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© 2021 Conscientia Beam. All Rights Reserved. 

PERFORMANCE EVALUATION OF CHINESE COMMERCIAL BANKS BASED ON THE 
MALMQUIST INDEX  

 

 

 Wenjing Xie1+ 

 Meiling He2 

 Guohui Huang3 

 Lu He4 

 Fan Lin5 

 Wen-Tsao Pan6 

1,2,3,4,5,6Hunan University of Science and Engineering, School of  Economics and 
Management, Hunan, Yongzhou, Lingling, District, China. 
1Email: 1269244811@qq.com Tel: 17077378829 
2Email: 1438758365@qq.com Tel: 15399977785 
3Email: 2062705347@qq.com Tel: 18176775344 
4Email: he1125@foxmail.com Tel 18373461057 
5Email: 1403561680@qq.com Tel: 18674686031 
6Email: teacherp0162@126.com Tel: 13426703155 

 
 

 
(+ Corresponding author) 

 ABSTRACT 
 
Article History 
Received: 4 August 2021 
Revised: 6 September 2021 
Accepted: 30 September 2021 
Published: 22 October 2021 
 

Keywords 
DEA  
Malmquist 
Performance evaluation 
Technological progress 
Performance analysis 
Business performance analysis 
Efficiency evaluation 
Commercial bank. 

 
JEL Classification: 
G29. 

 
Commercial banks have the function of promoting the raising and rational distribution 
of funds in economic construction in China. Commercial banks are also important in 
promoting the smooth development of socialist economic activities and the 
development of national economy and other socialist productive economic activities. At 
present, one of the biggest difficulties faced by China's commercial banks is the 
improvement of their efficiency and competitiveness in the face of continuous 
development and change. This paper establishes the efficiency evaluation model of 
commercial banks using the DEA-based Malmquist index; it also uses a data 
envelopment analysis (DEA) to analyze the financial data of nine listed banks in China 
from 2011 to 2020, studies the efficiency of commercial banks in China, and finds the 
efficiency differences. Based on empirical research, this paper puts forward 
corresponding suggestions. The research shows that the key to dealing with this 
situation depends on the banks’ effective utilization of scientific and technological 
innovation and technological progress. In order to achieve the goal of innovative and 
sustainable development of commercial banks, it is necessary to integrate the 
continuous developments of science and technology with finance.  
 

Contribution/Originality: The paper's primary contribution is finding that in the face of continuous 

technological innovation and technological progress, the effective way to improve the performance of Chinese 

commercial banks is to effectively integrate technology and finance. 

 

1. INTRODUCTION 

With the development of China and the progress of technology, the financial industry is becoming more and 

more efficient, the growth of the market and the main bodies of operation are also increasing, and the competition in 

the Chinese and the international financial industries is becoming more and more fierce. The operating efficiency of 

commercial banks not only represents their sustainable development level, but also feeds back the potential of 

efficient resource allocation. As an important indicator of a company's operation, efficiency evaluation plays an 

important role in the sustainable development of banks. Banks can judge their own strength level through the 

results of efficiency evaluation, plan in advance and formulate the route of future development. The main activity of 

commercial banks is to offer industrial and commercial loans and deposits for profit. Commercial banks play a role 

in planning money, credit goods and other financial services. The existence of commercial banks is conducive to 

Financial Risk and Management Reviews 
2021 Vol. 7, No. 1, pp. 60-66. 
ISSN(e): 2411-6408 
ISSN(p): 2412-3404 
DOI: 10.18488/journal.89.2021.71.60.66 
© 2021 Conscientia Beam. All Rights Reserved. 

