Profit-maximising firms will want to be on the efficiency frontier, but can go no further unless there is technological change which actually moves it downwards. In a perfectly competitive market, any firm that fails to reach the efficiency frontier will be forced out of the market. However, in markets where firms have some degree of monopoly power (due, for example, to entry barriers, scale economies or regulation), some firms are likely located somewhere inside the X-efficiency frontier. X-inefficiencies may be due to expense preference behaviour or when the managers are able to maximise their own utilities,3 if these diverge from shareholders’. Inefficiency may be registered by higher than minimum total costs [e.g. point D in Figure 9.1(a)]. It will imply a sacrifice of profits – the gap between B and D in Figure 9.1(b). Profits could be even lower if a different output level had been chosen.
Cost X-efficiency gets far more attention than profit X-efficiency. Consider them in relation to scale and scope economies, which were mentioned briefly in Chapter 2 and are discussed in more detail below. Scale or scope economies provide measures of the extent (if any) to which unit costs could be lowered by offering the total volume of production, or range of products, respectively. Allocative inefficiencies are caused by the sub-optimal use of the input mix, and X-inefficiencies are attributed to failures to minimise the cost of producing the given scale and range of outputs, which can be due to administrative costs or deliberate choices by management or staff. Reaping scale economies involves getting bigger, while scope economies are exploited by diversifying outputs. Lowering X-inefficiencies means reducing costs (through, for example, improved management, greater employee productivity), which moves the firm closer to the most efficient way of harnessing a given set of resources. Berger et al.’s (1993) review of the (mainly US) literature showed that in banking, X-inefficiencies explain about 20% of the costs, and less than 5% of the costs are due to inefficiencies arising from the failure to exploit scale and scope economies to the full. Allen and Rai (1996), looking at banks in 15 countries over the period 1988 – 92, report that countries which prohibit banks from combining commercial and investment banking have the largest bank X-inefficiency, amounting to 27.5% of total costs. In other countries where integrated banking is allowed, banks are more cost X-efficient: X-inefficiency was about 15% of total costs. Berger and Humphrey (1997) review 122 studies of bank cost efficiency, and report a mean level of 15% for 60 studies using a parametric approach; 28% for the 62 studies which adopted non-parametrictechniques – the distinction between these two techniques is discussed immediately below.
Data envelope analysis
Data envelopment analysis (DEA) is one way of testing for X-efficiencies, and was briefly discussed in Chapter 6. DEA is a ‘‘non-parametric’’ approach because it is not based on any explicit model of the frontier. The methodology was originally developed for non- profit-making organisations, because accounting profit measures are difficult to compute. DEA compares the observed outputs (Yjp) and inputs (Xip) of several organisations. If
3 For example, spending more on managerial comforts, or awarding themselves higher salaries.
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measuring cost X-efficiency, the relatively more efficient firms can be compared against the relatively less efficient by identifying a ‘‘best practice’’ firm or firms. To do this, maximise
the following:4
(9.2)
Ep = ujYjp/
viXip
subject to Ep ≤ 1 for all p; where p represents several organisations and weights vi, uj > 0. A linear programming model is run repetitively with each firm appearing in the objective function once to derive individual efficiency ratings. Each firm will have a derived rating of E, a measure of relative efficiency. The closer E is to 1, the higher the relative efficiency. E = 1 is for the ‘‘best practice’’ unit, and will be lower for all other firms in the study. Thus, E < 1, which implies relative inefficiency.
Numerous studies have used DEA to measure the cost X-efficiency of banks. Here, only a selection are reported. Rangan et al. (1988, 1990) tried to break down the efficiency of 215 US banks into that originating from technical inefficiency (arising from wasted resources) and scale inefficiency (operating at non-constant returns to scale). Bank output was measured using the intermediation approach. In the first study (1988) the results showed the average value of efficiency for the sample was 0.7, implying that, on average, the banks in the sample could have produced the same output using 70% of the inputs. Thus, there was, apparently, much waste, almost all of it due to technical inefficiencies.
