# Evaluation of Innovation Efficiency on Chinese Commercial Banks under the Internet Finance: A DEA-Malmquist Index-Based Approach

Authors: Kun Zhao; Jiaming Pi; Tao Zhang
Journal: Security and Communication Networks
 (2022)

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## Abstract

The development of the digital economy and internet finance greatly impacts the technological innovation of Chinese commercial banks. Therefore, most of the Chinese commercial banks have invested a lot of money in the new information technology applications to adapt to the impacts of internet finance. Consequently, whether these investments have achieved the expected effect and efficiency has been concerned by these banks. For these concerns, we have used relative data from 49 Chinese commercial banks from 2010 to 2020 period and used the DEA-BCC model and DEA-Malmquist index to analyze their innovation efficiency from both static and dynamic perspectives. Our study found that from the static perspective, the innovation efficiency greatly varies among the banks in the study, and most banks have room for improvement in pure technical efficiency and scale efficiency. From the dynamic perspective, the innovation efficiency of the banks in the study is generally on the rise. Changes in technical efficiency play a major role in improving their overall efficiency, and technological progress is the second driving force. Therefore, technological investment should be increased, and technological levels should be improved to improve innovation efficiency. Our study also shows that, according to the ownership types, different groups of banks have differently shown their innovation efficiencies. Joint-stock commercial banks have the highest innovation efficiency, while rural commercial banks have the lowest innovation efficiency. Our study suggests that all Chinese commercial banks should overcome their own shortages in information technological innovation capability to elevate their innovation efficiency, under the background of internet finance.


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## Body

## 1. Introduction

As an important part of the financial system, the commercial bank plays a very important role in the economic development of China, and it has been greatly affected by the rising of the digital economy and internet finance. Internet finance has the characteristics of low entry threshold, high efficiency of resource allocation, and low degree of information asymmetry, which have made the competition more fierce among commercial banks so that they affect the performance of the banks. The digital economy calls for the wide use of new technologies, which lead to the innovation of products and services of commercial banks. Therefore, many Chinese commercial banks have increased their innovation investment, which is characterized by the use of information technology. Consequently, if the innovation investments of the Chinese commercial banks have achieved their expected efficiency goals, and whether there are rooms and in which directions for these banks to improve their innovation efficiency, these questions are worthy to answer.To answer these questions, we use the DEA-BCC model and DEA-Malmquist index to calculate the innovation efficiency of Chinese commercial banks, in which the data of 49 banks during the period from 2010 to 2020 are obtained. By analyzing the results we have got, the factors that influence the innovation efficiency and the path to improve their innovation efficiency of Chinese commercial banks are derived in our discussion. Our study is of value for Chinese commercial banks in their decision-making on their technology investment.


## 2. Literature Review

The widely used efficiency measurement methods can be roughly divided into two categories, the accounting indicator analysis (AIA) method and the stochastic frontier analysis (SFA) method [1]. AIA has several problems in the process of selecting indicators, such as randomness, relevance, and collinearity. Moreover, it only reflects the operating status of a certain period, and the overall efficiency cannot be well reflected. With the enrichment of efficiency research theory and the expansion of measurement models and methods, this method is gradually out of focus among researchers. SFA is also divided into two categories, the parametric stochastic frontier analysis (PSFA) method and the nonparametric method. PSFA has been applied to all kinds of sectors [2–5]. PSFA needs to set a specific frontier production function and estimate the unknown parameters by econometric regression. Different frontier production functions will affect the efficiency value. Though the nonparametric method has several specific methods, the data envelopment analysis (DEA) method is the most used one. Because the DEA method does need not to define the form of production function or estimate the parameters of the production function, it is more and more popular in estimating efficiency. Although the choice of different input and output variables will affect the efficiency estimation, empirical study shows that results obtained by using the DEA method are robust [1].The DEA method has been widely used in efficiency estimation in various industries, including manufacturing industry (Walheer & He, 2020) [6]; agricultural sector (Wang & Feng, 2020) [7]; iron and steel industry (Lee et al., 2019) [8]; energy industry (Wanke et al., 2020) [2]; hospital sector (Rouyendegh et al., 2019) [9]; education sector (Aparicio et al., 2019) [10]; high-technology industry (An et al., 2020) [11]; petroleum industry (Wang et al., 2019) [12]; telecommunications industry (Sahoo & Sahoo, 2020) [13]; tourism industry (Song & Li, 2019) [14]; transportation industry (Stefaniec et al., 2020) [15]; insurance industry (Eling & Jia, 2019) [16]; and hotel sector (Yin et al., 2020; Yu & Chen, 2020) [17, 18]. In addition, the DEA method has been applied to analyze the efficiency level including innovation system (Kalapouti et al., 2020) [19]; sustainability and environmental performance (Allevi et al., 2019) [20]; and supply chain management (Malesios et al., 2020) [21], and so on.In the banking industry, the DEA method is also widely used in the efficiency estimation. Antunes et al. [1] proposed a new DEA model to estimate the efficiency of 39 Chinese commercial banks from 2010 to 2018. The study found that the efficiency level of Chinese banks in the sample continued to improve up to 2015; subsequently, the efficiency level decreases and then slightly fluctuates. Xie and He (2021) [22] established an efficiency evaluation model for commercial banks by using the DEA-Malmquist index, to analyze the financial data of 9 listed banks in China from 2011 to 2020, and found that there are differences exist in the efficiency of commercial banks. Li et al. (2021) [23] used the DEA-Malmquist index to estimate the efficiency and decomposition efficiency of 101 commercial banks from 2011 to 2018, which are in the 29 provinces of China. Shi et al. (2021) [24] proposed a model called slack-based model-network data envelopment analysis (SBM-NDEA) with bad output and used it to calculate the efficiency of 16 listed Chinese commercial banks from 2012 to 2016, which is used to evaluate the performance of complex structure production processes including both series and parallel processes. Tan et al. (2021) [25] used the two-stage network DEA model to calculate the efficiency level of 27 commercial banks in China from 2007 to 2017. Their research shows that the concentration of credit in a few banks will lead to the improvement of bank productivity. Liu et al. (2019) [26] proposed a two-stage DEA model based on element frontier boundary and intermediate output target setting. Compared with the traditional model, this model can deal with the technical heterogeneity of the DMU by aiming at the intermediate output. They use this model to estimate and analyze the efficiency of 28 commercial banks in China from 2013 to 2017. Hu Wei (2017) [27] took 13 city commercial banks in China from 2007 to 2016 as samples and measured their comprehensive innovation performance using the DEA method to analyze the impact of internet finance on the innovation performance of city commercial banks.From the above studies, we can see that most studies on Chinese commercial banks focused on the analysis of the comprehensive efficiency and total factor productivity, and less on the innovation efficiency. Under the background of a vigorously developing digital economy and many Chinese commercial banks have invested more and more in information technology, it is of practical significance to measure the innovation efficiency of these banks. For this consideration, we present our study on 49 Chinese commercial banks in this study. First, we use the DEA-BCC model to make a static analysis of the efficiency of the sample banks in 2013 and 2020. Second, we use the DEA-Malmquist index to dynamically analyze the changes in the innovation efficiency of the sample banks from 2010 to 2020, in order to find out the main factors affecting the innovation efficiency of the studied banks.The main contributions of this study are as follows. First, our study on the estimation of Chinese commercial banks’ innovation efficiency can enrich the application field of the DEA model and provide a new perspective on the commercial banks’ efficiency. Second, our analysis based on static and dynamic point of views can not only help to understand the innovation efficiency of commercial banks in a specific year but also can help to understand the development trend of commercial bank in technology innovation under the background of the digital economy in recent ten years. Finally, the suggestions we provided based on our studies are helpful for commercial banks to make reasonable decisions in their resource allocation so as to improve their innovation efficiency.


