TRENDS IN NEW ZEALAND BANK EFFICIENCY OVER TIME
TRIPE, David* Centre for Banking Studies
Massey University Palmerston North
Abstract
This paper explores the extent of efficiency improvements achieved by New Zealand banks over the period 1996 to 2002, using data envelopment analysis (DEA), on a time-series, rather than cross- sectional basis.
Evidence is found for improvements in bank efficiency through time, some of which can be attributed to falls in the general level of interest rates, although a further portion may be due to either management effort to improve bank efficiency or technical progress.
Because some of the results obtained appear to be a consequence of the methodology, rather than necessarily being consistent with other interpretations of the data, the paper also provides insights into complications that can arise with use of DEA.
JEL classification: C1, G2.
Keywords: Data Envelopment Analysis, Banking, New Zealand.
1. Introduction
All round the world, efforts are being made to achieve improvements in bank efficiency. The idea is that if banks are more
* Thanks are due to Necmi Avkiran and Lifen Wu, and to participants at the New Zealand Finance Colloquium, February 2002, and at seminars at Monash and Curtin Universities for comments on earlier versions of this paper.
efficient, they will be able to run at lower cost, leading to improved profitability and better returns to shareholders.
Banks are not the only businesses engaged in this pursuit, of course, but bank managements are inclined to be single-minded in the belief that cost cutting will be the answer to problems in bank performance. Bank management typically discuss cost performance in terms of two ratios – the ratio of (non-interest) operating costs to (average) total assets, and the ratio of operating costs to gross income (net of interest expense).
Both of these ratios have limitations as measures of cost performance, particularly in that they are capable of being manipulated through changing accounting practices, and because they take no account of differences between the pattern and structure of business undertaken by the banks whose ratios are being compared. The cost to income ratio is probably the more popular with bank managements, and it has an intuitive appeal in terms of incorporating both key elements in the profit equation, so that, other things being equal, a lower cost to income ratio should imply greater profitability.1 Banks in New Zealand and Australia achieved significant reductions in their cost ratios during the 1990s, with a major cause being reductions in staff numbers. This is a different outcome from that observed, for example, in the United States (based on OECD figures for bank profitability), and there is thus a question as to whether this may be a consequence of special characteristics of the Australia and New Zealand banking markets.
To take account of the different mix and pattern of business from bank to bank, we cannot confine ourselves to looking at simple ratios, but must look at financial firms on a multiple input and multi- product basis.2 Banks use a mixture of inputs to produce a mixture of outputs, and their reported aggregate cost figures will depend just as much on the mix of inputs and outputs as on the rate at which they use those inputs to produce outputs (Mester, 1987). Against this background, a financial firm may be said to be operating inefficiently if it can produce more output without a corresponding relative
increase in inputs, or if it can reduce its use of inputs without a corresponding relative decrease in output.
This article looks at changes in New Zealand bank efficiency through time, in an attempt to ascertain the extent of improvements achieved. During the course of this exploration we identify a number of practical issues with methodology and model structures, which can be expected to impact upon future research. This research is also part of a broader programme looking at performance issues in New Zealand banking.
The rest of this paper proceeds as follows. In the next section we provide some brief background information on the New Zealand banking market, while in Section 3 we discuss the methods of efficiency analysis in banks in general terms, making reference to previous studies. In section 4 we describe the data and methodology used for this study, the results from which are reported and discussed in section 5. In response to these findings, section 6 strives to draw conclusions from the analysis undertaken, and suggests ways in which this line of research may be pursued further.
2. The New Zealand banking sector
The deregulation of the New Zealand financial system in the 1980s wrought substantial changes for the New Zealand banking sector. Prior to deregulation, the banking sector was dominated by four trading banks, which undertook a broad range of banking business, very little of which, however, was home mortgage lending.
There was also a significant savings bank sector, including the so- called private savings banks (which were owned by the trading banks), and a number of other domestically-owned financial institutions such as building societies, finance companies and the government-owned Rural Bank.
One of the effects of deregulation of the financial sector was to remove barriers to the entry to and exit from banking, by establishing a system for bank registration. The original four trading banks were deemed to be registered as of 1 April 1987, and over the
following few months and years the number of registered banks grew substantially, to reach a peak of 23. Banks to achieve registration included both multinational banks seeking a presence in the New Zealand market, and existing savings and other financial institutions which were keen to change their status.
Relatively free entry was accompanied by relatively free exit, and a number of the newly arrived institutions have subsequently retired from the New Zealand market. Other institutions have disappeared as a result of acquisition, with the result that, since the acquisition of Trust Bank New Zealand by the Westpac Banking Corporation in 1996, approximately 99% of the assets of the New Zealand banking system have been under foreign- ownership.3
The high degree of foreign ownership is thus a distinctive feature of the New Zealand banking system, with the extent of foreign ownership being unrivalled elsewhere in the developed world (and in most of the developing world as well). Consumer and business banking is dominated by five foreign-owned banks, four of which are Australian-owned, one of which is British-owned, and which together controlled 83.7% of banking system assets as at 31 March 2002. The only locally owned registered banks are TSB Bank (TSB) and Kiwibank. TSB is a small retail bank with total assets of only NZ$ 1.63 billion at the end of March 2002, and which operates only in the Taranaki region (on the West Coast of the North Island).
