A DEA study to evaluate the relative efficiency and investigate the reorganization of the credit department of farmers’ associations in Taiwan

In this study data envelopment analysis models were applied to evaluate the relative efficiencies of the credit departments of farmers' associations (CDFAs) in Taiwan. The findings show that the overall efficiency scores are not best and scale for CDFAs in Taiwan is relative small. It implies that the reorganization of the CDFAs may be appropriate if more efficient organization is to be pursued. Thus, this study investigated CDFAs reorganization to increase the efficiency. The proposed CDFAs reorganization alternatives have higher average efficiency scores than the current CDFAs.

This article presents a case study in which data envelopment analysis (DEA) (Charnes et al., [6]; Banker et al., [1]) was applied to evaluate the relative efficiencies of the credit department of farmers' associations (CDFAs). Efficiency measurement is an important issue for CDFAs in Taiwan. However, little research has been done to evaluate the relative efficiencies of the CDFA (Liu, 2002). Many existing evaluation techniques measure the efficiency applying variations in accepted accounting or by means of ratio analysis (Golany and Roll, [13]). In practice, few techniques have been satisfactorily applied for measuring the relative efficiency. However, lack of vertical and horizontal integration, overlapping institutional regulations, rapid technological change and increased competition from the deregulated banking industry have strongly influenced the profitability of CDFAs and to a certain extent, the long-term viability of the rural financial market (Chang and Hsieh, [5]). Hence, CDFAs need an effective method to evaluate the relative efficiencies, to understand the CDFAs resource utilization and to be able to communicate the results with the stakeholders. The problem of efficiency evaluation usually involves multiple input and multiple output factors.

In this study, we conducted DEA to distinguish between the efficient and inefficient CDFAs. The use of DEA for evaluating the relative efficiencies of CDFAs showed a good understanding of the resources utilization of each CDFA. Based on the efficiency analysis, this study investigated the reorganization of the CDFAs and proposed different alternatives for reorganizing the CDFAs to improve the overall efficiency of CDFAs.

The organization of this article is as follows. Section II presents the foundations of the DEA models and reviews the related literatures. Section III reports the results and the final section is the conclusion.

The efficiency is measured applying the ratio of the aggregated output to the aggregated input. Following Charnes et al. ([6]), an evaluated entity is said to be efficient if it is not possible to increase (decrease) the level of an output (input) without increasing the use of at least one other input or decreasing the generation of at least one other output. This definition has the same concept as that in the Pareto optimality that all of the nondominated entities have the highest efficiency score. The entities that lie on the efficiency frontier are efficient in the DEA model. In contrast, the entities that do not lie on the efficiency frontier are regarded as inefficient. Data envelopment analysis models have been effectively applied for measuring the relative efficiency of the decision-making units (DMUs) in many fields. The original DEA model, Charnes et al. ([6]) and subsequent extensions of it can be found in Cooper et al. ([10]) and Thanassoulis ([20]).

The DEA method is a deterministic nonparametric frontier approach that adopts the concept of relative comparison. In comparing the credit departments of farmers' associations being evaluated with one another, a mathematical programming approach that originated with Farrell ([12]), who used mathematical programming techniques to search for the efficient frontier, namely the efficient production function, this frontier being one of the so-called deterministic nonparametric frontiers. Farrell then used the actual observation points, as well as their positions in relation to this frontier to determine the technical efficiency.

This concept was further expanded by Charnes et al. ([6]), who, in performing an evaluation of nonprofit institutions, formed linear combinations of each of the output and input factors being evaluated and took the relative values of two of these linear combinations to represent the efficiency of the institutions being evaluated, namely in making the optimal choice under the most advantageous conditions among the units being evaluated, the efficiency values of the various institutions would all lie between 0 and 1, with the most efficient DMU having an efficiency value of 1. That is, it was hoped in the DEA model that all of the efficiency values of the DMUs would be less than or equal to 1, which would give one particular DMU the best weighted values for its factors, which would in turn increase the efficiency value of the DMU. For this reason, the DEA model may be expressed as a linear programming model with fractional components. Because the model is such a linear programming model with fractional components, as well as a nonlinear model, it is extremely difficult to solve and involves the use of a series of mathematical and technical transformations which take the form of a linear programming model, referred to here as the CCR model. Subsequently, Banker et al. ([1]) developed the BCC model, which was based on scale efficiency considerations. The principal difference between this model and the CCR model is that the BCC model allows for variable returns to scale, while the CCR model assumes constant returns to scale. The BCC model may thus be used to calculate the pure technical efficiency of each decision-making unit.

