sou · GOB311d5 · 2001-01-01 00:00:00 — A total productivity index, can then be defined as Mi = MC x MFi: For a fully efficient observation both years, MC = 1. The index is then a pure frontier – distance measure. In general, the choice of reference technology is important for the empirical result. If there is no strong reason to choose a certain base, an alternative originally suggested in Färe et al (1994), is to take the geometric mean of Mt and Mt+1, MG = [Mt Mt+1]1/2 Volym D:276 Supplement 28 In calculating the efficiency measures in Section 3.2 on which the subsequent index is based, we have confined ourselves to the model with returns to scale. With regard to comparisons over time, this is fully plausible, since differences in returns-to-scale assumptions have greater implications for efficiency measures between production units in a cross section. However, in the other cases we apply both CRS and VRS models. 2.3Interpretation of efficiency scores and productivity change There are several reasons to be careful with interpretation of the empirical results of efficiency and productivity studies. For a start, what has come to be called efficiency measures is nothing but measures of distances from production units to a frontier. Especially in with variable returns to scale, the frontier envelops closely around the data set. This means that a production unit may be at the frontier not because it is a well performing unit, but just because it lacks competition in that segment of the frontier. Typically, a closer look at a small frontier unit reveals it to be a rather poorly performing unit in terms of partial productivities. But given its size, it is still a frontier unit with efficiency score of 1. One should therefore check which units are so-called self- evaluators, in the sense that they lack competition, from other units. In this respect, returns to scale is more robust, and in general one should, expect rather large differences between efficiency scores generated by DEA-VRS compared to DEA-CRS for small and large units. As discussed above, because of the inherent properties of the frontier techniques applied here, one should expect SFA to give higher mean efficiency, a smaller dispersion in a cross-section, and smaller variation over time than . The reason for this is that, in the case of SFA, part of the variation in data is referred to random noise, while in all deviations from the frontier are assumed to be inefficiency. Moreover, in the case of panel data estimation, another share of the variation in data is picked up the bank-specific effect. This component is meant to adjust for permanent differences in bank behaviour, which means that permanent inefficiency is caught by this component. Thus, the bank specific effect may also contain inefficiency, and then further reduce the explicit inefficiency scores. In comparison with many other industries, one should also expect a lower degree of mean efficiency and a larger dispersion in efficiency scores; i.e., between best practice and worst practice in the banking industry. The main reason for this is the rather low competitive pressure in the banking industry in combination with a mixture of banks with different types of ownership and objectives, commercial banks, cooperative banks, and not-for-profit savings banks. A related reason is the regulatory structure facing banks in different countries, which may further increase the distance between best practice and worst practice in international comparisons. The rate of productivity change may also influence the distance between best practice and worst practice. During periods of rapid technical progress at the frontier, many production units may have difficult catching up and lag behind for some time, causing a decrease in mean efficiency. On the other hand, during periods of slow technical progress at the frontier, one would expect units below the frontier to catch up, causing an increase in mean efficiency. Concerning interpretation of productivity change measures, one should bear in mind that, in general, productivity measures are rather model-dependent; see Kumbhakar et al (1999). This is also the case for productivity indexes. Usually Laspeyre and Paasche indexes constitute the outer bounds, with, for example the Tornkvist index in between. This is also true for the index: The index based on the reference technology for year t (Laspeyre) often shows higher values than the index based on the reference technology for year t+1 (Paasche). Volym D:278 Supplement 28 3.1Swedish branch office productivity change Analyses of productivity or efficiency at the branch office level are very rare; one of the few studies is et al (1991). This study covers the period 1983 to 1989 for the branch offices of one of the biggest Swedish commercial banks. The main reson for including this somewhat old study here is to show the large variation in productivity change between years at the bank office level and the large variation in efficiency among offices within a single bank. Data was derived from a computerised statistical system for labour-input measurement. The overall activity at the bank offices is specified and divided into about 700 points of measurement, then translated into time using the MTM standard. The various measurement points can be aggregated into a smaller number of activities or outputs. The following output variables are included in the analysis: Deposits; this refers to activities directed to the acquisition of savings and to related services. Cashing; this refers to cash-payment activity either in the bank offices or via a . Loans; this refers to activities related to the granting of credit. Trusteeship (Notariat); this refers only to the administration of assets which is related to the branch offices' depots. In the big cities, there are central notary (trust) departments that administer assets for a large number of . These departments are not included in the