Thay đổi năng suất của các ngân hàng ở Đài Loan và Trung Quốc

Nội dung text: Thay đổi năng suất của các ngân hàng ở Đài Loan và Trung Quốc

1. PRODUCTIVITY CHANGE OF BANKS IN TAIWAN AND CHINA THAY ĐỔI NĂNG SUẤT CỦA CÁC NGÂN HÀNG Ở ĐÀI LOAN VÀ TRUNG QUỐC Yu-Hui Lin Taipei Chengshih University of Science and Technology, Taiwan Jia-Ching Juo Lunghwa University of Science and Technology, Taiwan Abstract In order to find out the competitive advantages and disadvantages of input usage, Mahlberg and Sahoo (2011) and Chang et al. (2012) have decomposed the Luenberger productivity indicator into input-specific components. We extend their works, the input- specific decomposition, to the non-oriented decomposition of the Luenberger productivity indicator, which accounts for not only the conventional components, the changes in technical efficiency and technology, but also the productivity gap between the group technology and the meta technology. The decomposition enables us to recognize the contribution of each output and each input toward productivity change under the meta technology and the above gap. Especially, the productivity gap attributed to individual output- and input-specific components is newly developed in this study. Our decomposition framework is used to illustrate productivity performance of Taiwanese and Chinese banks over the period 2006-2009. JEL classification: G21; D24 Keywords: Metafrontier; Luenberger; Productivity change; Data envelopment analysis (DEA); Productivity gap Túm tắt Để tỡm ra lợi thế và bất lợi trong cạnh tranh của cỏc nguồn lực đầu vào, Mahlberg và Sahoo (2011) và Chang et al. (2012) đó phõn tỏch chỉ số năng suất Luenberger thành cỏc nhõn tố đầu vào cụ thể. Chỳng tụi mở rộng việc phõn tỏch cỏc nhõn tố đầu vào cụ thể này sang việc phõn tỏch khụng định hướng chỉ số năng suất Luenberger, chỉ số này khụng chỉ cho thấy cỏc nhõn tố thụng thường, việc thay đổi trong hiệu quả kỹ thuật và cụng nghệ mà cũn cho thấy khoảng cỏch năng suất giữa cụng nghệ nhúm và cụng nghệ meta. Việc phõn tỏch này cho phộp chỳng tụi nhận ra mức độ đúng gúp của mỗi nhõn tố đầu ra và nhõn tố đầu vào vào sự thay đổi trong năng suất trong cụng nghệ meta và khoảng cỏch giữa cụng nghệ nhúm và cụng nghệ meta. Đặc biệt, khoảng cỏch năng suất do cỏc nhõn tố đầu ra và đầu vào riờng biệt cũng được phỏt triển trong nghiờn cứu này. Khung phõn tỏch của chỳng tụi được sử dụng để minh hoạ cho năng suất hoạt động của cỏc ngõn hàng Trung Quốc và Đài Loan trong giai đoạn 2006 - 2009 Từ khoỏ: Metafrontier; Luenberger, thay đổi năng suất, phõn tớch phỏt triển dữ liệu DEA, khoảng cỏch năng suất JEL classification: G21; D24 229
2. 1. Introduction One of the limitations faced by researchers of the conventional Malmquist productivity index (MPI) is to choose either an output- or an input-oriented perspective. To deal with this difficulty, Chamber et al. (1996a, 1996b) used the directional distance functions (DDFs) to develop the Luenberger productivity indicator (LPI) as a measure of the change in total factor productivity. LPI appears in an additive form which is constructed on the basis of difference rather than ratio. According to the discussions of Boussemart et al. (2003), the ratio and difference approaches to index number differ in terms of following properties. First, while the ratio form is unit independent, the difference form may be not. Second, the ratio form faces problems of dealing with zero observations, while it poses little difficulties for the difference form. Furthermore, the difference form is invariant to changes in the origin, while the ratio form is not. DDF is a very flexible approach since it can be used to account for inefficiencies of both outputs and inputs at the same time. However, the Luenberger indicator based on the radial DDFs does not provide proper guidance for productivity change since it cannot account for non-radial slacks of inputs and outputs. Non-radial slacks of outputs and inputs often occur in the non- parametric reference technology. Recognizing the limitation of the radial approach, Fukuyama and Weber (2009) introduced the directional Russell measure of inefficiency that accounts for both non-radial output expansions and non-radial input contractions. Mahlberg and Sahoo (2011) and Chang et al. (2012) developed, based on the directional Russell measure, the non-radial Luenberger productivity indicator to address the concerns of non-radial slacks. Their indicator can also be shown as the sum of the individual input- specific Luenberger indicators so as to trace the contribution of a specific input to productivity