# X-efficiency, Scale Economies and Scope Economies - Modern Banking

Cost X-efficiency

X-efficiency2 can be measured in terms of cost or profit but the emphasis of much of the banking literature is on cost X-efficiency. Since managers have the ability to control costs (cost X-efficiency) or revenues (profit X-efficiency), greater X-efficiencies can be achieved by superior management. The cost efficiency frontier is shown in Figure.

Cost and Profit X-efficiency 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 translogcost 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 a locative 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) ----(XX)

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 a locative 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 equation gives:

ln TC = f(q, p, y, z) + ln μc + ln εc

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 + θ) = F(q, x, y, z) + ln μπ+ ln επ

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

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%.

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 labor 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) ----(XXI)

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, labor – 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 maximize 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, 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.

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