study. Foreign Related; this includes, foreign currency and travellers cheques as well as payments to abroad undertaken directly by the office. The bulk of foreign transactions are executed at centrally based and specialised departments using computers. These are left out of the analysis. Fund; this refers to that portion of the securities trade that is undertaken at the offices (delivery, swaps, payments etc.). Even here there exist centrally-placed functionaries who administer transactions and operate on the market (the stock exchange). These are not included either. Lawyer; this is a collective expenditure item used for those few offices which have their own bank lawyer. The following inputs are included: Time worked: full-time white-collar workers are assumed to put in 92400 minutes, in other words 1540 hours. Information technology, IT: costs for administrative data processing, measured in kSEK. Office space: measured in square meters. to a statistical reorganisation between 1987 and 1988, these two years are not fully comparable. We thus divide the sample period into two parts: 1983-1987 and 1988-1989. The number of offices in the sample varies from 133 to 135. We also note the following: 1984 and 1985 were years of low production across the board, the sharp decline having set in during 1983. This decline was reversed into an increase for 1986-87. Costs for information technology increased for all years. Office space, not unexpectedly, remained for the most part . Table 1a shows productivity growth for a constructed average office (using the arithmetic mean), while mean (unweighted) productivity growth for the offices is presented in Table 1b. Productivity changes for the average office, per cent MTP is the total productivity index, MC the catching-up – lagging-behind component and MF the frontier shift component derived in section 2.2. (Here, the first year is the reference year.) Productivity changes for the office mean, per cent The MTP value of -22 from 1983 to 1984, in Table 1a, indicates that total productivity fell by 22 per cent. The catching up component, MC, shows that the average fell slightly further behind the frontier, in spite of the large negative shift of the frontier itself, MF. After a notable decline in productivity between 1983-85, it rose by 34 per cent between 1985 and 1986, levelled out between 1986/87, and rose once again, by 14 per cent, between 1988 and 1989. Thus, the first two years show a negative productivity growth, which is hardly surprising given the sharp decline in all the output variables during these years. The MC measure suggests that the distance between the frontier and the average remained, roughly, over the sample period. The development of the unweighted arithmetic mean for the offices is slightly different from that of the constructed average office, reflecting the effects of the size distribution. The catching-up effect varies much more substantially here. The distance between the frontier and the average fell during 1983/84, rose during 1984-86, and fell for the remaining years of the sample. The differences between Tables 1a and 1b with regard to figures for 1983/84 indicate that it was the slightly larger offices on the frontier which experienced a reduction in efficiency. Though there was a reduction in labour input from 1983 to 1985, computer input increased, while office-space remained . The decline in labour productivity was, therefore, much less than that for the other inputs; see Table 2, which presents results from a model where labour is the only input, but where the outputs are the same as in the main model. Labour productivity change for the office mean, per cent The pattern is the same as that for total productivity although the labour productivity decline for 1983/84 was smaller. Moreover, labour productivity rose markedly in 1986/87, while MTP was almost . Development of the individual offices We have differentiated the individual offices with respect to their rate of productivity growth. Table 3 presents the number of offices with total productivity growth exceeding 5 per cent per year, the number from 5 to 2 per cent per year, those from 0 to 2 per cent per year, and the number of offices with negative productivity change. The drastic change in productivity growth between the periods 1983/85 and 1985/89 is indisputable. While only a few offices had some productivity growth during 1983/85, the reverse is true for the second sub-period, though during 1986/87 almost half of the offices showed negative productivity growth. Number of offices in different ranges of productivity change The spread of efficiency between offices together with the average offices efficiency; i.e., its distance from the best-practice frontier is highlighted in Table 4. Volym D:282 Supplement 28 Number of offices in different ranges of efficiency and structural 1 < E > 0,90 0,90 < E > 0,80 0,80 < E > 0,70 0,70 < E > 0,60 Structural efficiency during the period was within the interval 0.72-0.80. This implies that if all offices had been on the technology frontier observed output volumes could have been produced using between 20 and 28 per cent less inputs than was actually the case. Though this is a relatively common measure for structural efficiency in this type of analysis, the realisable productivity improvement potential is likely to be lower. The existence of a number of rigidities explains some of the differences in efficiency. Moreover, the offices are not as homogeneous as the analysis assumes. The shape of the efficiency distribution shows relatively variation. However, the number of frontier units varies considerably over the years. The results are summarised as follows: Total factor productivity increased strongly during 1985-89 Labour productivity grew somewhat more than total factor productivity Productivity growth was relatively uneven with a decline during 1983-1985, strong growth for 1985/86, low growth for 1986/87, and relatively strong growth for 1988/89. The distance between the frontier and the average has changed only minimally. Productivity growth varies markedly between branch offices. The structural efficiency measure suggests a productivity- improvement potential of 20-28 per cent; however, the realisable potential could be much lower. The spread of efficiency varies relatively over the years. 