Kiwibank was established more recently by the government as a personal sector bank, through New Zealand Post, and commenced business in February 2002.
The New Zealand banking system is also distinguished by a lack of regulation as to what functions banks may undertake (apart from a legislative requirement to be in the business of banking).
Despite this freedom, banks’ diversification into other activities such as stockbroking has often not been particularly successful, and their main business remains the borrowing and lending of money, with
this reflected in a ratio of non-interest income to total income for the major banks of 34.1% in the March 2002 quarter.
3. Some background to efficiency analysis
Efficiency can be discussed in a variety of different forms.
Traditional microeconomic theory has long talked of economies of scale, where increased volumes of output are supposed to be able to be produced with less than proportionate increases in quantities of inputs (increasing returns to scale). In due course, however, economies of scale will be exhausted, and increased output will require a more than proportionate increase in inputs, a situation described as diseconomies of scale (decreasing returns to scale).
Another type of efficiency is economies of scope. The essence of these is that firms should be able to produce multiple outputs from the same group of inputs at lower cost, in terms of inputs, than if they specialised in producing only one type of output.
In a banking context, we might be looking at a situation where a firm produced both loans and deposit services, using the same staff and branch networks, rather than specialising in just one of these functions by itself.
These discussions of economies of scale and scope in the previous paragraphs assume a uniform production function that applies to all firms in the market: if two firms are producing the same mix of outputs at the same volume, their costs will be the same. This may not be a reasonable assumption, and we thus come to the concept of X-efficiency, which itself has two components – technical efficiency and allocative efficiency. Technical efficiency might be conceived in simple terms as a measure of whether the firm is maximising production from the inputs it is using, while allocative efficiency looks at whether the best combination of inputs is being used, having regard to their relative cost.
Attempts to specify and measure X-efficiency generally occur relative to an efficiency frontier, with firms’ efficiency being defined in terms of their relative distance from the frontier (which
then becomes the benchmark for optimum performance). Previous research has suggested that variations in banks’ X-efficiency are much greater than any effects that might arise from economies of scale or scope (Berger & Humphrey, 1991). This should not deter us from looking for scale efficiency effects, however, although prior research generally suggests that these are exhausted at relatively low levels.4
Because there is no agreed set of engineering relationships defining a standardised set of production processes in banking, there is no simple readily agreed approach for specifying the efficiency frontier. Attempts to determine the position of the efficiency frontier are thus dependent on use of accounting information and any other measures of input or output volume that may be available. Berger &
Humphrey (1997) identify five different approaches to determining the efficiency frontier. The three main parametric approaches to specification of the efficiency frontier are the stochastic frontier approach (SFA), the distribution-free approach (DFA) and the thick frontier approach (TFA), while the two non-parametric approaches are data envelopment analysis (DEA) and the free disposal hull (FDH) method.5
The major difficulty with the non-parametric approaches is that they cannot distinguish random error arising from measurement error or extraordinary financial performance (arising from accounting practice or some other source). The parametric approaches are better able to deal with random error, and they are then distinguished by the way in which this random error is broken down to allow identification of inefficiency.6 An issue with the parametric approaches is that they have to specify a functional form for the cost, profit or production relationship between inputs, outputs and environmental factors. The problem with specifying a functional relationship is that it presupposes the shape of the efficiency frontier, and for the translog approximation in particular, this has the potential to generate misleading interpretations in relation to economies of scale and scope (Berger & Humphrey, 1997; McAllister &
McManus, 1993).
The previous study of bank efficiency in the New Zealand market (Su & Tripe, 2001) was based on the methodology used by Avkiran (1999) in his study of the Australian market. In both these cases, the frontier technique used was DEA, as also used by Avkiran (2000) and Sathye (2001). The other study looking at X-efficiencies in Australian banking was that of Walker (1998), who used a fixed effects version of SFA,7 although he identified the difficulty posed by the limited number of banks for establishing a suitable efficient frontier.
Another important classification of approaches to modelling bank efficiency is the distinction between the production and intermediation models, with the intermediation model existing in a number of different forms. Under the production approach, banks are regarded as using labour and capital to produce deposits and loans (with outputs potentially being measured by number of accounts, rather than dollars). The intermediation approach sees deposits and other funds being transformed into loans: Favero & Papi (1995) suggest that this is a particularly apposite description of the activities undertaken by banks. The different versions of the intermediation approach include the asset approach, which uses funds as inputs and loans as outputs, the user cost approach, which looks at the various contributions to banks’ net revenue, and the value added approach, where inputs and outputs are identified according to their share of value added.