In Rangan et al. (1990), the study was extended to include a sample of banks from unit banking as well as branch banking states. The pooled sample was split into two subsamples, and separate production frontiers calculated. No sizeable differences in efficiency as between the two types of banking were found. Field (1990) applied the DEA method to a crosssection of 71 UK building societies in 1981 – 81% were found to be inefficient, due to scale inefficiencies. Unlike Rangan et al., Field found technical efficiency to be positively correlated with firm size. Drake and Weyman-Jones (1992) applied DEA to building societies in 1988 after deregulation in 1987 – 37% were found to exhibit overall efficiency, an increase compared to the Field study.
Berger (1993), Berger and Humphrey (1997) and Bauer et al. (1998) identify the advantages of using data envelope analysis and other non-parametric techniques.5 DEA is advantageous because it can vary over time and all outputs and inputs are handled simultaneously. It produces a true frontier from which relative efficiencies can be derived and no functional form is imposed on the data. However, no allowance is made for a random error arising from measurement problems, such as inaccurate accounting data, random effects which have a temporary effect on outputs or inputs, or specification error (e.g. due to excluded outputs and inputs). Also, the DEA frontier is defined on the outliers rather than on the whole sample and, therefore, is susceptible to extreme observations and measurement error. Data problems also arise because it is necessary to obtain the same output and input measures for all the firms in the sample. Nor is it possible to draw statistical inferences from this approach, and the efficiency scores are not independent of market structure.
4 This equation and some of the discussion is taken from Colwell and Davis (1992). Their working paper provides a more complete review of earlier empirical studies.
5 Another non-parametric technique is free disposal hull analysis, but DEA is by far the most common approach used.
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Stochastic frontier analysis and other parametric techniques
Over the last two decades, the use of parametric techniques to estimate bank efficiency has increased. The most common includes a stochastic frontier approach, which uses a translog cost function. Parametric approaches allow a more explicit breakdown of the constituents of X-efficiency, namely technical inefficiency, which arises from factor inputs being over-used (e.g. expansion of staff) and allocative inefficiency – resources are not allocated efficiently, due to lax management or expense preference behaviour.6
The most common parametric method, the stochastic frontier approach, involves estimating a cost (or profit) function for a sector. A bank is inefficient if its costs exceed those of the most efficient bank using the same input – output combination. Or it is profit inefficient if its profits are inside a profit frontier, that is, its profits are lower than the best practice bank. To test for cost inefficiency the stochastic cost model is given as:7
TC = TC(q, p, y, z, µc, ε)
(9.3)
where
TC : variable total costs
q : a vector of quantities of variable outputs p : a vector of prices of variable factor inputs
y : other variables (environmental or market) which might affect output z : quantities of fixed inputs or outputs which could affect variable costs
µc : an error term − µc picks up allocative inefficiencies, which can arise because the bank fails to react optimally to the vector of input prices (w) plus inefficiencies from employing too many of the inputs to produce q
ε : a random error term
Using natural logs (ln) on both sides of the equation8 gives:
ln TC = f(q, p, y, z) + ln µc + ln εc
(9.4)
Profit efficiency measures show how close a bank is to producing the maximum profit possible given input prices, output prices and other variables. The standard profit function is:
ln(π + θ ) = F(q, x, y, z) + ln µπ + ln επ
(9.5)
where
π: variable profits
θ: constant to ensure the natural log is of a positive number x : vector of prices of the variable outputs
µπ : inefficiency that reduces profits
6 This interpretation is taken from Berger and Hannan (1998). 7 Following Aigner et al. (1977).
8 The inefficiency and random terms are assumed to be multiplicatively separable from the rest of the cost function.
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Berger and Humphrey (1997), in a comprehensive survey of 122 cost X-efficiency studies, report that most studies of cost X-efficiency among banks range from 0.7 to 0.9, that is, banks’ efficiency ranges between 70% and 90%. Better management would improve efficiency by between 10% and 30%. The X-efficiency scores from other studies include the following.
žBerger and Mester (1997): 0.868, based on 5949 US commercial banks over 1990 – 95. Thus, US banks could improve their cost X-efficiency by 13.2%.
žAltunbas et al. (2001a): for Japanese commercial banks, 0.94 and 0.96 over the period 1993 – 96, with between 136 and 139 observations per year.
žHao et al. (2001): 0.889 for private banks in South Korea, 1985 – 95; 19 banks per year, 17 in 1986.
žIsik and Hassan (2002): 0.895 for Turkish banks, 1988 (36 obs), 1992 (50 obs.), 1996 (53 obs.).
