Two-Stage DEA Model

The input and output of operating process of traditional DEA model should be considered as a single stage, and at the same time , processing multiple input and multiple output and obtained a comprehensive efficiency value, it can be seen that the overall efficiency of a DMU, by ignoring the important connotation in the process of industrial production, so not a deep layer of exploring in the process of industrial production of each process are real efficiency ( Ming-Zhong Yu, Heng-Zhi Guo, Geng Yi, 2008) .

Chen, Cook, & Zhu (2010) mentioned that recently the DEA method has extended to two phase process to evaluate efficiency, two-stage DEA seemed to the expansion of the DEA efficiency evaluation model and import the concept of intermediate goods, will be subjected to a review of the unit of production process which is divided into two sub DMU. All of the first stage output wills become the second stage inputs. And the results of the two-stage DEA model do not only provide overall efficiency value in the whole process, but also can be used for calculating the value of efficiency for each individual stage,, whereDMU1 and Sub-DMU2 are acting respectively as input and output to the production process of intermediate goods as in addition to the efficiency relation of input and output, the two-stage DEA is also the relationship between the input and the efficiency of intermediate goods, and the efficiency relationship between money and output. In addition, the basic model of the two-stage DEA and DEA model are the same, all can be used to evaluate efficiency of CCR model and BCC model (Jih-Hwa Wu, Bai-Zheng He, 2008).

Because of traditional DEA method cannot fully reflect the production stage in the process of the management information, Seiford and Zhu (1999) are the first people using data envelopment analysis, puts forward two stages of the production process of DEA analysis method to analyze the former U.S. 55 Banks' Profitability and market capacity (Marketability).

Seiford and Zhu (1999) then divide the production process of commercial bank profitability

and market capacity into second order section. The number of employees, assets, and shareholders equity are three variables as input in the first stage. Then to measure profitability, revenues and profits after tax are two variables as output. The input of the second stage contains revenues, profits after taxes, and market value, and the total reward of investment and earnings per share as output to measure the market efficiency. This research aims to explain the banking profitability and market capacity. Study found that nearly 90% of bank profitability and market capacity is inefficient; and large Banks profitability performance is better than small Banks in the market; in addition, the large Banks show increasing state on profitability pay scale, and decreasing on ability to pay in the market scale which point out what the Bank of America said size presents negative correlation with the ability to market efficiency.

Zhu (2000) inherited Seiford and Zhu (1999) for the two-stage data envelopment analysis method used to analyze revenue in the U.S. Fortune magazine ranked 500 companies financial performance. In practice, the first stage and second stage present by Seiford and Zhu (1999) is similar to the first stage of which is a measure of profitability to the number of employees, assets and shareholder equity as three input variables, revenues and profits after taxes for the output variables; second stage is to measure the ability of the market with two inputs is revenues and net income, market value, the output of the three variable is total return to investors and earnings per shares. The results show that there is not necessarily higher yielding corporate profitability and marketability in terms of good performance and diminishing returns to scale showing. The state also found that most companies presenting serious technical and scale inefficiencies. Furthermore studies have shown that by reducing the existing staff, assets and equity can actually increase revenue and profit levels.

Afterwards Luo (2003) also adopts the same assessment method, discusses the 245 large bank profit efficiency (Profitability Efficiency), and the market efficiency (Marketability Efficiency), to explore whether the location is on the efficiency of bank influence. Assess the

input variables of profit efficiency for the number of employees, assets and shareholders equity, output variables for revenue and profit; assess the input variables of market efficiency for revenue and profit, output variables with market value, earnings per share and stock price.

Study found that the inefficient problem for large Banks really comes from the market inefficiency there are 34 (i.e. 14%) Banks have high profit but they have no efficiency to market, so the bank should put emphasis on the value of the produce market activities; In addition, the results also refers to the position of the bank for a profit or the impact of market efficiency is not significant, and find the overall technical efficiency of profit efficiency of profit efficiency rate can predict bank failure.

Domestic and foreign scholars have presents the two stage DEA model in various related researches. This study summarizes the important literature as shown in the following table：

Table 2-4: Two-stage DEA model used in the empirical research

Reseacher Study object The first stage The second stage

Seiford and input, revenue, net income for two outputs variable.

Market Capacity

evaluation：With earnings, after-tax profit binomial for input, to reward of market value, the total investment and earnings per share three as output. and net profit after tax binomial as inputs, to reward of market value, the total investment and earnings per share three as outputs.

Table 2-5: Two-stage DEA model used in the empirical research ( cont )

Source: Summarized by this study

Reseacher Study object The first stage The second stage Luo(2003) The American 245

big bank profits and three inputs, two on revenue and profit as outputs. fees, the number of employees, the number of branches, the total amount of paid-in capital five as inputs. To sign the bill of the premium income and premium income, the liability employ persons as inputs. In order to interest income, fees for inputs. To directly accept insurance premium, for inputs. As outputs on underwriting profit, and investment profit.

Variables are selected in the two stage of this study including input variables, i.e. total assets, fixed assets, operating cost, operating expenses, non-business expenses and output variables, i.e. net sales, operating profits. In the second stage, the net sales and operating profit are two input variables, and earning per share, equity per share, turnover per share, cash flow per share, revenue per person and each business interests are six output variables.This study refers to the previous related researches with DEA model and summarizes them in the following table:

Table 2-6: The papers related with DEA model to measure business performance

The Year Author Input variables Output variables 2001 Ting-Yu Huang Fixed assets

Table 2-7: The papers related with DEA model to measure business performance ( cont ) The Year Author Input variables Output variables

2007 Ren-Fu Shi

Operating cost Net Sales

2009 Bi-Zhu Jiang

Source: Summarized by this study