Decompositions of profit change: With an application to Taiwanese banking
|Keywords:||銀行;利潤拆解;資料包絡分析法;方向性距離函數;差額衡量法;banks;profit change;decomposition;data envelopment analysis;directional distance function;DEA;slacks;SBM||Issue Date:||2011||Abstract:||
在資料包絡分析法(data envelopment analysis, DEA)的架構下，有兩種衡量效率的方法：射線法DEA (radial DEA)與非射線法DEA (non-radial DEA)。射線法係源自於Charnes et al. (1978)的CCR模型，而非射法則以Tone (2001)的差額衡量法(slack-based measure, SBM)為代表。為分析企業利潤變動之來源，Grifell-Tatjé and Lovell ((Grifell-Tatjé, E., Lovell, C.A.K., 1999. Profits and productivity. Management Science 45, 1177-1193)以射線法DEA將其拆解為六種不同的成份， 而Sahoo and Tone (Sahoo, B.K., Tone, K., 2009. Radial and non-radial decompositions of profit change: With an application to Indian banking. European Journal of Operational Research 196, 1130-1146)則以SBM拆解利潤變動之來源，將非射線差額 (non-radial slacks)納入考量。然而，上述兩篇研究在拆解生產力效果的過程中，均未考量要素投入面 。事實上，利潤變動可追溯自收入面(產出面)及成本面(要素投入面)的變動。
因此，本文的兩篇研究將分別使用DEA體系中的方向距離函數法(directional distance function, DDF)及未定向差額衡量法(non-oriented SBM)，以萃取較完整的利潤變動來源，前者仍設定在射線法DEA的範疇中。且兩者均以1994-2002年的臺灣銀行業為樣本資料拆解其利潤變動來源，並獲得以下實證結果：第一，當拆解生產力效果時，兩種方法皆可額外萃取出產要素投入面的影響。第二，當使用Grifell-Tatjé and Lovell (1999)的DEA法，以及本文的DDF衡量技術變動效果及營運效率效果對利潤變動的影響方向時，兩者測得的影響方向在所有樣本期間皆相同。第三，.當以DDF進一步拆解生產力效果時可發現：在所有樣本期間產出面對利潤變動的負向影響略高於要素投入面。第四，就未定向SBM所萃取出的額外效果而言，在部分樣本期間，生產力效果的產出面對利潤變動的頁獻高於要素投入面。
In the framework of data envelopment analysis (DEA), there are two different measures of efficiency: radial and non-radial. The radial measure originated from the CCR model (Charnes et al., 1978), whereas the non-radial DEA methodology is represented by the slack-based measure (SBM) (Tone, 2001). Regarding the studies on decompositions of profit change, Grifell-Tatjé and Lovell (Grifell-Tatjé, E., Lovell, C.A.K., 1999. Profits and productivity. Management Science 45, 1177-1193) decompose profit change of banks into six exclusive components using the radial DEA framework so as to consider the linkage between productivity change and profit change. Sahoo and Tone (Sahoo, B.K., Tone, K., 2009. Radial and non-radial decompositions of profit change: With an application to Indian banking. European Journal of Operational Research 196, 1130-1146) adopt SBM to decompose profit change of a bank so as to address the concerns of non-radial slacks. However, both the above two studies never consider the input side when decomposing the productivity effect. In fact, the change in operating profit can be traced from the change in revenue (the output side) and the change in cost (the input side).
Therefore, the study will propose two DEA approaches, directional distance function (DDF) and non-oriented SBM, to extract more complete drivers of profit change and illustrate the decompositions with these two approaches. The former is set as a kind of radial DEA framework. Both the two approaches illustrate the decompositions of profit change to Taiwanese banks during the period 1994-2002 and arrive at the following results. First, in the process of decomposing the productivity effect, both of them can extract the additional effect (i.e. the input side) which cannot be found in previous papers. Second, the DEA approach of Grifell-Tatjé and Lovell (1999) analysis (GLA) and DDF of our study exhibit the same direction of contribution by the technical change effect and the operating efficiency effect over the entire period. Third, when we use DDF to decompose the productivity effect, we find that the negative contribution of the output side slightly outweighs that of the input side over the entire period. Fourth, with regard to the additional components extracted by the non-oriented SBM, the study finds that the output side outweighs the input side within the productivity effect during some of our sample periods.
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