## 3. Methodology and Data

### 3.1. DEA-BCC Model

The DEA is a method for evaluating the relative effectiveness of decision-making units (DMUs). It is first proposed by Charnes, Cooper, and Rhodes in 1978 [28]. Sherman and Gold first applied the DEA model to the efficiency evaluation of commercial banks in 1985. [29]. Since then, the DEA model has become a mainstream method to study bank efficiency.The DEA model has two forms: input oriented and output oriented. The model can be set as CCR constant return to scale model and BCC variable return to scale model, which can be set according to the actual research situation. Commercial banks are service-oriented enterprises by nature, and the input factors are mainly savings deposits and initial investment. In the operations, the goal of the banks is to reasonably allocate their resources to maximize their profits. Therefore, this study selects the output-oriented BCC model to study the static efficiency of the banks. The expression of the output-oriented BCC model is shown as formula (1).(1)MaxθBθB,λ,s.t.Xλ≤x0θBy0−Yλ≤0eλ=1λ≥0,where X is the input vector, Y is the output vector, θB is the target planning value, and λ is the planning decision variable.


### 3.2. DEA-Malmquist Index

While analyzing the static efficiency of commercial banks, in order to further explore the dynamic change trend of the banks’ innovation efficiency in time series, we introduce the Malmquist index. The Malmquist index was originally proposed by Swedish economist Sten Malmquist in 1953. However, due to the lack of empirical tools, its application is greatly limited. Only after the DA method was proposed, there are researchers combined it with the Malmquist index that made the Malmquist index from theoretical index to empirical index, and it opened a wide application prospect in practice.Assuming thatt is the base period, the Malmquist index, which measures the change rate of innovation efficiency from t period to t + 1 period, can be expressed as formula (2).(2)Mt,t+1xt,yt,xt+1,yt+1,=Dtxt+1,yt+1Dtxt,yt×Dt+1xt+1,yt+1Dt+1xt,yt1/2,where (xt, yt) and (xt+1, yt+1) represent the input and output vectors of t period and t + 1 period, respectively. If M > 1, it means that the efficiency is improved from t period to t + 1 period; if M = 1, it means that the efficiency is at a standstill from t period to t + 1 period; and if M < 1, it indicates that the efficiency is decreasing from t period and t + 1 period.The Malmquist index can be further decomposed according to the work of Ray and Desli (1997) [30]. The decomposition results are shown as formula (3)–(6).(3)Mt,t+1xt,yt,xt+1,yt+1,=DVt+1xt+1,yt+1DVtxt,yt×DVtxt,ytDVt+1xt,yt×DVtxt+1,yt+1DVt+1xt+1,yt+11/2×DCtxt+1,yt+1/DVtxt+1,yt+1DCtxt,yt/DVtxt,yt×DCt+1xt+1,yt+1/DVt+1xt+1,yt+1DCt+1xt,yt/DVt+1xt,yt1/2,(4)Tech=Dtxt+1,yt+1Dt+1xt+1,yt+1×Dtxt,ytDt+1xt,yt1/2,(5)Pech=DVt+1xt+1,yt+1DVtxt,yt,(6)Sech=DCtxt+1,yt+1xt,yt/DVtxt+1,yt+1DCtxt,yt/DVtxt,yt×DCt+1xt+1,yt+1/DVt+1xt+1,yt+1DCt+1xt,yt/DVt+1xt,yt1/2,where Effch = Pech × Sech, so the final result of Malmquist exponential decomposition can be expressed as formula (7).(7)M=Effch×Techch=Pech×Sech×Techch,where Effch is the technical efficiency index, Techch is the technical progress index, Pech is the pure technical efficiency index, and Sech is the scale efficiency index.We use the DEA-Malmquist index to study the innovation efficiency of Chinese commercial banks and calculate the Malmquist index of their innovation efficiency and its decomposition. The Malmquist index and its decomposition we used in the study are shown in Table1.Table 1
Malmquist index and its decomposition index of the innovation efficiency.
Index nameContent of measurementMalmquist index of commercial banks’ innovation efficiency (Cbiem)Used to measure the efficiency of commercial banks’ innovation input and output.Technical progress index (Techch)Used to measure the technological progress produced by commercial banks using new technologies or inventing new products.Pure technical efficiency index (Pech)Used to measure the minimum input of commercial banks based on the maximum output under the premise of variable return to scale.Scale efficiency index (Sech)Used to measure whether the scale adjustment of commercial banks is close to the optimal production scale.As shown in Table1, the improvement of innovation efficiency is divided into three aspects, the progress of technical level, the improvement of management ability, and the improvement of scale efficiency.


