Looking at the derivative of each product’s marginal cost with respect to changes in output of the other product, Hardwick did not find evidence either for or against economies of scope for A1 and A2 firms. For building societies with assets of up to £1.5 billion, Hardwick found significant diseconomies of scope, suggesting diversification could actually raise the average operating costs of the society. Thus, there appeared to be virtually no case for diversification of building societies into the broader banking market.
Drake (1992), using a multiproduct translog cost function, found evidence for economies of scale in the asset value range of £120 – £500 million. He could find no evidence to support the earlier Hardwick (1989) finding of diseconomies of scale for building societies with assets in excess of £1.5 billion. Nor did Drake find economies or diseconomies of scope for the building society industry or subcategories of building societies, except for the second largest group (assets in the range of £500 million – £5 billion), which demonstrated significant diseconomies of scope. Drake was also able to test for product economies of scope. Mortgage lending showed significant diseconomies of scope, but scope economies were found for unsecured consumer lending and secured commercial lending.
Numerous US studies have tested for Economies of Scope in banking, with mixed results. Gilligan and Smirlock (1984) used balance sheet data from 2700 unit state banks in the period 1973 – 78. Two definitions of output were used, the dollar amount of demand and time deposits, and the dollar amount of securities and loans outstanding. Their test results supported the hypothesis of economies of scope, because they found the structure of bank costs to be characterised by jointness, that is, the cost of production of one output depended on the level of other outputs. Lawrence (1989) used a generalised functional form to test for economies of scope in a multiproduct production function. He employed the Federal Reserve’s functional cost data for the period 1979 – 82. The deposit size for banks in the sample ranged between $6 million and $2.6 billion – excluding the largest US banks. Lawrence used three output measures: deposits, investments and loans; and three factor inputs: interest costs, wages and computer rental costs. He found cost complementarities to be present in the joint production of the three outputs.
Hunter et al. (1990) used a sample of 311 out of 400 of the largest US banks at the end of 1986. Bank production was analysed using an intermediation approach and multicost production function. Deposits were treated as an output and as an input. The authors found no evidence to support the presence of subadditive cost functions, meaning cost complementarities (and scope economies) were not present. Mester’s (1987) review of eight US multiproduct studies published between 1983 and 1986 led him to conclude there was no strong evidence either to support or refute the presence of economies of scope.
Altunbas et al. (1996)18 used the intermediation approach. A translog cost function was estimated to examine the 1988 cost structure in four European countries – France, Germany, Italy and Spain. They use income and balance sheet data from the IBCA database, which includes 201 French, 196 German and 244 Italian banks. The data for 209 Spanish banks came from a Spanish source. The outputs and inputs were defined as:
18 Some of these results (on economies of scale) were reported in Altunbas and Molyneux (1996).
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Outputs
Q1: total loans
Q2: securities
Inputs
P1: average annual wage per employee (Italy, Spain); average annual wage per branch (France, Germany)
P2: average interest cost per dollar of interest bearing total deposits P3: average price of capital (capital expenses/total fixed assets)
Economies of scale and scope are tested for banks in different assets categories: $0 – $100 million, $100 – $300 million, $300 – $600 million, $600 million – $1 billion, $1 – $3 billion, $3 – $5 billion and greater than $5 billion.
