Applying Data Envelopment Analysis in Measuring the Efficiency Of

mathematics

Article Applying Data Envelopment Analysis in Measuring the Efﬁciency of Chinese Listed Banks in the Context of Macroprudential Framework

Huichen Jiang 1,* and Yifan He 2 1 School of Economics and Management, Beihang University, Beijing 100191, China 2 International College, Zhengzhou University, Zhengzhou 450052, Henan, China; [email protected] * Correspondence: [email protected] or [email protected]

Received: 29 August 2018; Accepted: 25 September 2018; Published: 29 September 2018

Abstract: China is a bank-dominated country; therefore, the sustainability of the Chinese banking industry is important for economic development. In this paper, data envelopment analysis (DEA) was combined with the Malmquist index, and we statically and dynamically analyzed the efficiency of listed banks during the period 2012–2017. The results showed that 12 of the 17 banks improved their technical efficiency. The technical efficiency of three banks remained the same, whilst that of two banks had dropped slightly by less than 1.0%. The Chinese government has learned from the lessons of past financial crises to find a way to forestall financial crisis, and implemented macroprudential policy, therefore the banking industry has actively served the real economy and promoted economic development while paying attention to the prevention of financial risks. According to the report of The Banker in 2018, for the first time, the four biggest banks in China topped the list of the Top 1000 World Banks. The research showed that, the Chinese government applied macroprudential framework in the banking supervision, and the listed banks effectively resisted financial risks and realized steady growth. We believe that the macroprudential framework plays a positive role in the economic development and financial stability in China.

Keywords: data envelopment analysis (DEA); efficiency; total factor productivity; listed banks; finance; macroprudential framework; financial supervision; financial risks; financial stability; economic development

1. Introduction Finance is the core element of the modern economy. As a bank-dominated country, it is important for the national economy to achieve sustainable and healthy development of the Chinese banking industry. Therefore, the Chinese government has been paying significant attention to policy making and planning of the banking industry. In 2012, the former Chinese president Hu Jingtao pointed out that the Chinese government was going to enhance financial supervision and improve the competitiveness of financial institutions, including banks [1]. In the following year, the report on the work of the government also underlined the importance of improving the competitiveness of banks [2]. Recently, the five-year plan (2016–2020) stressed that the government should accelerate financial reform, enhance the efficiency of finance in serving the real economy, and improve the service quality and management levels of financial institutions [3]. In 2017, Chinese president Xi Jinping pointed out that the Chinese economy has been transitioning from a stage of rapid growth to an era of high-quality growth, which means that China will pursue an economy with better quality, higher efficiency, and an increased total factor of productivity. In addition, the reform of the financial system should be strengthened in order to serve the real economy better, and the financial supervision framework should be enhanced to forestall financial risks [4].

Mathematics 2018, 6, 184; doi:10.3390/math6100184 www.mdpi.com/journal/mathematics Mathematics 2018, 6, 184 2 of 18