### 3.3. Indicators and Data

When using DEA to evaluate the efficiency of commercial banks, there are three main selection methods of input and output indicators: production approach, intermediate approach, and asset approach, as shown in Table2.(1)
The production approach regards the bank as the producer of financial products. The number of deposit accounts and loans is regarded as bank’s output, and the capital and labor are regarded as input.(2)
The intermediary approach regards banks as intermediaries that convert savings into investment. The amount of deposits and loans is regarded as bank’s output, and the labor and capital are regarded as input.(3)
The asset approach also regards banks as financial intermediaries, but only the asset items in bank’s balance sheet are regarded as output, and deposits are not included in the output as liabilities.Table 2
Characteristics of input and output indicators’ selection approach.
ApproachInput indicatorsOutput indicatorsDefectProduction approachCapitalLabourFixed assetsNumber of deposit accountsNumber of loansIn the actual operation process of the bank, the number of deposit accounts and loans is generally unavailable.Intermediate approachHuman resourcesDepositCapitalOperating costsLoanInvestment and other profitable assetsWithout considering the loan quality, only considering the number of loan assets, ignoring the potential risks, it cannot fully show the profitability of bank assets.Asset approachDeposit itemsLoanInvestmentWithout considering the income and profit of commercial banks, it is difficult to evaluate the actual use efficiency of funds.Combined with the respective characteristics of the above three approaches in Table1, we select the following indicators as the input and output indicators for the evaluation model. The specific indicators are shown in Table 3.Table 3
Input and output indicators for the innovation efficiency of commercial banks.
Indicator typeIndicator nameInput indicatorsFixed assets-net valuePayroll payableBusiness and management expensesOperating expensesOutput indicatorsFee and commission incomeOperating revenueTotal assetsThe four selected input indicators are fixed assets-net value, payroll payable, business and management expenses, and operating expenses.The innovation and development of commercial banks cannot be separated from the investment of fixed assets such as technology equipment, and the impact of its change on the innovation and development of commercial banks cannot be ignored.Employee compensation is an essential expenditure of any enterprise. In addition, innovation is inseparable from a high-quality employee team, and a high-quality employee team needs higher salary expenditure.The operation of commercial banks is inseparable from management. The expenses incurred in the organization and management of commercial banks are business and management expenses, which reflect the investment of commercial banks in management.The scale of a bank is reflected in the volume of business. Operating expenses are various business-related expenses incurred by commercial banks in the process of business operation, which reflects the business scale and investment of commercial banks.The three selected output indicators are fee and commission income, operating revenue, and total assets.The innovative income of commercial banks is mainly reflected in intermediary business income such as handling fees and commission income other than credit business. Therefore, measuring the innovation efficiency of commercial banks with intermediary business income has high reliability and validity.Operating revenue refers to the income obtained by commercial banks from providing financial products and services. It is also an important indicator to measure the product and service innovation of commercial banks.Total assets can measure the scale of commercial banks, and its increase also reflects the scale growth brought by the innovation.After determining the input and output indicators, based on the development status of Chinese commercial banks and taking into account the availability and effectiveness of data, we select 49 Chinese commercial banks from 2010 to 2020 as samples to measure and analyze their innovation efficiency. The data are from the China Stock Market & Accounting Research (CSMAR) database, the Wind database, and the annual reports of commercial banks. The 49 samples are 5 state-owned commercial banks, 9 joint-stock commercial banks, 26 city commercial banks, and 9 rural commercial banks. The sample selection covers a wide range, which can reflect the overall innovation efficiency of Chinese commercial banks.When using the DEA-BCC model to calculate efficiency, the input indicators and output indicators must comply with the “same direction” hypothesis, that is, the input quantity shall increase, the output quantity shall not decrease, and vice versa. Therefore, the selected input and output indicators must have a positive correlation. Pearson’s correlation analysis test method is often used to detect this hypothesis. We use the software Stata 15 for Pearson’s correlation analysis, and the analysis results are shown in Table4. It can be seen from Table 4 that the four input indicators and three output indicators have passed the test at the significance level of 1%. This shows that the selected input and output indicators of commercial banks comply with this hypothesis, and the DEA-BCC model can be used for empirical analysis.Table 4
Pearson’s correlation analysis results of the sample data.
IndicatorFixed assets-net valuePayroll payableBusiness and management expensesOperating expensesFee and commission income0.9487∗(0.0000)0.9427∗(0.0000)0.9412∗(0.0000)0.9892∗(0.0000)Total assets0.9576∗(0.0000)0.9394∗(0.0000)0.9243∗(0.0000)0.9794∗(0.0000)Operating revenue0.9183∗(0.0000)0.9076∗(0.0000)0.9378∗(0.0000)0.9665∗(0.0000)Note. “∗” means significant at a 1% confidence level, and “0.0000” in brackets is the P statistical value.


## 3.1. DEA-BCC Model

The DEA is a method for evaluating the relative effectiveness of decision-making units (DMUs). It is first proposed by Charnes, Cooper, and Rhodes in 1978 [28]. Sherman and Gold first applied the DEA model to the efficiency evaluation of commercial banks in 1985. [29]. Since then, the DEA model has become a mainstream method to study bank efficiency.The DEA model has two forms: input oriented and output oriented. The model can be set as CCR constant return to scale model and BCC variable return to scale model, which can be set according to the actual research situation. Commercial banks are service-oriented enterprises by nature, and the input factors are mainly savings deposits and initial investment. In the operations, the goal of the banks is to reasonably allocate their resources to maximize their profits. Therefore, this study selects the output-oriented BCC model to study the static efficiency of the banks. The expression of the output-oriented BCC model is shown as formula (1).(1)MaxθBθB,λ,s.t.Xλ≤x0θBy0−Yλ≤0eλ=1λ≥0,where X is the input vector, Y is the output vector, θB is the target planning value, and λ is the planning decision variable.


