انتخاب شاخص ورودی/خروجی برای ارزیابی کارایی تحلیل پوششی داده: مطالعه تجربی از بانک های تجاری چینی

One of the interesting research subjects in DEA is to choose appropriate input and output indicators. In the process, one may encounter many problems, such as the selection tools, correlation analysis, and the classification of input versus output status. In this paper, we propose a new method for choosing DEA variables. Unlike previous research, it is based on the conception of cash value added (CVA), and can make a selection according to the statistic results. This new method has some advantages: first, it is more objective, avoiding the influence of subjective factors on the subsequent calculation; second and most important is that it provides managers and researchers with measurement variables and exact classifications of these factors; third, all variables under discussion come from financial statements which are easily available. This variable selection method has been applied to 14 Chinese commercial banks, and both regression and statistic test results are satisfactory.

Data envelopment analysis (DEA) is a non-parametric technique for measuring the relative efficiency of a set of similar units, usually referred to as DMUs which convert multiple inputs to multiple outputs. Since the advent of DEA (Charnes, Cooper, & Rhodes, 1978), this methodology has been applied in a wide range of applications, such as schools, banks, and hospitals. A substantial amount of scholarly effort has been devoted to its development over the past three decades (Cook & Seiford, 2009). In the seminal work of Charnes et al., efficiency is represented by the ratio of weighted outputs to weighted inputs. Some expanded forms were proposed by other researchers later. Central to each formulation is the need to account for variables’ selection. Just as Paradi, Vela, and Yang (2004), pointed out, besides the choice of DEA technology (model), selecting inputs and outputs is the other crucial consideration that the analyst must keep in mind. Unfortunately, there has been inadequate attention to this issue, while most attention has been given to building models. Several researchers have just chosen variables subjectively or calculated efficiency based directly on others’ selection results. Lack of publicly available data is perhaps one of the reasons behind this trend. In some cases, there are too many variables, which violate the rule of the thumb (Cooper, Seiford, & Zhu, 2004) and causes bad discrimination between DMUs. Actually, certain factors may be eliminated because some variables prove to be very highly correlated. Several methods can be used to address this problem. Principal component analysis (PCA) is one of the most common techniques, which is widely used in multivariate statistics (Luukka, 2009, Ramalingam and Charles, 2007 and Wang and Du, 2000). Azadeh and Ghaderi (2007) integrated DEA and PCA for quality assessment of products. However, PCA just provides a way to reduce the number of inputs and outputs when there is a large-dimension data set after the choice of variables. There is also a graphic display method, called Co-Plot, which can be used to run a correlation analysis on all variables and DEA results (Raveh, 2000). But before calculation, one must decide the classification of every variable, because the process begins with the ratio of output/input (Adler & Raveh, 2008). In fact, the above two methods cannot solve the problem with variables selection. As is known, the usual variables in DEA are such that more is better for output, and less is better for input. However, the behaviors of many variables are just opposite to this in some situations, such as air pollution. Traditional DEA may cause confusion when dealing with such problems. Several researchers solve this problem by making restrictions to specific variables (Fare and Grosskopf, 2004 and Hua and Bin, 2008). However, these ideas are more related to defining models rather than variables selection, and how to deal with such variables depends on what the model is intended to achieve. In the traditional application of DEA, it is assumed that the status of variables is provided with a priori. However, in the real world, there exists a kind of variable characterized as “flexible”, i.e., a variable that acts as an input and an output at the same time. Beasley (1995) first discussed this issue and presented a formulation for this situation in evaluating universities in the UK. Cook, Green, and Zhu (2006) later gave an alternative version of Beasley’s. No matter what the models are, they should not consider the influence of such variables in both places, but rather consider it in the most appropriate place. In this paper, we propose a new methodology for choosing variables and making decisions on which variables to include as inputs and which ones as outputs at the same time. The new method is based on the concept of cash value added (CVA), which was first introduced by Erik Ottosson and Fredik Werssenrieder. In the theory of modern business management, cash flow plays a more and more important role in an enterprise’s development. It reflects the state of a business most accurately and decides the growth and decline of the enterprise in a certain degree. Many companies go bankrupt due to the deterioration of their cash flow. Unfortunately, the financial crisis that broke out in 2008 has made it hard for many enterprises to operate, and cash flow risks have gradually emerged. Under this situation, we consider cash flow in the DEA framework for efficiency evaluation. Appropriate variables are selected by our method in view of their influence on the DMUs’ cash flow. A factor can be taken as an output if it has a positive influence on a DMU’s cash flow or as an input otherwise. Finally, statistic tests are applied to analyze the selection results, demonstrating the validity of our method. What distinguish this research from those exists in the literature above mainly three issues. First, it is more objective. We are to control the influence of subjective factors and let the data speak for itself. Second, also the most important, it provides the managers and researchers with relevant variables and exact status designations of them. Third, the data can be easily obtained since all variables concerned are from balance sheet and statement of cash flows. The rest of the paper is arranged as follows. Section 2 gives a simple introduction to CVA and discusses how variables are selected. In Section 3, an example of 14 Chinese commercial banks is presented to illustrate the proposed method. Conclusions are drawn in Section 4.

One of the basic tasks for the application of DEA efficiency evaluation is to determine the input and output variables. However, there are many problems in existing methods for selecting variables, such as the choice means, correlation analysis on variables, and the classifications of input versus output status. A better way which can overcome these problems is highly necessary. Our new method for choosing DEA variables, unlike previous models, is an objective process based on CVA, and can make decisions as to which variables to include as inputs and which ones as outputs at the same time, according to the value based management. In addition, our process successfully avoids the correlation analysis, since it can be done by PLS automatically. The application in Section 3 illustrates its usefulness and rationality. As pointed out, the approach obtains data from the annual report, which provides easier data access. However, this characteristic also limits the application of our method. For instance, in the case of performance appraisal for sub-DMUs within a large organization, or for DMUs that have not gone public, the usefulness of the proposed process is limited. Nevertheless, the combination of cash value added and variables selection provides a meaningful direction for performance evaluation using DEA models.