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.

金融監理制度影響一國商業銀行經營績效的相關議題，一直受到學者與政府當局的重視，為瞭解亞洲地區銀行業在中央銀行與監理單位不同管理下的利潤效率，找出最適的制度設計，本研究根據Huang、Huang與Liu（2014）提出之隨機共同利潤邊界（stochastic meta-profit frontier），採用兩階段估計法，蒐集中國大陸、香港、印度、日本、韓國、馬來西亞、巴基斯坦、菲律賓、新加坡、斯里蘭卡、泰國以及阿拉伯聯合大公國等十二國商業銀行資料，分成開發中和已開發國家兩個群組，將環境變數納入無效率模型中，進行實證分析，比較不同群組的利潤效率差異，發掘影響效率的主要變數與方向，從而獲得重要政策意涵。 根據實證分析結果，中央銀行介入銀行監理程度越高，商業銀行利潤效率越低；金融監理單位整合程度越高，商業銀行利潤效率越高；中央銀行獨立程度越高，商業銀行利潤效率越低；已開發國家群組的平均技術缺口比率與共同邊界技術效率值皆高於開發中國家群組，符合預期。共同利潤效率最高的是日本，最低的是韓國。平均而言，各國若在共同利潤邊界上從事生產，能提升41.9%至75%的利潤。 / The effects of degrees of financial supervision on performance of commercial banks have long been important issues and drawn much attention to academic researchers and government authorities. This study applies the stochastic meta-profit frontier, recently developed by Huang, Huang, and Liu (2014), to estimate and compare profit efficiencies of commercial banks from 12 Asian countries, i.e., Mainland China, Hong Kong, India, Japan, South Korea, Malaysia, Pakistan, Philippines, Singapore, Sri Lanka, Thailand, and United Arab Emirates. We divide the sample countries into two groups, i.e., developing and developed countries. This enables us to further investigate the effects of different supervisory systems, enforced by central banks (CB) and supervisory authorities, on commercial banks’ profit efficiencies, as well as to make a suggestion about the optimal supervision regimes in the area. Note that a set of supervisory indices are considered as environmental variables that explain profit inefficiency. Using the two-stage estimation procedure, the empirical results are summarized as follows. First, it is found that bank’s profit efficiency decreases with the increase in a CB’s supervision sectors. Second, the unification of supervisory authority has positive effect on bank’s profit efficiency. Third, the more independent is the CB, the less profit efficient the commercial bank is. Fourth, banks in the group of developed countries are found to have higher technology gap ratios and meta-profit efficiencies than those in the group of developing countries, as expected. Fifth and finally, Japan and South Korea has the highest and the lowest level of meta-profit efficiency, respectively. Evidence is found that if an average commercial bank were adopting the best technology, it can earn roughly 41.9% to 75% more profits than otherwise.