Measuring Bank Output - Modern Banking

The definition of output and productivity is not straightforward for a bank. For example, should demand deposits be treated as an input or an output? Are bank services best measured by the number of accounts and transactions, or values of accounts? If it is shown that one bank is more productive than another, as measured by assets per employee, employees per branch, or assets per branch, is it also possible to conclude that the bank is more efficient?

The measurement of ‘‘output’’ of services produced by financial institutions has special problems because they are not physical quantities. Additionally, it is difficult to account for the quality of banking services. For example, customers opting to use cash dispensing machines/ATMs and electronic delivery of standard banking services instead of a bank cashier at a branch usually view these changes as improvements in the quality of banks services, because of greater convenience such as better access and the increased speed of transactions. ATM technology is also known to reduce bank operating costs, but if customers access the machine more frequently than they would visit the branch, the cost savings may be lower than expected. Also, to the extent that visits to a branch help foster a relationship, banks may find that electronic delivery methods reduce their ability to cross-sell other financial products.

Banks provide customers with many services, including intermediation (deposits, loans), liquidity and payment services, and non-banking financial services ranging from management of investment portfolios to protection of valuables.

In some bank systems, direct payment for these services is the exception rather than the rule. For example, demand deposits may be paid interest, in exchange for ‘‘free’ services. Or ‘‘free retail banking’’ may be offered to all customers in credit, but those with an overdraft are charged very high fees and interest, meaning these customers are effectively subsidising those in credit. Corporate clients normally receive a package of banking services to accompany a loan or overdraft facility, but depending on the size of their custom, are often charged for every transaction (direct debits/credits, fund transfers, etc.) they use.

In aggregate, bank output, for the purposes of a country’s national accounts, should be based on value-added, that is, adjusted operating profits less the cost of shareholder equity. When looking at the financial sector as a share of GDP, net interest receipts are normally included in value-added; in the USA these are attributed to depositors, while in the UK they include depositors and borrowers. However, empirical studies on banking do not normally use the national accounts definition of bank output. Instead, a ‘‘production’ or ‘‘intermediation’’ interpretation of bank output is employed.

The Production Approach

The production approach measures bank output by treating banks as firms which use capital and labor to produce different categories of deposit and loan accounts. Outputs are measured by the number of these accounts or the number of transactions per account.

Total costs are all operating costs used to produce these outputs. Output is treated as a flow, that is, the amount of ‘‘output’’ produced per unit of time, and inflation bias is absent. An example of the use of this type of measurement may be found in Benston (1965). There are several problems with this approach. First, there is the question of how to weight each bank service in the computation of output. Second, the method ignores interest costs, which will be important if, for example, deposit rates fall as the number of branches increase.

Furthermore, data from banks in countries using different accounting systems may not be comparable, making accurate measures of relative efficiency difficult to obtain. It is hoped the move towards International Accounting Standards (IAS) will address this problem.

The total factor productivity (TFP) approach employs a single productivity ratio, using multiple inputs and outputs. Humphrey (1992) measured productivity and scale economies using flow and stock measures of banking output in identical models. He employed both a non-parametric growth accounting procedure and the econometric estimation of a cost function. A structural model of bank production was used, which incorporated both the production of intermediate deposit outputs as well as ‘‘final’’ loan outputs. Thus, both the input and output characteristics of deposits were simultaneously represented.

With data on 202 US banks from the Federal Reserve’s 1989 Functional Cost Analysis survey, Humphrey employed a general production function:

Q = Af(K, L,D, S, F)----(XIX)

Q : bank output
A : efficiency
K, L : capital and labor, respectively
D : demand deposits
S : small time and savings deposits
F : purchased funds

Humphrey used three different measures of bank output

QT: a transactions flow measure – the number of deposits and loan transactions processed
QD: a stock measure – the real $ value of deposit and loan balances
QA: a stock measure of output – the number of deposit and loan accounts serviced

The growth of production efficiency is the residual, obtained after subtracting the growth in inputs from the growth in outputs. The residual from the dual cost function also shows productivity growth: the shifts in the average cost curve after controlling for changes in input prices. Expenditure share weights were estimated rather than being computed directly.

A translog cost function1 was used for the econometric estimation. TFP was derived from these equations, decomposed into cost reductions arising from either technical changeover time or scale economies. Humphrey specified scale economies of 0.9 (slight scale economies), 1.00 (constant costs) and 1.1 (slight diseconomies). Humphrey reported on the equation that assumed constant costs because the total factor productivity results did not appear to be sensitive to the scale economies imposed.

Humphrey’s key findings are as follows.

  • Using the QT definition (number of deposits and loans processed), banking productivity was found to have been flat over 20 years, with an annual average rate of growth of only 0.4%.
  • If output is defined as QD (dollar value of loans and deposits), TFP actually fell between 1968 and 1980 but rose thereafter. The overall average rate of TFP growth was 1.8%per annum.
  • The real value of total assets (QTA): the average TFP rate fell by about 1.4% per year.

Humphrey finds the TFP result using the parametric/econometric approach is virtually the same as when a growth accounting approach (non-parametric) is used. Nor was there much difference in the predictive accuracy of the stock and flow measures of bank output. By the flow measure, productivity growth was slightly positive; it was slightly negative when the stock measure was used. During the 1980s, both measures generated a small positive productivity growth. Two reasons are offered for the relatively low US bank productivity growth. First, banks lost low-cost deposit accounts as corporate and retail customers shifted to corporate cash management accounts and interest-earning cheque accounts. Second, the study largely ignored quality differences in bank output. For example, the quality of bank services may have improved because banks started to pay interest on most accounts but did not raise charges for bank services such as transfer of funds, cheque clearing and monthly statements.

The Intermediation Approach

This approach recognises intermediation as the core activity – banks are not producers of loan and deposit services. Instead, output is measured by the value of loans and investments. Bank output is treated as a stock, showing the given amount of output at one point intimae. Total cost is measured by operating costs (the cost of factor inputs such as labor and capital) plus interest costs. Sealey and Lindley (1977) argued that earning assets (loans, securities, etc.) make up bank outputs, so deposits, capital and labor should be treated as inputs. Others favour deposits being treated as outputs. However, if banks offer an extended range of services, such as trust operations or securities, the intermediation approach will make their unit costs appear higher than for banks that engage in traditional intermediation.

The relative importance of different bank products may also be ignored in the computation, unless weighted indices are used. Greenbaum (1967) suggested one method for obtaining weights: he used linear regressions to obtain average interest rate charges on various types of bank assets.

Most bank productivity studies use the intermediation approach because there are fewer data problems than with the production approach. They tend to follow Sealeyand Lindley (1977), where earning assets are produced from several factor inputs. In the more recent literature, in an attempt to recognise the multiproduct nature of the firm, outputs typically include loans, other earning assets (e.g. securities, interbank assets), deposits and non-interest income, which acts as a proxy for off-balance sheet’ output’’. Inputs include the price of labor, the cost of physical capital (proxied by non-interest expenses/fixed assets) and the price of financial capital (proxy: interest paid/purchased funds).

The empirical work suffers from a number of difficulties. First, the way output is measured varies considerably. Some studies use the number of deposit accounts because customers are getting services (e.g. intermediation, liquidity) from the account. Though banks incur costs from offering these services, all but a fraction of deposits earn revenue when they are loaned out. Studies that rely on the underlying production and cost functions for banks encounter these problems. The literature on X-efficiency, scale and scope economies and structure–conduct–performance often employ different definitions of output. Furthermore, deposits may be treated either as inputs, outputs or, in some studies, both.

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