Limitations in the data available for the New Zealand and Australian markets tend to mean that the production approach cannot generally be used, although it would provide some basis for looking at customer transaction behaviour, which is an important contributor to both banks’ costs and revenues. Favero & Papi (1995) note that the asset approach omits consideration of the non-lending activities that banks undertake, while it can be difficult to obtain accurate data for the user cost approach, because of the potentially distorting effects of cross-subsidisation. The value added approach generally treats deposits as outputs, although Hughes & Mester (1993) show that they ought more appropriately be classified as inputs.
4. Data and Methodology
Because the relatively small number of banks in the New Zealand market would make use of parametric techniques potentially unreliable, this study has used DEA.8 We believe that the alleged disadvantages of the user cost approach are not sufficient to cause us to prefer any alternative approach to selection of inputs and outputs, having regard to the available data, which are derived from New Zealand banks’ quarterly disclosure statements, produced (in terms of requirements) since the end of the March quarter 1996.9
These data are subject to some limitations, but they allow a time series analysis for quarters ending from 30 June 1996 to 31 March 2002. Because of a change in accounting policy, data for the ANZ Banking Group (NZ) Ltd (ANZ) for the quarter ending 31 December 1997 are not useable, but we otherwise have 24 quarters of data available for ASB Bank (ASB), Bank of New Zealand (BNZ), Citibank, Hong Kong Bank (HSBC), the National Bank of New Zealand (NBNZ or the “National Bank”), TSB and WestpacTrust.10 To economise on use of both input and output variables so as to enhance the discriminatory power of the analysis, we limit ourselves to two of each.
The variables used in other small sample analyses in the Australian and New Zealand markets are summarised in Table 1.
Data for staff numbers in New Zealand are not available on a quarterly basis, which precludes their use as an input variable.
Capital is not a suitable variable in New Zealand, as a number of the banks studied operate as branches, and therefore have no capital in New Zealand. Difficulties also arise in using deposits as either an input or output variable, as banks do not always provide sufficient detail to allow deposits to be distinguished from other sources of funding.
For this study, we have therefore chosen a model with interest and non-interest expense as inputs, and net interest income and non-interest income as outputs. These variables incorporate
more-or-less the whole gamut of activities that banks undertake, consistent with the user-cost approach to the specification of bank production. The input and output variables are all expressed as dollar amounts, at current prices.11 An earlier paper (Tripe, 2002) tried an alternative model on a similar data set with total interest income and non-interest income as outputs, but the model now used was found to display greater discriminatory power.
We begin with a constant returns to scale (CCR) model, but follow that with a variable returns to scale (BCC) model.12 This allows us to test for the existence of scale economies, which might emerge as a result of increases in banks’ assets. A constant returns to scale efficiency measure is the product of a variable returns to scale efficiency measure and a scale efficiency factor, which allows us to solve for the scale efficiency measure (Coelli et al, 1998, p 151).
Analysis using DEA was undertaken for each bank on a time-series basis. This contrasts with the approach followed in Su &
Tripe (2001) and Avkiran (1999), where efficiency frontiers were determined for each time period in isolation, and each bank’s performance was assessed relative to other banks in the same time period. That approach could not tell us how the efficiency of banks changes over time: all it could provide us with was a trend in banks’
efficiency relative to each other. On the other hand, the approach followed in this paper means that we cannot compare banks’
efficiency relative to each other.
For the DEA, the software used was DEA-Solver, developed and described by Cooper et al (2000). This has an advantage over some other DEA software in that it allows for negative output values (which was necessary to handle some observations for one of the banks studied).
It also identifies, in the variable returns to scale models, whether a decision making unit (firm) is operating at increasing, constant or decreasing returns to scale.
5. Analysis and Results
Results for efficiency for each of the banks analysed for each period are reported in Table 2 for the constant returns to scale model and Table 3 for the variable returns to scale model. The symbol N/A is used for the ANZ case where data were not meaningful because of changed accounting policy (the December quarter 1997).
From the constant returns to scale models we find that efficiency appears to have increased through time, with this confirmed by positive correlation coefficients (not reported), all but one of which are significant at the 1% level (with the remaining one, for Citibank, significant at the 5% level). For the variable returns to scale model, correlation coefficients are also positive, although for only 4 out of 8 banks are these significant at the 1% level, with one further bank showing a significant coefficient at the 10% level. The average efficiency (across the 6 banks that dominate the retail market, not reported) was also strongly positively correlated with the time trend (at the 1% level in each case). This would suggest that banks have been becoming more efficient over time, with one possible reason being that they have achieved more efficient scale.
5.1 Scale efficiency effects
We therefore look at scale efficiency effects, estimates for which for each bank for each quarter are reported in Table 4. We have also calculated an average scale efficiency factor for each bank, with the figures reported at the bottom of Table 4. The extent of scale inefficiency for some banks is greater than might have been expected,13 although this result is potentially distorted by our time- series approach to DEA.
