sou · GOB311d5 · 2001-01-01 00:00:00 — While deposits decreased somewhat, loans and guarantees decreased substantially, and it was obviously not possible to adjust labour use at the same rate. The 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 minor impact on the efficiency distribution. 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 deviation between models is striking for some savings banks. In a Scandinavian comparison, the Swedish banking sector in 1990 was much more productive than the Finnish, Norwegian, and Danish This conclusion also holds for the largest banks. The large gap between Swedish and Finnish average productivity is mainly due to the efficiency component, although also has a technology advantage. In a European comparison, Swedish commercial-banking efficiency ranks second from the bottom, both in a two-input model and in a labour use model. Important caveats here are the small sample of banks included in the study, and the small number of inputs and outputs covered. In general, there is large variation in efficiency between banks both within each country analysed and across countries. In comparison with many other industries, one should also expect lower 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 different regulatory structures facing banks in different countries, which may further increase the distance between best practice and worst practice in international comparisons. Concerning the international competitiveness of Swedish banking, we thus observe a large variation between best practice and worst practice banks in all countries and across countries. In a European comparison the results suggest the average productivity of Swedish banks to be rather low, while in a Scandinavian comparison, we get the opposite conclusion. Volym D:264 Supplement 28 The purpose of this report is to analyse relative efficiency and productivity growth in the Swedish banking sector. We will survey some previous results for the Swedish banking industry, in addition to presenting some new results. One analysis focuses on productivity change at branch-office level. We are also investigating the impact on productive efficiency and productivity growth of the deregulation of the Swedish banking industry in the mid-1980s and the consequent banking crisis. The distribution of productive efficiency for Swedish banks in 1996 is analysed on the basis of a third data set. The final analysis compares the efficiency of large Swedish banks internationally. The purpose of this report is to analyze relative efficiency and productivity growth in the Swedish banking sector. In recent years, relative efficiency and productivity change in banking have been the focus of a lively debate, though there is still a lack of clarity as to its actual development. The banking sector has also received considerable attention in international studies. Traditionally, the areas of main interest have been analyses of economies of scale and economies of scope, though more recently a number of efficiency and productivity studies have been undertaken. In the aftermath of liberalisation, restructuring, and deregulation of financial markets around the world, there is a recent boom, in activities directed to evaluating the performance of financial institutions. In a recent paper, and (1997) survey and contrast the results of 130 financial-institution efficiency studies. In addition to the many international studies, there are also a few studies based on data for Swedish banks; see (1999), Battese et al (1997), et al (1993), Heshmati (1997), et al (1991), (1998), and Kumbhakar et al (1998). In this paper we will summarise some previous results for the Swedish banking industry, in addition to presenting some new ones. A major problem related to the measurement of banking sector productivity is how to define, let alone measure, the sector's output. Triplett (1992), pointed out that progress in measurement of banking has been inhibited by two major unresolved but related questions: (1) What are the outputs? (2) What are the inputs? For instance, are deposit accounts inputs or outputs in its activity? This ambiguity of inputs and outputs was also highlighted by Wykoff (1992): When deposits are outputs, why are they so cheap? When they are inputs, why do people provide them to banks? Are bank services best measured by the number of accounts held and transactions executed, or should the value of transactions be used instead? Is the administration of these accounts really the most important aspect of banking? Is not the bank's role as intermediary between savers and investors the most important from the economic point of view? How would this be measured? For a thorough theoretical and conceptual discussion of these issues, see and (1992), Fixler and Zieschang (1992) and Colwell and (1992). Volym D:266 Supplement 28 Even in 'practical' work, there is an intense discussion relating to the measurement and valuation of a bank's output. Valuing bank production in national accounts has always been controversial. Given the guidelines used today, the banking and financial sector has only a weak contribution (positive or negative) to the growth of GDP. In relation to the revised international system of national accounts (SNA), a number of alternatives regarding the treatment of banking and financial activities have been suggested. In most cases, the suggestions would imply a marked increase in the sector's contribution to GDP. (1984) divided studies of banks' production into two distinct strands, depending on the nature of the analytical approach: the production approach, also called the service provision or value added approach the intermediation approach, also called the asset approach In the production approach, banks provide services to by