本研究利用方向距離函數與Luenberger生產力指標，估計台灣銀行業2000年至2009年的無效率值與生產力變動情形，並利用Ray and Desli (1997)生產技術內部一致的分解法將Luenberger生產力分解為純技術效率變動、規模效率變動、技術變動三個部分，最後根據方向距離函數具備的可加性，將個別銀行的無效率值與生產力變動作一致性的整體銀行業加總。 主要的研究結果為：以2000-2009年投入產出樣本平均數為效率評估方向，全程樣本平均無效率值為0.0209，平均無效率值最高的銀行分別為台北富邦銀行、萬通銀行、新光銀行；平均生產力變動為0.2615，進步最多的銀行為國泰世華銀行，退步最多的銀行為華僑銀行，且台灣的生產力變動的來源最主要來自於技術變動，其次源自於規模效率變動。另外，金控子銀行在規模效率變動與技術變動方面顯著優於非金控子銀行；泛公股銀行在無效率值、規模效率變動、技術變動部分顯著優於民營銀行。 / In this study, we estimate inefficiency and productivity changes of Taiwanese banks for period 2000-2009 using directional distance function and Luenberger productivity indicator. In addition, we decompose the Luenberger productivity indicator into pure efficiency change, scale efficiency change and technical change utilizing internal consistency approach of Ray and Desli (1997). At the end, we make the consistent aggregation across firms to industry level according to additive structure of directional distance function. Main results are as follows: setting the sample mean during 2000-2009 for the directional vector, the average inefficiency is 0.0209，and the most inefficient banks are Taipei Fubon Bank, Grand Commercial Bank and Shin Kong Commercial Bank; the average productivity change is 0.2615, the most progressive bank is Cathay United Bank, and the most regressive bank is OCBC Bank. Besides, the sources of productivity change are mainly attributed to technical change, then from the scale efficiency change. Moreover, financial holding banks are significantly better in scale efficiency change and technical change; pan-public banks are significantly better in inefficiency, scale efficiency change and technical change.

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).

本文利用可以同時捕捉到銀行增加意欲產出、減少投入與減少非意欲產出的方向距離函數，評估台灣銀行業與個別銀行在民國93年至97年的無效率值與生產力變化。設定逾期放款為銀行生產放款時的非意欲產出，以考量銀行的放款品質，也考慮到銀行都會付出成本來提供服務給存戶，因此以交易性存款作為銀行提供服務的替代變數，使銀行的服務包含在效率評估內，並以固定的方向向量作為無效率值加總的基礎，來衡量台灣整體銀行業的無效率。實證結果是台灣銀行業的無效率值隨著雙卡風暴的遠去，有逐年遞減的趨勢，生產力的變化則是退步的情況較多。 / In this paper we estimate Taiwanese banks’ efficiency and productivity change during 2004-2008. The estimates are derived from the directional distance function. We treat non-performing loans as an undesirable output arising from the production of loans to measure the quality of loans. Considering every bank would make costs to serve customers, we choose transaction deposits as an alternative variable to capture the service provided by banks. The way we set the directional vector allows the aggregation of individual bank inefficiency and productivity change to the industry level. Our findings indicate that inefficiencies of Taiwanese banking industry were decreasing after the over of credit and cash card debts. And Taiwanese banking industry experienced productivity regress during this period.

本文以貝氏方法估計方向距離函數，加入單調性與曲度限制，同時考慮環境變數於模型中。為了凸顯考慮非意欲產出方向距離函數的優點，本文同時估計產出面射線距離函數，並與方向距離函數模型比較。實證分析資料為1970至2010年間各國總體經濟變數，分別在有無加入限制條件與環境變數的狀況下，估計兩種距離函數，從無效率值、效率分數與技術進步率等角度分析彼此間的差異。發現射線距離函數模型由於忽略非意欲產出，傾向高估生產單位的技術效率。另一方面，其係數估計值容易違反射線距離函數的先天性質，較不具參考性。而方向距離函數模型當中，有無加入限制條件與有無考慮環境變數的模型結果各不相同，其中同時加入限制條件與環境變數的模型結果最為合理。

本研究發展新的計量方法，運用隨機邊界法將單調性和曲度條件等性質納入迴歸模型，使用聯立迴歸模型進行估計，藉此讓係數估計值不易出現違反經濟理論的情況。 採用台灣2002年至2015年，51家商業銀行進行實證分析，發現本研究方法估計產出方向距離函數時，僅有5%以下的樣本點不符合單調和曲度等性質，用於估計產出面距離函數時，僅有2%以下的樣本點不符合。進一步探討台灣銀行業之非意欲產出--逾期放款--對估計技術效率的影響，顯示不考慮此非意欲產出造成整體銀行業、非金控本國銀行與外商銀行的技術效率被高估，而金控本國銀行的技術效率則被低估，此外，分析2007年金融風暴前後銀行業經營效率變化，顯示考慮非意欲產出銀行業經營效率顯著提升，然而，未考慮非意欲產出銀行業經營效率卻下降，兩者結果有著極大的差異。 / The aim of the paper is to develop a new approach, which is stochastic frontier analysis imposing monotonicity and curvature conditions, then using simultaneous regression model to estimate. By the approach, it can solve the problem of most of the coefficient estimates violating the economic theory. The study uses the data of 51 commercial banks in Taiwan from 2002 to 2015 to conduct the empirical analysis. It indicates that by output directional distance function, less than 5% sample points violate the monotonicity and curvature conditions; by output distance function, less than 2% sample points don’t obey the restricted conditions. Further, the paper discusses the effect of commercial banks’ undesirable output- non-performing loan- on estimating technical efficiency. The results show that ignoring the undesirable output cause the technical efficiency of overall banks, non-finance holding banks and foreign banks are overvalued, and the technical efficiency of finance holding banks are undervalued. Furthermore, analyze the change of business efficiency after financial crisis in 2007. It points out that using the model consider the undesirable output, the banks’ efficiency rises. However, using the model no consider the undesirable output, the banks’ efficiency decreases. There is an extremely conflict between two approach.