 
 
 

 
 
 

 

 

 

 
 

https://orcid.org/0000-0003-2388-6943
https://orcid.org/0000-0002-7624-7400
https://orcid.org/0000-0002-3946-5775
https://orcid.org/0000-0002-9083-4046
https://orcid.org/0000-0001-9907-6635
https://orcid.org/0000-0002-0999-5257
mailto:1269244811@qq.com
mailto:1438758365@qq.com
mailto:2062705347@qq.com
mailto:he1125@foxmail.com
mailto:1403561680@qq.com
mailto:teacherp0162@126.com
https://www.doi.org/10.18488/journal.89.2021.71.60.66


Financial Risk and Management Reviews, 2021, 7(1): 60-66 

 

 
61 

© 2021 Conscientia Beam. All Rights Reserved. 

promoting capital flow, reducing the cost of transaction processes, saving transaction time, improving the efficiency 

of resource allocation and promoting economic development. Yu-Dan (2018) proposed the improvement of the 

efficiency of China’s commercial banks by increasing the proportion of technology input, developing intermediary 

business, reducing the non-performing loan ratio, and increasing the capital adequacy ratio (Yu-Dan, 2018).The 

Zhao and Zhao (2021) representative cited the following reference papers: (Yu-Dan, 2018). Zhao and Zhao (2021), after 

much research in terms of scale efficiency, pure technical efficiency and operation efficiency, stated that listed 

commercial banks perform better than non-listed commercial banks. Therefore, one of the ways to improve the 

efficiency of commercial banks is to increase the listing construction of commercial banks (Yu-Dan, 2018).The 

operating efficiency of banks has great potential for development, and there are imbalances and mismatches in bank 

input and output. The aim of this study is to measure the financial data of nine listed banks in China from 2011 to 

2020 through the DEA-based Malmquist index method, clearly understand the correlation between input and 

output indicators, explore the effect of technological progress on bank efficiency, and find answers on how to 

improve the efficiency of Chinese commercial banks. 

 

2. LITERATURE DISCUSSION 

Bank efficiency can reflect the competitiveness and operating level of banks in the industry. The level of 

resource allocation of banks is reflected by the ratio of their inputs and outputs. Li and Hu (2015) mentioned that, at 

this stage, there are three types of methods for exploring bank efficiency: One method is to use non-parametric data 

envelopment analysis (DEA) to explore bank efficiency; the second method is to analyze bank efficiency based on 

relevant financial indicators; the third method is to use the parameter analysis method to construct a multiple linear 

regression model using the cost of production function. Using the DEA-based Malmquist index method to analyze 

the financial data of nine listed banks in China from 2011 to 2020 is the main content of this article. DEA is a linear 

programming method based on the research of Farrell (1957), who analyzed the technical efficiency of only one 

input and one output and clarified a way to help companies analyze the efficiency of measurement under multiple 

input conditions. Charnes, Cooper, and Rhodes (1978) developed the CCR linear programming model to further 

analyze the technical efficiency of multiple inputs and outputs. DEA can be applied to a bank's input and output 

indicator system. In view of the different national conditions and economic environments, the interpretation of bank 

input and output is also different. It is easier for commercial banks to manipulate input factors, so the use of input-

oriented models to evaluate efficiency is more in line with the actual situation. Zhang and Lei (2019) analyzed the 

financial data of 15 commercial banks from 2006 to 2015 as a sample and concluded that bank efficiency decreases 

from high to low from joint-stock banks, city commercial banks to state-owned banks, and the difference between 

these three diminishes with the passage of time. Feng (2020) found that, based on the data envelopment method, 

excessive input and insufficient output are due to uneven resource allocation and insufficient management 

capabilities. Banks in China need to optimize the allocation of resources through internal adjustments to solve the 

problem of low operating capabilities and improve their efficiency. Yang, Chen, and Tan (2020) used a two-stage 

slack-based measure (SBM) model that considers undesired outputs to analyze the efficiency of 24 commercial banks 

in China, and found that the traditional DEA model may overestimate the efficiency of banks (Yang et al., 2020). 

An, Hou, and Li (2021) concluded, based on the efficiency measurement of the three-stage DEA-Tobit model, that 

increasing the total amount of commercial bank loans can promote economic efficiency and resource allocation 

efficiency while hindering the improvement of management technology efficiency. One of the conditions for 

realizing the rapid development of economic benefits is to improve the innovation ability of commercial banks. Cao 

and Du (2021) analyzed the financing efficiency of listed commercial banks that issue preferred shares in China. The 

research data showed that one of the ways to improve financing efficiency is to allow listed commercial banks to 

issue equity-type preferred shares, which can increase the company's financial leverage and reduce the debt-to-asset 



Financial Risk and Management Reviews, 2021, 7(1): 60-66 

 

 
62 

© 2021 Conscientia Beam. All Rights Reserved. 

ratio. As a result of their study, Cao & Du called on commercial banks to promote technological innovation. Call on 

commercial banks to promote technological innovation. 