handling their financial transactions, deposits, issuing loans, cashing cheques, etc. Here the number of deposit accounts, outstanding loans, foreign exchange transactions, etc., are the output variables, with labour and capital as inputs In the intermediation approach, banks are performing the two major roles of mobilising and distributing resources efficiently, in order to smooth investment activities in the economy. In this approach, the inputs are labour, materials, and deposits, while outputs are loans and other income generating activities to the banks, see e.g. Mester (1997). In some studies, the monetary volume of the deposit accounts and the loans comprise the output, while the costs of operation and the interest due are the inputs in the production process. This approach has two major sub- groups: (a) the profit approach, and (b) the risk management approach. In the profit approach, the bank managers target is to optimise the use of resources to maximise the banks profit function. In this approach, the bank manager cares for all types of costs in the banks and the output is the net income generated after incurring certain costs in the production process. In the risk management approach, banks transform assets, on the basis of evaluation of the risks attached to various forms of asset. In risk management, banks take some risks to produce acceptable returns. A bank's performance will affect its valuation in the market, its ability to acquire other banks or to be acquired at a good price, and its ability to be funded through deposits or financial markets. In both the production approach and the intermediation approach, the definition of output is strictly limited to production within banking. To what extent banks actually fulfill their role as producers of financial services lies beyond the scope of this analytical framework. This limitation is acceptable if the intention, as here, is to estimate productivity growth separately for different sub-sectors of the economy. Spillover effects between sectors would then manifest themselves as higher (or lower) productivity in those sectors which are exposed to these services. Increased productivity in the communications network, for exampel could be expected to spill over into higher productivity within transport-dependent sectors, while well-performing banks could lead to higher productivity in the whole economy, etc. These external effects could be important but, nevertheless, fall outside the scope of a purely sectoral productivity analysis. This report contains several pieces of empirical research related to Swedish banks. For a start, we will survey (and slightly develop) a few studies of efficiency and productivity change in Swedish banking. Then we will focus on the efficiency and productivity of Swedish banking in international comparisons. In one part of this report the production approach is used to review how one of the largest Swedish commercial banks use labour and capital to produce certain well-defined services at branch offices. However, we are not in a position to make any judgements on their quality. Instead, we will study only the development of productivity in services, under the assumption that their quality remains unchanged over the sample period.1 In other parts of this report, the intermediation approach is used. In these cases the sample is collected from banks´ annual reports. Here micro units are entire banks, with one or more offices. Because this report focuses on productive efficiency and productivity change, we use various kinds of frontier models, described in Section 2. The empirical results are presented in Section 3. 1 Other studies with a similar approach are and Gold (1985), Tulkens (1993) and Vassiloglou and Giokas (1990). In these studies, the analysis is based on the spread of efficiency between bank offices for a particular year. Volym D:268 Supplement 28 2Measurement of efficiency and productivity change Measurement of efficiency in the sense of evaluating the performance of production units against a benchmark or yardstick, under the heading of frontier analysis, is becoming increasingly widespread. Frontier analysis provides a ranking of production units in terms of their efficiency, and it also attributes a numerical efficiency value to each production unit. This makes it possible to identify best practice and worst practice in a sector, and the measurement of efficiency has in fact been the main motivation for the intensive study of frontier functions. Thus, for a variety of reasons, in recent years frontier analysis has become a very attractive and rather sophisticated way to benchmark the relative performance of production units. First, the notion of a frontier is consistent with the underlying economic theory of optimising behavior. Second, deviations from a frontier have a natural interpretation as a measure of the efficiency with which economic units pursue their technical or behavioral objectives. Finally, information about the structure of the frontier, and about the relative efficiency of economic units has many policy applications. One example is the setting of productivity targets in price-cap regulation of natural monopolies like electricity distribution. To serve as a meaningful benchmark, the frontier should represent best-practice technology or behaviour. This benchmark may be profits, costs or production. Estimation or construction of profit frontiers, cost frontiers, or production frontiers can be done in various ways. But since there is not enough information available on the technology of banking, and since organisation is also of great importance, the frontier itself represents observed best practice. i. e., studies of banking efficiency rely on accounting measures of