## 3.2. DEA-Malmquist Index

While analyzing the static efficiency of commercial banks, in order to further explore the dynamic change trend of the banks’ innovation efficiency in time series, we introduce the Malmquist index. The Malmquist index was originally proposed by Swedish economist Sten Malmquist in 1953. However, due to the lack of empirical tools, its application is greatly limited. Only after the DA method was proposed, there are researchers combined it with the Malmquist index that made the Malmquist index from theoretical index to empirical index, and it opened a wide application prospect in practice.Assuming thatt is the base period, the Malmquist index, which measures the change rate of innovation efficiency from t period to t + 1 period, can be expressed as formula (2).(2)Mt,t+1xt,yt,xt+1,yt+1,=Dtxt+1,yt+1Dtxt,yt×Dt+1xt+1,yt+1Dt+1xt,yt1/2,where (xt, yt) and (xt+1, yt+1) represent the input and output vectors of t period and t + 1 period, respectively. If M > 1, it means that the efficiency is improved from t period to t + 1 period; if M = 1, it means that the efficiency is at a standstill from t period to t + 1 period; and if M < 1, it indicates that the efficiency is decreasing from t period and t + 1 period.The Malmquist index can be further decomposed according to the work of Ray and Desli (1997) [30]. The decomposition results are shown as formula (3)–(6).(3)Mt,t+1xt,yt,xt+1,yt+1,=DVt+1xt+1,yt+1DVtxt,yt×DVtxt,ytDVt+1xt,yt×DVtxt+1,yt+1DVt+1xt+1,yt+11/2×DCtxt+1,yt+1/DVtxt+1,yt+1DCtxt,yt/DVtxt,yt×DCt+1xt+1,yt+1/DVt+1xt+1,yt+1DCt+1xt,yt/DVt+1xt,yt1/2,(4)Tech=Dtxt+1,yt+1Dt+1xt+1,yt+1×Dtxt,ytDt+1xt,yt1/2,(5)Pech=DVt+1xt+1,yt+1DVtxt,yt,(6)Sech=DCtxt+1,yt+1xt,yt/DVtxt+1,yt+1DCtxt,yt/DVtxt,yt×DCt+1xt+1,yt+1/DVt+1xt+1,yt+1DCt+1xt,yt/DVt+1xt,yt1/2,where Effch = Pech × Sech, so the final result of Malmquist exponential decomposition can be expressed as formula (7).(7)M=Effch×Techch=Pech×Sech×Techch,where Effch is the technical efficiency index, Techch is the technical progress index, Pech is the pure technical efficiency index, and Sech is the scale efficiency index.We use the DEA-Malmquist index to study the innovation efficiency of Chinese commercial banks and calculate the Malmquist index of their innovation efficiency and its decomposition. The Malmquist index and its decomposition we used in the study are shown in Table1.Table 1
Malmquist index and its decomposition index of the innovation efficiency.
Index nameContent of measurementMalmquist index of commercial banks’ innovation efficiency (Cbiem)Used to measure the efficiency of commercial banks’ innovation input and output.Technical progress index (Techch)Used to measure the technological progress produced by commercial banks using new technologies or inventing new products.Pure technical efficiency index (Pech)Used to measure the minimum input of commercial banks based on the maximum output under the premise of variable return to scale.Scale efficiency index (Sech)Used to measure whether the scale adjustment of commercial banks is close to the optimal production scale.As shown in Table1, the improvement of innovation efficiency is divided into three aspects, the progress of technical level, the improvement of management ability, and the improvement of scale efficiency.


## 3.3. Indicators and Data

When using DEA to evaluate the efficiency of commercial banks, there are three main selection methods of input and output indicators: production approach, intermediate approach, and asset approach, as shown in Table2.(1)
The production approach regards the bank as the producer of financial products. The number of deposit accounts and loans is regarded as bank’s output, and the capital and labor are regarded as input.(2)
The intermediary approach regards banks as intermediaries that convert savings into investment. The amount of deposits and loans is regarded as bank’s output, and the labor and capital are regarded as input.(3)
The asset approach also regards banks as financial intermediaries, but only the asset items in bank’s balance sheet are regarded as output, and deposits are not included in the output as liabilities.Table 2
Characteristics of input and output indicators’ selection approach.
ApproachInput indicatorsOutput indicatorsDefectProduction approachCapitalLabourFixed assetsNumber of deposit accountsNumber of loansIn the actual operation process of the bank, the number of deposit accounts and loans is generally unavailable.Intermediate approachHuman resourcesDepositCapitalOperating costsLoanInvestment and other profitable assetsWithout considering the loan quality, only considering the number of loan assets, ignoring the potential risks, it cannot fully show the profitability of bank assets.Asset approachDeposit itemsLoanInvestmentWithout considering the income and profit of commercial banks, it is difficult to evaluate the actual use efficiency of funds.Combined with the respective characteristics of the above three approaches in Table1, we select the following indicators as the input and output indicators for the evaluation model. The specific indicators are shown in Table 3.Table 3
Input and output indicators for the innovation efficiency of commercial banks.
Indicator typeIndicator nameInput indicatorsFixed assets-net valuePayroll payableBusiness and management expensesOperating expensesOutput indicatorsFee and commission incomeOperating revenueTotal assetsThe four selected input indicators are fixed assets-net value, payroll payable, business and management expenses, and operating expenses.The innovation and development of commercial banks cannot be separated from the investment of fixed assets such as technology equipment, and the impact of its change on the innovation and development of commercial banks cannot be ignored.Employee compensation is an essential expenditure of any enterprise. In addition, innovation is inseparable from a high-quality employee team, and a high-quality employee team needs higher salary expenditure.The operation of commercial banks is inseparable from management. The expenses incurred in the organization and management of commercial banks are business and management expenses, which reflect the investment of commercial banks in management.The scale of a bank is reflected in the volume of business. Operating expenses are various business-related expenses incurred by commercial banks in the process of business operation, which reflects the business scale and investment of commercial banks.The three selected output indicators are fee and commission income, operating revenue, and total assets.The innovative income of commercial banks is mainly reflected in intermediary business income such as handling fees and commission income other than credit business. Therefore, measuring the innovation efficiency of commercial banks with intermediary business income has high reliability and validity.Operating revenue refers to the income obtained by commercial banks from providing financial products and services. It is also an important indicator to measure the product and service innovation of commercial banks.Total assets can measure the scale of commercial banks, and its increase also reflects the scale growth brought by the innovation.After determining the input and output indicators, based on the development status of Chinese commercial banks and taking into account the availability and effectiveness of data, we select 49 Chinese commercial banks from 2010 to 2020 as samples to measure and analyze their innovation efficiency. The data are from the China Stock Market & Accounting Research (CSMAR) database, the Wind database, and the annual reports of commercial banks. The 49 samples are 5 state-owned commercial banks, 9 joint-stock commercial banks, 26 city commercial banks, and 9 rural commercial banks. The sample selection covers a wide range, which can reflect the overall innovation efficiency of Chinese commercial banks.When using the DEA-BCC model to calculate efficiency, the input indicators and output indicators must comply with the “same direction” hypothesis, that is, the input quantity shall increase, the output quantity shall not decrease, and vice versa. Therefore, the selected input and output indicators must have a positive correlation. Pearson’s correlation analysis test method is often used to detect this hypothesis. We use the software Stata 15 for Pearson’s correlation analysis, and the analysis results are shown in Table4. It can be seen from Table 4 that the four input indicators and three output indicators have passed the test at the significance level of 1%. This shows that the selected input and output indicators of commercial banks comply with this hypothesis, and the DEA-BCC model can be used for empirical analysis.Table 4
Pearson’s correlation analysis results of the sample data.
IndicatorFixed assets-net valuePayroll payableBusiness and management expensesOperating expensesFee and commission income0.9487∗(0.0000)0.9427∗(0.0000)0.9412∗(0.0000)0.9892∗(0.0000)Total assets0.9576∗(0.0000)0.9394∗(0.0000)0.9243∗(0.0000)0.9794∗(0.0000)Operating revenue0.9183∗(0.0000)0.9076∗(0.0000)0.9378∗(0.0000)0.9665∗(0.0000)Note. “∗” means significant at a 1% confidence level, and “0.0000” in brackets is the P statistical value.