In 2008, the global financial crisis caused by the subprime mortgage crisis in the United States severely damaged the global financial system. At the annual meeting of the World Economic Forum held in January 2017, Chinese president Xi Jinping emphasized that the extravagant profit-seeking behaviours of the financial capital, as well as the serious lack of financial supervision, caused the global financial crisis. Therefore, we need to strengthen the ability of financial markets to resist risks [5]. Researchers found that the lack of effective macroprudential concept was an important reason for the crisis [6,7]. Over the years, international organizations, regulatory authorities of various countries, and academics have begun to pay more attention to the development of the theory and practice of constructing a macroprudential framework, and there is an international consensus on strengthening financial supervision and preventing risks [7,8]. The idea of macroprudential policy is that the rational behavior of individual financial institutions may be irrational from the perspective of the financial system. In boom times, the credit expansion of banks may result in financial crises; however, people find it hard to get a loan from banks during a credit crunch, which may contribute to worsening financial instability. Therefore, the aim of macroprudential policy is to reduce the probability and the huge costs of systemic financial risks. Furthermore, the proximate objective of macroprudential policy is to decrease stress on the financial system and its ultimate objective is to reduce the loss of output resulting from financial instability [9,10]. Macroprudential policy has played an important role in mitigating systemic risk and creating a suitable financial environment [7,11]. Additionally, Xu Zhong, the director of the research bureau of the People’s Bank of China, pointed out that during the process of opening China’s financial industry to the outside world, it is necessary to open up steadily and orderly on the premise of improving macroprudential management, strengthening financial supervision, and improving the transparency of the financial markets. Thus, international competitiveness of the financial system can be improved, and the reform and development of the financial sector can be pushed to a new level in the new era. Moreover, the reinforcement of macroprudential management concentrates on the interaction between finance and the economy, which is conducive to the better financial support for development of the real economy [12–14]. At present, the direction of financial supervision is shifting from microprudential policy to a combination of microprudential and macroprudential policies. For instance, Basel III emphasizes the concept of macroprudential supervision. According to the development and changes of the economic and financial situation, the People’s Bank of China, being the central bank of China, has continuously improved the macroprudential policy framework and constructed the Macro Prudential Assessment (MPA) system in 2016. The MPA system supervises the financial institutions in terms of capital and leverage, assets and liabilities, liquidity, pricing behavior, asset quality, cross-border financing risk, and the implementation of credit policy. Since the first quarter of 2017, the central bank incorporated off-balance-sheet financing into broad credit indicators for MPA. Moreover, in the report of the 19th National Congress of the Communist Party of China (CPC) in October 2017, it was formally put forward that macroprudential policy and monetary policy should be the two pillars of the regulatory framework of the financial system [4]. Benefiting from the deepening of reforms and the improvement of policy frameworks, China’s banking industry has achieved steady growth, even in the post-crisis period. According to the statistics disclosed by the China Banking Regulatory Commission (CBRC), the total assets of China’s Banking Financial Institutions (BFC) increased from 128.5455 trillion yuan to 252.4040 trillion yuan during the period from 2012–2017, with an average growth rate of 11.90%. Additionally, the number of employees who work in the BFC grew from 3,362,000 in 2012 to 4,090,000 in 2016. However, whether the efficiency of the banking industry is growing along with the rapid growth of the industry has become a focus of public attention. Moreover, whether a bank operates efficiently is associated with the sustainability of the bank. Additionally, as mentioned above, the sustainable development of the banking industry, especially in China, is important for economic growth as the banking industry could affect many other industries. In addition, according to Reference [15], most research focuses on the efficiency of banks in Mathematics 2018, 6, 184 3 of 18 developed countries. However, development of the banking industry is not the same in developed countries and in developing countries. Therefore, research on the banking industry in developing countries will be quite interesting. Moreover, the studies will be of importance as China plays a more important role in the development of the global economy [16–18]. In all, our study concerning Chinese banks will fill the gap in previous studies. Furthermore, the DEA-based efficiency evaluation based on the latest data can depict the status quo of the banking industry in China well. Therefore, to accurately and comprehensively measure bank efficiency, we review the related literatures which have evaluated banking efficiency in different ways. Some research concentrated on measuring the efficiency of a bank and compared the performance of different banks through statistical analysis using accounting ratios. However, the traditional measure of efficiency using a single input and output cannot fully evaluate the performance of banks. Moreover, the evaluation based on accounting indicators may aggregate the performance of a bank in certain perspectives [19–21]. Therefore, we aim to measure the efficiency of a bank with multi-inputs and outputs efficiently, and we have found that data envelopment analysis is suitable for our research. Data envelopment analysis (DEA) is an efficient way to measure the relative efficiency of a decision-making unit (DMU), in comparison to the best performer in the sample. Additionally, DEA is suitable for analyzing the efficiency of DMUs with multi-inputs and outputs which can comprehensively depict performance. In addition, we do not need to preassign the form of the production function. More importantly, the combination of DEA and the Malmquist index model contributes to the dynamic analysis of the efficiency of DMUs [22–24]. In recent years, DEA has been widely used for efficiency evaluation in different areas, especially in the banking industry (see Chen et al. [25] for the detailed development of the related studies). Moreover, DEA has been considered as an efficient way to explore banking efficiency [26]. For instance, Staub, Souza, and Tabak believed that efficiency evaluation using DEA was valuable for bank managers and financial supervisors [27]. LaPlante and Paradi applied DEA in evaluating the bank branch efficiency of a Canadian bank [28]. Chortareas et al. measured the productivity of commercial banks in Latin American countries using DEA [29]. More researchers are interested in analyzing the efficiency of the Chinese banking industry. Based on DEA, Zhang [23] calculated the efficiency of three types of commercial banks in China during the period from 1997–2001, and the results showed that the average technical efficiency of the joint-stock commercial banks was high and stable, whilst that of the city commercial banks was significantly lower and more volatile. Additionally, the average efficiency of the state-owned commercial banks was stable and only the efficiency of JSYH (for simplicity, we use the abbreviation of China Construction Bank Corporation based on the Chinese Pinyin) ranked in the Top 20 amongst commercial banks during the period. Liu [30] analyzed the technical efficiency of 15 commercial banks, including state-owned and joint-stock commercial banks, from 2000 to 2002 and found that the average technical efficiency of the banking industry was 0.797, which showed that input slacks existed for most banks. Moreover, the three-year average technical efficiency of the joint-stock banks was higher than that of the state-owned ones. Additionally, scale inefficiency had been the main cause of the decreasing technical efficiency for the two types of banks. Furthermore, using the methodology of DEA, we could measure a bank’s efficiency in a given year. However, if we want to know whether the efficiency of a bank increased or decreased between two time periods or we are interested in whether there exists technical progress during the periods, the best choice is to make a combination of the DEA and the Malmquist index. Using DEA, Pang [31] found that the efficiency of city and joint-stock commercial banks was higher than that of the state-owned ones. Additionally, the application of the Malmquist index showed that there was an increase of the total factor productivity of the banking industry during the period from 2000–2004. Based on panel data for 15 commercial banks from 2005 to 2009, Zhu et al. [32] found that the technical efficiency of the state-owned banks was higher than that of the joint-stock banks in each year within the sample period, which was different from the results of prior studies. Mathematics 2018, 6, 184 4 of 18

The rest of the paper is organized as follows. The next section introduces the methodology of the measurement of bank efficiency and shows the sample and the variable selection. In Section3, we describe the data. Then, we make an efficiency evaluation of the banking industry, statically and dynamically. Additionally, we classify the banks by their ownership types and analyze bank efficiency in detail. Section4 discusses the results and conclusions.

2. Materials and Methods

2.1. The Measurement of Bank Efficiency DEA is a non-parametric mathematical programming model suitable for analyzing the efficiency of DMUs which have multiple inputs and outputs, and measuring the relative efficiency of each DMU [33]. Currently, more researchers are interested in efficiency evaluation based on DEA. Basso and Funari [34] applied DEA to measure the performance of mutual funds. Allevi et al. [35] studied the environmental performance of green funds. Therefore, DEA is considered to be appropriate for analyzing the efficiency of listed commercial banks. The basic idea of the prototype of DEA can be traced back to the concept of technical efficiency proposed by Farrell in 1957 [36,37]. In 1978, Charnes et al. [38] designed the approach of data envelopment analysis and their model (namely CCR model) assumed that all the DMUs were in a state of constant returns to scale. In 1984, Banker et al. [39] developed the DEA model (namely BCC model) by allowing the variable returns to scale in the model, therefore we can analyze the pure technical efficiency and scale efficiency of a DMU [40]. Based on References [38,39], we can measure the technical efficiency, pure technical efficiency, and scale efficiency of a DMU. In this section, we study the efficiency of the listed commercial banks and treat each bank as a decision-making unit. The DEA model can be divided into the input-oriented and output-oriented models. As we are interested in whether input redundancy exists, we choose the input-oriented DEA model, and the following equations are based on the input orientation. Suppose the number of DMUs is n, and the types of the inputs and the outputs of each T DMU are m and q. The input and output vectors of DMUj are Xj = x1j ··· xmj > 0 and T Yj = y1j ··· yqj > 0, j = 1, 2, ··· , n. v and u are the vectors of the input and output weights, i = 1, 2, ··· , m, r = 1, 2, ··· , q. We can derive the pure technical efficiency (PTE) of a DMU based on the linear form of the BCC model, where the sign of µ0 is unstrained and it may be positive, zero, or negative. max z = TY − v,u,µ0 µ 0 µ0 T T s.t. µ Yj − v Xj − µ0 ≤ 0 (1) T v X0 = 1 µ ≥ 0, v ≥ 0 T The dual form can be written as follows, where λ = λ1 ... λn , e is a row vector and all the elements are equal to 1. min θ