outputs, inputs, costs, revenues, profits, etc. However, there are still several competing methods for determining the best-practice frontier. These methods differ primarily in the assumptions imposed on the data in terms of: Functional form of the frontier function, especially the choice between a parametric form and a non-parametric one. Stochastic properties, especially the choice between a deterministic and a stochastic approach. Distribution assumed for the inefficiency scores (usually half-normal, truncated normal, exponential, or gamma distribution). In this report we are only concerned with production frontiers; i.e., our data consists of output and input variables. In measuring efficiency we adopt the system introduced by Forsund and (1974), a generalisation of Farrells measures to a variable-returns-to-scale (VRS) technology2. The generalised Farrell measures are illustrated in Figure 1, where a one – input (X) and one – output (Y) production activity is assumed. The production units are denoted by A, B, C and D. In the case of returns to scale (CRS), the frontier is the straight line through B and only unit B is on the frontier; i.e., only unit B is a fully efficient best-practice unit, while units A, C, and D are inefficient. With the more flexible variable returns to scale technology, the frontier is supported by three units, A, B, and C; i.e., these units are fully efficient, while D is still inefficient. A measure of efficiency is the distance between an inefficient unit and the frontier, which can be measured in several ways. Here we focus on input-saving (or input-oriented) efficiency. Another option is output- increasing (or output-oriented) efficiency. In the case of CRS, these measures coincide; see Forsund and (1974 and 1979b). The input-saving measure shows what proportion of observed input would have been necessary to produce observed output, if the unit in question were on the efficient frontier. Similarly, the output-increasing measure shows the ratio between observed output and how much output could 2 The basic idea of measuring efficiency on the basis of frontiers goes back to Farrell (1957), who introduced a deterministic non-parametric programming approach. The next step was taken by and (1968), who introduced the deterministic parametric approach, which was then generalised by Forsund and (1979a). At the same time, Charnes, , and (1978) developed data envelopment analysis, , as a much more convenient way to calculate Farrell efficiency measures on the basis of a non-paramtreic programming approach. Econometric estimation of frontier functions was introduced by (1974), although the most popular so-called composed error model appeared in two independent papers by et al (1977) and Meeusen and van den Broeck (1977); for recent surveys, see (1993), Lovell (1993), and Grosskopf (1996). Volym D:270 Supplement 28 have been produced, with observed input and frontier technology. Efficient frontier units have a value of 1, inefficient ones less than 1. An illustration of efficiency measures VRS efficiency measures for any unit at D are: The CRS efficiency measure is = ND/NG = technical efficiency Unit D will be both input-saving and output-increasing inefficient under VRS, since HJ/HD < 1 and ND/NL < 1. There are several summary measures of the efficiency of the entire sector, so called structural efficiency measures. One such measure is the mean of efficiency scores, or a size-weighted mean of the efficiency scores. Another is based on the average unit (an arithmetic or geometric mean of the industry), for which input-saving or output-increasing efficiency measures can be calculated. As regards determination of the frontier, two approaches dominate today: SFA = Stochastic frontier analysis – the dominant econometric approach = Data envelopment analysis – the dominant programming approach SFA uses a parametric representation of technology, along with a two- part composed error term. One part of the composed error term represents statistical noise, and is assumed to follow a normal distribution. The other part represents technical inefficiency, and is usually assumed to follow a skewed distribution such as a half normal, truncated normal, exponential, or gamma distribution. One problem with cross-sectional data in efficiency measurement is that technical inefficiency cannot be separated from firm-specific effects, which may not be related to inefficiency. This problem can be avoided if panel data is available. (By panel data, we mean data on a cross-section of firms, each observed for a number of time periods.) Then the residual may be split into four components; a firm-specific effect, a time-specific effect, an inefficiency component, and random noise. Often the time specific effect is replaced by the explicit introduction of technical change in the production function. One weakness with SFA is that if the functional form is mis- specified, measured efficiency may be confounded with specification errors. Another weakness of this approach is its limited usefulness in the case of multiple output – multiple input production when input price data is not available. A third weakness is its sensitivity to heteroscedasticity; i.e., the impact on the estimated efficiency scores when firms in a cross-section vary widely in size. If this is not accounted for, one would expect overestimation of the intercept of the frontier function and underestimation of the slope coefficients; see Caudill and (1993). The major competing frontier approach is the very popular non- parametric data envelopment analysis () approach. This approach imposes less structure on the frontier, which is formed as the piecewise linear combination of best-practice units, yielding a convex production possibilities set. Moreover, it is easy to apply in the