In this study, two DEA models were applied: CCR model and BCC model. In particular, the CCR model produces constant returns to scale (CRTS) efficiency frontier. The evaluated relative efficiency of the CCR model is an overall (or aggregated) efficiency score. In addition, the efficiency scores of all DMUs are set to be between 0 and 1 in the DEA models.

The BCC model produces variable returns to scale (VRTS) efficiency frontier and evaluates both the technical efficiency and the scale efficiency. Thus, the overall efficiency can be decomposed into the technical efficiency and the scale efficiency. Indeed, the value of technical efficiency times the value of scale efficiency equal to the value of overall efficiency. Therefore, a DMU is overall efficient if and only if it is both technical efficient and scale efficient. A DMU that is not overall efficient could be either technical inefficient or scale inefficient or both technical and scale inefficient. Applying BCC model can specify the major sources causing overall inefficiency.

Relevant studies on mergers among financial institutions involve cost efficiency analysis based on data after the merger has taken place (Mester, [17]; Berger and Humphrey, [4]; Berger and Mester, [3]). Only a few such studies are concerned with cost efficiency models based on the institutions before the merger takes place (Savage, [18]; Shaffer, [19]). As for the method adopted to evaluate the results of the merger, the financial ratios are compared before and after the merger, especially those related to profitability, such as the return on assets (ROA) and the return on equity (ROE) ratios, to judge the results of the mergers. However, because Taiwan lacks real examples of mergers (Liu, 2002), such empirical methods are inappropriate. Many different views currently exist in Taiwan regarding mergers involving farmers' associations. In the past, mergers among farmers' associations took place because their operating structures were relatively weak, their membership was decreasing, agricultural conditions were inadequate and because administrative district boundaries were redrawn, leaving no alternative but to merge. However, the mergers did not strengthen operating structures, or have other positive effects. Furthermore, the past contributions of the literature can largely be classified as fitting into either one of two kinds, namely, the nonfrontier approach and the frontier approach. The former focuses on the statistical method used, which is based on the average concept of efficiency value, without considering the economic meaning of efficiency, while the latter focuses on the efficiency aspect, being based on the concept of Pareto-efficient outcomes. This latter approach incorporates the frontier concept and consequently conforms more closely to the economic meaning of efficiency. The nonfrontier method is frequently applied in financial management and involves applying factor analysis or principal component analysis to select certain financial ratios to serve as variables for constructing a statistical model to perform the analysis. The statistical models adopted include analytical models based on regions, PROBIT models and LOGIT models, which are mostly used in the selection process and which have statistical meaning. Furthermore, in terms of the approach adopted for performing the statistical analysis, numerous hypotheses must be developed before proceeding, which does not conform to the meaning of efficiency as originally defined by Farrell. Therefore, this study adopts the frontier approach, which has economic connotations, to conduct the analysis.

In terms of the empirical analysis, the evaluation of the efficiency of the frontier approach may also be divided into two further approaches, namely, the parametric and nonparametric approaches. In contrast with the parametric approach, the nonparametric approach does not determine a priori the functional form of the production frontier. For this reason, it is not limited by the functional form and also does not require the many assumptions that arise from the use of statistical methods for function estimation and efficiency measurement. Moreover, the nonparametric approach is more straightforward than the parametric approach in terms of dealing with the evaluation problems associated with many outputs and inputs. For this reason, this study adopts the nonparametric approach for the subsequent empirical analysis.

This section details an empirical study applying DEA to measure the relative efficiencies of the CDFAs. Furthermore, we discuss possible alternatives for the reorganization of the CDFAs. Following Golany and Roll ([13]), this empirical study involves the following tasks: (1) determination of input and output factors for measuring the relative efficiency of the selected DMUs and (2) the discussion of the DEA results from both the CCR model and the BCC model.

