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A DEA-Based Data Mining for the Evaluation of the Efficiency in ...


Proceedings of the 13th Asia Pacific Management Conference, Melbourne, Australia, 2007, 303-310

A DEA-Based Data Mining for the Evaluation of the Efficiency in the IT Venture Business
Taeho Honga,*and Jiyoung Parkb
a

Division of Business Administration, College of Business, Pusan National University
b

Business Administration, Graduate School , Pusan National University

Abstract Proposed in this paper, is a DEA-Based data mining approach. To predict the efficiency of an IT venture business, data mining was utilized, to discover advantageous patterns in data. To measure the efficiency of an IT venture business, the Data Envelopment Analysis (DEA) was employed. This is a typical approach among non-parametric methods for measuring the efficiency of companies. A selection of KOSDAQ firms were divided into two groups in accordance with the efficiency in the DEA model. Using a logit model through the stepwise, we finally acquired a model for evaluating the efficiency of an IT venture business. We applied our integrated model to companies listed on the KOSDAQ, which is a stock market division of Korea exchange for dealing the securities of the venture business, with the corporate information available from 2005. Our integrated model enabled us to evaluate an individual firm and provided efficiency information without comparing with other companies. In this paper, to examine the feasibility of SVM in efficient company prediction, we compared it with logit analysis, and discriminant analysis. The experimental results show that SVM provides a promising alternative for the prediction of an efficient company.

Keywords: IT Venture Business; Measuring Efficiency; Data Mining; Data Envelopment Analysis (DEA); Support Vector Machine
(SVM)

1. Introduction A report by the Ministry of Information and Communication of Korea in 2005 found that the Korean management environment of IT venture businesses has improved better than last year (Ministry of Information and Communication of Korea, 2006). Nevertheless, there are still many difficulties for IT venture businesses in Korea. These challenges include developing technology, securing financing, abiding by regulations set forth to protect the environment and providing fair dealings. Many Korean venture businesses started appearing in 2000. This was the so called “IT bubble”. While a lot of companies went bankrupt or were on the verge of bankruptcy, the companies which overcame the fierce competition for survival grew explosively. These days, technology has become not only an important dimension to the development of the IT venture company, but it is also essential for survival. Some companies have been listed on the KODAQ, which is the stock market division of the Korean exchange for dealing with the securities of the venture business. Decision makers, such as investors or credit evaluator want to know which companies have a competitive edge. Most investment banks make every effort to satisfy their investors’ desire for identifying competitive companies. Even though efficiency information of IT venture firms is crucial information for
* Corresponding Author. E-mail:hongth@pusan.ac.kr

decision makers, the information could be hardly attained from the investment banks in actuality due to the absence of appropriate tools for measuring the efficiency of companies. Efficiency of company can be measured by Data Envelopment Analysis (DEA). DEA is a non-parametric multiple input-output efficiency technique that measures the relative efficiency of decision making units (DMUs) using a linear programming based model. It is useful methodology in evaluating of the companies. DEA has been applied for evaluating the relative efficiency of DMUs in many places such as hospitals, schools, banks, factories, and retail stores. A number of DEA-based studies have evaluated the efficiency of various types of company, such as internet companies (Lee et al., 2007; Carlos et al., 2005; Barua et al., 2004) and KOSDAQ companies (Koo et al., 2006; Kim, 2004). It was applied to the corporate credit ratings too (Lee; 2006). DEA is useful methodology but has some problems. Hong et al. (1999) pointed out weakness of DEA application in their study about evaluating the efficiency of SI projects using DEA and machine learning. To measure efficiency of a new DMU, we have to develop entirely new DEA with the data of previously used DMUs. And it is not possible to predict the efficiency level of the new DMU without another DEA analysis.