## 4. Results and Discussion

### 4.1. Static Analysis of Innovation Efficiency

We use DEAP 2.1 to calculate the input and output indicators of the selected 49 Chinese commercial banks in 2013 and 2020 and obtain the comprehensive efficiency (Crste), pure technical efficiency (Vrste), and scale efficiency (Scale). The year 2013 is selected as the base year because 2013 is recognized as the “first year of internet finance era”, and 2020 is the nearest year when the data used for the study can be obtained. The calculation results are shown in Table5.Table 5
Innovation efficiency of the 49 banks in 2013 and 2020.
Commercial banks20132020CrsteVrsteScaleCrsteVrsteScaleBank of China0.8900.9570.930drs0.8480.9460.896drsChina Construction Bank0.9240.9570.966drs0.9921.0000.992drsIndustrial and Commercial Bank of China1.0001.0001.000-1.0001.0001.000-Agricultural Bank of China0.7530.7940.948drs0.7621.0000.762drsBank of Communications0.8351.0000.835drs0.9730.9750.998irsIndustrial Bank1.0001.0001.000-0.9611.0000.961drsChina Guangfa Bank1.0001.0001.000-0.8850.9660.916drsShanghai Pudong Development Bank0.9561.0000.956drs1.0001.0001.000-Ping An Bank0.9520.9870.964drs1.0001.0001.000-China Minsheng Bank1.0001.0001.000-0.8630.8640.999drsChina Merchants Bank0.9841.0000.984drs1.0001.0001.000-China CITIC Bank0.8890.9210.965drs0.8080.8810.917drsChina Everbright Bank1.0001.0001.000-0.8340.8770.952drsHuaxia Bank0.7810.8220.950drs0.8861.0000.886drsBank of Beijing0.9491.0000.949drs1.0001.0001.000-Bank of Shanghai0.8630.9810.880drs1.0001.0001.000-Bank of Nanjing0.8520.8780.971drs0.7160.7170.998irsBank of Guangzhou1.0001.0001.000-0.8260.8380.985irsBank of Chengdu0.8900.9150.973drs0.9460.9630.982irsBank of Lanzhou0.7400.7530.984drs0.9530.9540.998irsBank of Ningbo0.7920.8180.969drs0.7700.9320.826drsBank of Jinhua0.8310.8330.998drs0.5070.6250.811irsQilu Bank0.7470.7550.989drs0.8270.8520.971irsBank of Kunlun1.0001.0001.000-1.0001.0001.000-Bank of Jiaxing0.6330.6640.953irs0.8720.9330.935irsBank of Hangzhou0.8270.8520.971drs1.0001.0001.000-Hankou Bank0.9090.9630.945irs1.0001.0001.000-Bank of Guiyang0.8940.9060.988drs0.8620.8660.995irsChina Resources Bank of Zhuhai0.8950.9320.961irs1.0001.0001.000-Bank of Liuzhou0.7100.7130.996drs1.0001.0001.000-Xiamen Bank1.0001.0001.000-1.0001.0001.000-Bank of Ningxia0.8670.8820.983drs0.6130.6710.913irsBank of Cangzhou0.6410.6420.999drs0.6960.7270.958irsBank of Jiangsu0.8320.8730.953drs0.9291.0000.929drsZhejiang Mintai Commercial Bank0.5100.5270.968drs0.4310.4540.949irsHuarong Xiangjiang Bank0.8150.8230.991irs0.9680.9790.989irsBank of Huzhou0.5440.6010.905irs0.5880.7340.801irsBank of Changsha0.9911.0000.991drs0.8911.0000.891drsBank of Wenzhou0.6040.6060.998drs0.7690.8100.950irsLeshan City Commercial Bank0.8801.0000.880irs1.0001.0001.000-Shanghai Rural Commercial Bank0.6150.7160.859drs0.6990.7000.998irsNingbo Yinzhou Rural Commercial Bank1.0001.0001.000-0.7490.7670.977irsBeijing Rural Commercial Bank0.6830.7300.934drs0.6650.6710.991irsJiangsu Suzhou Rural Commercial Bank0.7480.7490.998drs0.6670.6800.982irsGuangdong Nanhai Rural Commercial Bank0.8340.8380.996drs0.8230.8360.985irsFoshan Rural Commercial Bank0.9371.0000.937irs0.6450.6860.940irsJiangsu Jiangyin Rural Commercial Bank0.8640.8950.966irs0.7190.7540.953irsZhejiang Wenling Rural Commercial Bank0.7010.8110.864irs0.8091.0000.809irsYuhuan Rural Commercial Bank1.0001.0001.000-0.9621.0000.962irsAverage0.8480.8790.9640.8510.8910.954Note. drs means diminishing returns to scale, and irs means increasing returns to scale.It can be seen from the Crste index that the average of Crste in 2013 and 2020 is 0.848 and 0.851, which did not reach the DEA efficiency. However, it shows an overall growth trend though at a low level. From the perspective of individual banks, there are some differences in the value of Crste. Except 21 banks such as Bank of China, China Guangfa Bank, Bank of Nanjing, and Beijing Rural Commercial Bank, the innovation efficiency of most banks is gradually improved. In 2013, 10 banks reached DEA efficiency, and in 2020, 13 banks reached DEA efficiency. Among them, three banks reached DEA efficiency both in 2013 and 2020. They are Industrial and Commercial Bank of China, Bank of Kunlun, and Xiamen Bank, accounting for 6.1% of the total sample. It shows that the innovation of these banks has achieved the optimal allocation, the innovation investment is reasonable, and the input and output have reached the best results in different values and different years. In 2020, 13 banks including Industrial and Commercial Bank of China, Shanghai Pudong Development Bank, Ping An Bank, Bank of Beijing, and Bank of Shanghai reached DEA efficiency, accounting for 26.5% of the total sample. Other banks have room to improve their Vrste and Scale to varying degrees. The last three banks are Bank of Huzhou, Bank of Jinhua, and Zhejiang Mintai Commercial Bank, but these banks are “irs” (increasing returns to scale). Therefore, these banks should increase their innovation investment, improve management level, and expand scale to improve their Crste.It can be seen from the Vrste index that the average of Vrste in 2013 is 0.879, with a distance of 0.121 from the production frontier. In 2020, the average of the Vrste is 0.891, with a distance of 0.109 from the production frontier. It shows that the management level still has room for improvement. The average of Vrste in 2013 and 2020 is lower than the average of Scale, which shows that innovation management and technical level are the main factors restricting the innovation efficiency of the banks. In 2013, the number of banks with Vrste reached DEA efficiency is 17, and in 2020, the number of banks with Vrste reached DEA efficiency is 21. It shows that these banks are doing well in innovative management and technology. Low Scale is the main reason for the low value of Crste. The scale of innovation investment should be adjusted to further improve Scale. The Vrste of Zhejiang Mintai Commercial Bank is at a low level, 0.527 in 2013 and 0.454 in 2020, which is far lower than the national average. It is necessary to further improve the management and technical level.Scale efficiency refers to whether the innovation of the banks is on the optimal scale. It can be seen from Table5 that the value of the Scale slightly decreased from 0.964 in 2013 to 0.954 in 2020. In 2013, the Scale of 10 banks reached DEA efficiency, accounting for 20.4% of the total sample. In 2020, the Scale of 13 commercial banks reached DEA efficiency, accounting for 26.5% of the total sample. Among them, three banks’ Scale reached DEA efficiency both in 2013 and 2020. They are Industrial and Commercial Bank of China, Bank of Kunlun, and Xiamen Bank, accounting for 6.1% of the total sample. From the value of Scale in 2020, it can be seen that the Scale value of the Agricultural Bank of China and Bank of Huzhou is at a low level, and these banks need to integrate innovation investment to achieve the best scale. Commercial banks with increasing returns to scale include Bank of Communications, Bank of Nanjing, Bank of Guangzhou, Shanghai Rural Commercial Bank, and other 24 banks. These banks should reasonably increase investment in innovation to achieve the best scale. However, banks with diminishing returns to scale have obvious efficiency losses because their innovation investments have not been effectively utilized. Special attention should be paid to improve the investment direction of these commercial banks’ innovation.