change. There have been papers aimed at extending the framework of productivity change to the metafrontier. When analyzing performance of decision making units (DMUs) belonging to different groups, it is necessary to establish a common production function (the metafrontier production function) and these DMUs are assumed to have potential access to the metafrontier. According to Battese and Rao (2002), the concept of metafrontier was first introduced by Hayami (1969) and Hayami and Ruttan (1970). Battese and Rao (2002) used a stochastic metafrontier to investigate technical efficiencies of firms in different groups. From then on, there are on-going papers focused on the framework of metafrontier to measure technical efficiencies and productivity change, such as Battese et al. (2004), O’Donnell et al. (2008), Chen et al. (2009), Oh (2010a), Oh (2010b), Oh and Lee (2010), Chen and Yang (2011). However, there must be technology gaps between different group-specific technologies and metafrontier. Thus, we should estimate separate production frontiers for these different groups. The group-specific technical difference may be attributed to characteristics of the physical, social, and economic environment (O'Donnell et al., 2008). The examples of parametric approach to empirically construct the metafrontier include Battese and Rao (2002), Battese et al. (2004) and Chen and Yang (2011). The non-parametric approach to define the metafrontier is 230
3. exemplified by Oh (2010a and 2010b), Oh and Lee (2010). O'Donnell et al. (2008) used parametric and non-parametric methods to estimate the metafrontier. In order to trace the sources of change in the gap between a group-specific technology and the meta technology, there have been papers aimed at combining the concept of the metafrontier with productivity indices. Chen et al. (2009) introduced a generalized metafrontier Malmquist productivity index (MMPI) which further accounts for the impact of scale efficiency change to analyze the dynamics of Chinese productivity over the period 1996-2004. Oh and Lee (2010) proposed MMPI, based on the global technology set which envelops group-specific intertemporal benchmark technology sets, to calculate efficiency and technical changes for DMUs operating under different group-specific technologies. It further allows for the computation of technological gap and its change under different technologies. Oh (2010a and 2010b) incorporated desirable and undesirable outputs into the global Malmquist-Luenberger productivity index, measuring the calculation of the change in technical efficiency, technology and the technological gap between regional and global frontier technologies. Chen and Yang (2011) used MMPI which accounts for the effect of scale efficiency change to analyze productivity change of Taiwanese and Chinese banks over 1993－ 2007. There are many concerns about the growing market in China, such as the performance of the Chinese banking industry. Chen et al. (2005) examined the impact of regulatory reform and liberalization on the efficiency and productivity of Chinese banks. Fu and Heffernan (2007) estimated Chinese banking X-efficiency. Ariff and Can (2008) compared the efficiency of banks across different ownership types in China and found that joint-stock banks are more cost and profit efficient than state-owned banks. Berger et al. (2009) also explored Chinese banking ownership and efficiency. The Taiwanese banking industry actively sought for new business opportunities in China since 1990s. Using the stochastic metafrontier framework of Battese et al. (2004), Huang and Fu (2013) propose to compare and measure the cost efficiency and cost frontier gap between the banking industry in Taiwan and China over the period 2005-2009. Taiwan and China has signed the Memorandum of Understanding (MOU) on cross-strait financial supervisory cooperation in 2009. The MOU was expected to offer Taiwanese and Chinese banks more favorable opportunities which allow each other to establish branches or subsidiaries in both countries. However, the performance comparison of banks belonging to different groups requires constructing the common production frontier. The MOU represents the possibility of a common production technology for Chinese and Taiwanese banks in the future. The main objective of this study is aimed at analyzing the banking performance of both two groups if they operate under the metafrontier. In this study, we develop a new framework to extend the work of Mahlberg and Sahoo (2011) to the field of metafrontier so as to trace the contributions of a specific output and a specific input to the aggregate productivity change under a metafrontier. Furthermore, we can also recognize the contributions of a specific output and a specific input to the gap between productivity change under the metafrontier and that under a group-specific technology. The output- and input-specific gaps in the field of productivity 231