The key findings for Molyneux et al. (1996) are reported in Table 9.2. The findings on scale economies suggest that for at least some size ranges, French, German and Italian banks
Table 9.2 Summary of Findings from Molyneux et al. (1996)
France
Germany
Italy
Spain
Scale Economies
–
–
–
Yes, all asset sizes
Constant Returns
Yes, all asset
–
Yes, all asset
–
to Scale
sizes
Yes, all asset
sizes
–
Scale
–
–
Diseconomies
Yes
sizes
No
Yes
Product-specific
Yes
Scale Economies
in Loans and
Securities
Scale Economies
Yes, except
Yes, for asset
Yes, for asset
Yes, for assets size <$1
at Branch Level
banks with asset
sizes of
size >$1 billion
billion
size >$5 billion
$100 – $300
million or >$5
Economies of
Yes
billion
No
Yes, for assets size up
Yes, if assets size
Scope
exceeded $3
to $600 million
Diseconomies of
No
billion
No
Yes, if assets size
Yes, for small
Scope
and
>$600 million
medium-sized
Branch Economies
Yes, if asset size
banks
Yes
Yes, for banks with
Yes
of Scope
>$300 million
asset size <$300
Branch
No, if asset size
No
No
million
Yes, except for banks
Diseconomies of
<$300 million
with asset size <$300
Scope
million
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could reduce their costs by expanding the size of their existing branches. The exception is Spain, where costs would fall by increasing the number of branches.
Based on the results for economies of scope, all banks in France, smaller banks in Spain and larger banks in Germany could reduce costs by increasing their output mix. Branches in Italy and Germany, together with those of large banks in France, should do the same. Branches of smaller French and Spanish banks should do the opposite, i.e. specialise more.
Altunbas et al. (2001b) estimate scale economies using the same data set (income and balance sheet data from the Bankscope database for banks from 15 EU countries between 1989 and 1997) as was used for their X-inefficiency scores. They find average scale economies range from between 5% and 7%, suggesting that if outputs were increased by 100%, total costs would rise by 93% to 95%, on average.19 If the banks are broken down by asset size, it reveals that the significant economies of scale are being enjoyed by the smallest banks in all countries, with assets ranging between 1 and 99 million ECUs.20 German and Greek banks also enjoyed economies of scale for most asset size categories. Banks in Germany, the UK, Denmark and the Netherlands with assets in excess of 5 billion ECUs (the largest asset category) have significant economies of scale of just under 5%, but the largest banks in Austria, Belgium, Finland, Greece, Ireland and Luxembourg all had diseconomies of scale: so doubling output would lower average cost for the first group by about one-twentieth, but raise it for the second group. However, when equity capital is removed as a factor input,21 scale economies are found for the largest banks. Thus, the results here are mixed, but it is notable that the scale economies are found for the UK, Germany and the Netherlands – countries with large banks active in global markets. If it is accepted that equity capital is a weak measure of risk taking, the findings for scale economies are strengthened. These findings are more consistent with US studies using post-1990s data.
Berger and Mester (1997) review the possible reasons for differences in efficiency estimates. They also used their data to examine scale economies. Recall the database: nearly 6000 US commercial banks over the period 1990 – 95. They use the Fourier flexible cost model to estimate Scale Efficiency, defined as the ratio of the predicted minimum average costs to average costs, both adjusted to be on the X-efficiency frontier. They find evidence of scale efficiency at every asset size classification, ranging from 0.851 for banks with assets of up to $50 million to 0.782 for banks with assets in excess of $10 billion. From this, scale economies are computed as the bank’s ratio of cost efficient size to its actual size. In column
(2) of Table 9.3, the ratio is >1, implying scale economies for all asset sizes. For a given bank’s product mix and input prices, the typical bank needs to be over two times larger to maximise cost scale efficiency. Another way of looking at it is based on column (4), the reciprocal of (3), i.e. the ratio of actual to cost efficient size. Given an average of about 0.4, it indicates that the US system would, on average, reach maximum efficiency by reducing the number of its banks by 60%, with each surviving bank producing, on average, 170% more.
19Except for Finland and France, when scale economies were not found to be significant in most years.
20ECU: European currency unit. The term used before the euro was introduced.
21By including equity capital as a factor input, the authors argue they are controlling for risk in the cost estimation.
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Table 9.3 Key Results from Berger and Humphrey (1997)
Bank Size (assets)
No. of Banks
Cost-Efficient Size/
Actual Size/
(M/B US$)
Actual Size
Cost-Efficient Size
0 – $50M
2218
2.2
0.455
$50 – $100M
1794
2.363
0.423
$100 – $300M
1344
2.523
0.396
$300M– $1B
392
2.815
0.355
$1B– $10B
171
2.986
0.335
>$10B
30
2.673
0.374
Average
–
2.723
0.389
Source: Berger and Mester (1997).
