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H ετερογένεια που χαρακτηρίζει τις τεχνολογίες των επιχειρήσεων που εντάσσονται σε διαφορετικά σύνολα και ενσωματώνουν στο τεχνολογικό τους σύνολο μια καινοτομία, δημιουργεί προβλήματα στην εκτίμηση της συνολικής παραγωγικότητας των εισροών (TFP). Σε αυτή την περίπτωση οι όποιες μεταβολές της παραγωγικής αποτελεσματικότητας, τεχνικής και κλίμακας, συναρτώνται άμεσα με τους ρυθμούς τεχνολογικής αλλαγής και ταυτόχρονα εξαρτώνται από τις διαφορές παραγωγικότητας και αποτελεσματικότητας των κλάδων που ανήκουν οι επιχειρήσεις. Στην διεθνή βιβλιογραφία το παραπάνω ζήτημα έχει αντιμετωπιστεί από αρκετούς ερευνητές (Battese et al., 2002; 2004, Orea and Kumbhakar, 2004; Caudill, 2003). Ωστόσο σε μια πρόσφατη έρευνα (Kounetas, Mourtos and Tsekouras, 2009) παρουσιάζεται ένα αναλυτικό μεθοδολογικό πλαίσιο που επιτρέπει, καταρχάς την εκτίμηση της διαφοράς των τεχνολογιών στις οποίες εντάσσονται οι επιχειρήσεις και στη συνέχεια αποτυπώνει τις όποιες μεταβολές μπορεί να επιφέρει η ενσωμάτωση των καινοτομιών, νέων τεχνολογιών κ.λ.π. στα επιμέρους συστατικά της παραγωγικότητας. Σκοπός αυτής της διπλωματικής εργασίας είναι η ανάπτυξη ενός αλγορίθμου που θα βασίζεται στο μεθοδολογικό αυτό πλαίσιο και θα εκτιμά την αποτελεσματικότητα επιχειρήσεων που λειτουργούν υπό διαφορετικά τεχνολογικά καθεστώτα και θα υπολογίζει εφόσον υπάρχουν τα τεχνολογικά χάσματα σε οποιοδήποτε από τα εξεταζόμενα επίπεδα τεχνολογικής ετερογένειας. / Ηeterogeneity that characterizes the technologies of enterprises that are included in different totals and incorporate in their technology a innovation, creates problems in the estimation of total productivity of inputs (TFP). In this case any changes of technical and scale productivity, are associated immediately with the rate of technological change and simultaneously depend from the differences of productivity and effectiveness of sectors that belongs the enterprises. In the international bibliography the above question has been faced by enough researchers (Battese et al., 2002;.2004, Orea and Kumbhakar, 2004 Caudill, 2003). However in a recent research (Kounetas, Mourtos and Tsekouras, 2009) is presented an analytic methodological frame that allows, firstly the estimation of the difference of technologies that belong the enterprises and then impress any changes that can effect the incorporation of innovations, new technologies etc in the individual components of productivity. Aim of this is the development of an algorithm that will be based on this methodological frame and will appreciate the effectiveness of enterprises that functions under different technological arrangements and will calculate, provided that exist, the technological gaps in anyone from the examined levels of technological heterogeneity.