žMertens and Urga (2001): 0.672 for banks in the Ukraine, 79 banks in 1998.
žHardy and Patti (2001): 0.272 for Pakistan banks, 33 banks in 1981 – 97; X-efficiency could improve by as much as 73%.
žFu (2004): 0.35 to 0.44 for 14 major state owned and joint stock banks in China, 1985 – 2002; within this range joint stock banks were found to be more efficient than state owned; X-efficiency fell in the second stage of banking reform.
The number of banks included in these studies varies considerably, from just under 6000 observations in Berger and Mester (1997), to 14 in the China study, with 187 observations. Note also the higher X-efficiency in Berger and Mester, where 1990s data are used, compared to earlier US studies which relied on 1980s data.
In a 1980s study of 5000 US commercial banks, Berger and Hannan (1998) estimate a translog cost equation for each individual bank to get a measure of efficiency (based on an average of the residuals), then use these efficiency estimates to test the relationship between concentration and efficiency. They were testing the standard ‘‘structure – conduct – performance’’ hypothesis (see p. 13 for details), and find strong evidence that banks in more concentrated markets exhibit lower cost efficiency. The social costs from these extra operating costs were found to be between 3 and 20 times greater (depending on how efficiency is measured) than the welfare losses arising from noncompetitive pricing.
Williams and Gardener (2000) review the efficiency studies for Europe, and complete a comprehensive study of cost and profit X-efficiency among regional banks in six European countries, for the period 1990 – 98. The sample size includes 990 savings banks and 6300 observations. Using the Fourier flexible form9 and the stochastic frontier approach, they are able to distinguish between cost X-efficiencies arising from operating costs and variable costs. They report a mean operating cost inefficiency of 15.1%, and a variable cost X-inefficiency
9 According to Altunbas et al. (2001) the Fourier flexible functional form is a semi-non-parametric approach used when the true functional form of the relationships is unknown (2001, p. 1936). It is used to estimate scale and scope economies, but not X-inefficiency. See Carbo et al. (2000) for more detail.
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of 8.3%. They argue operating cost inefficiencies are higher because they include the cost of monitoring loans and dealing with bad debt. Profit X-efficiency is estimated at just under 80%, meaning these European savings banks are losing 20% of their profits (relative to what the best bank can earn) because of inefficiency.
Altunbas et al. (2001b) use income and balance sheet data from the Bankscope database for banks from 15 EU countries between 1989 and 1997, to estimate X-inefficiency using a stochastic frontier approach.10 The traditional intermediation approach is adopted where labour, physical capital and deposits are used to produce outputs, which includes loans, securities and total off-balance sheet items. They find, on average, X-inefficiency levels ranging between 20% and 25% depending on asset sizes, suggesting that more output could be produced if the banks reduced their inefficiencies by this amount. Table 9.1 summarises the Altunbas et al. (2001b) results for 1989 and 1997, the first and last years for which X-inefficiencies are computed. Using their data, the means for the two years were computed – they show X-inefficiencies have declined very slightly between 1989 and 1997. When placed in rank order, UK banks are close to the bottom in terms of X-inefficiency. Though not shown, X-inefficiency peaked in the UK in 1992, at 0.333. Put another way, in 1992, the same output could have been produced with about 67% of current inputs had British banks been able to reduce their managerial and technical inefficiencies. Note Ireland goes from being the most efficient in 1989 to one of the least by 1997.