3.2Swedish banking efficiency and productivity change In this section we report on a study, Battese et al (1997), investigating efficiency and productivity change in Swedish banks during 1984-95 using the SFA approach, with an input requirement frontier model, in which the amount of labour used is a function of the outputs and the quasi-fixed inputs, the number of branches and total inventories. The data set was obtained from the annual reports of Swedish banks. The data is not from a sample, but the entire population of Swedish banks. The data involved are for the years, 1984 to 1995. During the period some banks ceased to exist and others were established. Some of the changes were due to amalgamations of banks, or to take-overs. The data is at the bank level rather than at individual branch level. the large national banks with a large number of branches report only aggregate data. Other small regional banks may involve only one branch, and so the data are for that bank which is identical to a branch. Data for some small banks was deleted from the analysis because the values of one or more of the variables were missing or were clear outliers. This was particularly the case with some banks with only one or two part-time employees. A total of 1275 observations for 156 banks are used in the analyses reported below. In the first year, 1984, the number of banks in the data set was 140 and after a peak of 146 in 1985, the number declined to 65 in the last year, 1995. A total of 59 of the banks were observed in all twelve years. The variables, public loans, guarantees, and deposits, are regarded as outputs. A key input variable of interest in a study of the efficiency of the banking industry is labour, because it is a significant component in the cost structure of banks. The efficiency of the use of labour in producing the relevant outputs, given the values of the quasi-fixed inputs, branches and inventories, is the focus of this study. Data on Other Loans and Other Costs were considered in preliminary analyses, but these variables were subsequently deleted because it was evident that there were problems with this data, perhaps due to changes in the definitions of the variables over the period. Data on variables, originally expressed in current money values, were deflated according to the values of the Consumer Price Index (CPI). , all money values are expressed in terms of 1980 prices. Volym D:284 Supplement 28 Labour use varied from about 800 to over 20 million employee hours per year. The values of public loans, guarantees, and deposits, also indicate the considerable variation in the size of the banks. The average number of years for which the banks were observed was about 10 years. The individual technical inefficiencies of labour use for the banks range from to over the period. Thus, one bank was estimated to be fully technically efficient in labour use in at least one year, whereas another bank was estimated to use more labour than for a fully efficient bank with the same level of outputs and quasi-fixed inputs. The overall mean for the 156 banks was inefficiency. This is rather low, but one should keep in mind that a stochastic frontier model with bank-specific effects absorbs part of the inefficiency (in addition to the random noise component). Of the 13 banks with inefficiency more than in the last year they were observed, 10 disappeared from the data set before 1995. Of the three surviving banks, two were savings banks and the other was a recently started international bank with a non-typical output structure. Mean technical inefficiencies of labour use for the banks are graphed by year in Figure 3. Mean technical inefficiency of labour use for Swedish banks, 1984- 1995, per cent Mean technical inefficiency tended to increase from 1984 to 1991, during the period of rapid expansion when the banks were in vigorous competition for market shares. After the crisis in 1992, mean technical inefficiency decreased slowly. Overall, there was a slight increase in mean technical inefficiency of labour use over the twelve-year period. The results also indicate that the efficiency by the banks tend to: be larger for , banks than for Other Banks; be smaller for SE-banken than for Other Banks; decrease as the number of branches increase; increase as the total inventories increase; Because inventories are measured by book values, they reflect the modernity of these and especially for computer equipment with short depreciation periods. Thus, the efficiency-increasing effect of inventories should reflect the productivity-enhancing effect of more modern computer equipment. The mean technical inefficiencies of the five types of banks, considered in the study, are given in Table 5. The difference between the two largest commercial banks is striking. Volym D:286 Supplement 28 Mean technical inefficiency of labour use by bank type, 1984-95 Technical Inefficiency (%) 1: () (Co-operative; Particular bank 2: () (Commercial; Particular bank) 3: Sparbanker (SB) (Savings; Several banks) 4: SE-banken (SE) (Commercial; Particular bank) 5: Other Banks (Commercial; A few banks) While had an inefficiency level below for all years, SE-banken exceeded for all years, except 1984. During the banking crisis, was never perceived as a crisis bank, while SE-banken was. One reason for the somewhat lower loan losses at , compared with SE-banken and certain other Swedish banks, is usually attributed to the fact that never abandoned its local branch networks as sources of decision-making about credit allocation. Moreover, the