s.t. θx0 − Xλ ≥ 0

Yλ − y0 ≥ 0 (2) eλ = 1 λ ≥ 0 The technical efficiency (TE) can be derived based on the CCR model, by removing the condition of eλ = 1 in Equation (2). We can compute the scale efficiency (SE) based on the equation which shows that technical efficiency is the product of scale efficiency and pure technical efficiency, and Mathematics 2018, 6, 184 5 of 18 we can analyze the efficiency of a DMU in detail. Note that technical efficiency and pure technical efficiency respectively represent the efficiency under the assumption of constant returns to scale and variable returns to scale. In the DEA model, for technical, pure technical, and scale efficiency, the score of efficiency is greater than 0 and less than or equal to 1. If technical efficiency is 1, we consider the DMU to be DEA-efficient, which means that both the scale efficiency and pure technical efficiency equal one. If pure technical efficiency equals 1 or scale efficiency equals 1, the DMU is considered to be weak-efficient. If neither the pure technical efficiency nor the scale efficiency equal one, the DMU is not efficient in terms of both pure technical efficiency and scale efficiency. Note that if both the pure technical efficiency and the technical efficiency equal one, the size of the bank is appropriate and is neither too big nor too small. Otherwise, if the pure technical efficiency exceeds the technical efficiency, the bank size may be too big or too small to achieve an efficient operation. Moreover, if the optimal solution of µ0 > 0 or < 0, the size of the bank is too big or too small, and it is in a state of decreasing or increasing returns to scale, respectively. The above section discusses the DEA methodology of studying bank efficiency under the static condition. In this section, the dynamic analysis is carried out by introducing the Malmquist total factor productivity model (Malmquist index model). The Malmquist index model originated from the idea proposed by Malmquist in 1953 [41] and further developed by Caves et al. and Färe et al. [42–44], and it is used to analyze the change of the total factor productivity of banks between two time periods. Based on References [42–44], before defining the input-oriented Malmquist index, we need to assume that the production technology that converts the inputs into outputs for each time period t t can be represented as P = {(xt, yt) : xt can produce yt}. Given the output yt, the distance function is defined by the maximum proportional contraction of the inputs xt for each time period s and can be s s written as follows: D (xt, yt) = sup{λ : (xt/λ, yt) ∈ P }. Thus, the Malmquist index which computes the total factor productivity change (TFPC) of a bank from period t to period t + 1 is as follows.

1 Dt(x , y ) Dt+1(x , y ) 2 ( ) = t+1 t+1 t+1 t+1 M xt, yt, xt+1, yt+1 t t (3) D (xt, yt) D (xt, yt)

Furthermore, a Malmquist index equals 1 indicates that the total factor productivity of a DMU remains unchanged. If a Malmquist index is greater or lesser than 1, there is an increase or decrease of the total factor productivity, respectively. Based on prior studies, we can decompose the Malmquist index and measure the change in technical efﬁciency (CTE), and the technical change (TC), as shown in Equation (4).

1 Dt+1(x , y ) Dt(x , y ) Dt(x , y ) 2 = t+1 t+1 = t+1 t+1 t t CTE t , TC t t+1 (4) D (xt, yt) D (xt+1, yt+1) D (xt, yt)

Note that the technical change represents the effect of the shift of the frontier. In addition, as shown in Equation (5), the change in technical efficiency can be decomposed into the change in pure technical efficiency (CPE) and the change in scale efficiency (CSE), respectively. The decomposition of the Malmquist index and its factors would be beneficial for a further detailed study of the banking industry.

1  t+1 t  2 Dv (xt+1,yt+1) D (x ,y ) t+1 v t t D (x , y ) Dt+1(x y ) Ds(x y ) = v t+1 t+1 =  c t+1, t+1 c t, t  CTE t , CSE t s ( ) (5) D (xt, yt)  Dv(xs,ys) Dv xs,ys  v t s Dc(xs,ys) Dc(xs,ys)

2.2. Data Source and Variable Selection In this paper, to consider the accuracy, consistency, and accessibility of data, the commercial banks listed in the Chinese A-share stock markets were chosen as our research object. By the end of 31 December 2017, there were 25 banks listed on the A-share stock market according to the industrial Mathematics 2018, 6, 184 6 of 18 classification of listed companies. Moreover, we excluded firms with data which was not publicly disclosed in the sample period, and 17 firms were subsequently selected as the sample. The financial figures of the listed firms were manually collected from the publicly-disclosed financial reports over the period of 2012–2017. On 2 July 2018, “The Banker”, which is considered to be a leading magazine in the field of banking and its ranking of banks considered to be the standard in the global banking industry for more than 50 years, released the latest ranking of the Top 1000 World Banks. From the publicly-disclosed information, we manually collected the data, and the ownership types and rankings of the sample banks are listed in Table1. According to Table1, we found that GSYH was ranked number one and it has been ranking first for six years. Additionally, for the first time, China’s “Big Four” banks—GSYH, JSYH, ZGYH, and NYYH—topped the list of the Top 1000 World Banks [45,46].

Table 1. The list of the banks in the sample.

