最差績效前緣資料包絡分析法之研究與應用

Abstract

本研究針對企業組織在最不利情境下發展評量其最差績效表現之資料包絡法分析模式。傳統的資料包絡分析法係以對受評之決策單位最有利的一組權重（視同在最有利情境下） 來評量其最佳績效表現，所得到的最佳績效表現單位可建構成一個最佳績效前緣，故可將傳統的資料包絡分析法模型稱為最佳績效前緣資料包絡分析法模型。然而此類資料包絡分析法模型並不適用於投資風險評估及破產預測，因為最有可能破產或最具投資風險者往往是那些在產業環境日趨惡劣、經濟蕭條或金融風暴來臨時最不具競爭力的企業。為了在最不利情境下評量企業的最差績效表現，以利找到最有可能破產或最具投資風險者，本研究試圖發展建構適用的資料包絡分析法模型，此類模型係建構在最不利情境下，以對受評之決策單位最不利的一組權重來評量其最差績效表現。 本研究共建構了兩類可供在最不利情境下評量最差績效表現之資料包絡法分析模式，將其稱之為最差績效前緣資料包絡分析法，一類係針對輻射型績效值無法直接處理差額變數之缺點同時加以改進，另一類則是針對銀行業特具之兩階段生產過程建構出適用之兩階段最差績效前緣資料包絡分析法，最後均各以包含破產實例的本國銀行真實財報資料，對所提出之模型進行實證研究，研究結果證實其預測破產銀行之實用性及精確度。本研究在預測破產銀行之成效外，另開發了最差績效前緣資料包絡分析法之其他實用途徑，可供最差績效表現適切結合最佳績效前緣資料包絡分析法模型所得到的最佳績效，對受評之決策單位進行樂觀及悲觀雙面向的評估，使績效評量結果更具客觀及全面性。

The global financial crisis has been spreading since the subprime mortgage financial crisis in the United States started in 2006. The increasing number of corporate bankruptcies has reemphasized the need for research in the area of identifying early warning indicators of corporate distress. The identification of bankrupt firms and quantification of investment risk are of critical importance. Data envelopment analysis (DEA) has been proven as an excellent performance evaluation method. However, conventional DEA model is considered suitable to identify good (efficient) performers in the most favorable scenario. The best-practice frontier DEA (BPF-DEA) models select potentially distressed companies by measuring how inefficient they are in the most favorable scenario. I argue that the struggling companies should be picked out based on how worst they perform in the worst-case scenario since the companies who will potentially go out of business first are usually the ones of least competitiveness in comparison with others as the scenario is getting worse (less favorable) especially when they confront economic depression or financial crisis. Therefore, it is necessary and more meaningful to develop some appropriate model formulations other than the BPF-DEA models for evaluating and ranking units in the least favorable (worst-case) scenario and therefore identifying bad performers as potentially failed firm(s). This study proposes some types of DEA models based on the concept of worst-practice frontier (WPF). First, to identify bad performers together with the slack values I formulate the WPF-SBM model. Then I develop the HypoSBM model to distinguish the worst performers from the bad ones evaluated by the WPF-SBM model. And a solution approach is suggested to fully rank worst efficiencies in the worst-case scenario. The results of an empirical study shows that combining the proposed models and the solution approach can effectively and accurately identify the potentially failed banks. Second, to fit the two-stage production process in the banking industry, this study introduces a two-stage WPF-BCC model that can deal with negative profit data and effectively identify failed bank(s) in the worse-case scenario. This model is applied in an empirical study. The result is then compared with the result from a two-stage BPF-BCC model to show the adequacy of the WPF-DEA model for identifying failed bank(s) in the worst-case scenario. Third, there are no feasible super-efficiency evaluations for some DEA models such as the MEA model, which makes it difficult to discriminate the efficient units evaluated by the MEA model. This study proposes the WPF-MEA model and suggests a ranking approach to rank the efficient units evaluated by the MEA model. On the other hand, I can also rank the worst efficient units evaluated by the WPF-MEA model using the similar ranking approach and the MEA model. As a result, I can get a ranking list among the efficient units and among the worst efficient units. Finally, this research provides some possible limitation and drawbacks when using the proposed WPF-DEA models. Then I conclude this research with some directions of future research.