4. change are also newly developed in this study. Our decomposition will be illustrated by the panel data of Chinese and Taiwanese banks during the period 2006-2009. The remainder of this study is organized as follows. In Section 2 we propose the analytical structure to decompose the metafrontier Luenberger productivity indicator using the directional Russell measures. Section 3 executes the above decompositions. Definitions of variables and data descriptions are presented in Section 4. Section 5 deals with the empirical results. The conclusions follow in Section 6. 2. The metafrontier Luenberger productivity indicator The conventional framework of Luenberger productivity index is illustrated in terms of DDF proposed by Chambers et al. (1996b). DDF can completely characterize technology, since it allows DMUs to optimize their production by simultaneously adjusting inputs and outputs, and is a measure of technical inefficiency. We assume that all DMUs N M use xR∈ + inputs to produce yR∈ + outputs. Technology (S) for each DMU is defined as the set of all feasible input and output vectors. S= {( x , y ) : x can produce y } (1) In order to further consider non- radial slacks, Fukuyama and Weber (2009) extend the work of Fọre and Lovell (1978) to propose directional Russell measure (DRM) to measure technical inefficiency. To define N the framework of DRM, we first specify the directional vector, g=(-gx, gy), where g x ∈ R+ M and gRy ∈ + . The directional vector determines the direction in which technical inefficiency is assessed. The technical inefficiency measured by DRM in period t (t=0, 1, 2, , T) is then defined as ⎧⎫1 ⎛⎞NN 11ββββ+−+∈x gy,, g S r ⎪⎪⎜⎟NM∑∑iriirr()xyir (2) Rtxy(,;xy−= gg, ) sup⎨⎬2 ⎝⎠ii==11 ⎪⎪ ⎩⎭ββir≥≥∀=∀=0; 0, iNrM 1, , ; 1, , r where R(,xy ;−≥ ggxy, ) 0 and its value is independent of unit. Our study lets g=(－gx, gy) be taken as the quantity vector of the observed production point-that is, g=(－x, y). The th parameters, βi and βj, respectively represent the proportional contraction of the i input and the proportional expansion of the rth output in order to reach the efficient level. Then the objective function in Eq. (2) means that a DMU seeks to maximize the average degree of contraction in inputs and expansion in outputs along the directional vector (-x, y). For constructing a common meta production frontier, we further assume that there is a DMU k (k=1, 2, , Kh) in group h (h=1, 2, ., H) to produce M outputs with N inputs in each period and there is a total of K (K=K1+K2+ +Kh+ +KH) DMUs in our analytic framework. For a DMU in the specific group h, we denote the output and input vectors in h M h N period t by yRt ∈ + and xRt ∈ + respectively. The production technology set of a DMU h hh h h within group h in period t can be denoted by St = {( xtt , y ) : x t can produce y t }. Besides, *12 H all the H technology sets operate under the common technology set Sxtttt( )=∪∪∪{} S S S . Thus, DRMs with respect to the metafrontier in base period 0 can be represented as 232
5. r R* (,xy ;− g, g ) 0 00 xy00 ⎧⎫1 ⎛⎞NN 11ββββ +−+∈xgygS, ; (3) and the ⎪⎪⎜⎟NM∑∑iriirr()00x00iry 0 = sup ⎨⎬2 ⎝⎠ii==11 ⎪⎪ ⎩⎭ββir≥≥∀=∀=0, 0, iNrM 1, , ; 1, , frontier of group h in base period 0 can be denoted as follows. r R h (,xy ;− g, g ) 0 00 xy00 ⎧⎫1 ⎛⎞NN 11ββββhhhhh+−+∈xgygS, ; (4) ⎪⎪⎜⎟NM∑∑iriixrry()0000ir 0 = sup ⎨⎬2 ⎝⎠ii==11 ⎪⎪hh ⎩⎭ββir≥≥∀=∀=0, 0, iNrM 1, , ; 1, , DRMs in the current period 1 can be expressed in a similar way as above. We next use DRMs to define the technology gap (TG) between the metafrontier and the frontier of group h in two periods 0 and 1as rr TGhh(, x y ; −≡ g , g ) R* (, x y ; −− g , g ) R (, x y ; −≥ g , g )0 (5) 000xy00 000 xy 00 000 xy 00 rr TGxyhh(,;,)(,;,)(,;,)0 −≡ g g Rxy* −− g g Rxy −≥ g g (6) 111xy11 111 xy 11 111 xy 11 The technology gap measures the degree to which the current technology (the group- specific frontier) can approach its best potential technology (the metafrontier). The value h of TGt is smaller if the current technology of group h is closer to the meta technology in time period t. It also means that the production technology of the hth group is better than those of other groups under the common meta technology. On the other hand, we define two