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近年來台灣景氣持續低迷，台灣綜合商品零售業的成長也受到不小的衝擊，在市場漸趨成熟與飽和的情況下，產業內競爭也漸趨激烈。如何在外在經濟環境欠佳，內在市場飽和下，有效提升經營效率，加強產業競爭能力，是目前台灣綜合商品零售業者最重要的課題。 　　本研究以資料包絡分析法（Data Envelopment Analysis）為基礎，並結合Metafrontier分析法，針對台灣地區2000年到2006年25家綜合商品零售業者，以客觀的投入產出資料進行廠商的經營效率分析。本研究結果顯示： 　　1.整體而言，連鎖式便利商店的經營績效平均處於相對有效率狀態，購物中心的經營績效平均處於相對無效率狀態。 　　2.廠商技術無效率的原因主要為純粹技術效率的問題。廠商的規模報酬狀態與所屬業態關聯不大，而與廠商是否屬於連鎖集團較有關聯。 　　3.比較metafrontier模型與group frontiers模型所評估的效率值，顯示各業態廠商的平均技術水準有顯著差異，連鎖式便利商店的效率水準較接近metafrontier的效率邊界。 　　4.依據Norman and Stoker（1991）的效率值強度分類方法，發現在兩模型之下，各業態廠商屬於「邊緣無效率單位」與「確實無效率單位」的比例都較大，表示經營績效有很大的改善空間。 　　5.差額分析與敏感度分析方面，百貨公司業與超級市場業在兩模型之下的結論不一致，推論應是兩者評估的廠商樣本，其衡量的技術水準不同。各廠商依循group frontiers模型所得結論改善經營績效，將可以在業態內成為相對有效率的廠商，但如果想要進一步提高效率，則必須改變廠商本身所處的業態環境所造成的技術水準限制，便可依循metafrontier模型所得結論改善經營績效，所以選用何種結論，仍須由業者依據廠商未來發展自行判斷。 / Since the recession in Taiwan economy has arrived in recent years, it has a great effect on the growth of the Taiwan retail sale of general merchandise. Because the market has been saturated, the competition has become fierce in this industry. How to improve the management efficiency and the industrial competitiveness in the present economic environment is the most important issue of the Taiwan retail sale of general merchandise. 　　This study uses inputs and outputs data of 25 DMUs of the Taiwan retail sale of general merchandise from 2000 to 2006, applying Data Envelopment Analysis with Metafrontier model to evaluate the operational efficiency of those firms. The findings of this study are as below: 　　1. On average, the chain convenience store industry shows more technically efficient than the shopping mall industry. 　　2. The main source for the firms being inefficient is pure technical inefficiency. The returns of scale of the firms are not much related to the types of business operation, but to the firms being the chain store ones or not. 　　3. Comparing meta-frontier model with group frontiers model, we find that there are significant differences in the average technical efficiency levels among the various types of business operation, and the chain convenience store industry is most close to meta-frontier. 　　4. According to the classification of the efficiency by Norman and Stoker (1991), we find a major part of the firms is marginally inefficient and distinctly inefficient. It implies there is a great room for the firms to improve their managerial performance. 　　5. The slack analysis indicates there are differences in the resource wastes between the department store industry and the supermarket industry. The differences mainly come from the technological differences between the two industries. The information generated from the group frontier model is helpful to improve the firms’ efficiency within the group. However, if the firms want to further improve their efficiency, they should rely on the information from the meta-frontier model, which sheds light on the technology gap among sub-industries.

本文欲利用方向距離函數 (DDF) 來驗證中東歐國家銀行業之效率。不同的國家之銀行業者會由於不同的文化、資源稟賦和環境而採取不同的經營模式。因此，本文藉由共同邊界方向距離函數，其允許我們在跨國間不同的技術下，得以估計出銀行的技術效率並加以比較。使用方向距離函數，得以讓我們的模型中納入非意欲產出，此外，其亦允許銀行廠商同時增加產出與縮減投入和非意欲產出，相較於傳統模型，方向距離函數屬於較有彈性之模型。重要的是，不良貸款被視為是貸款過程中之副產品，其可能會降低銀行的利潤和績效。因此，為了減少不良貸款之產生，銀行管理者必須花費額外的成本，以確保借貸者是否有良好的信用，此舉亦可能影響銀行的績效。 本文試圖發展新的共同邊界隨機方向距離函數，其不同於Battese et al. (2004) 所提出的方法，該方法是屬於線性規畫法。此數理規畫法是屬於確定邊界，其無法針對有興趣之參數估計出該標準誤，因此，無法做有效地統計推論。因為本文提出的新共同邊界方向距離函數是隨機的，所以參數之標準誤可以被估計，其亦允許我們建造信賴區間和假設檢定。此外，共同邊界方向距離函數之無效率項可以被進一步設定成環境變數之函數，即Battese and Coelli (1995)所提出之模型。 / This study plans to employ directional technology distance function (DDF) to examine bank efficiency of Central-East European countries. Banks from different countries choose to operate under distinct technologies due to their differences in culture, endowments, and environments. A metafrontier directional distance function will be established, which allows for calculating comparable technical efficiencies for banks under different technologies relative to the potential technology available to the industry across nations. The salient feature of the DDF is its ability to include undesirable outputs into the model. In addition, it allows for a bank to simultaneously expand outputs and contract inputs, as well as undesirable outputs. It is important to note that the