Bank 1 Name Type 2 Rank 3 GSYH Industrial and Commercial Bank of China Limited A1 1 JSYH China Construction Bank Corporation A1 2 ZGYH Bank of China Limited A1 3 NYYH Agricultural Bank of China Limited A1 4 JTYH Bank of Communications Co., Ltd. A1 11 ZSYH China Merchants Bank Co., Ltd. A2 20 PFYH Shanghai Pudong Development Bank Co., Ltd. A2 25 XYYH Industrial Bank Co., Ltd. A2 26 ZXYH China CITIC Bank Corporation Limited A2 27 MSYH China Minsheng Banking Corp., Ltd. A2 30 GDYH China Everbright Bank Company Limited Co., Ltd. A2 39 PAYH Ping An Bank Co., Ltd. A2 57 BJYH Bank of Beijing Co., Ltd. A3 63 HXYH Hua Xia Bank Co., Limited A2 65 SHYH Bank of Shanghai Co., Ltd. A3 76 NJYH Bank of Nanjing Co., Ltd. A3 143 NBYH Bank of Ningbo Co., Ltd. A3 166 1 The abbreviation of the name of a sample bank is based on the bank’s stock name in Pinyin; 2 For simplicity, A1, A2, and A3 refer to the bank being a state-owned commercial bank, a joint-stock commercial bank, or the city commercial bank, respectively; 3 Rank refers to the ranking of a bank in the Top 1000 World banks.

Based on the statistics derived from the China Banking Regulatory Commission (CBRC), we made the following bar chart which describes the trends of total assets of the sample banks and all the commercial banks in China. According to Figure1, in recent years, the total assets of both the sample and all the commercial banks in China have realized a steady growth. Furthermore, the total assets of the sample, including the state-owned commercial banks, the joint-stock commercial banks, and the city commercial banks, account for more than 80% of the total assets in the Chinese banking industry during the sample period. This is indicative that the sample banks have a good representativeness in China’s banking industry. Based on previous literatures and considering the availability of data on banks in China, during the process of modelling and measuring the efficiency of listed banks, we chose the net value of the fixed assets of listed banks and the salaries of employees to reflect the capital and human inputs of the banks, respectively. Additionally, the operating cost which reflects the cost related to the main business, was chosen as the input variable. Regarding the output indicators, the operating income and net profit disclosed by the listed banks were selected as the outputs to comprehensively represent banks’ profitability. All the data were manually collected from the publicly-disclosed financial reports of the commercial banks, and the units of the indicators were one billion Renminbi (RMB, namely Chinese yuan). Mathematics 2018, 6, x FOR PEER REVIEW 6 of 18 rankings of the sample banks are listed in Table 1. According to Table 1, we found that GSYH was ranked number one and it has been ranking first for six years. Additionally, for the first time, China’s “Big Four” banks—GSYH, JSYH, ZGYH, and NYYH—topped the list of the Top 1000 World Banks [45,46].

Table 1. The list of the banks in the sample.

Figure 1. The trends of the total assets (the unit of thethe total assets is 100 million RMB) of commercial banks (2012–2017).

3. Results

3.1. Descriptive Statistics Table2 shows the descriptive statistics of the sample banks.

Table 2. The descriptive statistics of the input and output variables.

Salaries of Operating Operating Statistical Fixed Assets Net Proﬁt Employees Expenses Income Indicators (Billion RMB) (Billion RMB) (Billion RMB) (Billion RMB) (Billion RMB) Mean 52.048 12.624 102.633 73.543 196.814 Min 2.173 0.333 4.157 4.045 9.114 Median 14.483 7.863 64.701 41.763 119.534 Max 220.651 47.697 364.66 287.451 726.502 Std. Deviation 1 66.557 12.574 101.015 80.977 202.259 C.V. 2 1.279 0.996 0.984 1.101 1.028 1 “Std. Deviation” represents standard deviation; 2 “C.V.” refers to the coefﬁcient of variation.

3.2. The Overall Analysis of the Banking Industry (2012–2017) Firstly, we calculated the average total factor productivity of the seventeen listed commercial banks. According to Table3, on the whole, the average of the banks’ total factor productivity declined slightly, with a decrease of 3.6%. Based on the basic idea of DEA, we can divide the change of total factor productivity into the 4.6% decline of the technical change index and the 1.0% enhancement of the technical efficiency. Moreover, by analyzing the parts of the technical efficiency change index, we observed a 0.7% increase in pure technical efficiency and a 0.3% improvement in scale efficiency. From the perspective of the firm level, during the sample period, there was an increase of 0.9% for PAYH’s average total factor productivity (TFP), whilst that of NYYH remained the same. Meanwhile, the six-year average TFP for BJYH, PFYH, ZSYH, XYYH, and MSYH significantly dropped, with decreases of 14.4%, 6.4%, 5.4%, 5.3%, and 5.1%, respectively. For the other banks, their average TFPs decreased slightly. In terms of the factors of the TFP, according to the results, all the banks faced a regression of frontier technology in varying degrees. The TC index of BJYH, ZXYH, ZSYH, PFYH, and XYYH decreased by 13.9%, 6.7%, 6.4%, 6.4%, and 5.3%, respectively, which directly led to a dramatic decline of the TFPs. Mathematics 2018, 6, 184 8 of 18

Table 3. The Malmquist total factor productivity index and its factors 1 (2012–2017, ﬁrm level).

ID Firm CTE TC CPE CSE TFPC 1 BJYH 0.994 0.861 1.000 0.994 0.856 2 GSYH 1.000 0.961 1.000 1.000 0.961 3 GDYH 1.001 0.966 1.003 0.999 0.967 4 HXYH 1.015 0.972 1.014 1.001 0.987 5 JSYH 1.009 0.968 1.013 0.996 0.976 6 JTYH 1.012 0.953 1.014 0.998 0.965 7 MSYH 0.990 0.959 0.985 1.005 0.949 8 NJYH 1.008 0.973 1.000 1.008 0.981 9 NBYH 1.011 0.966 1.002 1.009 0.977 10 NYYH 1.032 0.969 1.038 0.995 1.000 11 PAYH 1.032 0.977 1.000 1.032 1.009 12 PFYH 1.000 0.936 1.000 1.000 0.936 13 SHYH 1.020 0.973 1.012 1.008 0.992 14 XYYH 1.000 0.947 1.000 1.000 0.947 15 ZSYH 1.012 0.936 1.000 1.012 0.946 16 ZGYH 1.012 0.969 1.012 1.000 0.981 17 ZXYH 1.030 0.933 1.030 1.000 0.961 Mean 1.010 0.954 1.007 1.003 0.964 Std. Deviation 0.013 0.028 0.013 0.009 0.034 1 “TFPC”, “TC”, “CTE”, “CPE” and “CSE” refer to the total factor productivity change, the technical change, the change in technical efficiency, the change in pure technical efficiency and the change in scale efficiency.