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Proceedings of the 13th Asia Pacific Management Conference, Melbourne, Australia, 2007, 303-310

To resolve the above limit of DEA we propose an integrating method, which is called DEA-based data mining for evaluating the efficiency of IT Ventures. Data mining for evaluating company has been applied to the bankruptcy prediction and the credit ratings in a lot of studies (Lee, 2007; Huang et al., 2007; Wu et al., 2007; Chen and Shih; 2006, Min and Lee, 2005; Shin et al., 2005; Min and Lee, 2005; Gestel et al., 2004; Huang et al.; 2004). We employed Support Vector Machine (SVM), known as the most powerful among data mining techniques in prediction and classification problems, to predict efficient companies. In this paper, our research objectives are to predict directly the efficiency of the specific company, using DEA-based data mining for evaluating the efficiency of IT Ventures. Consequently, using proposed model, decision makers who want to know about their interesting individual company can get the prediction information without bother. In the next section, we present a brief review of the IT venture business and explanation of the DEA and SVM. Section 3 describes the proposed research framework. Section 4 explains the experiments and results. The final section ends the paper with some concluding remarks. 2. Prior Research In this section, we present the previous studies related to IT venture businesses and the DEA. The DEA is a typical approach among non-parametric methods for measuring efficiency, and was employed as our model. 2.1 IT Venture Business For years, one of the fastest growing business fields has been the IT venture businesses in Korea since the economic crisis of 1997, the International Monetary Fund (IMF) (Cho, 2003). Many Korean venture businesses started appearing in 2000. This was the so called “IT bubble”. The number of IT venture businesses has been fully explored but some of them become unprofitable. There are several reasons, one of them is the environment influence. Especially, venture firms are affected by environment such as narrow markets, resources, degree of competition and investments (Sandgerg and Hofer, 1987). Although adequate expenditure is very important in an emerging industry, there must be a limit to how much a firm can spend in order to establish itself in the marketplace. Some venture firms cannot convert their initial expenditure into a positive income because of their inefficiency and inability. Most inefficient companies failed in the year 2000 (Min and Lee, 2005). The rational is generally that one of the objectives of the IT venture firms have many advantages of returns, making the best use information technology. Venture in the IT industry is defined as small companies of high risk and high revenue. They are fast growing, and research 304

based. This points to growth and an IPO based on innovative technological products and efficient management. Korean regulation of financial support to new technology businesses in all parts of the IT service, including the development of instruments, software and IT supplement is dependent upon the preceding factors (Lee, 2005; Yu and Park, 2000). Therefore, it is important to find efficient companies, with little expenditure, which still manage to obtain high levels of income. Because achieving a high income is a very important element in any emerging industry the IT venture businesses have been no exception. Therefore, it is necessary to evaluate the efficiency of the firms and to understand the important factors which determine their efficiency. To determine the efficiency of the firms, we tried to measure the relative efficiency of software companies with the DEA. 2.2 Data Envelopment Analysis Efficiency can be measured in many ways. Generally, efficiency can be defined as a ratio of a single output to that of the single input:

efficiency =

output input

(1)

In this study, we employed the DEA. The DEA is a non-parametric multiple input-output efficiency technique that measures the relative efficiency of decision making units (DMUs) using a linear programming based model. It is non-parametric because it requires no assumption on the shape or parameters of the underlying production function. Traditional DEA is based on the pioneering work of Farrell’s efficiency measure (1957). Then, Charnes et al. (1978) introduced CCR measures, and Banker et al. (1984) developed BCC measures. In the DEA model, the efficiency is calculated to multiple inputs and outputs. Two models of DEA efficiency measures are the CCR and the BCC model. There are two types of DEA models. Equation 2 is the CCR model and Equation 3 is the BCC model.
min
θ ,λ

θ
(2)
Yλ ≥ y 0

subject to θ x0 ? Xλ ≥ 0

λ≥0
min
θ B ,λ

θB
Yλ ≥ y 0 eλ = 1 λ≥0

subject to θ B x0 ? Xλ ≥ 0

(3)

The CCR model is calculated with the constant return

Proceedings of the 13th Asia Pacific Management Conference, Melbourne, Australia, 2007, 303-310