cross-period TGs as rr TGxyhh(, ; −≡ g , g ) Rxy* (, ; −− g , g ) Rxy (, ; − g , g ) (7) 011x11yxyxy 011 11 011 11 rr TGxyhh(, ; −≡ g , g ) Rxy* (, ; −− g , g ) Rxy (, ; − g , g ) (8) 100x00yxyxy 100 00 100 00 The former measures the gap, based on the observed points of period 1, between the metafrontier and the group frontier of period 0. The later measures the gap, based on the observed points of period 0, between the metafrontier and the group frontier of period 1. As the conventional Luenberger indicator, the indicator LPIh with respect to group h can be represented by the sum of group-specific technical efficiency change ( ∆TE h ) and technical change ( ∆T h ): LPIh (, x y ,,; x y −− g , g , g , g ) 0,1 0 0 1 1 xy00 xy 11 rr =−−−⎡⎤Rxyhh(, ; g , g ) Rxy (,; g , g ) ⎣⎦000xy00 111 xy 11 rr ⎧⎫⎡⎤Rxyhh(, ; −− g , g ) Rxy (, ; − g , g ) (9) 1 ⎪⎣111xy11 011 xy 11 ⎦ ⎪ + ⎨⎬rr 2 ⎪⎪+−−−⎡⎤Rxyhh(, ; g , g ) Rxy (, ; g , g ) ⎩⎭⎣⎦100xy00 000 xy 00 hh =∆TET0,1+∆ 0,1 h A value of LPI0,1 greater than 0 indicates the improvement in productivity of a DMUin group h, a value less than 0 denotes productivity deterioration and a value equal to 0 233
6. implies unchanged productivity. The change in the group-specific technical efficiency, h ∆TE0,1 , captures the average change of output gain/loss and input saving /wasting within th h the h group-specific technology over time. The change in technology, ∆T0,1 , captures the gain/loss of outputs and the saving /wasting of inputs due to the shift in the group-specific technology over two time periods. The values of ∆TE h and ∆T h greater than 0 suggest improvement, while the values of less than 0 suggest deterioration. Similarly, LPI * of a DMU under the metafrontier can also be defined by the sum of the metaforntier technical efficiency change ( ∆TE* ) and technical change ( ∆T * ): LPI* (, x y ,,; x y −− g , g , g , g ) 0,1 0 0 1 1 xy00 xy 11 rr =−−−⎡⎤Rxy (, ; g , g ) Rxy (,; g , g ) ⎣⎦000xy00 111 xy 11 rr ⎧⎫⎡⎤Rxy (, ; −− g , g ) Rxy (, ; − g , g ) (10) 1 ⎪⎣111xy11 011 xy 11 ⎦ ⎪ + ⎨⎬rr 2 ⎪⎪+−−−⎡⎤Rxy (, ; g , g ) Rxy (, ; g , g ) ⎩⎭⎣⎦100xy00 000 xy 00 =∆TET0,1+∆ 0,1 Since the metafrontier envelops all the group-specific frontiers, the indicator LPI* and its components are more suitable for comparing performance across different technologies. Based on Eqs. (5), (6), (7) and (8), the indicator LPI* in Eq. (11) can be further decomposed as follows. * LPI0,1(, x 0 y 0 ,,; x 1 y 1 −− gx , gyxy , g , g ) 00 11 (11) hh h h =∆TE0,1 +∆ T 0,1+ ∆ TEG 0,1 +∆ TG 0,1 Eq. (11) attributes the source of the indicator LPI* not only to the change in technical efficiency and technology within a specific group but also to the convergence rate of the above two components to those under the metafrontier. 3. Decompositions of the indicator with respect to inputs and outputs As proportional measures in the field of the conventional DEA, the radial DDF methodology overestimates the efficiency of a firm when there are non-radial slacks that remain in the constraints after the full radial efficiency is achieved. In order to take account of these slacks, we adopt DRM of Fukuyama and Weber (2009) to the decompositions of the Luenberger indicators. In addition to the decompositions of the Luenberger indicators across DMUs with different group technologies, this section will further execute the above decompositions across outputs and inputs. The meta productivity indicator in Eq. (11) can further be decomposed into the input- and output-specific components as LPI* (, x y ,,; x y −− g , g , g , g ) 0,1 0 0 1 1 xy00 xy 11 ⎛⎞⎛⎞NM NM hh hh (12) =⎜⎟⎜⎟∑∑ ∆TEir0,1 +∆ TE 0,1 + ∑∑ ∆ T ir 0,1 +∆ T 0,1 ⎝⎠⎝⎠ir==11 ir == 11 NM NM ⎛⎞⎛⎞hh hh +∆⎜⎟⎜⎟∑∑TEGir0,1 +∆ TEG 0,1 +∆ ∑∑ TG ir 0,1 +∆ TG 0,1 ⎝⎠⎝⎠ir==11 ir == 11 234
7. h h where ∆TEGi 0,1 and ∆TEGr 0,1 represent the change in the gap of technical efficiency h h change with respect to inputs and outputs, and ∆TGi 0,1 and ∆TGr 0,1 denote the change in the gap of technical change with respect to inputs and outputs. 