In the smallest asset category the number of banks should be reduced by 54% and banks in the second largest category, which would benefit by reducing their numbers by 67%.
These findings differ from most of the US studies that used 1980s data, where scale economies tended to be found for small banks; larger banks exhibited diseconomies or constant returns to scale. Berger and Mester identify a number of factors which could help to explain the difference:
žThe Fourier flexible function was used rather than a translog cost function, but they re-estimated using the translog and found the scale economies to be even larger for the bigger banks.
žOpen market interest rates were low in this period, about half what they were in the 1980s. The lower rates would reduce interest rate expenses which are normally proportionately higher for large banks because a greater proportion of their liabilities tend to be market sensitive. For example, they use wholesale funds.
žRegulatory changes tending to favour large banks. In the 1980s, with unit banking, or inter/intrastate branching restrictions, and restrictions on activities, it was costly to become large. For example, branching restrictions meant fewer branches for collecting deposits, contributing to scale diseconomies for large banks.
žNew technology has altered the way basic services are delivered, making it possible for banks to expand faster rather than having expensive branch outlets.
Drake and Sniper (2002) revisited UK building societies in light of more recent US studies (such as Berger and Mester, 1997) and found more evidence of scale economies. They use a translog cost function but extend it to allow for entry/exit22 and to estimate two types of technical change. They apply their estimating equation to a sample of UK building societies over the period 1992 to 1997. In their preferred model, the economies of scale estimate is highly significant and indicates that economies of scale exist for all different asset classes. Potential scale economies decline with size. Technical progress is shown to
22 The authors have an unbalanced panel set because the building societies exist through the period. Rather than discarding them, they extend the Dionne et al. specification based on the translog cost function.
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reduce the costs of larger societies relative to smaller ones, suggesting one strategy: mergers to reduce costs. Smaller societies are particularly vulnerable because they have the largest unexploited scale economies.
Cavallo and Rossi (2001) uses a translog cost function to estimate X-inefficiencies, scale and scope economies for several European countries (France, Germany, Italy, Netherlands, Spain and the UK) between 1992 and 1997. They have an unbalanced panel set of 442 banks and 2516 observations. The banks include commercial, saving and loans, cooperatives, investment, mortgage, non-banks, some government credit institutions. X-inefficiency is present in all the banking systems, with a mean cost X-inefficiency of 15.64%. The small financial institutions are significantly more efficient, especially those involved in traditional activities, and the coop banks do best among those involved in core banking services. They find evidence of economies of scale of similar magnitude, across the banking systems. They also report evidence for economies of scope, though it is not always significant. The best evidence is for large banks, while medium and small banks did not have significant coefficients. While these results are at odds with most other studies, they are similar to the findings of Berger and Mester (1997), which used 1990s data.
All the studies reviewed looked at the question of whether joint production reduces costs because of complementarities in production. Berger et al. (1996) used data from US banks over the period 1978 to 1990, looking for evidence of revenue economies of scope, that is, if complementarities in consumption raise revenues. Based on samples of small banks, large banks, specialists and banks offering a wide variety of products, they find no evidence to support this idea. The authors conclude that banks do not gain (in terms of higher revenues) by offering, for example, deposits and loans.
9.3.3. Technological Change
Altunbas et al. (1999) argue a time trend can act as a proxy for technical change.23 It was found to be significant, and reduced the real annual cost of production by 3%. Also, the bigger the bank, the greater the reduction in costs. In a recent paper, Molyneux (2003) summarises the econometric approach to measuring technical change, which involves using the cost or profit functions summarised in equations (9.3) to (9.5). Using the cost function, estimated with a time trend, technical change is measured by taking the partial derivative of the estimated cost function with respect to a time trend. Following Molyneux (2003, p. 13):
∂ ln TC/∂T = t1 + t2T + ψi ln Pi + φi ln Qi
(9.10)
where
ln TC : natural log of total costs
ln Qi
: natural log of bank outputs
ln Pi
: natural log of ith input prices (wages, interest rate, price of capital)
T
: time trend
23 Though they note it must be treated with caution because of problems identified in the literature when using a time trend for this purpose. Also, technical progress rates are not constant.