 

3. RESEARCH METHOD 

3.1. DEA-based Malmquist Index Method 

The data envelopment analysis (DEA) model is an analytical tool used to identify the efficiency of resource 

allocation within a company; however, one of its disadvantages is that it cannot analyze the numerical changes of 

efficiency in different periods. Traditional DEA models can be divided into the CCR model (based on constant 

returns to scale) and the BCC (Banker Charnes Cooper) model (based on variable returns to scale), which is also the 

difference between them. Fare, Grosskopf, and Norris (1994) proposed the DEA-based Malmquist model, which 

combines the Malmquist index theory with the DEA method to describe the dynamic changes in efficiency. 

Suppose there is n  decision-making unit (DMU) and each DMU obtains s  types of outputs through m  types 

of inputs in the t period.
T

mj
t

j
t

j
t

j
t xxxx )...,( ,2,1= represents the investment index value of the Jth DMU in 

period t . 
T

nj
t

j
t

j
t

j
t yyyy )...,( ,2,1= represents the output indicator value of the Jth DMU in period t , and they 

are all positive numbers ( Tt ,...,2,1= ).
 

Assuming that ),( tt yx  represents the input and output of period 

t , ）（ 11, ++ tt yx
 
represents the input and output of the t+1 period. In ),(),( 111 +++ tt

c
ttt

c
t yxDyxD 、 , the c  

return to scale is stable, and ),(),( 111 +++ tt
c

ttt
c

t yxDyxD 、  is the output distance function in the corresponding 

period. Under the technical conditions in period t , the change in technical efficiency from period t  to period t + 1 

is expressed as Equation 1 and Equation 2, respectively: 

 

),(

),( 11

tt

C

t

tt

C

t

t

yxD

yxD
M

++

=    (1) 

),(

),(
1

111

1

tt

C

t

tt

C

t

t

yxD

yxD
M

+

+++

+ =   (2) 

We calculate the geometric mean of the two Malmquist indices in Equation 1 and Equation 2 to obtain Equation 3: 

 2

1

1

11111

111 ]
),(

),(

),(

),(
[),,(

tt

c

t

tt

c

t

tt

c

t

tt

c

t

ttttt

yxD

yxD

yxD

yxD
yxyxMtfp

+

+++++

+++ == ，   (3) 

The Malmquist index is combined with DEA to analyze the development of efficiency changes by calculating 

the change in productivity from period to period. The differences between total factor productivity and factor 

productivity are as follows: Total factor productivity refers to the comprehensive productivity of various factors in a 

certain period of a business process. The factors here refer to all other material factors except labor and capital, 

including organizational innovation, technological progress, and production innovation. 

Scale efficiency change (Sech) and pure technical efficiency change (Pech) constitute technical efficiency change 

(EFFch), technical efficiency (EFFch) and technological progress (Tech) constitute total factor productivity (TFP), 

and Equation 4 is obtained: 

Sech×Pech×TECHch =EFFch ×TECHch =TFPch  （4） 



Financial Risk and Management Reviews, 2021, 7(1): 60-66 

 

 
63 

© 2021 Conscientia Beam. All Rights Reserved. 

EFFch represents the change in technical efficiency from period t to period t+1; TECHch represents the 

technological progress index from period t to period t+1; TFPch represents the change of TFP from period t to 

period t+1; Sech represents the change of scale efficiency from period t to period t+1; Pech represents the pure 

technical efficiency change from period t to period t+1. 

Input-oriented and output-oriented are two methods of the DEA-based Malmquist index method: (1)How to 

minimize the input when the output level is determined;(2)How to maximize output when the input level is 

determined. Since bank input factors are easier to control than output factors, a more appropriate method is the 

output-oriented DEA-based Malmquist index method. 

 

3.2. Selection of Indicators 

This paper selects nine listed banks in China as samples: Bank of China, Industrial and Commercial Bank of 

China (ICBC), Agricultural Bank of China, Bank of Communications, Construction Bank, Industrial Bank, China 

CITIC Bank, China Everbright Bank, and Minsheng Bank. The relevant indicator data comes from the financial 

statements of each bank for each year. Input and output indexes constitute the efficiency evaluation index system. 