Table 9.1 X-inefficiencies for European Countries
1989
1997
1989
1997
Austria
0.209
Austria
0.181
Ireland
0.166
Italy
0.126
Belgium
0.369
Belgium
0.322
Finland
0.193
Germany
0.135
Denmark
0.222
Denmark
0.191
Sweden
0.194
Sweden
0.165
Finland
0.193
Finland
0.296
Austria
0.209
ALL
0.179
France
0.288
France
0.244
Netherlands
0.213
Austria
0.181
Germany
0.218
Germany
0.135
Italy
0.217
Denmark
0.191
Greece
0.28
Greece
0.238
Germany
0.218
Spain
0.237
Ireland
0.166
Ireland
0.323
Denmark
0.222
Greece
0.238
Italy
0.217
Italy
0.126
Luxembourg
0.234
Netherlands
0.238
Luxembourg
0.234
Luxembourg
0.33
Spain
0.234
MEAN
0.241
Netherlands
0.213
Netherlands
0.238
MEAN
0.245
France
0.244
Portugal
0.335
Portugal
0.289
ALL
0.245
Portugal
0.289
Spain
0.234
Spain
0.237
Greece
0.28
Finland
0.296
Sweden
0.194
Sweden
0.165
France
0.288
UK
0.297
UK
0.298
UK
0.297
UK
0.298
Belgium
0.322
ALL
0.245
0.179
Portugal
0.335
Ireland
0.323
MEAN
0.245
0.241
Belgium
0.369
Luxembourg
0.33
10 The authors also use a flexible Fourier functional form.
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9.3.2. Scale and Scope Economies
There is an extensive literature and debate on the degree to which scale economies are present in banking. The term ‘‘economies of scale’’, or ‘‘scale economies’’, is a long-run concept, applicable when all the factor inputs that contribute to a firm’s production process can be varied. Thus, if a firm is burdened with any fixed capital, property or labour then, strictly speaking, it is not possible to test for economies of scale. Assuming all factor inputs are variable, a firm is said to exhibit:
Increasing Returns to Scale or Scale Economies: if equiproportionate increases in factor inputs yield a greater than equiproportionate increase in output. Firms are operating on the falling part of their average cost curves – the curve shows the average cost per unit of output, and firms with economies of scale can reduce average costs by increasing output. However, at some point scale diseconomies may set in, that is, if a firm/bank increases its output, average costs will rise.
Decreasing Returns to Scale or Scale Diseconomies: if equiproportionate increases in factor inputs yield less than equiproportionate increases in output.
Constant Returns to Scale: if equiproportionate increases in factor inputs yield an equiproportionate increase in output.
Product Specific Economies of Scale: this term applies if the firm produces more than one product (e.g. a bank can produce loans, deposits and securities), and is asking whether there is economies of scale with respect to a particular product. It is determined by looking at average incremental cost (AIC) – the effect on total cost if a product is produced at a specific level rather than not at all. Thus:
PSESi = AICi/(∂TC/∂Qi)
(9.6)
where
TC : total cost
Qi
: output vector for product i
PSESi
> 1 implies product specific economies of scale; diseconomies of scale if PSESi < 1.
Consider the case of a simple bank, which has three factor inputs: capital from deposits, labour – the bank’s employees – and property, in the form of a branch network. The bank produces one output, loans. Then economies of scale are said to exist if, as a result of doubling each of the three factor inputs, the bank is able to more than double its loan portfolio. Even in this simple example, the concept is fraught with difficulties when applied to a financial institution. First, unless a new bank is setting itself up from nothing, not all of its inputs will be completely variable. It is difficult to imagine a bank being able to double the number of deposits at short notice. Second, even if they could there is a potential problem with risk. If a bank more than doubles its loan portfolio the risk profile is bound to change, a critically important consideration for any bank wanting to maximise shareholder value-added. Third, there is a problem of indivisibilities. A bank branch could not add one-third of a bank cashier (teller) or half an ATM. Additionally, in banking, as has been noted, there is the question of what constitutes output. Some authors, including this one,
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have argued that deposits, in addition to loans, must be treated as bank products, because deposits provide customers with intermediary services. Furthermore, most banks produce multiple outputs, namely, a fairly broad range of financial services. These observations make it difficult to apply the term ‘‘economies of scale’’ in the financial sector, which may partly explain the widely varying empirical evidence on the degree to which economies of scale exist. Yet they are normally cited as one of the key reasons why a merger between financial institutions will be a profitable one for shareholders.
The concept of economies of scope is another one that, employed loosely, can lead to unrealistic expectations of the benefits of a merger or acquisition. Economies of Scope exist if the joint production cost of producing two or more outputs is lower than if the products are produced separately. For example, suppose a bank offers three services to its customers: deposit, loans and a payments service. If a bank can supply these services more cheaply through a joint production process it is said to enjoy economies of scope. The core banking business, where the bank intermediates between borrowers and lenders by lending out a percentage of its deposits, is one example of economies of scope. Though the payments service offered by banks is a byproduct of intermediation, it is not obvious that lower costs result from the joint production of this service with intermediation. This may explain why some countries, such as the UK, have a highly integrated payments system while in others (e.g. the USA) it is more fragmented (see Chapter 1).
