Two-stage DEA Model

As mentioned above, original one-stage DEA model is a useful technique to evaluate managerial performance of organizations. Its results help managers as well as decision makers identify the strengths and weaknesses of their organization. Based on that, they could have an appropriate adjustment in management to obtain better results. However, the original one-stage DEA model with initial inputs and ultimate outputs only can characterize operational performance;

it does not reflect profitability or market valuation of companies and organizations (Seiford &

Zhu, 1999).

Moreover, along with rapid development of global economy, companies and organizations have been changing significantly in structures as well as scales. There is an urgent need for organizations to seek more effective performance measurement methods. In addition, if the input and/or output are imprecise, Kao (2006) claimed that the efficiency scores which calculated by the traditional one-stage DEA model would appear in a range rather than being exact values. Huang and Kao (2006) also judged that the original one-stage DEA technique is

“incapable of providing reflecting sufficient management information about a company’s production process”. As a result, a two-stage DEA model, which was first introduced by Seiford and Zhu (1999) has been being adopted in many kinds of industries to provide managers with more precise and sufficient management information about their organizations. A two-stage DEA model can be illustrated as the figure below:

Figure 2.1 Two-stage DEA model

In their study, Seiford and Zhu (1999) suggested using the two-stage DEA model to evaluate production progress of the top 55 U.S. commercial banks. They measured the marketability in the first stage and the profitability in the second stage. The inputs to the first stage are: employees, assets and shareholders’ equity. The mediator factors connecting these two stages are revenues and profits. The three factors that play the role as the outputs of the second stage are earnings per share, market value, and total investment return.

Applying the same method of the two-stage DEA method introduced by Seiford & Zhu (1999), Zhu (2000) analyzed the financial efficiency of the best 500 companies, which were ranked by Fortune magazine. The methods of measuring used in the first and second stages were identical those of Seiford & Zhu (1999). In particular, the researcher employed three factors - employees, assets and shareholders’ equity – to be the inputs. The other three factors, which play the role as the outputs, are market value, total investment returns and EPS. Subsequently, Chen (2002) applied a similar method to evaluate managerial performance of 22 banks in Taiwan between 1996 and 2000. However, in this study, the researcher divided the services of banking industry of these companies into three stages to evaluate the financial efficiency, the business operations and the marketability separately.

Moreover, Sexton & Lewis (2003) utilized the two-stage DEA model to measure the

efficiency of the production activities of the American Major Baseball. In the first stage, the researchers treated the resources which include salary of all players as the inputs factor. The mediator factors are total bases gained and total bases surrendered in the games. In the second stage, game victories are the outputs factors which can be achieve from the mediator factors. Also relative to banking industry, Luo (2003) measured profitability and marketability efficiency of 245 large banks by utilizing two-stage DEA model.

Hwang and Kao (2006) followed up the two-stage DEA method to measure managerial efficiency of 24 non-life insurance companies in Taiwan. In this study, marketability was evaluated in the first stage and profitability was evaluated in the second stage. In the first stage, the researchers selected business and administrative expenses, and commissions and acquisition expenses as the inputs; direct premiums written and reinsurance premium received as the outputs.

In the second stage, they treated the first stage outputs as the inputs in the second stage and chose net underwriting income and investment income as the outputs to measure profitability. In addition, the data of these companies was recalled one more time in their study in 2008 to investigate efficiency decomposition in a two-stage network structure.

The above literatures analyze the production process using a mediator for being the outputs of the first stage, yet the inputs of the second stage. The same idea can be applied to a more than two-stage DEA model, where the outputs of the previous stage can be treated as the inputs of the next stage to enhance a production process; this could be called a multiple-stage DEA model. Based on the above discussion, it can be observed that, a two-stage DEA model can reflect managerial efficiency of companied and organizations better than the traditional one-stage model can. The main point is that all the studies mentioned above only focused on applying the model; there is no study that examines the relationship among efficiency values in one-stage and two-stage DEA model. Is there any connection and what can the results reveal? And the set of weights are the major elements that determine the values of efficiency. However, there is also no

study that attempts to explore the effect of set of weights on efficiency values. This paper is going to discuss those issues.

Table 2.1 List of researches that used a two-stage DEA model

Year Author(s)

Method

Stage 1 Stage 2

1999

Seiford Zhu

CCR model BCC model

CCR model BCC model

2000 Zhu CCR model CCR model

2002 Chen CCR model CCR model

2003

Luo CCR model CCR model

Sexton Lewis

CCR model CCR model

2006

Hwang Kao

CCR model CCR model

2008

Hwang Kao

CCR model CCR model