### 4.2. Dynamic Analysis of Innovation Efficiency

The DEA-Malmquist index can dynamically reflect the changing trend of innovation efficiency. We use DEAP 2.1 to calculate the input and output indicators of the studied 49 Chinese banks from 2010 to 2020 and obtain the Malmquist index of their innovation efficiency. Through the analysis of the index and its decomposition index, we further investigate the dynamic changes and heterogeneity of their innovation efficiency. The results of the index and its decomposition of the 49 banks are shown in Table6.Table 6
Malmquist index and its decomposition index of the 49 banks from 2010 to 2020.
YearEffchTechchPechSechCbiem2010-20111.1600.9171.0451.1101.0642011-20120.9911.0711.0030.9881.0612012-20131.0830.9421.0281.0541.0202013-20140.9910.9910.9911.0000.9822014-20151.0350.9181.0390.9950.9502015-20161.0160.9801.0161.0000.9962016-20170.9901.0141.0080.9821.0042017-20180.9571.0960.9590.9981.0492018-20191.0111.2511.0031.0081.2652019-20201.0030.9610.9981.0050.964Average1.0221.0101.0091.0131.032Notes: Effch is the technical efficiency index; Techch is the technical progress index; Pech is the pure technical efficiency index; Sech is the scale efficiency index; and Cbiem is the Malmquist index of commercial banks’ innovation efficiency.It can be seen from Table6 that the average of Cbiem is 1.032, and an overall increase is 3.2%. It can be seen from Figure 1 that the Cbiem of the sample banks decreased first and then increased from 2010 to 2020, but the value of Cbiem is less than 1 in 2020. It shows that the value of Cbiem is steadily rising after being impacted by internet finance. In 2020, their innovation efficiency is less than 1, which may be due to the impact of the COVID-19 epidemic.Figure 1
The change trend for efficiency of the 49 banks from 2010 to 2020.It can be seen from Table6 that the Effch increased by 2.2%, and the Techch increased by 1%. It indicates that the innovation management level and resource utilization efficiency play a major role in improving the Cbiem of the sample banks, followed by the driving role of technological progress. These banks need to further realize efficient innovation by improving their technical level.From 2011 to 2012, the Effch is 0.991 and the Techch is 1.071; from 2016 to 2017, the Effch is 0.990 and the Techch is 1.014; from 2017 to 2018, the Effch is 0.957 and Techch is 1.096; and from 2018 to 2019 the Effch is 1.011 and the Techch is 1.251. In these years, the Techch has made a major contribution to the improvement of innovation efficiency of the sample banks. In other periods, the Effch has a great impact on the improvement of innovation efficiency. From 2010 to 2020, the average of Sech is 1.013 and the average of Pech is 1.009, both of which are greater than 1. They both show an upward trend. The Sech in 2011-2012, 2014-2015, and 2016-2018 is less than 1, reflecting that scale efficiency inhibits the growth of their innovation efficiency.The calculation results of the Malmqusit index and its decomposition of innovation efficiency of the 49 banks are shown in Table7.Table 7
Malmquist index and decomposition index of innovation efficiency of the 49 banks.
BankEffchTechchPechSechCbiemBank of China0.9901.0150.9990.9911.005China Construction Bank0.9991.0321.0000.9991.031Industrial and Commercial Bank of China1.0001.0521.0001.0001.052Agricultural Bank of China1.0091.0341.0230.9861.043Bank of Communications1.0131.0220.9981.0151.034Industrial Bank0.9961.0431.0000.9961.039China Guangfa Bank1.0151.0351.0180.9971.050Shanghai Pudong Development Bank1.0321.0101.0001.0321.043Ping An Bank1.0311.1001.0241.0071.135China Minsheng Bank0.9851.1220.9851.0001.106China Merchants Bank1.0021.0341.0001.0021.036China CITIC Bank1.0071.0190.9951.0121.027China Everbright Bank1.0171.0520.9971.0201.070Huaxia Bank1.0640.9871.0321.0311.050Bank of Beijing1.0081.0091.0001.0081.017Bank of Shanghai1.0591.0091.0191.0391.068Bank of Nanjing1.0060.9960.9811.0261.002Bank of Guangzhou0.9811.0190.9830.9991.000Bank of Chengdu1.0480.9771.0131.0341.024Bank of Lanzhou1.0660.9470.9951.0711.009Bank of Ningbo1.0190.9931.0171.0021.012Bank of Jinhua0.9881.0121.0080.9801.000Qilu Bank1.0510.9771.0221.0281.027Bank of Kunlun1.0000.9301.0001.0000.930Bank of Jiaxing1.0501.1281.0520.9991.184Bank of Hangzhou1.0421.0261.0251.0171.069Hankou Bank1.0361.0651.0241.0111.104Bank of Guiyang1.0410.9801.0151.0251.020China Resources Bank of Zhuhai1.0751.0141.0001.0751.090Bank of Liuzhou1.0580.9961.0471.0101.053Xiamen Bank1.0710.9621.0551.0151.030Bank of Ningxia1.0070.9570.9891.0190.964Bank of Cangzhou1.0290.9781.0231.0061.006Bank of Jiangsu1.0570.9841.0221.0341.041Zhejiang Mintai Commercial Bank0.9930.9900.9771.0160.983Huarong Xiangjiang Bank1.0050.9600.9981.0070.964Bank of Huzhou1.0120.9771.0310.9810.989Bank of Changsha0.9991.0251.0080.9911.025Bank of Wenzhou1.0561.0101.0311.0241.067Leshan City Commercial Bank1.0561.0821.0001.0561.143Shanghai Rural Commercial Bank1.0461.0051.0031.0421.052Ningbo Yinzhou Rural Commercial Bank1.0010.9850.9881.0130.986Beijing Rural Commercial Bank1.0201.0431.0071.0131.064Jiangsu Suzhou Rural Commercial Bank1.0130.9791.0001.0130.992Guangdong Nanhai Rural Commercial Bank1.0540.9941.0301.0231.048Foshan Rural Commercial Bank0.9570.9450.9630.9940.904Jiangsu Jiangyin Rural Commercial Bank0.9960.9760.9851.0110.973Zhejiang Wenling Rural Commercial Bank1.0331.0111.0490.9851.043Yuhuan Rural Commercial Bank1.0131.0231.0001.0131.037State-owned commercial banks1.0021.0311.0040.9981.033Joint-stock commercial banks1.0171.0451.0061.0111.062City commercial banks1.0311.0001.0131.0181.032Rural commercial banks1.0150.9961.0031.0121.011Average1.0221.0101.0091.0131.032It can be seen from Table7 that from 2010 to 2020, there are 40 banks for which their Cbiem is greater than equal to 1, while 9 banks for which their Cbiem is less than 1. It shows that the Cbiem of most sample banks is constantly improving and presents a well development trend. Through the analysis of Cbiem, it can be seen that the Techch of Huaxia Bank, Bank of Nanjing, Bank of Chengdu, Bank of Lanzhou, Jiangsu Suzhou Rural Commercial Bank, and other commercial banks has decreased, and the improvement of their Cbiem mainly comes from the improvement of Effch. The Cbiem improvement of Bank of China, China Construction Bank, Industrial Bank, Bank of Guangzhou, Bank of Jinhua, and Bank of Changsha mainly benefits from Techch. The Effch and Techch of commercial banks such as Agricultural Bank of China, China Merchants Bank, Bank of Beijing, and Beijing Rural Commercial Bank synchronously change, that is, Effch and Techch play a synergistic role in promoting the improvement of Cbiem. The Effch and Techch of Zhejiang Mintai Commercial Bank, Foshan Rural Commercial Bank, and Jiangsu Jiangyin Rural Commercial Bank are less than 1. These banks should improve their innovation efficiency by improving their technical level and management level and adjusting the scale of innovation investment.From 2010 to 2020, the Cbiem average of large state-owned commercial banks, joint-stock banks, city commercial banks, and rural commercial banks is 1.033, 1.062, 1.032, and 1.011, i.e., they are in the order of joint-stock commercial banks > state-owned commercial banks > city commercial banks > rural commercial banks. Although the Cbiem of various commercial banks fluctuated up and down in different years, it showed an upward trend on the whole. The Cbiem of joint-stock commercial banks has rapidly increased, mainly due to the rapid Techch. The Sech of state-owned commercial banks shows a downward trend so that they should adjust the scale of innovation to improve their Sech. The Techch of city commercial banks is slowly growing, and this indicates that they should use new technologies and increase technological investment to improve their Techch. The Techch of rural commercial banks shows a downward trend, which shows that technological progress is the main restrictive factor for these banks to improve innovation efficiency, and they should improve their technical level.