From the perspective of technical efficiency, twelve of the seventeen banks improved in technical efficiency during the sample period. The technical efficiency of three banks remained the same, whilst that of two banks dropped slightly with a decrease of less than 1.0%. Therefore, the listed banks have suffered from the negative technical progress experienced during the period from 2012–2017. Meanwhile, the technical efficiency of most banks improved during the period, reducing the influence of the technical regression on the total factor productivity to some extent.

3.3. The Year-by-Year Analysis of Banking Industry (2012–2017) In this section, we did a year-by-year analysis of the banking industry, as shown in Table4.

Table 4. The average Malmquist total factor productivity of banking industry.

Year CTE TC CPE CSE TFPC 2013 1.013 1.019 1.013 1.000 1.032 2014 0.971 0.981 0.993 0.978 0.953 2015 1.050 0.863 1.025 1.025 0.907 2016 0.948 1.015 0.967 0.981 0.962 2017 1.074 0.901 1.040 1.033 0.968 Mean 1.010 0.954 1.007 1.003 0.964 Std. Deviation 0.053 0.070 0.028 0.025 0.045

In 2013, the industrial TFP increased by 3.2%, compared to 2012. This was due to the technical progress and the enhancement of the technical efficiency of the listed banks on the whole. Moreover, the increase in technical efficiency stemmed from the growth of pure technical efficiency rather than the improvement of scale efficiency. In the following year, the TFP of the banking industry dropped by more than 4%, which can be attributed to negative technical progress of 1.9% and a technical efficiency decrease of 2.9%. The decline of technical efficiency was mainly due to the decrease of scale efficiency. In 2015, the industrial TFP continued to decrease, with a drop of more than 9%. Meanwhile, the change of the TFP was different from that of previous years, where the negative technical progress increased by as much as 13.7%. However, the pure technical efficiency and scale Mathematics 2018, 6, 184 9 of 18 efficiency increased and contributed to the 5.0% increase in technical efficiency of the banking industry during that year. In 2016, the industrial TFP fell whilst the decline narrowed to 3.8%. Furthermore, there was a 1.5% increase in technical progress. Additionally, both the pure technical efficiency and the scale efficiency decreased, which resulted in a drop of the technical efficiency. In 2017, the average TFP of the banking industry continued to drop by 3.2%. Meanwhile, though the technical regression of the banking industry enlarged, the technical efficiency increased, which softened the negative impact by the technical regression. More importantly, both the pure technical efficiency and scale efficiency increased by more than 3.0%.

3.4. A Comparative Analysis of the Banks of Different Types of Ownership Tables5–7 show the efficiency evaluation of the listed banks with different ownership types in 2017: state-owned, joint-stock, and city commercial banks. In the tables, “RTS” refers to the “returns to scale” of a bank. “c”, “d”, and “i”, respectively, represent whether the bank is in a state of constant returns to scale, decreasing returns to scale, or increasing returns to scale. Clearly, there was a huge difference between the banks of different types. In 2017, there were seven banks belonging to the efficient banks group: a state-owned commercial bank (GSYH), a city commercial bank (SHYH), and five joint-stock commercial banks (PAYH, PFYH, XYYH, ZSYH, and ZXYH). They were in a state of DEA-efficiency, which meant they were efficient in terms of both pure technical efficiency and scale efficiency.

Table 5. The efﬁciency evaluation 1 of the state-owned banks in 2017.

Type Bank TE PTE SE RTS GSYH 1.000 1.000 1.000 c State-owned JSYH 0.978 1.000 0.978 d commercial JTYH 0.934 0.956 0.977 i banks ZGYH 0.929 0.930 0.999 i NYYH 0.900 0.924 0.974 d 1 “TE”, “PTE” and “SE” refer to the technical efficiency, the pure technical efficiency and the scale efficiency.

Table 6. The efﬁciency evaluation of the joint-stock commercial banks in 2017.

Type Bank TE PTE SE RTS PAYH 1.000 1.000 1.000 c PFYH 1.000 1.000 1.000 c XYYH 1.000 1.000 1.000 c Joint-stock ZSYH 1.000 1.000 1.000 c commercial ZXYH 1.000 1.000 1.000 c banks GDYH 0.925 0.941 0.983 d MSYH 0.871 0.873 0.998 i HXYH 0.848 0.857 0.989 d

Table 7. The efﬁciency evaluation of the city commercial banks in 2017.

Type Bank TE PTE SE RTS SHYH 1.000 1.000 1.000 c City NJYH 0.974 1.000 0.974 i commercial BJYH 0.971 1.000 0.971 i banks NBYH 0.889 1.000 0.889 i

