過去十幾年間歐洲金融市場經歷了一系列的變革，歐盟的形成促使歐洲市場朝一元化方向邁進。透過歐盟的整合，在1990年間，可以發現歐洲金融市場已經和過去大不相同了，各成員國金融市場的特徵越來越相近。因此各國的生產技術、技術效率及其變動便成為一有趣且重要的議題。 在進行跨國生產效率比較時，當廠商面對不同的技術集合，將因衡量基準不一致，而無法相互比較。無論是在各國邊界或共有邊界(common frontier)基礎下進行比較，都可能會高估或低估個別廠商的效率值。故本研究使用Rao(2006)共同邊界 (metafrontier)的概念，使用共同邊界生產函數的估計架構。並引入麥氏生產力指數，即可衡量各廠商生產力之跨期動態變動過程，且引用陳谷劦與楊浩彥(2008)拆解共同邊界麥氏生產力指數，以了解生產力變動的來源。 實證結果發現多數環境變數都達到顯著水準，然而，各國環境變數的係數符號沒有一致為正或為負，故無法明確推論這五項環境變數對於技術無效率一致的影響方向。TE*於樣本期間下滑的速度更甚於TEK，顯示TGR下降的趨勢加速了共同邊界下技術效率的退步。平均RTS值各年皆很接近一，也就是已很接近固定 (最適) 規模報酬。研究期間GMPI與MMPI於多數年間變動方向不一致，從GMPI與MMPI的歧異性，說明忽略各群組技術水準的差異對效率比較影響的嚴重性。因為潛在技術變動上升幅度剛好抵銷技術追趕下降幅度，使得技術缺口比率變動全部樣本期間的平均值恰等於一。綜而言之，各國技術變動均呈現穩定成長或平穩的走勢，顯示西歐銀行業的技術改變是較穩定漸進的。亦可看出各年生產力變動是來自於各要素微幅的波動，沒有哪一項成份強烈得支配著生產力變動的現象。若以MMPI平均值作為西歐國家的分組依據，發現這15個樣本國家可分成六個組，其中一組包含歐洲北部的六個國家，另一組則為法國與德國，由此可見地域與經貿關係在生產技術交流扮演了重要的角色。

本研究以Rao(2006)的MMPI為基礎，在距離函數觀念下將MMPI進行拆解，分解成技術效率變動、技術變動、規模變動以及追趕項，再將追趕成份，進一步拆解為「技術追趕」(catch-up in technology, 簡稱CUT) 與「潛在技術變動」(potential technological change, PTC)，其中，CUT又可再分解為變動規模報酬之下的效率追趕(catch-up in efficiency, CUE)及規模追趕 (catch-up in scale, CUS)。實證上，利用1993-2007年間，15個歐洲國家的財務報表資料，運用DEA法分析西歐金融機構之經營效率，並進行生產力的推估與拆解，同時結合共同邊界的分析架構，從事群組國家間比較分析。 實證結果發現，MMPI表現突出的群組，主要來自於技術效率的進步，例如：北歐三國群組和奧地利；其次是規模效率的進步，例如：北歐三國與法國；最後才是技術變動，例如法國。而在十個國家群組中，除了義大利的MMPI退步以及奧地利的規模效率呈現持平外，其餘八個群組的MMPI與其三個構成項目，都呈現同升同降的相同趨勢，不同處僅在於變動幅度大小。例如MMPI都呈現進步的情形，其構成項目，分別表現出技術退步、技術效率進步以及規模效率進步。這樣的結果可能來自於歐洲單一市場的運作方式。 又依MMPI統計差異性檢定的結果，我們可以將原先依MMPI數值大小排序的十個國家群組，重新考慮群組間統計上差異及無差異的情形，合併為五個層次的生產力成長情形，第一層為北歐三國，MMPI成長最快，其次為奧地利、法國、比利時，再次為荷葡西英群組，第四層是盧森堡、瑞士，最末層則為德國、丹麥及義大利。