## 4.1. Static Analysis of Innovation Efficiency

We use DEAP 2.1 to calculate the input and output indicators of the selected 49 Chinese commercial banks in 2013 and 2020 and obtain the comprehensive efficiency (Crste), pure technical efficiency (Vrste), and scale efficiency (Scale). The year 2013 is selected as the base year because 2013 is recognized as the “first year of internet finance era”, and 2020 is the nearest year when the data used for the study can be obtained. The calculation results are shown in Table5.Table 5
Innovation efficiency of the 49 banks in 2013 and 2020.
Commercial banks20132020CrsteVrsteScaleCrsteVrsteScaleBank of China0.8900.9570.930drs0.8480.9460.896drsChina Construction Bank0.9240.9570.966drs0.9921.0000.992drsIndustrial and Commercial Bank of China1.0001.0001.000-1.0001.0001.000-Agricultural Bank of China0.7530.7940.948drs0.7621.0000.762drsBank of Communications0.8351.0000.835drs0.9730.9750.998irsIndustrial Bank1.0001.0001.000-0.9611.0000.961drsChina Guangfa Bank1.0001.0001.000-0.8850.9660.916drsShanghai Pudong Development Bank0.9561.0000.956drs1.0001.0001.000-Ping An Bank0.9520.9870.964drs1.0001.0001.000-China Minsheng Bank1.0001.0001.000-0.8630.8640.999drsChina Merchants Bank0.9841.0000.984drs1.0001.0001.000-China CITIC Bank0.8890.9210.965drs0.8080.8810.917drsChina Everbright Bank1.0001.0001.000-0.8340.8770.952drsHuaxia Bank0.7810.8220.950drs0.8861.0000.886drsBank of Beijing0.9491.0000.949drs1.0001.0001.000-Bank of Shanghai0.8630.9810.880drs1.0001.0001.000-Bank of Nanjing0.8520.8780.971drs0.7160.7170.998irsBank of Guangzhou1.0001.0001.000-0.8260.8380.985irsBank of Chengdu0.8900.9150.973drs0.9460.9630.982irsBank of Lanzhou0.7400.7530.984drs0.9530.9540.998irsBank of Ningbo0.7920.8180.969drs0.7700.9320.826drsBank of Jinhua0.8310.8330.998drs0.5070.6250.811irsQilu Bank0.7470.7550.989drs0.8270.8520.971irsBank of Kunlun1.0001.0001.000-1.0001.0001.000-Bank of Jiaxing0.6330.6640.953irs0.8720.9330.935irsBank of Hangzhou0.8270.8520.971drs1.0001.0001.000-Hankou Bank0.9090.9630.945irs1.0001.0001.000-Bank of Guiyang0.8940.9060.988drs0.8620.8660.995irsChina Resources Bank of Zhuhai0.8950.9320.961irs1.0001.0001.000-Bank of Liuzhou0.7100.7130.996drs1.0001.0001.000-Xiamen Bank1.0001.0001.000-1.0001.0001.000-Bank of Ningxia0.8670.8820.983drs0.6130.6710.913irsBank of Cangzhou0.6410.6420.999drs0.6960.7270.958irsBank of Jiangsu0.8320.8730.953drs0.9291.0000.929drsZhejiang Mintai Commercial Bank0.5100.5270.968drs0.4310.4540.949irsHuarong Xiangjiang Bank0.8150.8230.991irs0.9680.9790.989irsBank of Huzhou0.5440.6010.905irs0.5880.7340.801irsBank of Changsha0.9911.0000.991drs0.8911.0000.891drsBank of Wenzhou0.6040.6060.998drs0.7690.8100.950irsLeshan City Commercial Bank0.8801.0000.880irs1.0001.0001.000-Shanghai Rural Commercial Bank0.6150.7160.859drs0.6990.7000.998irsNingbo Yinzhou Rural Commercial Bank1.0001.0001.000-0.7490.7670.977irsBeijing Rural Commercial Bank0.6830.7300.934drs0.6650.6710.991irsJiangsu Suzhou Rural Commercial Bank0.7480.7490.998drs0.6670.6800.982irsGuangdong Nanhai Rural Commercial Bank0.8340.8380.996drs0.8230.8360.985irsFoshan Rural Commercial Bank0.9371.0000.937irs0.6450.6860.940irsJiangsu Jiangyin Rural Commercial Bank0.8640.8950.966irs0.7190.7540.953irsZhejiang Wenling Rural Commercial Bank0.7010.8110.864irs0.8091.0000.809irsYuhuan Rural Commercial Bank1.0001.0001.000-0.9621.0000.962irsAverage0.8480.8790.9640.8510.8910.954Note. drs means diminishing returns to scale, and irs means increasing returns to scale.It can be seen from the Crste index that the average of Crste in 2013 and 2020 is 0.848 and 0.851, which did not reach the DEA efficiency. However, it shows an overall growth trend though at a low level. From the perspective of individual banks, there are some differences in the value of Crste. Except 21 banks such as Bank of China, China Guangfa Bank, Bank of Nanjing, and Beijing Rural Commercial Bank, the innovation efficiency of most banks is gradually improved. In 2013, 10 banks reached DEA efficiency, and in 2020, 13 banks reached DEA efficiency. Among them, three banks reached DEA efficiency both in 2013 and 2020. They are Industrial and Commercial Bank of China, Bank of Kunlun, and Xiamen Bank, accounting for 6.1% of the total sample. It shows that the innovation of these banks has achieved the optimal allocation, the innovation investment is reasonable, and the input and output have reached the