sou · GOB311d5 · 2001-01-01 00:00:00 — Input saving efficiency for Swedish banks, 1996: A comparison between variable and returns to scale Reduction in the number of variables also has a strong impact on the number of frontier units; see Figure 8, where the number of outputs is decreased from 4 to 3, or Figures 10 and 11, with labour as the only input. In the former case the number of frontier units decreased from 31 to 25. The choice between labour costs and labour hours has only a minor impact on the efficiency distribution; see Figures 7 and 9, in which Models 1 and 2 almost coincide, as do Models 3 and 4. Under VRS, four to six units (all savings banks) which are on the frontier in Model 1 become inefficient in the other models. Under CRS, four to seven banks become inefficient when moving from Model 1 to the other models; all these are savings banks except Nordbanken which becomes inefficient in Models 2 and 4 (efficiency scores 0.94 and 0.88, respectively), i.e., when labour hours are substituted for labour costs. On the other hand, there is a substantial difference between Models 1 and 2 on the one hand and Models 3 and 4 on the other; i.e., the results are very sensitive to the inclusion or exclusion of net provisions as an output variable. This is even more clear from Figure 8, which illustrates the difference between Model 1 and Model 3. Mean efficiency decreases from 0.89 in Model 1 to 0.73 in Model 3. All commercial banks (except ) are on the frontier in both models. For three units (Finn, and Roslagen savings banks) there is a deviation in efficiency scores exceeding 0.50. Input saving efficiencyfor Swedish banks, 1996, variable returns to scale Volym D:292 Supplement 28 Efficiency distribution with and without net provisions as an output variable, variable returns to scale When labour is used as the only input, the number of frontier units decreases from 31 to 10 in Model 1 under VRS and from 14 to 3 under CRS; see Figures 10 and 11. Variation between the models is very large.Under VRS mean efficiency decreases from 0.79 in Model 1 to 0.45 in Model 4, and under CRS from 0.67 to 0.27. While all the commercial banks (except ) are on the frontier in Model 1 under VRS, only and are on the frontier in all four models. In CRS only and (along with sparbank in Model 1 only) are on the frontier in all models, while SE-banken and get efficiency scores of 0.75 and 0.62, respectively, in Model 1. Efficiency distribution for Swedish banks, 1996. Labour use efficiency for Swedish banks, 1996. Volym D:294 Supplement 28 Labour use efficiency for Swedish banks, 1996. Efficiency analysis of Swedish banks in 1996 illustrates the sensitivity of the results with respect to choice of variables. On the one hand, the choice between labour costs and labour hours has only a minor impact on the efficiency distribution, but on the other hand, the results are very sensitive to the inclusion or exclusion of net provisions as an output variable. While the results are robust for the commercial banks – which are all (with one exception) fully efficient – the differences between models for some savings banks are quite striking. 3.4Banking productivity in a Scandinavian comparison Because of low cultural barriers to entry into each others markets, the performance of Swedish banking in comparison with its Scandinavian neighbours is of great interest. This issue was analysed in a few studies about , and although there are plans to update these, this has not yet been realised; see et al (1993) and Bukh et al (1995) which will be dealt with here. The data set in et al (1993) consists of observations from 503 Finnish, 150 Norwegian, and 126 Swedish banks. Only a few, quite small, banks in each country have been omitted, due to data collection problems. The data were collected from official bank statistics in and , and from annual reports in , for the year 1990. The output variables are deposits loans, and the number of branches. The input variables are number of hours worked and the book value of machinery and equipment. To convert monetary values into a common unit, both the official exchange rate and the purchasing- power parity rate as computed by the were used, but it did not matter very much which rate was used. In Bukh et al (1995) the data set for 1990 was extended to include 182 Danish banks and the variables were extended to include guarantees as an output, and non-labour and non-capital operating expenses as input. et al (1993) uses the productivity index; is chosen as the technology base for productivity comparisons, due to the superior performance of its largest banks. A common technology base facilitates intercountry comparisons, but the choice of base country will influence the results. Productivity comparisons are shown in Table 7. Intercountry productivity comparisons, 1990, average and largest units tivity index (MTP) component (MC) The average Norwegian bank has about higher productivity than the Finnish average bank, under VRS, under CRS. For the largest bank the scale assumption is crucial, with higher Finnish productivity under VRS, as opposed to higher Norwegian productivity under CRS. The Swedish average bank is much more productive than both the Finnish and the Norwegian average