

x = 0.942 σ = 0.069 1.000

x = 0.956 σ = 0.062 1.000

x = 0.985 σ = 0.026 1.000

MPSS

ANZ

0.898

0.979

0.917

DRS

BankQLD

0.998

1.000

0.998

IRS

BankSA

0.887

0.916

0.968

IRS

BankWA

0.933

0.954

0.978

IRS

CBA

1.000

1.000

1.000

MPSS

Macquarie

1.000

1.000

1.000

MPSS

NAB

1.000

1.000

1.000

MPSS

SbankNSW

0.802

0.815

0.985

IRS

Westpac

0.900

0.900

1.000

MPSS

Advance

Notes:

Nature of Returns to Scale

CRS denotes constant returns to scale. VRS denotes variable returns to scale. MPSS denotes most productive scale size. DRS denotes decreasing returns to scale. IRS denotes increasing returns to scale. Technical efficiency = Pure technical efficiency x Scale efficiency

36

Table 6. Annual Mean Relative Efficiency Scores, 1986-1995 Technical Efficiency

Pure Technical Efficiency

Scale Efficiency

(CRS)

(VRS)

1986

.977

.986

.991

1987

.955

.965

.989

1988

.951

.969

.982

1989

.946

.970

.975

1990

.919

.943

.974

1991

.825

.844

.979

1992

.860

.901

.957

1993

.909

.942

.967

1994

.883

.899

.983

1995

.942

.956

.985

37

Table 7. Window Analysis of Pure Technical Efficiency Scores of Trading Banks, 1986-1995

1986 .895

Advance

Bank

1.000 1.000

ANZ

.827

1987 .881 .840

BankQLD

1.000

BankSA

.883

BankWA

.839

.883 .804

.835 .805

.843 .808

CBA

.903

1.000 1.000

Macquarie

.893

.959 .915

SBankNSW

NAB

.918

1.000 1.000

.883

.850 .815

1988 .882 .863 .879

1.000 1.000 1.000

1.000 1.000 1.000

.897 .814 .809

.975 .932 .934

.994 .994 .994

1.000 1.000 1.000

1.000 1.000 1.000

.876 .839 .852

1989 .818 .819 .761

.910 1.000 .756

1.000 1.000 1.000

.913 .925 .827

.963 .965 .902

.973 .973 1.000

1.000 1.000 1.000

1.000 1.000 1.000

.879 .881 .816

Efficiency Scores 1990 1991 .814 .755 .754

.924 .724 .724

1.000 1.000 1.000

.977 .866 .866

.733 .677 .677

.905 .898 .970

1.000 .973 1.000

1.000 .993 .999

.802 .762 .791

.836 .858 .851

.803 .803 .803

1.000 1.000 1.000

.301 .301 .301

.628 .627 .627

1.000 1.000 1.000

1.000 1.000 1.000

1.000 1.000 1.000

.827 .846 .840

1992

.929 .907 .900

1.000 .923 1.000

1.000 1.000 1.000

.450 .450 .468

.730 .728 .777

.933 .902 .899

1.000 1.000 1.000

1.000 .967 .964

1993

1.000 .981 .976

.988 .932 .943

1.000 1.000 1.000

.773 .813 .824

.825 .824 .829

.886 .826 .822

1.000 .964 1.000

1.000 .980 .973

1994

1.000 1.000

.976 .982

1.000 1.000

.647 .650

.863 .865

.857 .854

1.000 1.000

1.000 1.000

1995

Mean

.883

.079

.060

.246

.915

.097

.244

.276

.999

.003

0

.013

.723

.220

.111

.676

.813

.114

.063

.348

.924

.065

.072

.192

.988

.034

.036

.130

.986

.025

.044

.085

1.000

.930

.987

.913

.951

.940

.870

1.000

.821 .798 .790 .802

.786 .794 .795

.775 .781

Descriptive Statistics SD LDY LDP

.036

.065

.813

38

.121

Westpac

Bank

Notes:

1986 .857

1987 .874 .857

Mean SD LDY LDP

1988 1.000 1.000 1.000

1989 1.000 .953 1.000

Efficiency Scores 1990 1991 1.000 1.000 1.000

1.000 1.000 1.000

1992

1993

1994

1995

Mean

.943 .940 .814 .832

.973 .966 .981

.846 .847

Descriptive Statistics SD LDY LDP

.069

.126

.887

(average score for the ten year period) (standard deviation for the period) (largest difference between scores in the same year) (largest difference between scores across the entire period)