There are also significant differences in size between the banks, and varying degrees of growth in assets observed over the period studied. Table 5 summarises the size of each bank (by assets) at the beginning and end of the period, and also summarises the
returns to scale results reported for each bank by the individual bank BCC models.
A review of Tables 4 and 5 together sends confusing and contradictory messages about the relationship between size and returns to scale, even though we are unable to compare results for individual banks against each other (as the efficiency scores have not been determined from cross-sectional analysis). Overall in Table 5 we find 105 observations characterised by increasing returns to scale, 68 by constant returns to scale, and 18 by decreasing returns to scale.
These would seem to suggest that banks had improved their efficiency scores by increasing their assets in an environment of increasing returns to scale.
Some of the potentially conflicting and contradictory effects may be attributable to the non-parametric basis of DEA (which fails to allow for random effects or errors). Results for individual banks where we can comment are as follows.
* For ASB, a high incidence of increasing returns to scale appear consistent with its strong asset growth: constant or decreasing returns to scale were observed only where the bank showed as efficient under the variable returns to scale model.
* In the BNZ case, the decreasing returns to scale cases were all in 2001, during a period when the bank’s assets peaked.
* HSBC shows as having achieved some improvement in scale efficiency, although total assets are virtually unchanged. This might mean that the point at which efficient scale could be achieved has changed with time.
* The NBNZ achieved an improvement in scale efficiency, most noticeably around the end of 1998/beginning of 1999, following its merger with Countrywide Bank, which caused a sharp growth in assets. The opportunity to realise economies of scale was one of the arguments put forward in support of this merger, and, contrary to more usual findings (Su & Tripe, 2001), they may actually have been realised. We also find that, prior to the merger, NBNZ was generally showing increasing returns to scale, while constant returns to scale are reported more frequently subsequently.
*TSB changed from increasing to constant returns to scale at around the end of 1998, by which time it was generally showing as being scale efficient. This was at about the time its assets passed $1 billion.
The inconsistencies between scale efficiency measures and bank size, except in the case of the National Bank, generally confuse interpretation of the results obtained, with the problem compounded by the wide diversity of sizes at which banks appear to achieve scale efficiency. It is perhaps helpful to look at how the observed scale effects have been generated from the data used in this study.
The reported scale effects can be attributed to the significant increase in efficiency shown by the variable returns to scale models during the earlier part of the period analysed. A variable returns to scale model must report a greater proportion of observations as on or close to the efficiency frontier, when compared to a constant returns to scale model, and this will sometimes occur because of a lack of other adjacent efficient observations.14 The increases in the reported efficiency for earlier observations when the variable returns to scale model is used may therefore simply be a reflection of the relative dearth of efficient observations in that zone when the constant returns to scale model was being used:15 it is possible that scale efficiencies are being exaggerated by the method employed. This is consistent with the point made by Dyson et al (2001), that “… the VRS model will always envelop the data more closely than the CRS model, irrespective of whether variable returns to scale exist” (p 248).
We cannot rule out the existence of scale effects, but we would have to be wary of assuming that the observed increase in efficiency through time, evident from the constant returns to scale model, should be attributed to scale effects arising from increases in banks’ assets. Concern over the validity of the scale efficiency measures would also be raised by their relative volatility, particularly during the earlier part of the period studied: such instability would seem to be inconsistent with the theoretical and logical underpinnings for the existence of scale economies.
5.2 Other impacts on efficiency
The unreliability of scale as a cause of improved efficiency obliges us to look at other potential causes. One argument is that some of the efficiency improvement observed may be a logical outcome of the use of DEA and frontier analysis in general, against the background of a reduction in the general level of interest rates over the period studied. We explain this as follows, based on the principle that DEA relies for efficiency measurement on the ratio between inputs and outputs.
Suppose as a simplifying assumption that net interest income is constant over time, and that we look at two separate time periods, one of which is characterised by high interest rates and the other by low interest rates. All other aspects of bank cost and efficiency (i.e.
non-interest expense and income) are unchanged. Let us pick some numbers as examples – an aggregate average cost of funds of 8% in the high interest case and a cost of funds of 4% in the low interest rate case, with a net interest income of 2% in each case.16 We thus have, in the high interest case, interest expense of 8% being used to generate net interest income of 2%, and in the low interest environment, interest expense of 4% being used to generate net interest income of 2%. The ratio of the output price to input price is thus higher (and the bank will therefore appear to be more efficient) when interest rates are lower.17
The 90-day bill rate can be regarded as a reasonable proxy for the general level of interest rates impacting on New Zealand banks. We explore the relationship between bank efficiency and the general level of interest rates using the following regression model, for both the constant and variable returns to scale models.
EFF = α + β(INTRATE) + γ(TIMETREND) + ε (1)
Where EFF is the efficiency score; INTRATE is the average 90-day bill rate for the quarter; TIMETREND is a time trend variable (to incorporate the effects of technological change, managerial effort to reduce X-inefficiency, etc); and Ε is an error term.
Results are reported in Table 6.