4. Variables and data Description In the section, we adopt the intermediation approach which regards a bank as an intermediary producer of services through the transformation of funds received from depositors into investment or loans. According to the discussions of Berger and Humphrey (1997), each output in our study is measured in value terms but not in terms of the number of transactions or accounts. Generally, the intermediation approach views labor, funds, operating cost and interest as major inputs. On the other hand, it views loans and investments as major outputs. Thus, banks in this study are considered to have two outputs: loans (y1) and financial investment (y2), and three inputs: labor (x1), fixed assets (x2) and funds (x3). Our sample includes 27 banks in Taiwan and 18 banks in China for each year. The sample periods cover four years starting from the year 2006 to 2009. The descriptive statistics of variables shows in Table 1. On average, loans of the Chinese banks has 8.87 times amount as much as those of the Taiwanese banks and the investment of the Chinese banks has 13.57 times amount as much as those of the Taiwanese banks. With respect to the input variables, the Chinese banking industry has 21.54 times employees, 6.23 times fixed assets and 11.57 times funds as many as the Taiwanese banking industry. Table 1 Descriptive statistics of variables, 2006-2009 Taiwan China Outputs Mean S.D. Max. Min. Mean S.D. Max. Min. Total loans (Y1, millions of USD) 16,840 14,777 61,997 1,512 149,404 201,892 788,310 1,784 Investments (Y2, millions of USD) 8,301 8,962 48,297 151 112,665 163,511 627,254 982 Inputs Labors (X1, no. of employees) 4,055 2,361 9,290 287 87,358 142,526 452,464 1,228 Net fixed assets (X2, millions of USD) 451 500 2,556 40 2,808 4,244 16,370 30 Funds (X3, millions of USD) 24,418 21,697 103,171 2,565 282,589 390,548 1,567,713 2,630 5. Empirical results Table 2 shows the results for average technical inefficiencies and the technology r gaps of banks in China and Taiwan. The values of R* (,x ygg ;− , ) in Eq. (3) are used 0 00 xy00 to compare technical inefficiencies of banks across different groups. The values of 235
8. r Rh (,x ygg ;− , ) in Eq. (4) are used to observe performance of banks within a specific 0 00 x00y group h (h=Taiwan; China). On average, technical inefficiencies of the Taiwanese and Chinese banks were 14.53% and 5.78% respectively if they operate under the metafrontier. The average degree of the required increment of outputs and the decrement of inputs in Taiwanese banks was 14.53%, versus the degree of 5.78% for Chinese banks. This result suggests that the Chinese banks outperformed Taiwanese banks in technical efficiency. Regarding the panel results, Chinese banks still outperformed Taiwanese banks in technical efficiency over all the sample periods. However, the group-specific frontier of the Taiwanese benchmark banks was closer to the metafrontier in each period. Although it is not appropriate to directly compare the group-specific technical efficiency across groups due to technological heterogeneity, Table 2 nevertheless shows that, during the entire sample period, the Chinese banks are much closer to their own cost production frontiers r with an average technical inefficiency Rh (,x ygg ;− , )=4.10% than the Taiwanese 0 00 x00y banks to their own production frontier with an average technical efficiency r Rh (,x ygg ;− , )=13.65%. It can also be found that both the Chinese and Taiwanese 0 00 x00y banks showed the highest degree of inefficiency in 2008. However, we find that the Taiwanese banking industry has the lower average value of TGh (0.88%), compared with that (1.68%) of the Chinese banking industry. It means that the benchmark banks located in Taiwan were closer to the potential technology (the metafrontier) even though the Chinese banking industry outperformed the former in technical efficiency. Table 2 Average inefficiency and technology gap Year β* βh TGh 2006 13.88 13.69 0.19 2007 14.50 13.81 0.69 Taiwan 2008 15.39 13.99 1.40 2009 14.36 13.10 1.26 Mean 14.53 13.65 0.88 2006 4.77 3.35 1.42 2007 7.19 4.95 2.24 China 2008 6.18 4.74 1.44 2009 4.98 3.36 1.62 Mean 5.78 4.10 1.68 The figures in this table are the average annual percentages over all outputs and inputs. The average values of productivity growth, technical efficiency change, technology change, ∆TEGh and ∆TGh are listed in Table 3. The first three columns provide LPI * and its components which are the conventional works by Chamber et al. (1996a, 1996b), and the following three columns provide those of the LPI h . We first examine the results on LPI h of banks within a specific group and its components, the change in technical efficiency and technology. They are not suitable to execute comparison across groups as a result of different technologies. Average productivity of both Taiwanese and Chinese banks improved slightly by 0.47% and 0.97% respectively. Regarding the panel results, the former improved and the later deteriorated in two out of three sample periods. Especially, productivity deteriorated within both the two groups during the period 2007-2008, in 236