to scale (CRS) assumption. Banker et al.(1984) presented the BCC model, which allows for a variable return to scale and computes the scores of technical efficiency (TE) and scale efficiency (SE) for each firm in a data set. In these models, the DMUs were not penalized for operating at a non-optimal scale. These models yield the same results if achievement of efficiency or failure is the only topic of concern (Cooper et al., 2000). DEA results are classified as either an efficient group or an inefficient group. DEA yields projections of inefficient DMUs onto an efficient piecewise linear frontier (Golany and Roll, 1989). Although DEA is a powerful tool for the efficiency measurement, there are some important things that have to be considered. One of them is the selection of inputs and outputs. It is important to select appropriate inputs and outputs, because combinations of selected inputs and outputs generate different efficiency rankings for DMUs. DEA has been applied for evaluating the relative efficiency of DMUs in many places such as hospitals, schools, banks, factories, and retail stores. Particularly, DEA is applied to the evaluation of company and corporate credit ratings (Lee, 2006). A number of DEAbased studies have evaluated the efficiency of various types of company; for example, Lee et al. (2007), Carlos et al. (2005) and Barua et al. (2004) applied DEA to measure the efficiency of internet companies. Lee et al. (2007) used the 4 inputs of capital, assets, salary, and advertising expenditure. The 2 outputs used were visitors and sales. Carlos et al. (2005) applied the 3 inputs and the 2 outputs. The inputs were employees, expenses and assets, and the outputs were visitors and revenues. Barua et al. (2004) employed IT capital, NIT capital, labor, and number of years in business for inputs, and they used sales and gross margins for outputs. Koo et al. (2006) and Kim (2004) researched KOSDAQ companies by using the DEA. Koo et al. (2006) used total assets, employees, cost of sales, selling and administrative expenses for inputs, and sales for output. Kim (2004) used total assets, employees, and cost of sales for inputs and sales for the output in his study. The review of research shows that many researchers are applying DEA to evaluate companies. In this study, DEA was employed for the evaluation of the efficiency of an IT venture business. 2.3 Support Vector Machine The Support Vector Machine (SVM) is a popular technique for solving data classification problems. We employed SVM to predict the efficiency in IT venture companies. The SVM method was developed by Vapnik (1995) SVM, one of many machine learning techniques, is based on statistical theory. It has shown good performance and a generalizing capacity in classification tasks. It is applied to the many areas of business (Tay and Cao, 2001).

SVM is the algorithm that finds the maximum margin hyperplane, which is the maximum separation between classes. In here, support vectors are the closest to the maximum margin hyperplane. If it is impossible to divide into two classes, we can use the kernel function. In the case of nonlinear class boundaries, we can transform the inputs into a high-dimensional feature space. This is the original input space and is mapped into a highdimensional dot-product space.

classes, A is defined as xi ∈ R , yi = 1 , B is defined n as xi ∈ R , yi = ?1 . If it is possible to separate them linearly, they can be represented in Equations 4 and 5.
n

f : R n → {±1} using a training set. In the separated two

In the separating case, we can presume the function

w ? xi + b ≥ +1, ?xi ∈ A
w ? xi + b ≤ ?1, xi ∈ B
?

(4) (5)

Where x is the input vector, w is the weight vector and b is bias. w and b represent the parameters used to determine the hyperplane. Using Equations 4 and 5, we can derive Equation 6, as follows:

yi ( w ? xi + b) ≥ 1, ?xi ∈ A ∪ B

(6)

The maximum margin classifier optimizes data within the maximum margin hyperplane. This is an optimization problem expressed Equation 7:

min
w ,b

s.t.

w? w 2 y i ( w ? xi + b ) ≥ 1

(7)

Finally, the equation for an optimal separating hyperplane is shown in Equation 8.

f ( x, α i , b) = ∑ yiα i ( x ? xi ) + b

(8)

Where α i and b are parameters for determining the separation of the hyperplane. x is the training data, and xi is the support vector. In the case of nonlinear class boundaries, we can implement the idea by transforming the inputs into the high-dimensional feature space. A nonlinear separating case, is represented in Equation 9.

f ( x,α i , b) = ∑ yiα i K ( x, xi ) + b

(9)

Where K ( x, xi ) is called the kernel function. The examples of the kernel functions are the polynomial kernel K ( x, xi ) = ( x ? xi + 1) d , and the Gaussian radial basis function K ( x, xi ) = exp( ?

1

δ2

( x ? xi ) 2 ) .