It might reasonably be argued that, because our response variable is efficiency, which must be in the range 0 to 1 (100%), we ought to be using logit regression.18 The actual fitted values obtained from the regression are not of particular interest, however, and in any case the estimated constants are not significantly greater than 1 (100%). It is therefore considered that the OLS regressions used provide adequate outcomes, while offering us a coefficient of determination that is simple to interpret. Use of linear regression is also consistent with usual practice in the banking literature (Berger &
Mester, 1997).
The general finding from the results reported in Table 6 is that there are relationships between the reported efficiency and interest rates, time trend, or both for many of the banks studied. In the constant returns to scale model, the coefficients for interest rate are consistently negative, while coefficients on the time trend variable are consistently positive.19
We have explored these issues further by investigating the efficiency of banks with predominantly retail business as if they were a single entity20. Efficiency scores are not reported, but we find a strong correlation (significant at less than 0.1%) between scale efficiency measure and the time trend, which once again causes us to question the validity of the scale efficiency measures obtained.
Regression results are reported in Table 7, and these support the existence of relationships between efficiency and both interest rates and time trend for the constant returns to scale model.
6. Conclusion
This paper has taken a different approach to that which is usually followed in using DEA for exploration of bank efficiency, looking at it on a time-series, rather than cross-sectional basis. It is part of a larger research programme, which also looks at efficiency in
other ways, to try and understand more about the performance of New Zealand banks.
Major findings from this study are as follows. New Zealand banks have become more efficient, in general, over the period 1996 to 2002, although part of the improvement in efficiency appears to be a consequence of the fall in the general level of interest rates. The rest of the improvement in efficiency may be accounted for either by improved managerial practice in improving X-efficiencies, or by technical progress that has allowed banks to improve their efficiency (reflected in a movement in the efficient frontier). This is reflected in time trend appearing to account for a further portion of the observed efficiency improvements (although time could ever only be a relatively crude proxy for technical progress or for the effects of managerial effort to be realised).21
The data generated by our research also suggest that scale factors may impact on bank efficiency, but the generally inconsistent relationships between estimated scale efficiencies and actual bank size make us reluctant to ascribe particular importance to this effect, except perhaps for the National Bank of New Zealand.
Another aspect of this research has been the suggestion that some of the findings emerging from DEA studies may be a reflection of the methodology, rather than the data. We are thus very cautious of our findings in respect of scale economies, but our findings in respect of the impact of the general level of interest rates are perhaps more important. If we are looking at efficiencies through time, we need to be careful in our selection of inputs and outputs to make sure that these are not being influenced by factors that are not part of the study. General levels of interest rates are an obvious example of such a factor, and we will be alert to this in future research.22
With the guidance that this research has provided in model selection, we are now better positioned to undertake further research on New Zealand bank efficiency. This should entail cross-sectional analysis, so as to allow us to extend the results reported in Su and Tripe (2001), but also panel data using the Malmquist index
(Fukuyama, 1995; Worthington, 1999; Avkiran, 2000; Alam 2001), which is particularly attuned to measurement of productivity changes through time.23 The research agenda also includes attempting some cross-country analysis, to allow us to better understand the relative performance of the New Zealand banking system.
Table 1: Approaches followed in previous Australasian DEA analysis
Source Inputs Outputs
Avkiran (1999) Model A
Interest expense Non-interest expense
Net interest income Non-interest income Avkiran (1999)
Model B
Deposits Staff numbers
Net loans
Non-interest income Avkiran (2000) Interest expense
Non-interest expense
Net interest income Non-interest income Sathye (2001) Labour
Capital
Loanable funds
Loans
Demand deposits Su & Tripe (2001)
Model A
Interest expense Non-interest expense
Net interest income Non-interest income Su & Tripe (2001)
Model B
Interest expense Non-interest expense
Customer deposits Net loans and advances Operating income Su & Tripe (2001)
Model C
Interest expense Non-interest expense
Deposits
Loans and advances Operating income This Study Interest expense
Non-interest expense
Net interest income Non-interest income Beyond that, there is also the possibility that we may be able to look at parametric techniques for efficiency measurement, as the passage of time allows us to expand our data set. We also want to explore the impact of using a wider range of DEA models, such as the additive and slacks-based models (Cooper et al, 2000, pp 91- 104).
That is beyond the scope of this paper, however. What this paper has achieved is some appreciation of the methodological problems likely to be faced in other research.
Table 2: Constant returns to scale model results (percentage efficiencies).