Additionally, according to the above tables, there were four banks belonging to the DEA weak-efficient banks group: a state-owned commercial bank (JSYH) and three city commercial banks (NJYH, BJYH, and NBYH). Take JSYH and NBYH, for example. They were, respectively, a state-owned Mathematics 2018, 6, 184 10 of 18 commercial bank and a city commercial bank. In 2017, China’s economy had achieved steady growth and the Chinese government proposed building a dual-pillar regulatory framework, which comprised monetary policy and macroprudential policy. Additionally, the demands on liquidity management had been further strengthened. JSYH improved the management of liquidity risk, concentrated on the prudential use of funds, and ensured the security of payments and settlements. Because of the increase in net interest income by 34.66 billion yuan with a growth rate of 8.30%, the bank realized a net profit of 243.62 billion yuan, with an increase of 4.83%. NBYH conducted the diversification of its business, adhered to the idea that controlling risks contributed to the reduction of costs, and improved asset quality. The net profit of NBYH in 2017 was 9.33 billion yuan, with a growth rate of 19.50%. The other banks were neither efficient in pure technical efficiency nor in scale efficiency, which indicated that they still had great potential for improvement in terms of their efficiency. Based on the Tables8–10, we found that, in terms of the six-year average technical efficiency, the efficiency scores of the joint-stock commercial banks, the city commercial banks and the state-owned banks were respectively 0.921, 0.918 and 0.912. It was clearly that the efficiency gap of the three types of banks was small. Then we analyzed the efficiency of the banks amongst the three ownership types on a year by year basis. The average technical efficiency of the state-owned banks had been increasing since 2012 and reached its peak in 2015. However, the technical efficiency began to decrease in 2016, though it rebounded and surpassed the historical high in 2017. The directions of the technical efficiency change of the joint-stock commercial banks and the city commercial banks from 2012 to 2017 were the same, except for the slight difference in their magnitudes. The only difference between them and the state-owned banks was that in 2014, the efficiency of both joint-stock and city commercial banks decreased by more than 4%, whilst that of the state-owned banks increased by 1.12%. Overall, although the technical efficiency of the three types of banks fluctuated during the sample period, their technical efficiency in 2017 exceeded their historical highest levels.

Table 8. The average efﬁciency of the state-owned commercial banks (2012–2017).

State-Owned Year Commercial Banks TE SE PTE 2012 0.891 0.998 0.894 2013 0.896 0.970 0.927 2014 0.906 0.963 0.942 2015 0.936 0.969 0.967 2016 0.895 0.948 0.944 2017 0.948 0.986 0.962 Mean 0.912 0.972 0.939

Table 9. The average efﬁciency of the joint-stock commercial banks (2012–2017).

Joint-Stock Year Commercial Banks TE SE PTE 2012 0.910 0.968 0.941 2013 0.926 0.980 0.946 2014 0.889 0.967 0.920 2015 0.942 0.988 0.954 2016 0.903 0.989 0.912 2017 0.956 0.996 0.959 Mean 0.921 0.981 0.939 Mathematics 2018, 6, 184 11 of 18

Table 10. The average efﬁciency of city commercial banks (2012–2017).

City Year Commercial Banks TE SE PTE 2012 0.922 0.937 0.984 2013 0.932 0.948 0.982 2014 0.890 0.899 0.989 2015 0.929 0.944 0.983 2016 0.878 0.896 0.977 2017 0.959 0.959 1.000 Mean 0.918 0.930 0.986

4. Discussion

4.1. The Validity of the Efficiency Evaluation Model In this section, we check the validity of the model in terms of the model specification and the existence of potential outliers in the sample. First, we introduced the isotonicity test for checking the validity of the model specification, namely, we checked whether an increase in input indicators brought a growth in outputs rather than a decrease in outputs (see Avkiran [47]; Adusei [48]; Hwang, Park and Kim [49]). By calculating the inter-correlations of the input and output variables (see Table 11, where all the numbers in the brackets refer to the p-values under the null hypothesis that the variables are not inter-correlated), we found that the inter-correlations of all the indicators were positive and significant at the 1% level, suggesting that the specification of our model was valid.

Table 11. Test of Isotonicity.

Statistical Operating Salaries of Operating Net Profit Fixed Assets Indicators Income Employees Expenses Net profit 1.0000 Operating 0.9934 *** 1.0000 income (0.0000) 0.9444 *** 0.9539 *** Fixed assets 1.0000 (0.0000) (0.0000) Salaries of 0.8974 *** 0.9214 *** 0.9039 *** 1.0000 employees (0.0000) (0.0000) (0.0000) Operating 0.9716 *** 0.9914 *** 0.9537 *** 0.9324 *** 1.0000 expenses (0.0000) (0.0000) (0.0000) (0.0000) *** Represent the 1% significance level.

Second, we conducted the outlier detection with the idea of box plot methodology. According to Reference [50], this methodology is simple and has been widely used. Following the procedures of the method, we calculated the related indicators, see Table 12. In the table, Q1, Q2, Q3, and IQR represent the ﬁrst quartile, median, third quartile, and inter-quartile range (IQR). The idea of the methodology is that if the value is greater than Q3 + 1.5IQR or less than Q1 − 1.5IQR, it may be an outlier. We performed the procedure and calculated the accumulated times that the data of a bank is considered to be an outlier, see Figure2. For instance, if the net proﬁt and operating income of a bank were considered to be outliers in 2012, the accumulated times of the bank was two in the year. According to following Figure2, we found that the Big Four banks in China including GSYH, JSYH, NYYH, and ZGYH outperformed the other banks during the period 2012–2017. Mathematics 2018, 6, 184 12 of 18

Table 12. The statistical indicators of the box plot methodology 1.

Statistical Operating Fixed Salaries of Operating Net Proﬁt Indicators Income Assets Employees Expenses Q1 17.14 48.18 6.78 4.35 25.72 Q2 41.76 119.53 14.48 7.86 64.70 Q3 69.89 207.14 100.08 13.35 129.57 IQR 52.75 158.96 93.30 8.99 103.86 Mathematics 2018, 6, x FOR PEER REVIEW1 The unit of input and output variables is 1 billion RMB. 12 of 18 Mathematics 2018, 6, x FOR PEER REVIEW 12 of 18

FigureFigure 2. 2. TheThe The trends trendstrends of of the the inputs inputs and and outputsoutputs (2012–2017). (2012–2017).