Lee (2007), Huang et al. (2007), Chen and Shih (2006), Gestel et al. (2004), and Huang et al. (2004) 305

Proceedings of the 13th Asia Pacific Management Conference, Melbourne, Australia, 2007, 303-310

applied SVM to the problem of estimating credit rating. Wu et al. (2007), Min and Lee (2005), and Shin et al. (2005) studied the prediction of bankruptcy using SVM. In addition, Hao et al. (2007) employed SVM in categorizing the document. Tay and Cao (2002) used SVM to forecast a financial time series, and Like this, SVM is applied to many areas for the reliable prediction of performance 3. Research Framework Most corporate information provider companies make every effort to satisfy their investors’ desire for identifying competitive companies. These companies have to measure and analyze the efficiency of IT venture businesses in light of the efficient operations of technologies and utilization of assets. The efficiency information is generated and preselected. This efficiency information is necessary used to financial institutes’ investment or banks’ loan decision making. In this study, we proposed an integrated method using DEA and data mining techniques to evaluate and predict the efficiency of an IT venture business. Figure 1 shows our research framework. To measure the efficiency of IT venture businesses, we collected the corporate information. We are able to obtain this information from IR reports that companies give for customers or the corporate information provider companies. Generally, the corporation information contains information about an outline of a business, a value of company, and welfare of workers. An outline of a business includes the name of the firm, a representative, a main office or branch offices. The Quantitative items such as a statement of profit and loss and a balance sheet, safety, or potential represent a value of a company. Welfare of workers includes pay and benefit package. To evaluate efficiency of IT businesses using DEA, we need inputs and outputs in quantitative variables. Therefore, we used quantitative variables of collected many corporate information. Applying IT venture businesses to the DEA, we evaluated a relative efficiency of them. The selection of inputs and outputs is very important in DEA modeling because the performance of DEA generally depends on these variables. These variables have to be representative of the evaluated companies. In the case of internet-based companies (Lee et al., 2007; Carlos et al., 2005; Barua et al., 2004) inputs were IT capital, assets, employees, salary or advertising expenditure and outputs were sales, revenues or visitors. In the case of manufacturing companies (Koo et al., 2006; Kim, 2004), inputs were assets, employees, cost of sales or selling and general administrative expenses and the outputs were used sales, or revenue. In this paper, the subject of investigation is the IT venture business. We selected variables reflecting the features of these businesses. Figure 1. The Framework of DEA-Based Data Mining In lexical meaning, efficiency is the quality of being able to do a task successfully, without wasting time or energy. We obtained a relative efficiency of IT businesses. This value is between 0 and 1. If the relative efficiency score of a company is 1, we are able to come to the conclusion that the company is an efficient compared to other companies. If the score is below one, the company is a relatively inefficient. As a result, companies were divided into two groups in accordance with their relative efficiency in the DEA. To our approach for the prediction, we introduced data mining such as logit and SVM. We acquired the prediction efficiency. 4. Experiments and Results The objective of this section is to analyze the efficiency of an IT venture business. This section starts by describing the data collection. Then it continues with a discussion of the model specifications, which includes the selection of inputs and outputs that enter the model. It ends by producing DEA efficiency estimates and analyses. 4.1 Data In this study, we chose 93 KOSDAQ companies associated with software in the IT venture business. Among them, we used the information of 71 companies, excepting the companies for which information was insufficient. We obtained company information from 2005 from the KIS (Korea Information Service, Inc.). The KIS is the first credit rating agency in Korea. It was founded in February 1985 with the mission of facilitating the advancement of a credit economy (http://www.kisvalue.com). 4.2 Model Specification and Results

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Proceedings of the 13th Asia Pacific Management Conference, Melbourne, Australia, 2007, 303-310

Table 1. The Descriptive Statistics
Variables Employees Total assets Input Development cost Selling & General admin. expenses Output Sales 1) the standard deviation (Unit: the number of person, mil. won) Mean S.D1) Max. Min. 106.44 10.452 37,625 1,841 6,452 18,646 3,841 378 664 1,407 679 203,220 21,112 35,840 53,558 21 7,598 3 742 3,600