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Equation (9.10) can be broken down into three types of technical progress.
2.ψi ln Pi: non-neutral technical change, reflects changes in the sensitivity of total cost
(or profits) to changes in input prices. If ψi is negative then the share of cost of input 1
towards total cost (profits) is decreasing over time.
3. φi ln Qi: scale augmenting technical progress, reflects changes in the sensitivity of total cost (profits) to variations in the quantities of output produced. If φi is negative, then the scale of production which minimises average cost (or maximises profit) for a given output is rising over time.
Molyneux uses balance sheet income data for 4000 European banks for the period 1992 – 2000, giving a panel of 20 333 observations. His main findings are:
žThere was a reduction in costs of 5.62% arising from pure technical change (1.7%), and non-neutral technical change (3.92%). This was offset by a 1.8% increase in annual costs due to augmenting technical change. Overall annual costs fell by 3.8%.
žClassified by asset size, the small banks (with assets ranging from ¤1 million to ¤499.99 million) gained the most from cost reductions due to technical changes. The cooperative and savings banks benefited more than commercial banks, probably because these banks are normally smaller.
žTechnical change reduced annual average costs by 2 – 4% in most EU states. Austria, Denmark, France, Germany, Italy and Spain experienced the largest reduction in costs. The decline in costs was highest in Denmark (6.6%), followed by Germany (4.4%). In the UK, they fell by 2.2%.
The effect of technical progress on the profits/profit frontier is estimated in the same way as equation (9.10), but this time the dependent variable is profits – see also equations (9.3) to (9.5). Based on the estimated profit function, it appears that reduced costs due to technical change have not fed into higher profits.
žThe average annual reduction in profits as a result of technical change was 0.45% over the period, brought about by a fall in profits of 3.42% from pure technical change (1.9%) and from non-neutral technical change (1.52%), and an increase in profits (2.966) due to scale augmenting technical progress. In the early period, 1992 – 95, technical change improved profits but since then, it has reduced them by increasing amounts. Molyneux suggests this is due to ‘‘early mover’’ (p. 14) advantage: banks adopting the early technology earned enough revenue to offset the costs of adopting it but by the late 1990s, profits began to decline because all banks were adopting similar technologies, thereby incurring costs but not improving revenues.
žIt appears that the banks that benefited most in terms of cost reduction suffered from reduced profits and vice versa. Commercial banks and banks from the top three asset categories experienced an increase in profits, while technical change reduced profitability of the smaller banks including the savings and cooperative banks. Molyneux suggests there
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is a trade-off: banks using technology for large cost cuts (e.g. increasing ATMs and closing branches) ended up with poorer service quality, lower revenues and reduced profits. The commercial banks experience a smaller cost reduction because they use the technology to improve revenues through better services and risk management, etc. – reflected in higher profits.
žCountries that led the way in terms of annual cost reductions as a result of technical progress experienced the biggest declines in profits. For Danish banks, annual profits fell by 2.7% over the period; they also fell for the four other big cost cutters. Austria, Germany, Italy and Spain experienced annual declines in profits, though all except Austria were less than 1%. The other 10 countries experienced a rise in profits as a result of technical change. It is notable that in the UK, which (along with New York) led the way in generating new forms of commercial and investment banking business,24 technical change led to an annual increase in profits of 0.781, with a small annual cut in costs. Sweden did the best overall, where annual costs fell by 1.8% and profits increased by 1.7%. Luxembourg’s profit increase was about the same as Sweden’s, though costs fell by just 0.41%.