9. which technology deterioration dominated efficiency change. The decline seems to be temporary for Taiwanese banks as they recovered quickly in the following year. However, productivity decay of the Chinese banking industry still held in next year and its technology deteriorated up to a even higher level of 3.72%. In order to compare the results on productivity growth and its components across groups, we further examine them under the common technology (the metafrontier). It can be found that productivity change of the Taiwanese banking industry slightly outperformed the Chinese banking industry. The former’s average potential productivity increases by 0.63%. It was mainly attributed to the improvement in technology (0.79%), on average. However, average technical efficiency exhibits deterioration (－0.16%). Average productivity of Chinese banks also improved, up to a degree of 0.56%. The improvement in technology was main source. The panel results of LPI* and its components are also illustrated in Table 3. The Taiwanese banking industry outperformed the Chinese group only during 2008－2009. For the Chinese banking industry, its potential productivity decay (－2.54%) came from the metaproduction technology deterioration (－3.74%) of its benchmark banks even though its members showed catching-up in technical efficiency (1.20%). As discuss previously, if the group-specific Luenberger productivity index is greater than the meta Luenberger productivity index, i.e., LPIh > LPI * , then it implies a convergence of the group-specific productivity toward the meta productivity. The rate of convergence can further be attributed to various sources via Eq. (19). The last three columns of Table 3 summarizes the sources and rates of convergence. First of all, Table 3 shows that the meta Luenberger productivity of Taiwanese banks barely improves over the country-specific Luenberger productivity by 0.16% ( LPGh =0.16%). For Chinese banks, the country-specific productivity converged to the meta productivity by 0.41% ( LPGh =－0.41%) on average. When we further explore their components, it can be found that technical efficiency of the Taiwanese group converged to that of the metafrontier at the average rate of 0.35% ( ∆TEGh =－0.35%) annually. However, its country-specific technology diverged from the metafrontier at the average rate of 0.51% ( ∆TGh =0.51%) annually. On the other hand, both technical efficiency and technology of the Chinese group converge to those of the metafrontier at the average rate of, respectively, 0.07% ( ∆TEGh =－0.07%) and 0.34% ( ∆TGh =－0.34%) annually. The empirical findings shown in Table 3 seem to suggest that the important source of the path to the divergence of country-specific productivity from the meta productivity is the growth of production technology in the case of Taiwan. For Chinese banks, the production technology dominated the path to the convergence of the country-specific productivity to the meta productivity. 237
10. Table 3 Decomposition of the overall LPI* Metafrontier Group-specific frontier LPGh ∆TEGh ∆TGh LPI * ∆TE* ∆T * LPI h ∆TE h ∆T h 2006-2007 1.65 -0.62 2.27 1.26 -0.12 1.38 0.39 -0.50 0.89 Taiwan 2007-2008 -1.15 -0.89 -0.26 -1.32 -0.18 -1.14 0.17 -0.69 0.86 2008-2009 1.38 1.03 0.35 1.43 0.89 0.54 -0.05 0.14 -0.19 Mean 0.63 -0.16 0.79 0.47 0.20 0.27 0.16 -0.35 0.51 2006-2007 3.14 -2.42 5.56 7.78 -1.60 9.38 -4.64 -0.82 -3.82 China 2007-2008 1.06 1.01 0.05 -2.52 0.21 -2.73 3.58 0.79 2.79 2008-2009 -2.54 1.20 -3.74 -2.34 1.38 -3.72 -0.20 -0.17 -0.03 Mean 0.56 -0.07 0.63 0.97 0.00 0.97 -0.41 -0.07 -0.34 The figures in this table are the average annual change percentages over all outputs and inputs. We now turn to show the results on decomposition of LPI * with respect to output- specific and input-specific contributions. For comparison across countries, Tables 4 and 5 illustrate the results of decomposition for Taiwanese and Chinese banks. The individual output-specific and input-specific indicators with respect to LPI*, ∆TE* and ∆T * , when added up, yield their respective overall indicators. The relationship holds across banks in each period and on average. For example, Table 4 shows that Taiwanese banks exhibited productivity growth of 0.63% (see Table 3), which is nothing but the sum of productivity change in loans (0.05%), investment (－0.16%), labors (0.43%), fixed assets (0.35%) and funds (－0.04%). We can find that labors, especially for their technical growth (0.74%), played a dominant role in this industry. Furthermore, productivity growth of both labors and fixed assets, especially for their technical growth, made positive contributions