bank, higher than Finnish under VRS, under CRS, and and respectively, higher than Norwegian. The Swedish largest banks are also much more productive. As discussed earlier the productivity index can be decomposed into an efficiency component and a frontier technology component, the latter measuring the distance of the frontier technologies relative to the Swedish common-reference technology. The large gap between Swedish and Finnish average productivity is mainly due to the efficiency component, although also has a technology advantage. The efficiency component explains even more of the Swedish-Norwegian gap. In fact, under CRS, even has a technology advantage. Since the largest banks are on the frontier under VRS, there is in that case no efficiency component; i.e., its value is zero. There is just a difference in frontier technology levels. The extension of the data set to include Danish banks and inclusion of one more output and input variable does not change the previous picture very much; see Table 8. Intercountry productivity comparisons, 1990. index, average and largest units in each country The average Swedish bank still has a higher productivity than the average bank in the other Scandinavian countries, now including , both under VRS and CRS. In an inter-Scandinavian comparison, the Swedish banking sector in 1990 was much more productive than the Finnish, Norwegian, and Danish banking sectors. This conclusion also holds for the largest banks, except in comparison with . The large gap between Swedish and Finnish average productivity is mainly due to the efficiency component, although also had a technology advantage, which was the source of the Swedish-Danish productivity gap. The Swedish- Norwegian productivity gap is more model- dependent, and consists of both components. 3.5The efficiency of Swedish banks in a European comparison As the final step in this review of empirical studies, we draw on a study by (1999) on the relative efficiency of a set of large European banks observed in 1996. This analysis is based on a sample of 104 of the largest banks in eight countries, i.e., the , , , , , Great Volym D:298 Supplement 28 The German, British, Italian and French banking markets constitute the largest markets in Europe, while the remaining four are representing the smaller market places; see Table 9. The complete list of banks is reported in Appendix 2. The distribution of banks Most of the countries in the study have a few core banks, which are dominant players in their domestic markets, but their importance is largely balanced by equally important regional banking groups, particularly in , , and : Table 10 shows two size indicators for the sample. The size of the average bank in the sample, 1996 The main bank- types represented are commercial banks (67), savings/co-operative banks (26), and specialised banks (investment banks, mortgage banks-, and non-credit institutions) (11). The average bank in the sample had some 14 000 employees and a branch network of almost 700 branches. Here we report efficiency scores under both VRS and CRS, with two different choices of input variables and with the three output variables, loans, number of branch offices, and deposits. L-vrs and L-crs are the pure labour efficiency models i.e. hours worked as the only input under VRS and CRS respectively. X12-vrs and X12-crs include inventories as the second input under VRS and CRS respectively. Because the number of variables is small in this data set, one would expect rather low levels of efficiency and a large dispersion between best practice and average efficiency. This is in fact the case. There is a large variation in efficiency. The results are shown in Figures 12-15. The differences in mean efficiency scores are quite large. In the base model, X12-vrs mean efficiency varies from 0.31 for to 0.70 for the . ranks second from bottom with a mean efficiency score of 0.35. also ranks second from the bottom in the VRS labour-use model, with a mean efficiency score of 0.20 compared with 0.61 for the . Country mean efficiency scores for European banks, 1996 Figure 13 shows the efficiency distribution for the entire set of units. Volym D:300 Supplement 28 The efficiency distribution of large European banks, 1996 The number of frontier units in the base model X12-vrs is 23, where as it is only 13 in the labour-use model under VRS. All countries are represented at the frontier, with only one bank. The distance between best practice and worst practice is unusually large, with three worst performing UK banks at the very bottom (efficiency score 0.01-0.02) in all models. The worst-performing Swedish bank has an efficiency score of 0.07 both in the base model and the labour use model with VRS. The location of the Swedish banks in the base model is shown in Figure 14 and in the labour use model in Figure 15. The Swedish banks are spread along the entire efficiency distribution in the two-input model. In the labour use model none of the Swedish banks has an efficiency score exceeding 0.50. The location of Swedish banks in the efficiency distribution of European Banks, 1996, variable returns to scale The location of Swedish banks in the labour-use efficiency distribution of European banks, 1996, variable returns to scale There is a large variation in efficiency between banks, both within each country analysed and across countries. In a European perspective, Volym D:302 Supplement 28 Swedish commercial banking efficiency on average ranks second from the bottom, both in a two-input model and in a labour-use model. 