We referred to previous studies to select bank operating expenses, total shareholder equity, and deposits as input 

indicators, and we selected total profit and interest income as output indicators (see Table 1). 

 

Table-1. Input and output indicators of  efficiency. 

Indicator type Index Variable Unit 

Input indicators Operating expenses X1 100 million yuan 
Deposits taken X2 100 million yuan 

Total shareholder equity X3 100 million yuan 
Output indicators Interest income Y1 100 million yuan 

Total profit Y2 100 million yuan 

 

4. EMPIRICAL ANALYSIS 

The Malmquist index and DEA can analyze the dynamic changes of technological progress efficiency. This 

situation is also applicable to commercial banks. In Table 2, the technological progress efficiency of the nine listed 

banks from 2011 to 2020 is decomposed and the results are as follows: 

 

Table-2. The average Malmquist decomposition index of the technological progress of commercial banks in each year 

 Technical 
Efficiency 

Index 
(EFFch) 

Technological 
Progress 

Index (Tech) 

Pure Technical 
Efficiency 

Index (Pech) 

Scale 
Efficiency 

Index 
(Sech) 

Total Factor 
Productivity 
Index (TFP) 

2011–2012 0.995 1.014 0.988 1.008 1.010 
2012–2013 1.006 1.004 0.997 1.011 1.009 
2013–2014 0.975 1.009 0.992 0.983 0.984 
2014–2015 0.920 1.004 0.951 0.969 0.924 
2015–2016 0.905 1.235 0.853 1.061 1.163 
2016–2017 1.007 1.000 1.083 0.929 1.007 
2017–2018 0.956 1.000 0.987 0.970 0.956 
2018–2019 0.977 1.000 1.021 0.959 0.977 
2019–2020 0.942 1.000 0.974 0.969 0.942 

Average 0.965 1.030 0.983 0.984 0.997 

 

Analysis was carried out according to the values of the technical efficiency (EFFch) index, total factor 

productivity (TFP) index, scale efficiency (Sech) index, technological progress (Tech) index, and pure technical 

efficiency (Pech) index, and the values were compared with 1. If the value of TFP is greater than 1, it indicates that 

the total factor efficiency has improved; if the value of EFFch is greater than 1, it indicates that there is technical 



Financial Risk and Management Reviews, 2021, 7(1): 60-66 

 

 
64 

© 2021 Conscientia Beam. All Rights Reserved. 

efficiency; if the Tech value is greater than 1, it indicates that there is technological progress; if the value of Sech is 

greater than 1, it indicates that the expansion of the scale improves efficiency; if the value of Pech is larger than 1, it 

indicates that there are other factors that can promote efficiency. It can be seen from Table 2 that, on the whole, the 

M index of Chinese commercial banks from 2011 to 2020 is less than 1, indicating that the efficiency of 

technological innovation of Chinese commercial banks has declined, with an average annual decline of 0.3%, where 

the decline from 2014 to 2015 reached 7.6 %. When Tech is greater than 1, 1 is greater than Sech, and most of 

EFFch is less than 1. If the M value is less than 1, it can be concluded that the nine commercial banks sampled from 

2011 to 2020 have shown a decline in technological innovation efficiency. From this, we can see the scale efficiency 

change index of less than 1 is an important factor in the decline in efficiency of technological innovation of the 

sampled commercial banks. In addition, the average value of Sech is less than 1, and Pech fluctuates around 1, which 

means that it is in the stage of diminishing returns to scale. This means that the scale of commercial banks has not 

reached the optimal level with the continuous introduction of new technologies and technological progress. The 

degree of progress does not match the scale, and it has not reached the stage of increasing scale benefits. The 

operating efficiency of banks still has a lot of room for improvement, and the imbalance and mismatch of bank input 

and output hinders the improvement of the efficiency level regarding technological innovation. The detailed 

Malmquist index of each commercial bank's technological innovation efficiency and its decomposition are detailed in 

Table 3 below.  

 

Table-3. Malmquist index and its decomposition of urban technological innovation efficiency of commercial banks. 