Quarter
ended ANZ ASB BNZ Citib. HSBC NBNZ TSB Westpac
Trust
Jun 96 75.39 98.30 86.26 66.37 45.44 62.43 85.99 64.96 Sep 96 69.87 75.51 78.50 79.81 75.69 68.67 74.83 61.19 Dec 96 69.73 94.50 84.06 41.00 57.56 75.90 78.71 67.67 Mar 97 81.54 94.42 88.75 69.29 85.19 70.80 64.81 71.46 Jun 97 85.94 84.14 92.60 48.03 70.82 72.96 88.50 76.66 Sep 97 90.67 81.62 85.63 47.71 69.62 62.70 76.32 80.74 Dec 97 N/A 83.75 88.93 70.43 64.00 62.17 78.44 82.75 Mar 98 66.04 85.82 77.54 57.60 71.38 69.35 74.26 71.69 Jun 98 67.54 80.83 85.60 47.55 83.11 69.32 86.51 85.53 Sep 98 88.96 84.58 73.07 61.33 84.01 71.45 94.60 90.39 Dec 98 81.53 90.62 93.19 100 66.56 76.44 100 84.77 Mar 99 89.91 100 93.40 47.52 98.01 100 91.92 100 Jun 99 100 100 100 100 96.16 98.21 100 96.64 Sep 99 99.53 97.39 86.36 62.92 100 95.68 98.31 100 Dec 99 91.56 100.00 98.71 90.54 80.07 93.32 100 98.16 Mar 00 86.41 99.69 100 74.49 93.42 92.32 95.60 91.68 Jun 00 85.84 91.83 98.57 85.36 100 100 100 89.79 Sep 00 75.65 90.02 100 100 100 91.75 100 92.10 Dec 00 84.42 94.82 100 88.75 77.01 90.88 96.83 88.31 Mar 01 92.79 91.31 100 64.33 93.79 97.38 79.32 87.16 Jun 01 100 100.00 90.52 41.72 75.80 100 98.39 92.34 Sep 01 100 93.83 92.98 100 96.19 96.41 92.83 100 Dec 01 98.52 99.89 97.14 100 100 90.78 100 97.65 Mar 02 100 100 100 89.91 100 100 99.89 93.88
Table 3: Variable returns to scale model results (percentage efficiencies).
Quarter ended
ANZ ASB BNZ Citibank HSBC NBNZ TSB Westpac
Trust Jun 96 75.47 100 99.03 70.26 90.31 89.34 100 100 Sep 96 73.79 97.52 79.93 79.85 99.51 87.17 89.50 70.26 Dec 96 70.34 95.82 89.33 64.83 72.89 90.96 93.58 80.19 Mar 97 81.68 100 96.88 73.03 94.04 100 85.76 82.51 Jun 97 91.23 92.80 94.00 64.58 73.45 99.14 97.47 82.81 Sep 97 96.88 92.17 86.58 50.87 77.35 100 88.34 83.95 Dec 97 N/A 94.21 92.71 100 69.47 94.90 86.26 84.02 Mar 98 100 99.33 90.15 59.67 87.39 97.72 85.31 79.96 Jun 98 79.47 92.76 96.58 51.07 100 93.63 91.63 88.58 Sep 98 100 93.40 78.38 65.76 85.05 85.11 96.47 100 Dec 98 86.43 93.14 94.89 100 73.63 84.18 100 87.94 Mar 99 100 100 98.72 66.03 99.14 100 98.63 100 Jun 99 100 100 100 100 100 100 100 98.67 Sep 99 100 100 88.47 85.50 100 100 100 100 Dec 99 92.93 100 98.72 100 87.83 95.42 100 100 Mar 00 91.08 100 100 75.13 95.95 100 96.37 94.71 Jun 00 91.60 93.01 98.57 98.36 100 100 100 94.29 Sep 00 76.90 93.25 100 100 100 93.27 100 94.85 Dec 00 88.78 95.03 100 93.47 79.49 92.89 98.62 91.95 Mar 01 96.29 94.23 100 71.05 94.94 97.73 79.63 93.01 Jun 01 100 100 92.20 77.48 79.09 100 99.01 96.26 Sep 01 100 94.65 100 100 96.19 98.63 93.44 100 Dec 01 98.71 100 100 100 100 90.82 100 100 Mar 02 100 100 100 96.02 100 100 100 97.51
Table 4: Scale efficiency estimates (percentage)
Quarter
ended ANZ ASB BNZ Citib. HSBC NBN
Z TSB West.