disadvantageous scale conditions. In the score of the return to scale, as identified by the BCC model, companies with full efficiency in the CCR score were also efficient in the BCC model, the region where constant returns-to-scale prevails. DMU 3, 5, 25, 31, 46, 47 and 54 had this status, while all other companies displayed increasing return-toscale. 4.3 DEA-Based Data Mining We sorted relatively efficient companies by using the DEA methodology. This method is useful for distinguishing relatively efficient and inefficient companies. However, it cannot be used to evaluate a company’s absolute efficiency. Therefore, in this step, efficiency scores were applied to a logit model. First of all, we performed a paired t-test and then a logit analysis using significant financial variables. Logit analysis has been utilized to investigate the relationship between binary or ordinal response probabilities and explanatory variables. The method fits the linear logit model for binary or ordinal response data via the method of maximum likelihood (Hua et al. 2007). In our study, we divided IT venture businesses into the two classes according to their ranking in the CCR efficiency scores. The two classes were efficient companies and inefficient companies. Using the stepwise module in SPSS 12.0, we conducted the logit analysis. Table 2 presents the hit ratio in logit model at the 0.5 cutoff. The results from, the prediction probability of the classification accuracy is 88.2% for inefficient companies. In the case of the efficient companies, the prediction probability was 83.8%. Using this criterion, it correctly classified 85.9% of IT venture businesses.

The 71 IT venture businesses to be our DEA programming DMUs. In DEA modeling, the selection of inputs and outputs is important because selected inputs and outputs generate different efficiency rankings of DMUs. In this study, we employed four inputs. They were the number of employees, total assets, development cost, and selling and general administrative expenses. Sales was used for the output. The mean, standard deviation, and maximum and minimum were calculated for the input and output variables. The results can be seen in Table 1. The efficiency and ranking results of the DEA, are listed in the Appendix 1. These results represented the characteristics of each company. The CCR results showed the fact that 39 out of 71 companies were below the average, assuming the constant returns-to-scale of the DEA model. Seven of the 71 DMUs that were efficient companies, as they had DMUs of 3, 5, 25, 31, 46, 47 and 54. These companies were more frequently referenced when evaluating inefficient companies. If the CCR efficiency is not equal to 1, we have to examine whether the reason is a managerial problem, or a scale problem, especially when the efficiencies of DMUs of 7, 12 and 33 are under 0.2. These companies had high input variables, but sales which were relatively low. In these cases, there are managerial problems. The BCC scores provide efficiency evaluations using a local measure of scale, i.e. under the variable return-toscale. In this model, DMUs of 11, 18, 22, 30, 49, 58, 59, 66 and 67 were accorded efficient status in addition to the 7 CCR efficient companies which retained their previous efficient status. The DMU’s full efficiency with the BCC model was due to its use of the smallest amount of inputs even though it had the lowest CCR score. In the BCC model, the companies exhibited scores in which 32 out of 71 were below average. The scale efficiency as defined by the ratio, CCR efficiency/BCC efficiency. For example, DMU 1 had a low BCC score and a relatively high scale efficiency among the group, meaning that the overall inefficiency in the CCR column of DMU 1 was caused by inefficient operations rather than scale inefficiency. DMU 11 had a fully efficient BCC score and a low scale efficiency. This can be interpreted to mean that the global inefficiency of this company under is mainly attributed to

Table 2. The Hit Ratio in Logit Analysis
Observation Efficiency Inefficiency Total (%) Prediction Efficiency Inefficiency Classification Accuracy (%) 31/37 4/34 6/37 30/34 83.8 88.2 85.9

Table 3. The Selected Variables in Logit Analysis
Variables Total Capital Turnover Sales/Employee Constant B1) 5.818 0.000 -5.990 S.E.2) 1.696 0.000 1.475 Wald3) 11.771 4.581 16.490 Sig. Prob.4) 0.001*** 0.032** 0.000***

1) the coefficient estimates, 2) the standard error, 3) the wald statistics, 4) the significant probability

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Proceedings of the 13th Asia Pacific Management Conference, Melbourne, Australia, 2007, 303-310
* p<0.1 ** p<0.05 *** p<0.01

