This chapter deals with a number of questions. It begins by looking at what might be meant by efficiency, and then goes on to look at efficiency in the specific context of financial i nstitutions. This provides a basis for an examination of specific methods that have been used for studying effi ciency, and efficiency in financial institutions in particular.
The latter part of the chapter then looks at some of the specific practical issues which otherwise get in the way of research, and at how these have been dealt with 111 previous research. This section has more of a focus on one of those techniques m particular, Data Envelopment Analysis, as this is the teclmique used in this research, but it also i dentifies issues that need to be addressed in other approaches.
Following thi s outline of previous research, the following chapter explains the actual methods to be used in this research, results from which are reported in Chapter 5 .
3.1 What is efficiency?
The concept of efficiency may be regarded as one of the fundamental precepts of economics, and one which also has welfare connotations. Efficiency may be defined as the ratio of the \veighted sum of outputs to the weighted sum of inputs (Boussofiane et a!, 1 99 1 ). In general terms, a fin11 may be said to be operating efficiently i f it caru1ot produce more output without a corresponding relative increase in inputs, or if it caru1ot reduce its i nputs without a corresponding relative decrease in output .3 1 More generally, a decision-making unit (DMU) will be 1 00% efficient if there i s no scope for improvement i n the ratio in which it conve11s inputs to outputs.32
3 1 This assumes that there i s no change or d i fference in the qual ity of inputs or outputs.
32 This i s consi stent with what Cooper et al (2000) refer to as Pareto-Koopmans effici ency: a unit "is fu l ly efficient i f and only if it i s not possible to i mprove any input or output without worsening some other input or output" (p 45). For the background to the terminology on e ffi c iency, refer to their d iscuss ion on pp 68-69. See also Charnes et al ( 1 985).
Efficiency can be discussed i n a variety of different forms, not all of them necessarily totally consistent with the previous definition. Traditional microeconomic theory has l ong talked of economies of scale, where increased volumes of output are supposed to be able to be produced with less than proportionate i ncreases in quantities of i nputs ( increasing returns to scale). In due course, however, economies of scale will be exhausted, and increased output wil l require a more than proportionate increase in i nputs, a situation described as diseconomies of scale ( decreasing returns to scale). 33
This description of economies of scale is consistent with what is referred to as a U shaped average cost curve, one of the implications of which is that there is a particular l evel of output consistent with a minimum level of average cost. Under such a view, there is likely to be a fl at portion in the middle of the U, characterised by constant returns to scale, where there is a fixed (and minimum cost) relationship between o utput and uti l isation of inputs.
It is more common in practice to focus on the left side of the U-shaped average cost c urve, where increases in outputs are associated with l ess than proportionate increases in inputs. A possible source of such positive scale economies in banking might arise from using a computer system to process customer accounts: more accounts can be processed without a corresponding increase in computing costs (Mester, 1 987).
Another type of efficiency i s economies of scope . The essence of these is that firms should be able to produce multiple outputs from the same group of inputs at l o\ver c ost. in tern1s of inputs. than if they specialised in producing only one type of output. Clark ( 1 988) identi fied economies of scope as existing where the total costs from j oint production of all products in the mix were less than the sum of the costs of producing each product independently (p 1 8) . In the context of a financial institution, one might be looking at a situation where a firm produced both l oans and deposit services, using the same staff and branch networks, rather than special ising in just one of these functions by itself.
33 This discussion i s d irected at sca l e economies in a static context. I ssues relating to changes in e ffic iency arising from changing production functions through t i m e are discussed funher below.
Mester ( 1 987) notes that, at least in financial services, economies of scale and scope may arise at the same time. The use of a computer to reali se economies of scale in account processing may be accompanied by use of the same computer system to process several different types of account simultaneously.
Clark ( 1 988) identified a relationship between economies of scale and scope and the structure of firms in an industry. If the avai lable teclmology allows for both economies of scale and scope, the industry will tend to be made up of l arge diversified firms, producing at lower unit costs, and using this advantage to gain market share.34 I f the technology does not allow for economies of scale or scope, small specialised firms wil l dominate the industry. If there is an absence of significant economies of scale or scope, there is likely to be a mixture of larger diversified firms and smaller specialised firms (p 1 7).
These discussions of economies of scale and scope in the previous paragraphs may be construed as assuming that firms are operating on some so11 of production possibility frontier, and that it is only a matter of achieving an effi cient level of production or mix of outputs. This will often not be the case, thus providing a basis for the concept of X-efficiency, as proposed by Leibenstein ( 1 966). If a firm is X-inefficient, it is l ikely to be capable of producing more output for any given l evel of inputs, perhaps by a better utilisation of resources, reorganisation of the production process so as to make better use of avai lable technology. better purchasing of inputs, enhancing staff motivation. or by any one of a range of other improvements.35
X-ineffici ency is commonly broken down into 2 elements, allocative inefficiency and technical i nefficiency, in terms of the approach outlined by Farrell ( 1 957).36 Technical efficiency might be conceived in simple terms as a measure of whether the firm is max i mising 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. Frei et al (2000) distinguish X -efficiency, suggesting that :
34 Th i s is the so-called Efficient Structure hypothesis, wh ich may be contrasted with the Structure Conduct Performance hypothesis. See, for example, B erger ( 1 995) for a review of these.
35 Stigler ( 1 976) suggested that differences in X-efficiency should be attributed to differences in
technology.
" . . . X-efficiency describes all techni cal and allocative inefficiencies of i ndividual firms that are not scale/scope dependent. Thus X-efficiency is a measure of how wel l management is aligning technology, human resources and other assets to produce a given level of outputs." (p 260).
Attempts to measure X -efficiency generally occur relative to an efficiency frontier, with firms' teclmical efficiency being defined in tem1s of their relative distance from the frontier (which then becomes the benchmark for optimum performance). Allocative efficiency will then be identified according to whether firms are producing at that point on the effi cient frontier that minimises input costs. This can be explained using Figure 5 .
Fig u re 5: X-efficiency a n d its decom p osition into tec h n ical a n d a llocative efficiency.