case of multiple output and multiple input. It involves the construction of a technological frontier via the estimation of a piece-wise linear convex technology that envelops the data, as in Figure 1. The frontier technology encompasses the fully efficient units, while the efficiency of the rest of the units is measured as deviations from the frontier. A key drawback is that there is no random error; i.e., the approach is deterministic (although there have been attempts to introduce stochastic properties). Another weakness of this approach is its sensitivity to some factors: It is sensitive to outliers; i.e., units that are extreme in some sense (e.g. small offices run by workaholics) Volym D:272 Supplement 28 An increase in the number of outputs or inputs leads to an increase in efficiency scores. In small samples with many variables almost all units may be on the frontier. An increase in the number of production units yields a decrease in efficiency scores. Thus, a comparison of efficiency levels across industries requires adjustment for sample size; see and (1998). It is not possible to determine which of the two major approaches dominates the other, since the true level of efficiency is unknown. Because in all deviations from the frontier are interpreted as inefficiency, the SFA approach normally yields higher efficiency levels than . A more technical description of the two approaches is given in Appendix 1, which presents the mathematical formulation of the models applied in this report. The general definition of total factor productivity, TFP, is the ratio between an output index and an input index. This definition raises the question how outputs and inputs should be aggregated in the respective indexes. If a production function is used as an aggregator, the weights will be the marginal elasticities on both the output and the input side. This is the conventional aggregation approach. Another type of aggregation is the proportional shrinking of an input vector and proportional expansion of an output vector. This is the aggregation performed in the so-called productivity index discussed below. We are often not so much interested in TFP per se, but in comparisons of TFP over time or across regions. Thus, TFP comparisons are binary comparisons between two observations in time or in space, while as we saw above, efficiency is measured against a common reference technology – the frontier. For a parametric production function, the change in TFP over time is usually measured by the shift in production possibilities, which is the same as technical change. This is the time-trend approach. TFP is then the change in the output vector minus the change in the input vector; i.e., the residual factor of output growth net of changes in inputs. This is the definition used in the econometric, SFA, models discussed in this report. With however, which is non-parametric, productivity change can not be investigated by a time trend approach. Instead, the total productivity (MTP) index has come to dominate productivity research based on frontiers. The MTP index is only based on quantity variables, but nevertheless knowledge about at least one technology is required. This index and its parts can be expressed completely in terms of Farrell efficiency measures, so the need for technology information boils down to being able to calculate these measures. Thus, MTP fits very well as a complement to DEA3. Thus, the productivity index offers an alternative way to measure productivity at a sectoral level. A graphical presentation of the total productivity index is provided in Figure 2. Here we illustrate the construction of the input-oriented or input-based index. 3 Originally, within a consumer theory context, (1953) introduced the notion of proportional scaling of quantities observed in year t2 to allow a consumer the same utility level as in year t1. The proportional scaling factor was interpreted as a quantity index. Caves et al (1982) developed the idea to a productivity index proper. However, the link to was first developed by Färe et al (1994), (originally a working paper in 1989). They showed the relative ease with which the index could be calculated in the case of piecewise linear frontiers and since then there has been a rapidly increasing number of empirical applications. The additional attraction added by Färe et al (1994) was to maintain inefficient operations and decomposing productivity change into efficiency improvement and production frontier shift in the general case of multiple outputs and inputs, thus generalising the parametric single output approach in Nishimizu and (1982). Volym D:274 Supplement 28 Construction of the total productivity index, MTP P is a production unit observed for two years, t and t+1. Between these time points the frontier function has shifted from ft to ft+1. In year t, technical efficiency for Pt measured against ft is Et,t = OC/OD where the first index denotes the frontier year, and the second index denots the observation. Measured against ft+1 technical efficiency for pt is Et+1,t = OA/OD Correspondingly, technical efficiency for Pt+1 relative to ft+1 is Et+1,t+1 = OB/OE and measured against ft it is Et,t+1 = OF/OE The input-based productivity index with frontier technology ft as the reference may then be written as M t = Et,t+1 The input-based productivity index with frontier technology ft+1 as the reference may be written as M t+1 = Et+1,t+1 M >1 means productivity improvement, while M<1 means productivity decline. The index can be decomposed into two components, MC and MFi. MC is the change in efficiency relative to the frontier: i.e.,a catching up productivity index: MC = OE = Et+1,t+1 OC Et,t MF is the change in distance to the frontier; i.e., a productivity index: , i, j = t,t +1 i j