Berger (2003) and Berger and Mester (2003) use similar cost and profit equations but look at changes in cost productivity (caused by movements in the best practice frontier and changes in inefficiency) and profit productivity. Berger and Mester looked at US banks from 1991 to 1997 and found annual increases in profit productivity of 13.7% to 16.5%, but cost productivity declined by 12.5%. They argue that these findings are consistent with US banks adopting new technologies that improved a range of services (e.g. mutual funds, derivatives, securitisation) such that the rise in revenues exceeded the increase in costs, hence the rise in profit productivity. Their US results are consistent with Molyneux’s findings for commercial banks and for some European states.
9.4. Empirical Models of Competition in Banking
This section reviews different approaches that have been used to assess how competitive the banking sector is and to identify factors influencing competitive structure. The hypotheses most frequently tested are based on the structure – conduct – performance and relative efficiency models. Attempts to measure contestability in banking markets were briefly popular in the late 1980s/early 1990s, and are still mentioned in many papers. Finally, some studies have been trying to obtain more direct measures of competition by looking at bank pricing behaviour.
9.4.1. The Structure–Conduct–Performance Model
Since the Second World War, a popular model in industrial economics has been the structure – conduct – performance (SCP) paradigm, which is largely empirical, that is, it
24 It is unclear whether investment banks were included in the sample, but the large European commercial banks also offer investment banking services. Off-balance sheet business is not included in Molyneux’s model, though it would contribute to the profit figures.
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relies on empirical data but for the most part, lacks a theoretical base. Applied to the banking sector, SCP says a change in the market structure or concentration of banking firms affects the way banks behave and perform. The more concentrated the market, the more market power banks have, which means they can be inefficient (i.e. avoid minimising costs) without being forced out of the market. This approach assumes a well-defined link between structure, conduct and performance:
Structure of the market: determined by the interaction of cost (supply) and demand in a particular industry
Conduct: a function of the numbers of sellers and buyers, barriers to entry and the cost structure – a firm’s conduct is reflected chiefly in its pricing decisions
Performance: the bank’s conduct (e.g. its pricing behaviour) will affect performance, often measured by profitability
How the links between the three might work in practice is:
In the actual tests (see below), some authors treat profits as the dependent variable. Others look at the first link and try to explain prices by structure; the argument is that a concentrated market allows firms to set prices (e.g. relatively low deposit rates, high loan rates) which boost profitability.
Several theoretical models predict that fewer firms imply higher prices. Cournot oligopoly and Dixit – Stiglitz monopolistic competition models are examples. However, market structure is normally thought of as being endogenous, not exogenous, as assumed in the SCP model. So the SCP framework depends on the assumption that entry is effectively barred. In banking, the SCP model has been used extensively to analyse the state of the banking market in a given country or countries. Given there is no single generally accepted model of the banking firm, and since entry barriers are often high, emphasis on the SCP paradigm25 is understandable.
9.4.2. The Relative Efficiency Hypothesis26
This model challenges the SCP approach. Relative efficiency (RE) posits that some firms earn supernormal profits because they are more efficient than others. This firm specific efficiency is exogenous. Greater efficiency may well be reflected in greater output. When the number of firms is small, bigger efficiency differences between them would imply greater concentration. Though RE predicts a similar (positive) profits concentration relationship to the SCP model, its key claim is that firms’ profits should be correlated with this efficiency. Prices and concentration are inversely related, the opposite of SCP. Under the
25Hannan (1991) developed a theoretical model, from which the SCP relationship is derived.
26This model is sometimes known as the efficient markets model, but to avoid confusion with the well-known ‘‘efficient markets’’ hypothesis used in finance, this book uses the term ‘‘relative efficiency’’.
