Abstract
Parametric and nonparametric procedures are used to identify the apparent source of cost inefficiency in banking. Inefficiencies of 20–25% from earlier studies are reduced to 1–5% when, in addition to commonly specified cost function influences, variables reflecting banks’ external business environment and industry indicators of “productivity” are added. These productivity indicators explain most of the reduction in bank operating cost over 1992–2001 and was 5 times the reduction in the dispersion of inefficiency. Inefficiency appears stable over time because it is small relative to industry-wide cost changes occurring concurrently and because technology dispersion is imperfect.
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Notes
The assumption that most banks are close to the efficient frontier so that inefficient firms are skewed away from the frontier (as in a half-normal, Gamma, or truncated normal distribution of inefficiency) does not appear to be the case in practice (Bauer and Hancock 1993; Berger 1993). The distribution of inefficiencies is more like a symmetric normal distribution which would make it difficult to locally identify separately from normally distributed error.
The other approach is the Free Disposal Hull and will be either congruent with or interior to the DEA frontier. When it is interior, lower estimates of average inefficiency will result (Tulkens, 1993).
Using U.S. banking data, DeYoung (1997) devised a test to determine how many years of separate cross-section regressions may be needed to have the random error likely average out close to zero and achieve a stable measure of efficiency. Six years was the result. We have 10 years of data and, instead of positing that measured efficiency should be stable, we interpret our results as an average indicator of efficiency over our period.
The ratio \({\bar {u}_{\min} /\bar {u}_i =\left( {TC_{\min}/C(Q,P)_{\min}}\right)/\left({TC_i /C\left({Q,P} \right)_i} \right)}\) and when evaluated at the same output level and input prices, the predicted values of total cost \({C(Q,P)_{min}}\) and \({C(Q,P)_{i}}\) are equal as both are at the same point on the estimated total cost curve, leaving the ratio \({TC_{min}/TC_{i}}\) . EFF can vary from zero (where bank i uses multiple times the resources of the most efficient bank) to one (where bank i is just as efficient as the most efficient bank).
The level of inefficiency (INEFF) at the ith bank is INEFF = (1 - EFF)/EFF = (1/EFF) − 1.
We thank an anonymous referee for the comments on this section.
The nonparametric Malmquist index was not used here as it is not well-adapted to available banking data. The Malmquist index typically relates categories of balance sheet output (assets) to inputs (liabilities) plus labor and physical capital. This works well if outputs and inputs are actual quantities but in banking these are nominal or deflated values (using the same deflator for everything, not actual prices). Due to the balance sheet constraint, the sum of asset outputs always equals the sum of liability inputs so efficiency is equivalent to a simple ratio of labor and capital inputs to asset value. Other measurement problems also exist (c.f., Lozano-Vivas and Humphrey 2002).
The data are already separated along these dimensions and aggregation to obtain total cost or reflect all banks unnecessarily restricts the separate costs or different banks to have the same (average) efficiency response. Spanish savings banks are similar to mutual organizations and are managed by depositors and provincial/local government entities while commercial banks are privately (stockholder) owned. This has led to differences in internal goals associated with service provision and contribution to local communities.
Two intercepts are specified as the cross-section data used in each of the 10 separate regressions (one for each year) consists of two (pooled) semi-annual data periods. Specifying a single intercept would lower by three percentage points the efficiency value reported below for Technical Influences—the cost function. All the other operating cost efficiency values, however, are unchanged at the two digit level.
While past managerial decisions can affect bank size, in practice the vast majority of banks only grow slowly as their (externally influenced) market expands. The exception concerns those few banks that merge in a given year during which time inefficiency may improve (if costs are cut) or worsen (as back office integration problems arise). Consultant and other studies suggest that the net effect on the average bank merger on cost efficiency is close to zero (Rhoades 1993).
Our model specifications do not always follow a standard second order Taylor series expansion but instead reflect judgments about whether a relationship is likely to be quadratic versus linear and whether or not interaction relationships are likely to be important.
Unfortunately, publicly available data in Spain do not permit the specification of different types of loans.
The market interest rate is a constant for all banks in each 6-month period. However, our 10 separate annual cross-section regressions are composed of two 6-month periods so this variable is not a constant in each regression run.
