# Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in taiwan

TL;DR: The relational model developed in this paper is more reliable in measuring the efficiencies and consequently is capable of identifying the causes of inefficiency more accurately.

Abstract: The efficiency of decision processes which can be divided into two stages has been measured for the whole process as well as for each stage independently by using the conventional data envelopment analysis (DEA) methodology in order to identify the causes of inefficiency. This paper modifies the conventional DEA model by taking into account the series relationship of the two sub-processes within the whole process. Under this framework, the efficiency of the whole process can be decomposed into the product of the efficiencies of the two sub-processes. In addition to this sound mathematical property, the case of Taiwanese non-life insurance companies shows that some unusual results which have appeared in the independent model do not exist in the relational model. In other words, the relational model developed in this paper is more reliable in measuring the efficiencies and consequently is capable of identifying the causes of inefficiency more accurately. Based on the structure of the model, the idea of efficiency decomposition can be extended to systems composed of multiple stages connected in series.

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### Cites background from "Efficiency decomposition in two-sta..."

...Chen and Zhu [77], Kao and Hwang [78], and Chen et al....

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378 citations

### Cites background or methods from "Efficiency decomposition in two-sta..."

...For systems composed of two processes connected in series, Kao and Hwang (2008) developed a DEA model to measure the efficiencies of the system and component processes at the same time....

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...This study considers this company as efficient while Kao and Hwang (2008) gave it a rank of 7....

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...Based on this representation, the efficiency decomposition for series systems (Kao and Hwang, 2008) and for parallel systems (Kao, in review) can be utilized to obtain the mathematical relationship between the system efficiency and the processes efficiencies....

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...Kao and Hwang (2008) developed a relational model to calculate the efficiency of the system taking into account the series relationship of the two processes....

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...The largest difference occurs at Union (No. 12), which Kao and Hwang (2008) evaluated as the second best while this study gives it a rank of 8....

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370 citations

### Cites methods or result from "Efficiency decomposition in two-sta..."

...Throughout the paper, we use the Kao and Hwang [4] data set involving non-life insurance companies in Taiwan....

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...Using the notation of Chen and Zhu [10] and Kao and Hwang [4], we assume each DMUj (j=1, 2, y, n) has m inputs xij, (i=1, 2, y, m) to the first stage, and D outputs zdj, (d=1, 2, y, D) from that stage....

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...; s Model (3) is the Kao and Hwang [4] model and the centralized model developed in [6]....

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...As in Kao and Hwang [4], we have ej 1⁄4 e(1)j e 2 j at optimality provided we assumewd 1⁄4 ~ wd Note that such a decomposition of efficiency is not available in the standard DEA approach, and the network DEA approaches....

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...[25], Chen and Zhu’s [10] model under the CRS assumption is equivalent to the Kao and Hwang’s [4] model....

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##### References

22,924 citations

### Additional excerpts

...…returns-to-scale is the CCR model (Charnes et al., 1978): Ek ¼ max Xs r¼1 urY rk ,Xm i¼1 viX ik s:t: Xs r¼1 urY rj ,Xm i¼1 viX ij 6 1; j ¼ 1; . . . ; n; ur; vi P e; r ¼ 1; . . . ; s; i ¼ 1; . . . ;m; ð1Þ where e is a small non-Archimedean number (Charnes et al., 1979; Charnes and Cooper, 1984)....

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13,542 citations

### "Efficiency decomposition in two-sta..." refers background in this paper

...Banker et al. (1984) break the overall efficiency of a DMU into the product of scale efficiency and technical efficiency. Byrnes et al. (1984) further separate the congestion effect from the technical efficiency. Kao (1995) decomposes the overall efficiency into a weighted arithmetic mean of the efficiencies of individual outputs. A similar decomposition from the input side is also derived. Another type of decomposition emphasizes the stages of the production process. The complicated production process is divided into sub-processes, in that some intermediate products are the outputs of a sub-process on the one hand and the inputs of another sub-process on the other hand. The works of Färe and Grosskopf (1996, 2000) and Seiford and Zhu (1999) are some examples of this approach. In the former type of decomposition, there exists some mathematical relationship between the overall efficiency and the component efficiencies, while for the latter type there is no specific relationship between those two parts. The reason is because the sub-processes in the latter type are considered as independent processes in calculating their efficiencies. The model for calculating the efficiencies of the sub-processes does not reflect any relationship between the components and the whole system. The simplest case of a complicated production process is a tandem system, in which the whole production process is composed of two sub-processes connected in series. Seiford and Zhu (1999) divide a commercial bank’s production process into the stages of profitability and marketability....

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...Banker et al. (1984) break the overall efficiency of a DMU into the product of scale efficiency and technical efficiency. Byrnes et al. (1984) further separate the congestion effect from the technical efficiency....

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...Banker et al. (1984) break the overall efficiency of a DMU into the product of scale efficiency and technical efficiency....

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...Banker et al. (1984) break the overall efficiency of a DMU into the product of scale efficiency and technical efficiency. Byrnes et al. (1984) further separate the congestion effect from the technical efficiency. Kao (1995) decomposes the overall efficiency into a weighted arithmetic mean of the efficiencies of individual outputs. A similar decomposition from the input side is also derived. Another type of decomposition emphasizes the stages of the production process. The complicated production process is divided into sub-processes, in that some intermediate products are the outputs of a sub-process on the one hand and the inputs of another sub-process on the other hand. The works of Färe and Grosskopf (1996, 2000) and Seiford and Zhu (1999) are some examples of this approach....

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...Banker et al. (1984) break the overall efficiency of a DMU into the product of scale efficiency and technical efficiency. Byrnes et al. (1984) further separate the congestion effect from the technical efficiency. Kao (1995) decomposes the overall efficiency into a weighted arithmetic mean of the efficiencies of individual outputs. A similar decomposition from the input side is also derived. Another type of decomposition emphasizes the stages of the production process. The complicated production process is divided into sub-processes, in that some intermediate products are the outputs of a sub-process on the one hand and the inputs of another sub-process on the other hand. The works of Färe and Grosskopf (1996, 2000) and Seiford and Zhu (1999) are some examples of this approach. In the former type of decomposition, there exists some mathematical relationship between the overall efficiency and the component efficiencies, while for the latter type there is no specific relationship between those two parts. The reason is because the sub-processes in the latter type are considered as independent processes in calculating their efficiencies. The model for calculating the efficiencies of the sub-processes does not reflect any relationship between the components and the whole system. The simplest case of a complicated production process is a tandem system, in which the whole production process is composed of two sub-processes connected in series. Seiford and Zhu (1999) divide a commercial bank’s production process into the stages of profitability and marketability. The inputs of the bank production process are employees, assets, and shareholders’ equity, which are also the inputs of the first stage. The outputs of the bank production process are market value, total return on investments, and earnings per share, which are also the outputs of the second stage. In addition to the inputs and outputs of the system, there are two intermediate products, revenues and profits, which are the outputs of the first stage as well as the inputs of the second stage. The efficiencies of the first stage, second stage, and the whole production process are calculated via three independent DEA models for 55 US commercial banks. Decomposition of the production process helps identify the source of inefficiency. Zhu (2000) follows the same idea to analyze the financial efficiency of the best 500 companies as ranked by Fortune....

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