According to Keeney and Raiffa ([14]), a desirable set of measurement factors should be complete, decomposable, operational, nonredundant and minimal. There exists considerable disagreement in finance literature on the definition of outputs and inputs of a financial institution. In general, two alternative approaches–i.e. 'intermediation or asset' and 'value-added or production'–have evolved (Ellinger et al., [11]). In terms of measuring efficiency, the production approach lays emphasis on the operating costs of the bank and is suitable for measuring overall efficiency. Meanwhile, the intermediation approach, besides considering overall bank operating costs, also focuses on measuring bank competitiveness. This focus arises because the intermediation approach serves as the principle for determining the bounds of the input and output variables used in this study. Thus, two output items are obtained, namely, loans and noninterest income, along with three input items, namely, salaries, funds and noninterest expenditure. The present data are obtained from the annual reports for each level of farmers' associations in Taiwan for 2001.

For the validation of the developed DEA model, we examined the assumptions of the 'isotonicity' relationships between the input and output factors, i.e. an increase in any input should not result in a decrease in any output (Charnes et al., [7]). Following Golany and Roll ([13]), regression analysis on the selected input and output factors is a useful procedure to examine the isotonicity relationships between the input and output factors. If the correlation of the selected input and output factors is positive, these factors are isotonically related and can be included in the model. The factor that has a weak isotonicity relation to the other factors should be re-examined. Alternatively, a strong correlation may indicate that the information contained in one factor is already represented redundantly by other factors. In addition, according to Golany and Roll ([13]), the number of DMUs should be at least twice of the total number of input and output factors considered when applying the DEA model. In this study the number of DMUs was 277, at least twice of the selected five factors. We concluded that the developed DEA model of this study had high construct validity.

In this study, we applied the CCR model, with constant returns to scale, to evaluate the overall efficiencies of all DMUs. The results of the CCR model are shown in Appendix Table A1. In addition, we used the BCC model, with variable returns to scale, to evaluate the technical efficiency and the scale efficiency. The results of the BCC model are discussed in the next section. Both the dual linear programming formulations of the CCR and BCC models were run 277 times, i.e. one for every DMU.

Based on the CCR results, the efficiency values can be obtained for the farmers associations in each village, township and city, as listed in Appendix Table A1. The empirical results regarding the operating efficiency of the farmers' associations at the village, township and city level in Taiwan show that their average technical efficiency is low. This result appears to hide the fact that these DMUs, because of their relatively small regional spheres of operation, do not possess economies of scale, or possibly, because they have experienced problems with their internal controls, they have been unable to compete with other institutions and have also been hampered by poor quality staff. Therefore, we used BCC model to decompose the total efficiency and to evaluate the technical efficiency and the scale efficiency in the next section.

We used BCC model to evaluate the technical efficiency and the scale efficiency of the CDFAs. The results of BCC model can show the major sources of inefficiency among the 258 inefficient districts (as shown in Appendix 1 Table A1) and also provide possible improvement directions to promote the overall efficiency for each inefficient CDFA. We found that 190 of the 258 inefficient CDFAs had the technical efficiency scores higher than the corresponding scale efficiency scores. The CDFA that has the scale efficiency less than 1 is called scale inefficient. This result implies that the overall inefficiencies of the eight districts are primarily due to the scale inefficiencies. A scale inefficient DMU that exceeds the most productive scale size will present decreasing returns to scale. Alternatively, a scale inefficient DMU that is smaller than the most productive size will present increasing returns to scale. For example, as shown in Appendix Table A1, the DMU 5 and 9 CDFA have the technical efficiency scores equal to 1, but the scale efficiency scores are less than 1. These two districts are technically efficient yet scale inefficient. They can possibly increase (decrease) their operation scales to improve their overall efficiencies because they present increasing returns to scale and decreasing returns to scale as shown in Appendix Table A1. These results implied that the relative scales of these CDFAs have unbalanced status. Thus, reorganizing the existing CDFA is one way to adjust the unbalanced scales and thus improve the returns to scales.

Based on the efficiency analysis, this study investigated the reorganization of the CDFAs and proposed two reorganization alternatives for discussion. In this study, we investigated two possible reorganization alternatives to reduce the number of CFDAs and to improve the resource utilization of the CDFAs. Summaries of the two different reorganization alternatives are presented as follows.