NoteNote that that we we focused focused on on the the listed listed banks banks in in China in in thisthis paper,paper, and and the the following following table table clearly clearly showsshows that that the the Big Big Four Four banks banks took took a a large large proporti proportionproportion of of thethe netnet profit profit profit and and operating operating income income of of all all thethe banks banks banks in insample sample sample (see (see Figure Figure Figure 33), ),3), whichwhich which showsshows shows that thatthat thethe BigBigBig FourFour banks banksbanks play playplay an anan important importantimportant role rolerole in in inthe thethe developmentdevelopment of of thethe the industry.industry. industry. Therefore,Ther Therefore,efore, the thethe outlier outlieroutlier detection detection method methmethodod showsshows shows thatthat that thethe the performancesperformances performances of of the Big Four banks are superior to the other banks in the sample. However, if we excluded the Big ofthe the Big Big Four Four banks banks are are superior superior to to the the other other banks banks in in the the sample. sample. However,However, ifif wewe excludedexcluded the Big Four banks given that their performances were much better than the other banks, as well as ignored Four banks given that their performances were much better than the other banks, as well as ignored the importance of the Big Four banks in industrial development, the efficiency evaluation based on the importance ofof thethe BigBig Four Four banks banks in in industrial industrial development, development, the the efficiency efficiency evaluation evaluation based based on theon the other banks would be unrepresentative of the listed banks. Therefore, we should include the Big theother other banks banks would would be unrepresentative be unrepresentative of the of listedthe listed banks. banks. Therefore, Therefore, we should we should include include the Big the Four Big Four banks in the sample and the efficiency evaluation of the seventeen listed banks will be very Fourbanks banks in the in sample the sample and the and efficiency the efficiency evaluation evalua of thetion seventeen of the seventeen listed banks listed will banks be very will meaningful be very meaningful and interesting. meaningfuland interesting. and interesting.

Figure 3. The trends of indicators of all the banks in the sample and the Big Four banks (2012–2017). Figure 3. The trends of indicators of all the banks in the sample and the Big Four banks (2012–2017). 4.2.Figure Conclusions 3. The trends of indicators of all the banks in the sample and the Big Four banks (2012–2017). 4.2. Conclusions ConclusionsIn this paper, we collected the data of seventeen listed commercial banks, which covered more than 80% of the total assets of the Chinese banking industry, showing good representativeness. In this paper, we collected the data of seventeenseventeen listed commercial banks, which covered more thanFirstly, 80% ofwe the evaluated total assets the technical of the Chinese efficiency banking and calculated industry, showingthe Malmquist good representativeness.total factor productivity Firstly, thanof the80% banks of the during total theassets period of thefrom Chinese 2012–2017, banking based industry,on the methodology showing good of the representativeness. DEA model and Firstly,Malmquist we evaluated index model. the technical Secondly, efficiency the decomposition and calculated of the Malmquist the Malmquist index total provided factor a usefulproductivity way of tothe see banks the technicalduring the change period and from the 2012–2017,change in efbasedficiency on ofthe the methodology banks during of thethe sampleDEA model period. and MalmquistMoreover, index we subdividedmodel. Secondly, the banking the decomposition industry according of the Malmquistto the ownership index provided types of athe useful banks, way to analyzedsee the technical the changes change of the andbanks’ the efficiency, change inand ef conductedficiency of the the efficiency banks du comparison.ring the sample The findings period. Moreover,and policy we implications subdivided are the as follows.banking industry according to the ownership types of the banks, analyzedFrom the changesthe perspective of the banks’ of bank efficiency, performance, and conducted according the toefficiency Figures comparison.4–6, the central The findingsbank andstrengthened policy implications macroprudential are as follows. management and countercyclically adjusted the economy using the dynamicFrom adjustmentthe perspective of the differenof banktial performance, deposit reserve. according The banking to industryFigures realized 4–6, the a rapid central growth bank strengthened macroprudential management and countercyclically adjusted the economy using the dynamic adjustment of the differential deposit reserve. The banking industry realized a rapid growth

Mathematics 2018, 6, 184 13 of 18 we evaluated the technical efficiency and calculated the Malmquist total factor productivity of the banks during the period from 2012–2017, based on the methodology of the DEA model and Malmquist index model. Secondly, the decomposition of the Malmquist index provided a useful way to see the technical change and the change in efficiency of the banks during the sample period. Moreover, we subdivided the banking industry according to the ownership types of the banks, analyzed the changes of the banks’ efficiency, and conducted the efficiency comparison. The findings and policy implications are as follows. From the perspective of bank performance, according to Figures4–6, the central bank strengthened macroprudential management and countercyclically adjusted the economy using the dynamic adjustment of the differential deposit reserve. The banking industry realized a rapid growth in 2013, and the total factor productivity of the industry increased by 3.2%. The average net profit and operating income of the banks under different ownership types, including the city commercial banks, the joint-stock commercial banks, and the state-owned commercial banks, all realized double-digit growth in outputs, with average growth rates of the net profit and operating income of the city commercial banks and joint-stock commercial banks exceeding 16%. In 2014, there were severe fluctuations in the international financial markets and factors including the decrease of oil prices led to a slowdown of the world economy. The Chinese government adhered to the general trend of seeking progress while maintaining stability, and the national economy achieved stability. Moreover, the government continuously strengthened macroprudential management. The growth of the outputs of the city commercial banks continued to expand, with net profit and operating income increasing by 19.05% and 27.80%, respectively, whilst the operating income of the joint-stock commercial banks increased by more than 20%. Meanwhile, the growth of net profit slightly decreased. In the same year, the operating income of the state-owned commercial banks expanded by 11.78%. However, the net profit growth slowed. In 2015, the frequency and magnitude of volatility in international financial markets increased, and the total factor productivity of the banking industry decreased by more than 9%. Furthermore, negative technical progress was 13.7%. Therefore, the Chinese government reduced the deposit reserve ratio and lowered the interest rate five times, and the financial regulators also guided the banking industry towards strengthening risk prevention and better serving the real economy. The operating income and net profit growth slowed in 2015 for all the three types of banks, particularly in the cases of the city commercial banks and joint-stock commercial banks, where net profit growth slowed from 19.05% and 10.83% in 2014 to 13.62% and 4.63% in 2015, respectively. However, they still showed good profitability. For the state-owned banks, the growth rates of operating income and net profit were 5.17% and 0.69%, respectively. In 2016, with the positive progress in the supply-side structural reform, the downward pressure of China’s economy lessened. As the banking industry is closely related to the development of the economy, it showed strong procyclicality. The decrease in total factor productivity narrowed and we observed a 1.5% technical progress. The output growths of the city commercial banks and the joint-stock banks gradually stabilized, with the city commercial banks’ net profit and operating income increasing by more than 10%, whilst the joint-stock banks’ net profit and operating income increased by more than 4%. The state-owned banks’ net profit growth slightly expanded, whilst their operating income showed an average negative growth of 1.73%. In 2016, the Chinese government constructed the Macro Prudential Assessment (MPA). In 2017, the global economy was recovering and emerging markets were growing at a faster pace. The Federal Reserve had raised its interest rate three times and started to reduce the size of its balance sheet. The Bank of England also raised its interest rate, and global liquidity was tightening. Meanwhile, the central bank of China continuously enhanced the MPA and took account of the off-balance-sheet financing to forestall financial risks. China’s economy realized steady growth. The city commercial banks’ net profit realized an average growth rate of 10.16%, whilst their operating income grew by 1.14%. The net profits of the joint-stock commercial banks and the state-owned commercial banks increased slightly by 5.45% and 3.44%, respectively. However, for the joint-stock banks, there was a 0.65% negative Mathematics 2018, 6, 184 14 of 18 growth in the operating income, while the state-owned banks, which performed better than the past year,Mathematics increased 2018, 6 by, x FOR 4.09% PEER in REVIEW 2017. 14 of 18 Mathematics 2018,, 6,, xx FORFOR PEERPEER REVIEWREVIEW 14 of 18