strong local authority at branch-offices was combined with a system of profit sharing for bank staff. Among the savings banks, there was substantial variation in inefficiency not reflected in the aggregated figure in Table 5. Most of these banks are local or regional banks operating as not-for-profit organisations. The same holds for the local or regional branches of . This bank specialised in credit to agriculture and small businesses before it merged with the largest savings bank in 1997. Technical change and efficiency change The rate of technical change (TC) in labour use is estimated to be negative for all years, but small in absolute values, see Figure 4. This indicates that there was modest technical progress in the frontier labour use during the years of our study. Starting at technical progress of in 1984, the industry continued to have technical progress, but at a decreasing rate, until 1992, when technical progress in labour use was effectively exhausted. Among the bank types, only experienced technical regress in labour use over the entire period. Inefficiency (IC) change of labour use over time was positive during 1984-1992, see Figure 4. This indicates that the inefficiency of labour use increased over those years. Thus the average bank did not manage to catch up with the labour-use frontier, which was experiencing technical progress. However, when technical progress in labour use was effectively exhausted in 1992, the banks began to catch up, i.e., the distance between observed labour use and the best-practice labour use The dynamic interplay between changes in the frontier (technical change) and changes in inefficiency is discussed in more detail in (1973), Førsund and (1974) and Førsund, and Summa (1996). One might have expected a much stronger impact of deregulation and the subsequent banking crisis on the efficiency of labour use in Swedish banks. An important reason why this did not occur might be the rapid return of Swedish banks to profitability which restored their access to capital markets. Most of the so-called crisis banks recovered rather rapidly; some were able to raise money from the capital market as early as 1993. Moreover, competitive pressure from abroad remained weak. Technical change (TC) and inefficiency change (IC) in labour use by Swedish banks, 1984-1995 Figure 5 shows the relative movement of outputs, inventories and labour hours over the period, relative to 100 at the branch level in 1984. Volym D:288 Supplement 28 Development of mean output and mean input A major reason for the banking crisis in 1992 was the dramatic increase in the real rate of interest causing large changes in household and company portfolios with extensive repayment of old loans and less demand for new loans. Although deposits decreased somewhat in 1992, public loans, guarantees and inventories decreased substantially, and adjustments in the labour use was not at the same rate. Inefficiency of labour use varied considerably for different banks over the period; overall inefficiency was estimated to be about . This implies that banks, on average, were using about more labour than if they were fully efficient, given the levels of outputs and quasi-fixed inputs. An unexpected pattern emerges concerning the impact of deregulation and the subsequent banking crisis on technical change at the frontier. There was a decrease in technical change at the frontier and an increase in mean technical efficiency. While the development of efficiency seems to be driven by the frontier change, the change in the frontier is to a large extent driven by the development of output. Dramatic increases in the real rate of interest caused large changes in household and company portfolios, with extensive repayment of old, loans and less demand for In general, the frontier banks did not manage to adjust the labour use in proportion to the decline in output. 3.3The efficiency of Swedish banking in 1996 In addition to the analysis in the previous section, we have calculated efficiency scores for Swedish banks in 1996. To investigate the sensitivity of the results with respect to the choice of variables, we compare the outcomes of different specifications under variable returns to scale (VRS) and returns to scale (CRS). The variables in this data set overlap with the previous one. We use the same basic three output variables, loans, guarantees, and deposits, but now we also add net provisions, i.e., the difference between commissions and other service charges received and the costs related to these. On the input side we use the number of branch offices, inventories, other costs, credit losses, and labour costs, or alternatively, hours worked. Thus, one important part of this section is to investigate the sensitivity of the results with respect to the choice of variables. Not including net provisions might "punish" especially the commercial banks or the larger banks. On the other hand, banks with large net provisions may also have more high-salary staff; therefore, we also use labour costs as a quality-adjusted labour input variable. See Table 6 for the differences between the models. We will also look at labour efficiency; i.e., we have calculated efficiency distributions for Models 1-4 but with only one input, labour. The difference between the models applied Volym D:290 Supplement 28 Empirical results are illustrated in Figures 6-11. We regard Model 1 as the base model, while Models 2-4 are used for sensitivity analysis. In general, with so many variables one would expect a rather large number of fully-efficient units (efficiency score = 1) under VRS, and this is also the case: Somewhat more than half of the units are on the frontier in Model 1; see Figure 6. On the other hand, under CRS, less than one fourth of the units are on the frontier. Mean efficiency decreases from 0.90 under VRS to 0.79 under CRS. All 17 units, which are on the frontier under VRS but not under CRS, are savings banks.