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The stochastic frontier model We assume that the following translog stochastic frontier model defines labour use for the 156 banks in our data where the subscripts i and t represent the i-th bank (i = 1, 2, , 156) and the t-th year of observation (t = 1, 2, , 12); Y represents the total quantity of labour used (in hours per year); D is a dummy variable for guarantees, which has value one if guarantees were zero or not observed, and, otherwise zero 4 x1 is the logarithm of the total amount of public loans (in SEK1,000); x2 is the logarithm of the maximum of the guarantees (in SEK1,000); x3 is the logarithm of deposits (in SEK1,000); x4 is the logarithm of the number of branches; x5 is the logarithm of the value of machinery and equipment; x6 is the year of observation, where x6 = 1, 2, , 12; the Vits are random variables, associated with measurement errors in the labour variable or the effects of unspecified explanatory variables in the model, which are assumed to be independent and identically distributed with N(0, v2)-distribution, independent of the Uits; The Uits are non-negative random variables, associated with inefficiency of labour use, given the levels of the outputs and the quasi- fixed inputs, such that Uit is obtained by the truncation (at zero) of the N(µit, 2)-distribution; where 4 Some small banks had zero guarantees. This variable permits the intercepts to be different for banks with positive and zero guarantees, see Battese (1997). + å4 0j Djit + D1, D2, D3, and D4 are dummy variables which have value one if the observation involved is on a bank of types 1, 2, 3, and 4, respectively, and, otherwise zero; z1 is the logarithm of the number of branches (i.e., z1 = x4); z2 is the logarithm of total machinery and equipment (i.e., z2 = x5); z3 is the year of observation (i.e., z3 = x6); and z4 is the square of the year of observation (i.e., z4 = z32). The model incorporates non-neutral technical change in the use of labour in the production of the outputs, given the quasi-fixed inputs in the banking operations. The specification of the model for the inefficiency effects in equation (2) implies, in addition to accounting for the existence of inefficiency effects in the use of labour in producing outputs that the variations in the inefficiency effects are a function of other variables. In this case, we permit the level of the inefficiency effects in labour use to be different for five different types of banks (associated with the four dummy variables for types of banks), and they also depend on the number of branches in the banks and the year of observation. The parameters of the stochastic frontier model, defined by equations (1) and (2), were simultaneously estimated by the method of maximum likelihood using the computer program, FRONTIER 4.1, written by Coelli (1996). The technical efficiency of labour use for the i-th bank in the t-th year of observation (TEit, given the values of the outputs and quasi-fixed inputs, is defined as the ratio of stochastic frontier labour use to observed labour use. Stochastic frontier labour use is defined by the value of labour use if the technical inefficiency effect, Uit, were zero (i.e., it the bank were fully efficient in the use of labour). Given the specifications of the translog stochastic frontier labour-use function in equation (1), it can be shown that TEit = exp(-Uit) which indicates that technical efficiency is no greater than one. The reciprocal of this quantity, exp(Uit), is no less than one, and can be interpreted as a measure of the technical inefficiency of labour use.5 Computation of efficiency scores by The input-saving measure under VRS is found by solving the following LP problem for each plant, k, with output yk and input xk subject to the following restrictions: yrj , r = 1,...,m kj xij , i = 1,...,n åNj kj = 1 kj 0, j = 1,...,N where E1k is the input-saving efficiency measure for plant k, m is the number of outputs, n is the number of inputs and N the number of plants. Restriction (4a) implies that the reference plant must produce at least as much as plant k, while restriction (4b) implies that the efficiency- adjusted volume of input used by plant k must at least amount to the input volume used by the reference plant. Restriction (4c) is the condition for VRS. If this restriction is omitted, CRS is implied; E1 and E2 then coincide with each other. 5 precisely, the amount by which exp(Uit) exceeds one is a measure of technical inefficiency of labour-use, because it gives the proportion by which actual labour use exceeds the corresponding stochastic frontier labour value, given the level of outputs and quasi-fixed inputs. Volym D:310 Supplement 28 The selection of large European banks Cassa di Risparmio di Cassa diRisparmio di Parma et Piacenza Cassa di Risparmio di Volym D:312 Supplement 28 De Nationale Investeringsbank N.V. Crédit à L= Industrie