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relative efficiency hypothesis, causation runs from greater efficiency, lower prices and higher concentration/market share:
The relative efficiency hypothesis can be linked to the X-efficiency hypothesis: some firms have superior management or production technology, which makes them relatively more cost X-efficient with lower costs. They are able to offer lower prices (if products are differentiated), gain market share (which increases concentration) and earn more profit. Likewise the presence of scale economies would mean these firms produce at low unit cost, lower prices and higher profits per unit of output.
The evidence for or against these hypotheses is important because the policy implications are so different. Confirmation of SCP is a case for intervention to reduce monopoly power and concentration. Curbing the exercise of monopoly power may be done by policies to encourage more firms to enter the sector or through a regulator who monitors the prices set by existing firms and/or imposes rules on pricing; e.g. deposit rates may not be more than x% below the central bank official rate. Strong evidence for the relative efficiency hypothesis suggests policy makers should not interfere with deposit and loan rate setting in the banking markets. Mergers should be encouraged if they improve relative efficiency, but discouraged if all they do is increase concentration and market power (SCP).
9.4.3. Empirical Tests: Structure–Conduct–Performance and
Relative Efficiency
There are a multitude of studies testing the SCP and/or relative efficiency models in banking, especially for the USA. It would be impossible to do justice to them all. This section does not attempt a comprehensive survey of the published work.27 Instead, it provides a summary of the findings reported in some recent key papers, which will be discussed below. For the SCP model, the general form is:
P = f(CONC, MS, D, C, X)
(9.11)
where
P : measure of performance (profits or price)
CONC : market structure, with the degree of concentration in the market a proxy for the variable
MS : market share, more efficient firms should have a greater market share D : market demand
C : variables used to reflect differences in cost X : various control variables
27 For surveys of SCP and relative efficiency, see Gilbert (1984), Molyneux et al. (1996). Brozen (1982), Smirlock (1985), Evanoff and Fortier (1988), Molyneux et al. (1996) provide studies which have tested SCP. Berger (1995) and Goldberg and Rai (1996) review and extend the debate.
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The dependent variable, performance, is proxied by either the price of the good or service, or profitability. In the list of performance measures below, the first number in the brackets gives the number of times these measures have been used in 73 SCP studies between 1964 and 1991 using US data, as reported by Molyneux et al. (1996, table 4.1). The second number shows the number of times the performance measure was found to be significantly related to market structure.
Measures for price include:
žLoan rates, such as interest rates and fees on personal loans, business loans or residential mortgages (30;14).
žDeposit rates, for example the interest rate paid on a term or savings deposits, money market accounts (25;10).
žBank service charges, such as a monthly service charge levied on a current account, or service charges on a standard account (22;6).
Profitability measures include:
žReturn on assets: net income/total assets (24;12).
žReturn on capital: net income/capital (14;8).
žReturn on equity: used in more recent studies, net income/stockholder’s equity (NA).
There is an ongoing debate as to which performance variable should be employed. Profitability, it is argued, addresses the issue of banks supplying multiple products/services. However, it combines a flow variable (profit) with stock variables (assets, capital). The use of interest rates (prices, e.g. deposit or loan rate) has been criticised for the same reason (e.g. loan rates over one year and loans outstanding at the end of the year). Using service charges can be fraught with problems; the way they are computed can vary from bank to bank, and account charges will vary depending on the number of times a service is used, and some customers may be exempt provided they maintain a minimum balance.
Some studies employ a price measure as the dependent variable and others used a profit variable. For example, Berger and Hannan (1989) conducted direct tests of the SCP and relative efficiency models using the estimating equation:
rijt = αij
+ βjCONCjt +
δijxjit + εijt
(9.12)
rijt : the interest paid at time
t on one category of retail deposits by bank
i
located in the local banking market j
CONCjt : a measure of concentration in local market j at time t
xjit : vector of control variables that may differ across banks, markets or time periods εijt : error term
By the SCP hypothesis, β should be less than 0; that is, there is a negative relationship between concentration and deposit rates, the ‘‘price’’ of the banking service.28 If the relative
28 If loan rates are used as the dependent variable, then β should be positive for SCP, and non-positive under RE.