39

.186

Table 8. Window Analysis of Scale Efficiency Scores of Trading Banks, 1986-1995

1986 .989

Advance

Bank

1.000 .980

ANZ

1.000

1987 .962 .954

BankQLD

1.000

.995 .980

BankSA

.995

.925 .925

BankWA

.966

1.000 .986

CBA

1.000

.968 .967

Macquarie

.981

.999 .995

NAB

.999

1.000 1.000

SBankNSW

.991

.991 .998

1988 .996 .996 .985

.936 .923 .923

1.000 1.000 1.000

.996 .984 .990

.978 .979 .981

.982 .959 .958

1.000 1.000 1.000

1.000 1.000 1.000

.993 .999 .991

1989 .977 .978 .974

.940 .858 .992

1.000 1.000 .937

.999 .991 .964

.980 .982 .978

.992 .992 .934

1.000 1.000 1.000

1.000 1.000 1.000

.997 .998 .990

Efficiency Scores 1990 1991 .983 .935 .942

.879 .979 .979

1.000 .966 .973

.985 .972 .973

.974 .954 .975

.999 1.000 .986

1.000 .993 1.000

.957 .943 .992

.999 .993 .996

.976 .997 .998

.956 .956 .956

1.000 .991 .988

.987 .989 .989

.965 .999 .994

1.000 1.000 1.000

1.000 1.000 1.000

.966 .993 .985

.990 .997 .999

1992

.986 .999 .994

.804 .839 .804

1.000 1.000 1.000

.992 .992 1.000

.999 .997 .971

.944 .961 .952

.996 .996 1.000

.986 .981 .976

.995 .999 .997

1993

1.000 .997 .986

.809 .832 .838

1.000 1.000 1.000

.999 .981 .968

.993 .993 .978

.970 .978 .986

1.000 .996 .991

1.000 .986 .990

.998 .997 .988

1994

1.000 1.000

.884 .890

.970 .970

.995 .982

.995 .984

.990 .995

1.000 1.000

1.000 1.000

.995 .983

1995

Mean

Descriptive Statistics SD LDY LDP

.984

.019

.048

.065

.912

.066

.134

.196

.983

.025

.063

.075

.986

.010

.035

.036

.980

.012

.034

.045

.980

.020

.058

.066

.998

.004

.009

.019

.990

.015

.049

.057

.994

.004

.012

.016

1.000

.938

.951

.972

.980

.978

.996

1.000

.987

40

Westpac

Bank

Notes:

1986 .998

1987 .983 .963

Mean SD LDY LDP

1988 .971 .943 .943

1989 .910 .958 .850

Efficiency Scores 1990 1991 .977 .880 .895

.848 .848 .848

1992

1993

1994

1995

Mean

.916 .791 .860 .849

.895 .896 .894

1.000 .999

Descriptive Statistics SD LDY LDP

.061

.108

.982

(average score for the ten year period) (standard deviation for the period) (largest difference between scores in the same year) (largest difference between scores across the entire period)

41

.209

Table 9. Nature of Returns to Scale for Individual Trading Banks, 1986-1995 1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

Advance

IRS

IRS

DRS

IRS

IRS

IRS

DRS

MPSS

MPSS

MPSS

ANZ

DRS

MPSS

DRS

DRS

DRS

DRS

DRS

DRS

DRS

DRS

BankQLD

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

IRS

IRS

BankSA

MPSS

IRS

IRS

IRS

IRS

IRS

DRS

IRS

IRS

IRS

BankWA

IRS

IRS

IRS

IRS

IRS

IRS

IRS

IRS

IRS

IRS

CBA

MPSS

DRS

DRS

MPSS

DRS

MPSS

DRS

DRS

DRS

MPSS

Macquarie

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

NAB

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

MPSS

SbankNSW

IRS

IRS

DRS

IRS

IRS

MPSS

IRS

IRS

IRS

IRS

Westpac

MPSS

DRS

DRS

DRS

MPSS

DRS

DRS

DRS

IRS

MPSS

42

Table 10. Comparison of Bank Size with Nature of Returns to scale, 1993-95 1993 (mean = 17,705)

Bank Size (staff numbers) 1994 (mean = 16,749)

1995 (mean = 16,671)

DRS Banks ANZ CBA Westpac

41,737 42,329 33,724

ANZ CBA

39,642 37,269

ANZ

39,240

BankSA BankWA SBankNSW

3,375 3,312 5,269

BankQLD BankSA BankWA SBankNSW Westpac

745 2,980 2,959 4,687 31,396

BankQLD BankSA BankWA SbankNSW

786 2,388 2,872 4,441

Advance BankQLD

2,197 703

Advance

2,409

Advance

2,459

Macquarie NAB

1,351 43,053

Macquarie NAB

1,528 43,871

CBA Macquarie NAB Westpac

35,822 1,704 45,585 31,416

IRS Banks

MPSS Banks

43

1

An excellent historical perspective on the Australian financial system can be downloaded from the web site

http://www.treasury.gov.au/Publications/FSI/final_report/ (see Chapter 14). 2

Non-interest expense: before tax total expenses less interest expenses and charges for bad and doubtful

debts. Net loans: gross loans less specific and general provisions for bad and doubtful debts. Net interest income: interest income less interest expense. Non-interest income: all revenues less interest income and bad debt recoveries. 3

Peer weight is known as 'lambda'. It measures the degree of contribution by the efficient peer to calculation

of the inefficient unit's score. In Figure 1, unit M would have the highest lambda in unit K's peer group. 4

Given that trading banks share similar technology, staff members can be used as a proxy for bank size.

44