Table 3 shows the information for the financial variables included in the regression formula. The coefficient estimate of the total capital turnover was significant with a p < 0.01. The coefficient estimate of the sales/employee was significant with a p < 0.05. This model was found to be highly significant. We know that these two financial variables are good criteria for determining an efficient company. In this study, the Gaussian radial basis function was used as the kernel function of SVM. In SVM, the upper bound C and the kernel parameter δ 2 play an important role. C and δ 2 have a big effect on the performance of SVM. In this study, we used LIBSVM-2.83(Chang and Lin, 2006). For the SVM experiment, we applied 20, 40, 60, 80, and 100 to C. The value of δ 2 was set at 1, 25, 50, 75, and 100. When δ 2 was 25 in datasets 1, 2, 3, a better prediction performance was presented. In that case, the value of C was 60, 20 and 20 for each dataset. And when δ 2 was 50 in dataset 5, a better prediction performance was recorded. In that case, C was 60. In dataset 4, a higher prediction performance was found when δ 2 was 100 and C was 20. 4.4 Comparing Performances In this study, we divided data into a training data set and a test data set. Then we performed a 5-fold cross validation with 70 pieces of data to verify the findings of SVM, logit, and discriminant analysis. Table 4 shows the prediction results of the efficient and inefficient companies.

into two groups in accordance with the efficiency scores of the DEA model. Using the logit model through the stepwise method, we finally acquired a model for evaluating the efficiency of an IT venture business. In the case of analyzing a new company, the DEA model demands other companies to be compare with the new company to generate the relative efficiency. Our integrated model could evaluate the efficiency of a specific company. Through this process, we could find the financial variables which characterize an efficient company. Further through the application SVM, we could predict efficient companies. As a result, we applied our integrated model to companies listed on the KOSDAQ, with corporate information available from 2005. Our model enabled us to evaluate an individual firm and provide the efficiency information of an IT venture business without comparing it with other companies. For IT venture businesses in Korea, we found aspects, such as a total capital turnover, sales/employee, and the productivity of employees to be very important pieces of financial information to evaluate the efficiency of an IT venture business. Also, to examine the feasibility of SVM in efficient company prediction, we compared performances of logit analysis, and discriminant analysis. The experimental results show that SVM provides a promising alternative for efficient company prediction. We should generalize our integrating model by applying it to the IT venture businesses of other countries. Through this additional analysis, we will be able to better understand the general features of the IT venture business. References
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Table 4. The Prediction Results
Discriminant Train Test 82.1 78.6 78.6 92.9 87.5 78.6 83.9 78.6 82.1 78.6 82.8 81.5 logit Train 83.9 82.1 85.7 85.7 85.7 84.6 Test 85.7 92.9 71.4 78.6 85.7 82.9

(unit: %)

Set 1 Set 2 Set 3 Set 4 Set 5 average

SVM Train Test 80.4 85.7 78.6 92.9 82.4 78.6 82.1 78.6 85.7 85.7 81.8 84.3

We compared results of SVM, logit, and discriminant analysis. The hit ratio results show that SVM provides a promising alternative for the prediction of efficient companies. 5. Conclusion We proposed a DEA-Based approach to evaluate efficiency in an IT venture business and performed an empirical analysis for the companies listed on the KOSDAQ. In this study, we used data mining, to discover advantageous patterns in data for the prediction of an efficient IT venture business. We divided the companies