The business policy term for economies of scope is Synergy, though synergy may embrace broader ideas such as the newly formed, larger firm reducing input prices by exploiting its more powerful influence on suppliers, thereby enhancing profitability. Again, among financial firms, where skills and innovation may be the difference between success and failure, synergy may be costly to achieve if it requires a merger of different cultures, or stifles the entrepreneurial spirit typical of small, successful financial firms.
From the strategic standpoint of managers, the question of whether or not economies of scale and scope or synergy are present in the banking is important. Evidence of economies of scale will mean large banks have a cost advantage over small ones. If cost complementarities are present, multiproduct banks will be more efficient than the financial boutique. Though obtaining these measures is fraught with difficulty, it has not stopped a large number of investigators from testing for it. Not surprisingly, empirical studies of economies of scale and scope in financial institutions throw up mixed results for every country which has been tested, though most of the empirical work emanates from the United States. Here, the results of some of the key studies are reported.11
Recall Humphrey (1992) looked at productivity growth in US banking using different measures of output. He used the same data to obtain estimates of scale economies. Based on R2 and the predictive accuracy of the different output measures, he concluded that the stock measure QD (the real dollar value of deposit and loan balances) was more accurate than the flow measure of output, QT (the number of deposits and loan transactions processed) in tests for scale economies. Humphrey found slight economies of scale for small US banks (assets of $10 – $25 million), but slight diseconomies for larger US banks ($2 – $5 billion).
11 For a comprehensive review of published studies in this area up to the mid-1990s, see Molyneux et al. (1996).
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Allen and Rai (1996) use their data to test for scale and scope economies. No scope economies are found; scale economies are significant for the smallest banking groups,12 in the order of 2%. There are significant diseconomies of scale (about 5%) for banks which are prohibited from offering commercial and investment banking. This finding by Humphrey (1992) and these authors are fairly typical for studies of US banks using 1980s data.
One exception is Shaffer and David (1991), who questioned US empirical work that reported diseconomies of scale for very large US multinational banks. These results are inconsistent with the observation that very large banks are financially viable over long periods of time. Shaffer and David used data from the 100 largest commercial banks in the USA in 1984, with assets ranging from $2.5 billion to $120.6 billion. They relied on the Federal Reserve’s Call Report data.13 However, the aggregated nature of these data may obscure some of the factors which differentiate banks, such as output mix, input mix, strategy, regulatory environment, and so on. All of these factors will influence the bank’s level of costs. To correct for this problem a hedonic cost function14 was used. The scale variable in the cost equation is augmented with a vector of variables chosen to reflect qualitative differences (therefore, ‘‘hedonic’’ terms).
Shaffer and David estimated a translog cost function (In TC) (TC: total operating expenses) with the following independent variables.
y : assets
w1 : price of labour
w2 : price of physical capital
qj : the vector of hedonic terms – funding strategy, off-balance sheet activities, asset quality, the regulatory environment (unit versus branch banking) and target clientele
The translog cost function was estimated, with and without the hedonic terms. In the absence of hedonic terms, they found evidence of economies of scale which were exhausted in the region of $21 billion – $25 billion of assets. F-statistics rejected the hypothesis of constant returns to scale at the 1% level. With the hedonic terms included, scale economies were found at slightly lower sizes, between $18.9 and $23.6 billion.15
Hardwick (1990) tested for scale and scope economies using UK building society16 data. The author employed multiproduct statistical cost analysis. Building societies were assumed to supply one type of financial service to borrowers (mortgages) and another type to lenders
12Small is defined as any bank that falls below the median assets size for banks in that country.
13US studies of scale and scope economies normally use data from one of two sources. There is the Federal Reserve’s Functional Cost Analysis (FCA) data – supplied (on a voluntary basis) to the Federal Reserve System by commercial and savings banks from across the USA. Or there is data from the banks’ call and income reports. The FCA data exclude large banks with deposits in excess of $1 billion. This is why Shaffer and David opted to use call report data. See Molyneux et al. (1996, pp. 158– 159) for a critique of the two sources of data.
14The hedonic cost function was developed by Spady and Friedlaender (1978).
15Shaffer and David (1991) estimated cost functions with each hedonic variable at a time, and a full model that included every hedonic variable.