FigureFigure 4. 4. The The trendstrends of of inputsinputsts andand outputs outputs (2012–2017). (2012–2017).

FigureFigure 5. 5.The The trendstrends of inpu inputsts and and outputs outputs (2012–2017). (2012–2017). Figure 5. The trends of inputs and outputs (2012–2017).

FigureFigure 6. 6.The The trendstrends of inpu inputsts and and outputs outputs (2012–2017). (2012–2017).

For the change in inputFigure indicators, 6. The trends in termsof inpu ofts theand employees’ outputs (2012–2017). salaries, the growth rates of the city commercial banks were 24.82%, 19.43%, 26.65%, 48.52%, 30.45%, and 23.87%, respectively, from For the change in input indicators, in terms of the employees’ salaries, the growth rates of the city commercial banks were 24.82%, 19.43%, 26.65%, 48.52%, 30.45%, and 23.87%, respectively, from

Mathematics 2018, 6, 184 15 of 18

For the change in input indicators, in terms of the employees’ salaries, the growth rates of the city commercial banks were 24.82%, 19.43%, 26.65%, 48.52%, 30.45%, and 23.87%, respectively, from 2013 to 2017, with an average growth rate of 28.96%. The growth rates of the joint-stock commercial banks were 23.13%, 8.76%, 12.80%, 6.77%, 2.19%, and 6.38%, respectively, from 2013 to 2017. The average growth rate of the joint-stock commercial banks was 10.01%. For the state-owned commercial banks, the growth rates in terms of the salaries of employees were 5.88%, −1.10%, 0.35%, 2.11%, 1.87%, and 0.67%, respectively, and the average growth rate was 1.63%. In terms of the fixed assets, both the city commercial banks and the joint-stock commercial banks grew rapidly, with the increases of more than 17%. For the state-owned commercial banks, the growth rate of the fixed assets was 9.64%. In terms of the operating expenses, during the sample period, the city commercial banks achieved a rapid increase, and the average growth rate was more than 10%. Moreover, the operating expenses of the banks grew by more than 30% in 2014 and 2015. In 2016, the operating expenses changed from a phase of rapid increase to a stage of stability, followed by a decrease of 0.98%. For the joint-stock commercial banks, the operating expenses increased rapidly from 2013 to 2015, and the growth rates in 2014 and 2015 were more than 25%. However, the operating expenses stabilized in 2016, and the growth rates in 2016 and 2017 were −0.83% and 3.94%, respectively. The operating expenses of the state-owned commercial banks changed in the same direction as the joint-stock commercial banks. The joint-stock commercial banks achieved higher magnitudes while the maximum growth rate of the state-owned commercial banks was 16.61%. Similarly, its growth rate decreased slightly by 1.65% in 2016 and increased by 6.46% in 2017. In summary, since the global financial crisis and the European debt crisis, the global economy has been recovering slowly, and the volatility of the financial markets has intensified. The Chinese government responded to the crisis actively and implemented macroprudential policy. The Chinese banking industry actively served the real economy and promoted the development of the national economy, whilst paying attention to the prevention of financial risks. As mentioned above, all the banks in the sample suffered from the negative technical progress of different extents; however, we observed the growth of both pure technical efficiency and scale efficiency, which contributed to the development of the industry. In addition, we found that banks of different ownership types showed their own characteristics. Moreover, we found that, in terms of the six-year average technical efficiency, the joint-stock banks performed the best, which was consistent with the study of Zhang [23]. However, our study also showed that the technical efficiency of the three types of banks was stable and the efficiency gaps between banks of different types were small, which was different from Zhang [23]. Furthermore, we studied the development of pure technical efficiency and scale efficiency of the three types of banks, which fills the gap in prior studies (e.g., Zhu et al. [32]). For the first time, the four biggest banks in China topped the list of the Top 1000 World Banks released by The Banker in July 2018, and the rankings of GSYH, JSYH, ZGYH and NYYH were 1, 2, 3 and 4. This is a good start for the Chinese banking industry, and it showed the positive influence of macroprudential policy on the sustainability of the Chinese banking industry.

Author Contributions: H.J. finished the work including mathematic methodology, data collection, the search of information related to the study, investigation and research, modelling, and writing. Y.H. assisted the search of information related to the study. Funding: This research was funded and supported by the Academic Excellence Foundation of BUAA for PhD Students, the Chinese Academy of Social Sciences (CASS) Innovation Project under Grant No. 2017CJYA006, and National Natural Science Foundation of China under Grant No. 71673020 and Grant No. 71690244. Acknowledgments: We thank the helpful and important suggestions of the editors and reviewers. Conflicts of Interest: The authors declare no conflict of interest. Mathematics 2018, 6, 184 16 of 18

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