non-performing loans (NPL) can be regarded as a by-product of various loans granted, which lowers a bank’s profitability and performance. To reduce the occurrence of NPL bank managers have to spend extra costs to confirm whether the potential applicants for loans have good credit before granting loans to them. This may also affect the bank’s performance. This study attempts to develop a new metafrontier DDF in the context of the stochastic frontier approach, which differs from the one proposed by Battese et al. (2004) who suggest the use of a linear and/or a quadratic programming technique. The mathematical programming technique is known as deterministic, which is unable to estimate the standard errors for the parameters of interest. Hence, no statistical inference can be made. As our new metafrontier DDF is stochastic, the standard errors of the parameters are estimable, which permits establishing confidence intervals and hypotheses testing for the parameters. Moreover, the inefficiency term of the metafrontier DDF can be further specified as a function of several environmental variables of the form proposed by Battese and Coelli (1995).

本文採用新的隨機共同邊界方法，將其擴充至Fourier富伸縮成本函數，針對西歐地區十個國家的銀行業進行成本效率之分析，資料期間涵蓋1996年至2010年。不同於Battese et al. (2004), O’Donnell et al. (2008), and Huang et al. (2011a) 等人利用線性規劃法，本文應用隨機共同邊界法來估計技術缺口比率，進而做跨國間的效率比較，此法的特點在於技術缺口比率可以設為一些反映國家環境差異的外生變數之函數，而線性規劃法則無法做此設定。實證結果顯示採用線性規劃方法所估計出的技術缺口比率與共同成本效率會有低估的現象，技術缺口比率以及共同成本效率在1996年至2000年間逐步上升，此結果支持金融市場的整合可以增進效率，然而，到2000年之後則反轉向下，特別是在2007年至2010年次級房貸風暴時期明顯惡化。此外，進一步的分群進行分析的結果顯示，小規模、高獲利、或是較保守的銀行相對來說較具有效率。 / This paper aims to gain further insights into cost efficiency using the newly developed metafrontier approach under the framework of the Fourier flexible cost frontier for banking industries across 10 Western European nations during the period 1996-2010. Unlike Battese et al. (2004), O’Donnell et al. (2008), and Huang et al. (2011a), who suggest using programming techniques, the stochastic metafrontier is formulated and applied to obtain the technology gap ratio (TGR) for efficiency comparisons among countries. One salient feature of our method is that the TGR can be specified as a function of some exogenous variables that reflect group-specific environmental differences, while the mathematical programming is not allowed to do so. Empirical results show that both TGR and metafrontier cost efficiency (MCE) are underestimated by programming techniques. The TGR and MCE exhibit a gradual upward trend during 1996-2000 and then followed by a downward trend, especially after the subprime crisis of 2007-2010. This suggests that a more integrated financial market is able to improve banking efficiency. Smaller banks tend to be more cost efficient than larger ones. Higher profitable banks and more conservative banks are related to greater efficiency.

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兩岸在2001年底加入世界貿易組織（WTO），使得兩岸壽險市場受到經濟自由化及國際化的衝擊。因此，要如何提高自身的經營績效及競爭能力，便成為兩岸壽險公司最重要的目標。本研究以資料包絡分析法為基礎，並結合共同邊界（metafrontier）分析法，針對兩岸地區在2004年至2007年共59家壽險公司，進行經營效率與Malmquist生產力指數的實證研究。在生產力變動來源的拆解上，本文延伸Pastor and Lovell（2005）的固定規模報酬模型，利用變動規模報酬的生產邊界來衡量各公司的技術變動及技術差距比率變動，使生產力變動的來源上獲得更明確的意涵。最後本文利用Tobit迴歸模型，探討影響兩岸壽險公司經營效率的因素。 / After joining the WTO in December 2001, there is the advent of economic liberalization and internationalization on the life insurance market of Taiwan and Mainland China. Therefore, how to improve the operating performance and the industrial competitiveness in the present economic circumstance is the critical and important goal of the life insurance industry in Taiwan and Mainland China. This study applies data envelopment analysis with metafrontier model to measure the managerial efficiency and Malmquist productivity index of 59 firms of life insurance industry in Taiwan and Mainland China from 2004 to 2007. On decomposing the sources of productivity change, we extend Pastor and Lovell’ s CRS model (2005) to a VRS frontier benchmark to measure technical change and technical gap ratio change, which apparently provides us a more meaningful decomposition of productivity change. Finally, this study uses Tobit regression model to examine the factors which influence the managerial efficiency of the life insurance industry in Taiwan and Mainland China.