本文旨在探討台灣和大陸壽險公司的經營效率。由於台灣和大陸的環境背景、金融體制、經營理念等不同，使得兩岸壽險公司的生產技術水準也有所差異。本研究選擇25家台灣壽險公司和23家大陸壽險公司為研究對象，樣本期間為2003年到2008年。 迴歸模型為translog型式的投入距離函數，將模型中的隨機干擾項給予適當假定，並放入環境變數作為影響技術無效率的因子，採用最大概似法進行估計。其次，利用Battese et al. (2004)的共同邊界生產模型，將共同邊界生產函數定義為，依據不同技術組別間的隨機邊界生產函數，包絡各組別隨機邊界的確定性部份，形成具包絡性質的共同邊界，並藉此估計出屬於兩岸壽險業的共同邊界，比較台灣和大陸壽險公司在技術缺口比及共同技術效率上是否有顯著差異。 研究結果顯示:1. 台灣與大陸壽險公司的組別隨機邊界中，兩個組別在技術效率的表現上無顯著的差異。2. 台灣壽險公司的技術缺口比顯著的高於大陸，表示台灣壽險公司整體而言比較靠近共同生產邊界，隱含台灣的生產技術顯著優於中國大陸。3. 在共同邊界的技術效率中，台灣壽險公司的技術效率顯著的優於大陸壽險公司。

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.

隨著台海兩岸經貿往來密切，發展迅速，客觀上對銀行業提出了許多服務要求，為兩岸金融業的合作提供了廣闊的空間。本文通過採用數據包絡分析法和共同邊界成本函數比較分析了兩岸商業銀行的成本結構及效率差異，實證結果表示大陸商業銀行的成本效率要高於台灣銀行。對這一結果的可能性解釋是大陸銀行的資產規模要遠高於台灣銀行。銀行總資產越高，其獲取低投入要素價格的市場能力越強，因此生產成本更低，成本效率更高。台灣和大陸商業銀行有必要發揮自身的優勢，通過各種方式和渠道，加快兩岸銀行界合作的進程。 / With cross-strait rapid economic development and trade exchanges, huge business investments have induced a great demand for financial services and provided a broad space for cross-strait cooperation. This paper adopts data envelopment analysis and meta-frontier cost function to compare and analyze the different cost structure and efficiency of mainland and Taiwan commercial banks. The empirical results reveal that cost efficiency of mainland commercial banks is higher than Taiwanese ones, which is maybe caused by the larger bank size and total assets. The larger the size of banks, the higher the market power for reaping the benefits of low input prices, thereby resulting in a lower cost of production and a higher cost efficiency. It is necessary for mainland and Taiwan commercial banks to develop their own strengths to accelerate the process of cross-strait cooperation in the banking sector through various means and channels.

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.

本論文嘗試解決在文獻上估計生產函數時所產生內生性及樣本選擇的問題。在模型設定上，我允許生產函數存在未觀察到的生產力，並引入技術無效率。在隨機邊際模型架構下，我利用 Olley and Pakes (1996) 及 Levinsohn and Petrin (2003) 所提之演算法先行解決內生性的問題。之後再利用關聯結構法 (copula method) 將樣本選擇問題考慮至生產函數中。如此，既可解決生產函數時所產生內生性及樣本選擇的問題，又可在此基礎上估計技術效率值。另外，根據本文所提之估計方法基礎下，我們透過共同邊界分析法 (metafrontier analysis) 比較留下 (stayer) 與離開 (exit) 市場廠商的技術效率與技術差距比率 (technology gap ratio, TGR)。 / Plants in Taiwan’s manufacturing are characterized as small- and medium-size with frequent exit and entry and the scale of survivors varies considerably with business cycles. Plants' choices on whether to exit or to stay and continuing plants' options on input quantities count on both technical efficiency and productivity. This entails a selection and a simultaneity problems in the estimation of production frontiers. This dissertation proposes a new approach to solve both issues under the framework of the stochastic frontier approach. More specific, we extend Olley and Pakes' (1996) and Levinsohn and Petrin's (2003) approaches to a stochastic production frontier and use copula methods to deal with simultaneity and selection at the same time. Based on the proposed method, we further conduct a metafrontier analysis to compare the technical efficiency and technology gap ratio between exit and continuing firms, which are operating under different technologies and subject to simultaneity and selection. The data of Taiwan’s electronic and food products industries are arbitrarily chosen to illustrate our empirics. Some results are obtained in this dissertation: first, the proposed model solves the problems of simultaneity and selectivity in the production function that exists in ordinary least square estimation; second, there is a serious downward bias in technical efficiency when the conventional stochastic frontier approach ignores simultaneity or sample selection problem; third, the results of metafrontier analysis find that, there is little difference in technology gap ratio between exit and continuing firms. The primary determinant on whether a firm can keep operating in the industry is its managerial ability, rather than its adoption of technology.