Trust Jun 96 99.85 98.30 87.10 94.47 50.32 69.88 85.99 64.96 Sep 96 94.68 77.43 98.21 99.95 76.07 78.78 83.61 87.09 Dec 96 99.12 98.63 94.11 63.25 78.96 83.45 84.11 84.39 Mar 97 99.83 94.42 91.61 94.88 90.59 70.80 75.56 86.61 Jun 97 94.20 90.67 98.51 74.37 96.42 73.60 90.80 92.57 Sep 97 93.58 88.56 98.90 93.79 90.00 62.70 86.39 96.18 Dec 97 N/A 88.90 95.92 70.43 92.13 65.52 90.94 98.49 Mar 98 66.04 86.40 86.02 96.52 81.67 70.97 87.05 89.66 Jun 98 84.99 87.14 88.63 93.10 83.11 74.03 94.41 96.56 Sep 98 88.96 90.55 93.24 93.26 98.78 83.96 98.05 90.39 Dec 98
94.34 97.30 98.21 100.0
0 90.39 90.81 100.0
0 96.39 Mar 99
89.91 100.0
0 94.61 71.96 98.87 100.0
0 93.20 100.0
0 Jun 99 100.0
0 100.0
0 100.0
0 100.0
0 96.16 98.21 100.0
0 97.94 Sep 99
99.53 97.39 97.62 73.59 100.0
0 95.68 98.31 100.0 0 Dec 99
98.53 100.0
0 99.98 90.54 91.16 97.80 100.0
0 98.16 Mar 00
94.87 99.69 100.0
0 99.15 97.37 92.32 99.20 96.80 Jun 00
93.72 98.74 100.0
0 86.79 100.0
0 100.0
0 100.0
0 95.24 Sep 00
98.38 96.54 100.0
0 100.0
0 100.0
0 98.37 100.0
0 97.10 Dec 00
95.09 99.78 100.0
0 94.95 96.88 97.83 98.18 96.04 Mar 01
96.36 96.89 100.0
0 90.54 98.78 99.65 99.61 93.72 Jun 01 100.0
0 100.0
0 98.19 53.85 95.85 100.0
0 99.37 95.93 Sep 01 100.0
0 99.14 92.98 100.0
0 100.0
0 97.75 99.35 100.0
0 Dec 01
99.81 99.89 97.15 100.0
0 100.0
0 99.96 100.0
0 97.65 Mar 02 100.0
0 100.0
0 100.0
0 93.64 100.0
0 100.0
0 99.89 96.28 Averag
e 94.86 95.26 96.29 88.71 91.81 87.59 94.33 93.67
Table 5: Size growth and estimated scale effects for individual banks AN
Z AS
B BN
Z Citi b. HSB
C NB
NZ TS
B We
st.
Tru st Assetsat June
1996 ($B)
19.
45 9.0
9 23.
09 1.4
8
4.28 17.7 7
.63 26.
78 Assets at
March 2002 ($B)
27.
37 23.
05 35.
78 3.0
0 4.34 36.9 2 1.6
3 37.
26 Observ.incre
ase.
t t
12 17 0 13 18 16 11 18 Observ.
constant returns to sc.
4 5 21 8 6 8 12 4
Observ.decre
asing r. to s. 7 2 3 3 0 0 1 2
Table 6: Regression results for individual bank efficiency
ANZ ASB BNZ Citib. HSBC NBNZ TSB West.
Trust Constant returns to scale model
R2 66.4% 43.6% 48.3% 24.8% 54.3% 76.8% 57.9% 81.9%
Constant 1.10 (10.14)**
1.07395 (11.53)**
.93915 (9.76)**
.7350 (2.45)*
.8592 (4.89)**
.8930 (7.81)**
1.0385 (8.91)**
1.05674 (12.74)**
Interest rate
-.042 (-3.60)**
-.02487 (-2.46)*
-.01352 (-1.29)
-.02126 (-0.65)
-.02563 (-1.34)
-.03004 (-2.42)*
-.03036 (-2.40)*
-.040757 (-4.52)**
Time Trend
.003 (1.15)
.001271 (0.52)
.005228 (2.08)*
.010501 (1.34)
.011228 (2.45)*
.011739 (3.93)**
.005181 (1.70)
.006315 (2.91)**
F-stat. 19.75** 8.13** 9.82** 3.46* 12.47** 34.75** 14.44** 47.62**
d-w 1.64 1.74 1.81 2.44 2.44 1.14* 1.90 1.70 Variable return T scale model
R2 46.1% 7.5% 28.0% 35.5% 13.9% 10.1% 26.5% 51.2%
Constant 1.06 (8.73)**
1.01886 (19.74)**
.92339 (10.14)**
.9271 (4.02)**
.7793 (4.66)**
.97061 (11.82)**
1.09585 (12.51)**
1.02334 (10.35)**
Interest rate
-.029 (-2.22)*
-.006589 (-1.17)
-.003935 (-.40)
-.03216 (-1.28)
.00552 (.30)
-.004872 (-.55)
-.020385 (-2.14)*
-.02273 (-2.12)*
Time .002 -.000575 .004091 .007962 .006533 .001346 -.000662 .003788
Trend (.93) (-.43) (1.72) (1.32) (1.50) (.63) (-.29) (1.47) R2 46.1% 7.5% 28.0% 35.5% 13.9% 10.1% 26.5% 51.2%
F-stat. 8.56** .85 4.09* 5.79** 1.69 1.18 3.79* 11.03**
d-w 1.60 1.53 2.40 2.37 1.99 1.36 1.98 1.91
** indicates significance at the 1% level; * indicates significance at the 5%
level.
Table 7: Regression results for efficiency of all retail banks (treated as a single entity).
Constant returns to scale Variable returns to scale
R2 90.7% 52.6%
Constant .98454
(17.12)** .97166
(16.46)**
Interest rate -.32819
(-5.25)** -.009470
(-1.48) Time trend .008577
(5.71)** .003395
(2.20)*
F 102.65** 11.63**
d-w 2.10 2.04
** indicates significance at the 1% level; * indicates significance at the 5%
level.