The evaluation of efficiency is basically only a process, the ultimate objective of which is to find out where the shortcomings of an institution lie, enabling improvements and increased efficiency. The approach adopted to improve efficiency can be implemented by adjusting institution inputs or outputs, for example, through slacks variable analysis, thus increasing efficiency. This is the approach already explained by Charnes et al. ([6]) when referring to their version of the DEA analytical method (CCR). Additionally, another method exists for improving the efficiency of the CDFAs, which consists of increasing their overall efficiency. For this reason, this study adopts the reorganization principle and increases the operating scales of small institutions to an appropriate level, thus achieving economies of scale. The principles behind the reorganization cases mentioned below are based on the results of a study by Chiang and Chen ([9]) which indicated that mergers among credit departments most likely to succeed will be those involving credit departments located in adjacent districts, followed by those involving credit departments in nonadjoining districts and finally by those mergers in which credit departments are taken over by other financial institutions. For this reason, this study first enlarged the scale of operations of the CDFAs with excessively small scales of operations by reorganizing them with two or three adjacent credit departments. This study then applied the CCR model to calculate the respective efficiency values. Appendix Table A2 lists the results.

Based on the work of Chen ([8]), this study points out that merging the CDFAs located in townships or villages within the same county (city) is currently the best merger strategy for enhancing the scale of operations of these inefficient CDFAs. Therefore, in accordance with this principle of mergers taking place at the county- or city-level, 17 such credit departments existed after the mergers took place and these 17 credit departments served as the basis of the efficiency analysis. Following the mergers, the number of DMUs was also 17, and since there were a total of five inputs and outputs, the requirements of Thomas et al. ([21]) and Banker et al. ([2]) were met. This study then applied the CCR model to calculate the efficiency values. Table 1 lists the results.

Table 1. Operating efficiency of farmers' associations at the county- and city-levels after reorganization

The average efficiency scores of the new CDFAs from the two reorganization alternatives were between 0.83 and 0.85. The average efficiency score of the existing districts was 0.73. Thus, the average efficiency scores from the first and second reorganization alternatives are better than the current values. In particular, the second alternative is the best-proposed reorganization alternative because it has the highest average efficiency scores of the reorganized CDFAs. This result implies that combining adjacent inefficient districts that present increasing returns to scale and combining an inefficient CDFA with efficient CDFA can possibly increase the overall efficiencies. Although Taiwan has not reorganized the CDFAs, this study proposed the directions for reorganizing the CDFAs and provided feasible alternatives.

In this article, DEA models were applied to evaluate the relative efficiencies of the CDFAs in Taiwan. The empirical results regarding the operating efficiency of the farmers' associations at the village, township and city level in Taiwan show that their average technical efficiency is low. This result appears to hide the fact that these DMUs, because of their relatively small regional spheres of operation, do not possess economies of scale, or possibly, because they have experienced problems with their internal controls, they have been unable to compete with other institutions and have also been hampered by poor quality staff. Thus, this study also investigated reorganizing CDFAs by combining inefficient CDFAs to improve the current unbalanced status. The proposed reorganization alternatives can reduce the number of CDFAs from 277 to 96 or 17. The reorganized CDFAs of the proposed alternatives had better average efficiency scores than the current CCDFAs.

Although this study focused on the operation aspects of the CDFAs, external factors that are not controllable nor operational may affect the efficiency scores of the CDFAs. For example, NAN-TOU (DMU 131–143) that had the lowest average efficiency score covered the largest mountainous area. Thus, it was inherently more costly for NAN-TOU CDFAs to provide the same service as a compact urban CDFAs did. Nevertheless, NAN-TOU CDFAs has reorganized other CDFAs by merging several small CDFAs with a big CDFA to reduce the input resources to improve the efficiency.

The author would like to thank the Council of Agriculture of the Republic of China, Taiwan for financially supporting this research under Contract No. COA-91AS-1.6.1-FS-#1(3).

Table A1. Operating efficiency of credit departments of farmers' associations

Table A2. Operating efficiency of farmers' associations at the county- and city-level after partial reorganization