16UK building societies are mutually owned and some engage in functions that are similar to US savings and loans – see Chapter 5 for more detail.
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(personal sector savers). Hardwick argued that for a firm producing m outputs, the cost function may be written as:
where
TC = TC(y, p)
(9.7)
TC : total cost
y : vector of
m outputs
p : vector of
n input prices
Hardwick’s definition of overall economies of scale (OES) was
(∂ ln TC/∂ ln yi). OES
were measured by the elasticity of total cost with respect to a given composite input. If OES <1 (>1), there are overall economies (diseconomies) of scale. To identify the main sources of economies or diseconomies of scale, it was necessary to estimate the cost saving attributable to the jth input as the firm expands. Hardwick employed the following equation:
ln Cj = ln Sj + ln TC
(9.8)
where
Sj : jth input’s cost share
The OESj (input specific overall economies of scale) is given by:
OESj = (∂ ln Sj/∂ ln yi)
(9.9)
Hardwick also tested for product specific economies of scale. These measure the effect on the ith product’s incremental cost of a change in the quantity of product i, with the quantities of the other products unchanged. It is captured by the elasticity of the ith product’s incremental cost with respect to the output of the ith product. He used a marginal cost approach; a negative gradient of the marginal cost (∂2TC/∂y2i ) confirms product specific economies while a positive gradient is indicative of diseconomies.
Economies of scope are said to exist if the total cost of the joint production function is less than the sum of the costs of separate production. If a firm is producing two goods, then the appropriate test is (∂2TC/∂yi∂yj) to be significantly negative. If less than zero, the marginal cost of producing one good decreases with increases in the output of another good, implying cost complementarities and economies of scope.
Hardwick’s data come from the 1985 annual returns of a sample of 97 building societies. The variables included in the model were as follows.
TC: total operating cost – the dependent variable, measured by the sum of management expenses and depreciation, where management expenses include all staff expenses, auditors’ remuneration, office expenses, advertising and various commission and agency fees
y1: the average number of outstanding mortgage accounts y2: the number of outstanding share and deposit accounts p1: the effective wage rate
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p2: the effective price of capital – the rental rate on capital, measured as [(annual expenditure on office accommodation and equipment + depreciation)/mean assets] × 100
B: number of branch offices
M: average size of all outstanding mortgages and deposit accounts (D), to control for the heterogeneity of accounts
S1: labour’s cost share – the dependent variable in the derived share equations S2: capital’s cost share – the dependent variable in the derived share equations
Hardwick used a maximum likelihood procedure to estimate the full cost equation jointly with one of the share equations. Behind these equations lies the assumption that the technology of the building society industry can be represented by a translog multiproduct cost function, where the natural log of total cost is approximated by a quadratic in the natural logs of the two outputs, the two input prices and the other explanatory variables.
To test for overall economies of scale, the 97 building societies were put into one of eight groups, by value of mean assets.
A1: > £ 5.5 billion
A2: £1.5 billion to < £ 5.5 billion
B1: £450 million to < £ 1.5 billion
B2: £280 million to < £ 450 million
C1: £140 million to < £ 280 million
C2: £60 million to < £ 140 million
D1: £15 million to < £ 60 million
D2: < £ 15 million
Input specific overall economies of scale were found to be present and significant for all eight size groups except A1. Hence, economies of scale are present for all but the very largest building societies, where economies of scale could not be established (OES > 1 but was not statistically significant from unity), due to the presence of significant diseconomies in the employment of capital. For the other groups, the cost savings attributable to the employment of labour were found to be greater than those from the employment of capital.17
Hardwick tested for product economies of scale by looking at the gradient of each product’s marginal cost. For output supplied to mortgage borrowers, the marginal cost gradients were negative for all size groups, indicating the presence of product specific economies of scale, though the findings were not significant for groups A1 and A2. For the output supplied to depositors and shareholders (y2), none of the marginal cost gradients were significantly different from zero, so it was not possible to conclude whether there were economies or diseconomies of scale.
17 In an earlier study where the same methodology and data were employed, Hardwick (1989) reported a finding of significant diseconomies of scale for societies with assets in excess of £1.5 billion if an augmented economies of scale measure was used. The formula was augmented to account for the direct effect on TC of a change in output, and an indirect effect, arising from the induced change in the number of branches.