臺灣於1990年放寬銀行設立的限制後，本國銀行和外商銀行的數目快速增加，使得金融市場更加競爭，因此銀行的經營績效是個重要的議題，銀行可透過績效的評估結果找出可能的改善方向。本國銀行與外商銀行的進入條件、經營形態、銀行制度等因素可能使得兩種類型的銀行生產技術有所不同，因此本研究採用全域共同邊界法研究37家本國銀行與20家外商銀行在2005-2015年間效率與生產力的分析，並採用變動規模的方式拆解Malmquist生產力指數，使得生產力變動來源能更精準地衡量。最後使用Tobit迴歸分析找出影響銀行技術效率、最佳實務差距和技術差距比率之因素。 / Since Taiwan relaxed the restriction of setting up a bank in early 1990s, the number of both domestic and foreign banks in Taiwan had increased rapidly. This leads to the result that the financial market become more competitive. Consequently, the performance of bank is an important issue. It can be used to find some way for improvement. Due to the different entry conditions, types of operating system and bank systems between domestic and foreign banks, this paper uses global metafrontier approach to research the efficiency and productivity change of 37 domestic banks and 20 foreign banks during 2005-2015 in Taiwan. Furthermore, this research adopts VRS to decompose Malmquist productivity indexes, which makes the sources of the productivity change can be measured more accurately. Finally, Tobit regression analysis is used to investigate the factors accounting for the differences in technical efficiency, best practice gap and technology gap.

金控銀行和獨立銀行在傳統在做績效評估時，可能都只考慮相同的技術水準，如此可能無法正確來衡量不同群體的的差異，而忽略其潛在的效率改善指標。因此，本文將先採用隨機邊界模型(SFA)，估出兩體系的隨機邊界模型，接著，再運用Rao (2006)所提出的共同邊界模型(metafrontier)，來進行兩個體系的銀行效率評估。 本研究運用了民國91年到民國97年期間，13家金控銀行與24家獨立銀行的資料為樣本，去分析此兩個群體的效率比較，可得以下結論： 1.在金控銀行與獨立銀行的個別隨機邊界中，兩個群體在於技術效率的表現上差異不大。 2.金控銀行的技術效率變動有越來越小的趨勢；而獨立銀行術效率沒有明顯的縮小的趨勢。 3.獨立銀行的技術缺口比TGR有顯著的大於金控銀行的TGR。 4.在共同邊界的技術效率中，獨立銀行的技術效率顯著的大於金控銀行 / Most of traditional banking performance evaluation analyses assume both financial holding banks and independent banks share the same level of technology, thus it may not able to identify the managerial efficiency difference of different groups correctly . In this research, a SFA model (Battese and Coelli, 1995) is used first to estimate the technologies and inefficiency factors for both systems. Then a deterministic linear programming metafrontier (Rao, 2006) is adopted to evaluate the technology gap ratio between two bank systems. We collect data of 13 financial holding banks and 24 independentbanks from 2001~2008. After analyzing two systems and making comparison, the main conclusions are as follows: 1.Two bank systems have a minor difference in SFA. 2.The variance on technical efficiency becomes smaller with time in financial holding banks, but not in independent banks. 3.Independentbanks’ TGR is significantly larger than financial holding banks’. 4.In metafrontier, technical efficiency of independent banks is significantly larger than financial holding Bbnks.