Equations (3.1), (3.2), and (3.3) are alternative explanations of bank operating cost and, since the dependent variable (ln OC in Eq. (3)) is the same, these three equations are not a system of equations amenable to system estimation (so OLSQ is used). Cross-section estimation of the cost function (3.2) for each year for commercial (savings) banks yielded 20 (15) positive values for marginal costs for loan and security outputs. The 5 negative marginal costs were for securities, which is not surprising since the incremental cost of changing bank security holdings is close to zero in practice (all that is needed are a few traders, a small room, and phones).
The full DFA model contains 34–35 parameters. With semi-annual data on 46 (31) savings (commercial) banks, this gives 92 (62) observations for each year’s separate regression and 58 (27) degrees of freedom. Similarly, there is no problem of an insufficient number of observations for our DEA model.
Adding off-balance sheet (OBS) activities as a third banking output increased savings and commercial bank efficiencies by 1 percentage point (to 0.95 and 0.97, respectively) with a corresponding 1 percentage point reduction of inefficiency. As the effect was small, OBS activities were not added to the DEA model. Lagging by 6-months all but the ATM and BR variables in (3.3) reduced efficiency by 5 percentage points. However, decisions to alter loan and deposit rates do not generate a significant operating cost response since rate changes by one bank are typically matched by others and the small change in loan and deposit values is easily handled with the same number of branches and workers. Also, the time lag between decisions to add ATMs and branches and when they become operational is closer to 6 months for ATMs—the frequency of our data—and 9 months or more for branches (with little contemporaneous correlation).
The DFA model estimates a separate regression for each year so each bank’s residual for each year is determined by a different set of estimated parameters. Pooling the data and estimating a single set of parameters for all years with which to calculate each bank’s yearly residual may or may not have much effect on the results. For savings banks in Table 1, EFF was 0.94 with yearly estimation and only falls to 0.92 using pooled estimation. For commercial banks, the reduction was greater (falling from 0.96 in Table 1 to 0.89 with pooled estimation).
In contrast to the operating cost specification (3), two intercepts—one for each six-month period—is redundant here. The INTRATE variable in the External Influences Eq. (4.1) contains constant interest rates for each six-month period and reflects already our use of two periods for each annual cross-section regression. The exception is when Technical Influences (4.2) is separately estimated but here a two intercept specification yielded efficiency estimates that were the same at the three digit level.
The level of market interest rates, through a yield curve, helps to determine bank funding costs. It is a constant for all banks for each 6-month period but varies within each annual cross-section regression (which covers two 6-month periods) and reflects an important influence on the level of bank deposit/loan rates from year-to-year.
When a common frontier is specified, the parameters for savings and commercial banks are the same while when separate frontiers are used, these parameters can vary between these two sets of banks. If the efficiency values are quite similar, this means that allowing for different parameter values between savings and commercial banks (separate frontiers) has little or no economic significance (even if the parameter estimates may be significantly different in a statistical test).
As one of the purposes of efficiency or frontier analysis was to make efficiency/productivity comparisons using a single overall measure rather than rely on a set of sometimes conflicting partial indicators, this result is largely expected, although its importance was unknown.
Unfortunately, DEA estimates are serially correlated with unknown dependency among them. Consequently, we incorporate environmental variables on efficiency analysis using stage inference procedures that should solve this problem. In particular, we apply the Simar and Wilson (2007) algorithm. This algorithm is a coherent data generating process that allows environmental variables to influence efficiency. This model is estimated using a two-stage semiparametric bootstrap procedure.
This latter influence is more likely a result of previously locating branches in areas where incomes are relatively high than due to independent internal efforts by management at existing offices to raise deposits.
This reference to the diffusion theory of innovation was suggested by a referee.
With the non-parametric Data Envelopment Analysis model, operating cost efficiency was 0.98–0.99 while for interest cost it was 0.92–0.97.