 EFFch Tech Pech Sech TFP 

People’s Bank of China 0.969 1.007 0.986 0.987 0.974 
Industrial and Commercial Bank 0.952 1.207 1.000 0.952 1.187 
Agricultural Bank of China 0.961 1.005 0.994 0.970 0.965 
Bank of Communications 0.968 1.003 0.969 0.999 0.971 
China Construction Bank 0.958 1.009 1.005 0.960 0.965 

China's Industrial Bank 0.963 1.018 0.975 0.991 0.980 

China CITIC Bank 0.970 1.002 0.982 0.989 0.972 
China Everbright Bank 0.971 1.002 0.960 1.013 0.973 
China Minsheng Bank 0.970 1.013 0.973 0.998 0.982 

 

In the table, EFFch, Tech, Pech, Sech and TFP respectively represent technical efficiency index, technical 

progress index, pure technical efficiency index, scale efficiency index and total factor productivity index. 

From the perspective of banks, Industrial and Commercial Bank of China (ICBC), China Construction Bank and 

China Everbright Bank have developed better than the other six banks in the past ten years. It shows that the 

resource structure allocation of these three banks is relatively reasonable. The technological progress indexes 

(Tech) of all nine banks are greater than 1, which shows effectiveness; the pure technical efficiency index of the 

Industrial and Commercial Bank of China and China Construction Bank is equal to 1 or more than 1, respectively, 

which means that the invested resources are used efficiently; ICBC’s TFP is greater than 1, indicating that the 

efficiency of all factors has improved; Everbright Bank's scale efficiency index (Sech) is greater than 1, indicating 

that the expansion of scale has improved efficiency. ICBC recently increased its investment in financial science and 

technology innovation. It has not only achieved results in 5G, cloud computing, and big data, but has also achieved 

great results in areas such as artificial intelligence and blockchain. In 2020, ICBC’s investment in information 

technology increased by 20% year-on-year and it invested 207.8 billion yuan in funds. At the same time, China 

Construction Bank focused on building a new generation of core systems in 2010 and won the People’s Bank of 

China’s “2017 Banking Technology Development Award” to form efficient financial technology innovation 

capabilities. In terms of technology-driven processes, China Construction Bank has established a series of platforms 

in cloud computing, artificial intelligence, 5G, blockchain and other fields, and its innovative business continues to 



Financial Risk and Management Reviews, 2021, 7(1): 60-66 

 

 
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© 2021 Conscientia Beam. All Rights Reserved. 

develop. Everbright Bank insists on promoting business development with innovative technology and has 

established a scientific and technological innovation fund, including scientific research expenses and marketing. 

Everbright Bank also established the Everbright Digital Finance Academy. While cooperating with a number of 

institutions with technological innovation as the core theme, it launched a double investment plan in science and 

technology, and it supported financial technology innovation projects in terms of employees by cultivating 

innovative talents. 

 

5. CONCLUSION 

Based on the analysis of the financial data of nine listed banks in China from 2011 to 2020, we can draw the 

following conclusions. First, commercial banks need to adapt to the changing times and circumstances, increase 

capital investment, strengthen technological empowerment, further support businesses, improve customer service 

capabilities, and promote their own high-quality development. Second, from 2011 to 2020, the technical progress 

indexes of the nine listed banks showed a trend of volatility and that technology was steadily improving. Third, we 

have calculated that the technological progress indexes (Tech) are greater than 1, the scale efficiency change 

indexes (Sech) are less than 1, most of the technical efficiency indexes (EFFch) are less than 1, and the M value is 

less than 1. Therefore, it can be concluded that the efficiency of technological innovation of the nine commercial 

banks sampled from 2011 to 2020 has declined. Fourth, strengthening financial innovation capabilities can improve 

the efficiency of Chinese commercial banks. Technological attributes are the core and most basic attributes of new 

finance. One of the ways to improve the competitiveness of commercial banks is to promote the production of new 

financial products by increasing capital investment in innovative technologies. Finally, the overall operating 

performance of these nine banks is diminishing returns to scale. Banks can reduce the corresponding costs by 

reducing investment, which can improve their operating efficiency. 

 

Funding: This study received no specific financial support.    
Competing Interests: The authors declare that they have no competing interests.  
Acknowledgement: All authors contributed equally to the conception and design of the 
study. 

 

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