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Notes
1 For a more extensive discussion of deficiencies in the cost to income ratio, see Tripe (1998).
2 Berger & Humphrey (1992B), pp 559-560, provide an outline of why analysis of a bank’s costs should include both interest and non-interest costs.
3 This figure is the author’s calculation from bank disclosure statements. It is significantly higher than figures proposed on the basis of analysis of some other data sources, such as IBCA’s Bankscope database (Focarelli &
Pozzolo, 2002).
4 By contrast, Berger & Mester (1997) suggest that scale economies may still be relevant up to asset levels of US$10 billion or more, which is about the size of the larger New Zealand banks.
5 Lists of approaches to frontier analysis often omit the FDH approach, which may be regarded as a special case of DEA. Berger & Humphrey (1997) suggest that DEA is the most widely used, at least in banking.
6 Berger & Mester (1997) also note that the non-parametric techniques generally ignore prices and can therefore only account for technical efficiency, in terms of too many inputs or too few outputs. The non- parametric techniques thus focus on technological rather than economic optimisation (p 905).
7 A number of earlier studies have also been reported, such as Valentine &
Williamson (1982), but these were not focused on X-efficiency, while there have also been a number of studies of non-bank financial institutions, such as Esho & Sharpe (1996), Garden & Ralston (1999) and Worthington (1999).
8 This is not to say, however, that the usefulness of DEA is not also improved with larger data sets: it is rather, as Evanoff & Israilevich (1991) put it, that one can get away with smaller data sets in DEA analysis.
9 We would also believe that the extent of cross-subsidisation would not be sufficient to seriously distort results, as New Zealand banks have been moving increasingly towards cost recovery for the services they provide.
Berger & Humphrey (1992A) note a further complication with the user cost approach, in terms of differences in interest rates arising from different credit risk, liquidity and duration profiles of a bank’s assets and liabilities.
We do not believe that this is an issue for this research.
10 These are the only banks out of the 17 registered as at August 2002 which have been registered and conducting business in a significant way throughout the period under analysis. Rabobank New Zealand branch commenced business shortly before 30 June 1996, but the scale and scope of that business was only quite limited until the end of 1997. The business of Citibank and HSBC has been predominantly in wholesale markets (and in Citibank’s case, wholly in wholesale markets since it sold its retail business to AMP Banking in 1998), but these banks are still included on the basis of their reasonable scale of business, while they also expand the size of our sample.
11 Some previous studies have adjusted for the effects of inflation, but with inflation throughout the period studied having been low, ignoring this issue is unlikely to have a major impact on results.
12 Results are reported for use of an input-oriented BCC model. We also ran an output-oriented BCC model, and generally comparable results were obtained, although the improvements in efficiency (and therefore, estimated scale efficiencies) were not as great as for the input-oriented model. A detailed exploration of the results obtained from different models, and the reasons for these, is beyond the scope of this paper.
13 Berger & Humphrey (1991) suggest scale inefficiencies as being only of the order of 5%.
14 Thus Coelli et al (1998) report that “[The VRS] approach forms a convex hull of intersecting planes which envelope the data points more tightly than the CRS conical hull and thus provides technical efficiency scores which are greater than or equal to those obtained using the CRS model.” (p 150).
15 This is likely to reflect interest rates having been higher during the earlier period. The significance of this is explained in the following subsection of the paper.
16 These numbers are not inconsistent with figures actually observed in New Zealand over the period analysed.
17 We can thus observe that efficiency first peaked for most banks in early/mid 1999, which was when the general level of interest rates reached its lowest level (as can be seen in Figure 1).
18 Coelli et al (1998) recommend use of tobit regression (p 170), whereas Mester (1993, 1996) used logit.
19 Further checks, using simple regression and data from the constant returns to scale model, with interest rate as the sole explanatory variable generated significant coefficients (not reported) for those cases where coefficients were not significant in the regressions reported in Table 6.
Similar tests using time trend as the sole explanatory variable also generated significant coefficients (not reported).
20 Banks included in this group are ANZ, ASB, BNZ, Countrywide Bank (up until its acquisition by the NBNZ in 1998), NBNZ, TSB and WestpacTrust.
21 Moreover, as Walker (1999) notes, time trend may catch a number of other factors, even if his example of banking regulation is not obviously an issue in this case.
22 Berger & Humphrey (1992A) adjusted their frontier in an attempt to take account of this effect, although the effect of the adjustments on the efficiency scores would appear to be rather less than was found in this research.
23 If we were only interested in productivity change from period to period, we could also try the DEA window analysis approach discussed by Lovell (1993), p 47, and Cooper et al (2000), pp 272-276. Such an approach would give larger cross-sectional data sets so that the DEA output would be more likely to be meaningful, noting that the relatively small number of banks with sufficient similarity in their business might otherwise undermine cross- sectional DEA.