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Appendix 1.
CCR BCC DMU RTS2) S.E1) No. efficiency ranking efficiency ranking 1 0.4747 41 0.5072 58 0.9359 Increasing 2 0.5868 28 0.8397 25 0.6988 Increasing 3 1.0000 1 1.0000 1 1.0000 Constant 4 0.4002 51 0.5588 50 0.7162 Increasing 5 1.0000 1 1.0000 1 1.0000 Constant 6 0.8294 10 0.8365 26 0.9915 Decreasing 7 0.1919 66 0.4616 63 0.4158 Increasing 8 0.3443 55 0.8553 23 0.4026 Increasing 9 0.5053 37 0.7970 32 0.6340 Increasing 10 0.4212 49 0.5345 56 0.7880 Increasing 11 0.6497 24 1.0000 1 0.6497 Increasing 12 0.1760 68 0.3728 67 0.4720 Increasing 13 0.3803 53 0.5074 57 0.7494 Increasing 14 0.4704 42 0.5754 47 0.8176 Decreasing 15 0.2064 63 0.4803 61 0.4297 Increasing 16 0.7027 18 0.7036 39 0.9987 Decreasing 17 0.2732 59 0.2909 68 0.9391 Increasing 18 0.3806 52 1.0000 1 0.3806 Increasing 19 0.3002 58 0.4390 64 0.6839 Increasing 20 0.5301 36 0.5386 54 0.9843 Decreasing 21 0.8006 13 0.8492 24 0.9428 Increasing 22 0.6656 22 1.0000 1 0.6656 Decreasing 23 0.1964 65 0.8301 27 0.2366 Increasing 24 0.3039 57 0.5546 52 0.5480 Increasing 25 1.0000 1 1.0000 1 1.0000 Constant 26 0.8007 12 0.8262 28 0.9691 Decreasing 27 0.4478 48 0.7692 34 0.5821 Increasing 28 0.5400 34 0.5559 51 0.9714 Decreasing 29 0.5771 31 0.8233 29 0.7010 Increasing 30 0.6923 19 1.0000 1 0.6923 Increasing 31 1.0000 1 1.0000 1 1.0000 Constant CCR BCC DMU RTS2) S.E1) No. efficiency ranking efficiency ranking 32 0.4151 50 0.4963 59 0.8364 Increasing 33 0.1066 71 0.1071 71 0.9951 Increasing 34 0.7130 17 0.8012 31 0.8899 Increasing 35 0.4657 43 0.5654 49 0.8236 Increasing 36 0.4902 38 0.6904 40 0.7101 Increasing 37 0.4837 39 0.5865 46 0.8247 Increasing 38 0.4613 45 0.5510 53 0.8372 Increasing # of ref. CCR BCC 0 0 0 0 26 8 0 0 23 10 0 0 0 0 0 0 0 0 0 0 0 30 0 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 2 0 0 0 0 24 28 0 0 0 0 0 0 0 0 0 6 59 36 # of ref. CCR BCC 0 0 0 0 0 0 0 0 0 0 0 0 0 0

309

Proceedings of the 13th Asia Pacific Management Conference, Melbourne, Australia, 2007, 303-310 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 average S.D # effic. 0.8834 0.5845 0.7859 0.4583 0.6793 0.7156 0.1893 1.0000 1.0000 0.6554 0.9593 0.2453 0.4615 0.5858 0.7575 1.0000 0.4803 0.6082 0.1291 0.3321 0.6289 0.1973 0.1412 0.4515 0.2174 0.8223 0.2590 0.5613 0.5373 0.6414 0.3601 0.5443 0.6716 0.5426 0.2481 7 9 30 14 46 20 16 67 1 1 23 8 61 44 29 15 1 40 27 70 56 26 64 69 47 62 11 60 32 35 25 54 33 21 0.9308 0.6142 0.8824 0.5357 0.9098 0.7325 0.2247 1.0000 1.0000 0.7295 1.0000 0.3932 0.6434 0.9487 0.7960 1.0000 0.4816 0.6815 0.2255 1.0000 1.0000 0.6427 0.6790 0.4641 0.5700 0.8652 0.3910 1.0000 1.0000 0.7206 0.7672 0.9683 0.8167 0.7172 0.2313 16 19 45 21 55 20 36 70 1 1 37 1 65 43 18 33 1 60 41 69 1 1 44 42 62 48 22 66 1 1 38 35 17 30 0.9491 0.9517 0.8906 0.8555 0.7467 0.9769 0.8423 1.0000 1.0000 0.8984 0.9593 0.6238 0.7174 0.6175 0.9517 1.0000 0.9972 0.8925 0.5726 0.3321 0.6289 0.3070 0.2080 0.9728 0.3813 0.9504 0.6624 0.5613 0.5373 0.8901 0.4694 0.5621 0.8223 0.7555 0.2192 7 Increasing Increasing Increasing Increasing Increasing Decreasing Increasing Constant Constant Increasing Increasing Increasing Increasing Increasing Increasing Constant Decreasing Increasing Increasing Increasing Increasing Increasing Increasing Increasing Increasing Increasing Increasing Increasing Increasing Increasing Increasing Increasing Increasing 0 0 0 0 0 0 0 8 9 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 7 0 11 0 0 0 0 4 0 0 0 1 26 0 0 0 0 0 0 12 6 0 0 0 0

1) Standard error, 2) return to scale

310


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