References
Bauer P, Berger A, Ferrier G, Humphrey D (1998) Consistency conditions for regulatory analysis of financial institutions: a comparison of frontier efficiency methods. J Econ Bus 50:85–114
Bauer P, Hancock D (1993) The efficiency of the federal reserve in providing check processing services. J Bank Finance 17:287–311
Berger A (1993) Distribution-free estimates of efficiency in the U.S. banking industry and tests of the standard distributional assumptions. J Product Anal 4:261–292
Berger A, Humphrey D (1991) The dominance of inefficiencies over scale and product mix economies in banking. J Monet Econ 28:117–148
Berger A, Humphrey D (1997) Efficiency of financial institutions: international survey and directions for future research. Eur J Operat Res 98:175–212
Berger A, Mester L (1997) Inside the black box: what explains differences in the efficiencies of financial institutions. J Bank Finance 21:895–947
Carbó-Valverde S, Humphrey D, López del Paso R (2006) Electronic payments and ATMs: Changing technology and cost efficiency in banking. In: Balling M, Lierman L, Mullineaux A (eds) Competition and Profitability in European Financial Services. Strategic, Systemic and Policy Issues, Routledge, Abingdon (UK), pp 96–113
Charnes A, Cooper W, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Operat Res 2:429–444
DeYoung R (1997) A diagnostic test for the distribution-free efficiency estimator: An example using U.S. commercial bank data. Eur J Operat Res 98:243–249
Dietsch M, Lozano-Vivas A (2000) How the environment determines banking efficiency: a comparison between French and Spanish industries. J Bank Finance 24:985–1004
Frei F, Harker P, Hunter L (2000) Inside the black box: what makes a bank efficient? In: Harker P, Zenios S (eds) Performance of financial institutions: efficiency, innovation, regulation. Cambridge University Press, Cambridge
Humphrey D, Willesson M, Bergendahl G, Lindblom T (2006) Benefits from a changing payment technology in European banking. J Bank Finance 30:1631–1652
Lozano-Vivas A, Humphrey D (2002) Bias in Malmquist index and cost function productivity measurement in banking. Int J Product Econ 76:177–188
Lozano-Vivas A, Pastor J, Pastor J (2002) An efficiency comparison of european banking systems operating under different environmental conditions. J Product Anal 18:59–78
Maudos J, Pastor J, Pérez F, Quesada J (2002) Cost and Profit Efficiency in the European Banks. J Int Financial Markets, Inst Money 12:33–58
Rhoades S (1993) The efficiency effects of horizontal bank mergers. J Bank Finance 17:411–422
Sherman D, Ladino G (1995) Managing bank productivity using data envelopment analysis (DEA). Interfaces 25:60–73
Simar L, Wilson PW (2007) Estimation and inference in two-stage, semi-parametric models of production processes. J Econom 136:31–46
Tulkens H (1993) On FDH efficiency analysis: some methodological issues and applications to retail banking, courts, and urban transit. J Product Anal 4:183–221
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Comments by two referees and participants at seminars at the Federal Reserve Bank of Philadelphia, the Bank of Canada, the Bank of Spain, and De Nederlandsche Bank as well as the Universities of Valencia and Wales were helpful and appreciated. Financial support was provided by the Fundacion de las Cajas de Ahorros Confederadas.
Data Appendix
Data Appendix
Data are observed semi-annually over 1992–2001, giving 1,540 panel observations. The data set includes all savings banks, all but the very smallest commercial banks (which were excluded due to missing data), and no cooperative banks (who also had missing data). The sample covers 90% of total banking assets in Spain in 2001. Starting at the end of 2001, all data were backward aggregated to obtain the same number of banks with the same bank code in each year. If two banks had existed but merged before the end of the sample period, they are aggregated over the period they existed separately and so enter the data set as a single composite bank for the entire period. This permits the use of a balanced panel data set from which to compute the DFA average residual for each bank separately. Descriptive statistics are shown below.
Variable | Mean | Standard deviation |
|---|---|---|
TC | 524,826 | 1,306,915 |
LOAN | 5,650,417 | 13,640,000 |
SEC | 2,241,031 | 6,798,484 |
PF (interest rate) | 0.048 | 0.028 |
PL (annual price) | 44.725 | 44.766 |
PK | 0.135 | 0.0162 |
IC | 344,020 | 939,119 |
Q TA (ln of value) | 14.82 | 1.35 |
INTRATE=PM (percentage) | 7.107 | 3.385 |
GDPR | 46,980,000 | 29,130,000 |
MKSH (percentage) | 0.012 | 0.03 |
ATM/BR | 0.865 | 0.946 |
LOAN/TA | 0.737 | 0.097 |
DEP/TA | 0.884 | 0.075 |
OC | 180,806 | 379,849 |
WAGE | 1,217 | 181 |
IPP (index number) | 120 | 36 |
ATM (number) | 396 | 744 |
BR (number) | 391 | 690 |
L/BR (number per branch) | 8.14 | 13.3 |
DEP/BR (value per branch) | 33,583 | 162,821 |
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Carbó Valverde, S., Humphrey, D.B. & López del Paso, R. Opening the black box: Finding the source of cost inefficiency. J Prod Anal 27, 209–220 (2007). https://doi.org/10.1007/s11123-007-0034-x
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DOI: https://doi.org/10.1007/s11123-007-0034-x