to Taiwanese banks productivity over all the sample period even at the outset of the global financial crisis in 2007－2008. We can trace the sources of Taiwanese banking technical efficiency change (－0.16% in Table 3) and technical change (0.79% in Table 3) with respect to output and input components in the same way. Table 4 Decomposition of Taiwanese banking LPI* with respect to individual variables Y1 Y2 LPI* ∆TE* ∆T * LPI* ∆TE* ∆T * 2006-2007 0.28 0.31 -0.03 0.96 -0.20 1.16 2007-2008 0.00 -0.08 0.08 -2.11 0.11 -2.22 2008-2009 -0.13 0.15 -0.28 0.66 0.64 0.02 Mean 0.05 0.13 -0.08 -0.16 0.18 -0.34 X1 X2 X3 LPI* ∆TE* ∆T * LPI* ∆TE* ∆T * LPI* ∆TE* ∆T * 2006-2007 0.17 -0.62 0.79 0.23 -0.11 0.34 0.01 0 0.01 2007-2008 0.43 -0.5 0.93 0.58 -0.42 1.00 -0.05 0 -0.05 238
11. 2008-2009 0.68 0.18 0.50 0.24 0.06 0.18 -0.07 0 -0.07 Mean 0.43 -0.31 0.74 0.35 -0.16 0.51 -0.04 0 -0.04 The figures in this table are the average annual change percentages In Table 5, the average productivity growth of Chinese banks can be traced in the same way as above. The average productivity growth of labors (1.13%) not only played a dominant role within the Chinese banking industry but also outperformed that of the Taiwanese banking labors. Comparing the components of the productivity growth of labors across two groups, we find that technical improvement was major source. Furthermore, the labor technical improvement of Chinese banks outperformed that of Taiwanese banks. Referring to Tables 4 and 5, we can also compare the productivity contributions of other individual outputs and inputs toward LPI * across groups. The comparison reveals that Taiwanese banks outperformed Chinese banks only in the productivity growth of loans and funds. Table 5 Decomposition of Chinese banking LPI* with respect to individual variables Y1 Y2 LPI * ∆TE* ∆T * LPI * ∆TE* ∆T * 2006-2007 0.47 -0.40 0.87 1.32 -1.33 2.65 2007-2008 0.34 -0.10 0.44 0.48 1.66 -1.18 2008-2009 -4.28 0.35 -4.63 -0.31 -0.29 -0.02 Mean -1.16 -0.05 -1.11 0.50 0.01 0.49 X1 X2 X3 LPI * ∆TE* ∆T * LPI * ∆TE* ∆T * LPI * ∆TE* ∆T * 2006-2007 1.32 -0.08 1.40 0.57 -0.62 1.19 -0.54 0.01 -0.55 2007-2008 0.86 0.47 0.39 -0.08 -0.96 0.88 -0.54 -0.06 -0.48 2008-2009 1.21 0.38 0.83 1.06 0.70 0.36 -0.22 0.06 -0.28 Mean 1.13 0.26 0.87 0.52 -0.29 0.81 -0.43 0.00 -0.43 The figures in this table are the average annual change percentages Tables 6 and 7 show further decomposition of LPI * into output- and input- specific components and exhibit the relationship between LPI * and LPI h for each output and input. We first focus on Taiwanese banks. Table 6 shows that their average productivity growth was mainly driven by the labor usage (0.43%) which significantly came from the contribution of their group-specific technology improvement (0.55%). Similarly, Table 7 shows that the average productivity growth of Chinese banks was mainly driven by the labor usage (1.13%) which also came from the contribution of the group-specific technology change (0.65%). For Taiwanese and Chinese banks, Table 3 has shown negative values of ∆TEGh in two out of three sample periods and on average. Taking a further look at Tables 6 and 7, we find different sources for the two groups. For Taiwanese banks, catching-up in technical efficiency was mainly induced by inputs including labors (－0.16%) and fixed assets (－0.23%). On the other hand, catching-up in technical 239
12. efficiency for Chinese banks was mainly driven by investments (－0.23%). We finally turn to trace the source of catching-up of a group technology with the meta technology ( ∆TGh ). For Taiwanese banks, Table 6 shows that the divergence of their group-specific technology change from the potential technology change was mainly driven by loans ( ∆TGh =0.11%), investments ( ∆TGh =0.27%) and labors ( ∆TGh =0.19%). Table 3 has shown that technology of the Chinese group converged toward the potential technology at the average rate of 0.34% ( ∆TGh =－0.34%) annually. We further find in Table 7 that the above convergence was mainly pushed by loans ( ∆TGh =－0.13%), investments ( ∆TGh =－0.23%) and funds ( ∆TGh =－0.15%). Table 6 The relationship between LPI* and LPIh with respect to individual variables for Taiwanese banks Y1 Y2 * h h h * h h h LPI ∆TE ∆T h ∆TEG ∆TG LPI ∆TE ∆T ∆TEG ∆TG h 2006-2007 0.28 0.21 0.14 0.10 -0.17 0.96 -0.24 0.84 0.05 0.31 2007-2008 0 -0.14 -0.05 0.06 0.13 -2.11 0.68 -2.84 -0.57 0.62 2008-2009 -0.13 0.20 -0.66 -0.05 0.38 0.66 0.12 0.13 0.52 -0.11 Mean 0.05 0.09 -0.19 0.04 0.11 -0.16 0.19 -0.62 0 0.27 X1 X2 X3 * h h * h h h h * h h h h LPI ∆TE ∆T ∆TEGh ∆TG h LPI ∆TE ∆T ∆TEG ∆TG LPI ∆TE ∆T ∆TEG ∆TG 2006-2007 0.17 -0.25 0.42 -0.38 0.38 0.23 0.16 0.01 -0.27 0.33 0.01 0 -0.03 0 0.04 2007-2008 0.43 -0.56 0.94 0.07 -0.02 0.58 -0.16 0.91 -0.25 0.08 -0.05 0 -0.10 0 0.05 2008-2009 0.68 0.36 0.28 -0.18 0.22 0.24 0.21 0.78 -0.15 -0.6 -0.07 0 0.01 0 -0.08 Mean 0.43 -0.15 0.55 -0.16 0.19 0.35 0.07 0.57 -0.23 -0.06 -0.04 0 -0.04 0 0 The figures in this table are the average annual change percentages Table 7 The relationship between LPI* and LPIh with respect to individual variables for Chinese banks Y1 Y2 * h h LPI ∆TE h ∆T h ∆TEGh ∆TGh LPI * ∆TE ∆T ∆TEGh ∆TG h 2006-2007 0.47 -0.44 1.31 0.04 -0.44 1.32 -1.18 6.93 -0.15 -4.28 2007-2008 0.34 0.09 0.22 -0.19 0.22 0.48 1.39 -4.29 0.27 3.11 2008-2009 -4.28 0.22 -4.46 0.13 -0.17 -0.31 0.51 -0.48 -0.8 0.46 Mean -1.16 -0.04 -0.98 -0.01 -0.13 0.50 0.24 0.72 -0.23 -0.23 X1 X2 X3 * h h h * h h * h h h LPI ∆TE ∆T ∆TEGh ∆TG LPI ∆TE ∆T ∆TEGh ∆TGh LPI ∆TE ∆T ∆TEG ∆TGh 2006-2007 1.32 0.05 1.15 -0.13 0.25 0.57 0.02 0.60 -0.64 0.59 -0.54 -0.05 -0.61 0.06 0.06 2007-2008 0.86 0.02 0.31 0.45 0.08 -0.08 -1.28 1.05 0.32 -0.17 -0.54 -0.01 -0.02 -0.06 -0.45 2008-2009 1.21 0.46 0.48 -0.08 0.35 1.06 0.24 0.94 0.46 -0.58 -0.22 -0.05 -0.20 0.12 -0.09 Mean 1.13 0.18 0.65 0.08 0.22 0.52 -0.34 0.86 0.05 -0.05 -0.43 -0.04 -0.28 0.04 -0.15 The figures in this table are the average annual change percentages 240
13. 6. Conclusions The papers that compare productivity growth across different DMUs usually resort to the Malmquist productivity index or the Luenberger productivity indicator. However, it may be improper to directly compare productivity change of DMUs belonging to different groups with different production technology. Consequently, the proper measure of productivity comparison is assessed with respect to the meta production technology. Based on the Russell directional distance functions, this study develops the non-radial metafrontier Luenberger productivity indicator not only to execute the comparison across DMUs facing diverse technologies but also to deal with non-radial slacks. Furthermore, the relationship between meta Luenberger productivity indicator and group Luenberger productivity indicators can be expressed as the sum of output- and input-specific indicators so as to explore the contribution of a specific output and input to productivity change. Especially, the gaps of technical efficiency change and technology change attributed to individual output- and input-specific components are newly developed in this study. A panel data of 27 Taiwanese banks and 18 Chinese banks covering the period 2006-2009 are illustrated to measure the above decompositions and gaps. First, the benchmark banks located in Taiwan were closer to the potential technology even though the Chinese banking industry outperformed the former in technical efficiency. Second, the average productivity growth of Taiwanese banks under the metafrontier slightly outperformed those in China. The main source of productivity growth for these two groups was technology improvement. When we further explore the contributions of output-specific and input-specific productivity growth, we find that labors, especially for their technical growth, played a dominant role in this industry for both countries. Regarding the dynamics of productivity change and its components, Taiwanese banking technical efficiency change demonstrated convergence toward that under the metafrontier. Labors and fixed assets were the main sources. For Chinese banks, their group-specific productivity change and components, especially technology change, showed convergence toward those under the metafrontier. Loans, investments and funds were the main driving power. REFERENCES Ariff M, Can L (2008) Cost and profit efficiency of Chinese banks: A non-parametric analysis. China Economic Review 19:260-273 Battese GE, Rao DSP (2002) Technology gap, efficiency, and a stochastic metafrontier function. International Journal of Business and Economics 1:87－93 Battese GE, Rao DSP, O'Donnell CJ (2004) A metafrontier production function for estimation of technical efficiencies and technology potentials for firms operating under different technologies. Journal of Productivity Analysis 21:91−103 Berger AN, Hasan I, Zhou M (2009) Bank ownership and efficiency in China: what will happen in the world’s largest nation? Journal of Banking and Finance 33: 113-130 Berger AN, Humphrey DB (1997) Efficiency of financial institutions: International survey and directions for future research. European Journal of Operational Research 98:175-212 241
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