best results in different values and different years. In 2020, 13 banks including Industrial and Commercial Bank of China, Shanghai Pudong Development Bank, Ping An Bank, Bank of Beijing, and Bank of Shanghai reached DEA efficiency, accounting for 26.5% of the total sample. Other banks have room to improve their Vrste and Scale to varying degrees. The last three banks are Bank of Huzhou, Bank of Jinhua, and Zhejiang Mintai Commercial Bank, but these banks are “irs” (increasing returns to scale). Therefore, these banks should increase their innovation investment, improve management level, and expand scale to improve their Crste.It can be seen from the Vrste index that the average of Vrste in 2013 is 0.879, with a distance of 0.121 from the production frontier. In 2020, the average of the Vrste is 0.891, with a distance of 0.109 from the production frontier. It shows that the management level still has room for improvement. The average of Vrste in 2013 and 2020 is lower than the average of Scale, which shows that innovation management and technical level are the main factors restricting the innovation efficiency of the banks. In 2013, the number of banks with Vrste reached DEA efficiency is 17, and in 2020, the number of banks with Vrste reached DEA efficiency is 21. It shows that these banks are doing well in innovative management and technology. Low Scale is the main reason for the low value of Crste. The scale of innovation investment should be adjusted to further improve Scale. The Vrste of Zhejiang Mintai Commercial Bank is at a low level, 0.527 in 2013 and 0.454 in 2020, which is far lower than the national average. It is necessary to further improve the management and technical level.Scale efficiency refers to whether the innovation of the banks is on the optimal scale. It can be seen from Table5 that the value of the Scale slightly decreased from 0.964 in 2013 to 0.954 in 2020. In 2013, the Scale of 10 banks reached DEA efficiency, accounting for 20.4% of the total sample. In 2020, the Scale of 13 commercial banks reached DEA efficiency, accounting for 26.5% of the total sample. Among them, three banks’ Scale reached DEA efficiency both in 2013 and 2020. They are Industrial and Commercial Bank of China, Bank of Kunlun, and Xiamen Bank, accounting for 6.1% of the total sample. From the value of Scale in 2020, it can be seen that the Scale value of the Agricultural Bank of China and Bank of Huzhou is at a low level, and these banks need to integrate innovation investment to achieve the best scale. Commercial banks with increasing returns to scale include Bank of Communications, Bank of Nanjing, Bank of Guangzhou, Shanghai Rural Commercial Bank, and other 24 banks. These banks should reasonably increase investment in innovation to achieve the best scale. However, banks with diminishing returns to scale have obvious efficiency losses because their innovation investments have not been effectively utilized. Special attention should be paid to improve the investment direction of these commercial banks’ innovation.


## 4.2. Dynamic Analysis of Innovation Efficiency

The DEA-Malmquist index can dynamically reflect the changing trend of innovation efficiency. We use DEAP 2.1 to calculate the input and output indicators of the studied 49 Chinese banks from 2010 to 2020 and obtain the Malmquist index of their innovation efficiency. Through the analysis of the index and its decomposition index, we further investigate the dynamic changes and heterogeneity of their innovation efficiency. The results of the index and its decomposition of the 49 banks are shown in Table6.Table 6
Malmquist index and its decomposition index of the 49 banks from 2010 to 2020.
YearEffchTechchPechSechCbiem2010-20111.1600.9171.0451.1101.0642011-20120.9911.0711.0030.9881.0612012-20131.0830.9421.0281.0541.0202013-20140.9910.9910.9911.0000.9822014-20151.0350.9181.0390.9950.9502015-20161.0160.9801.0161.0000.9962016-20170.9901.0141.0080.9821.0042017-20180.9571.0960.9590.9981.0492018-20191.0111.2511.0031.0081.2652019-20201.0030.9610.9981.0050.964Average1.0221.0101.0091.0131.032Notes: Effch is the technical efficiency index; Techch is the technical progress index; Pech is the pure technical efficiency index; Sech is the scale efficiency index; and Cbiem is the Malmquist index of commercial banks’ innovation efficiency.It can be seen from Table6 that the average of Cbiem is 1.032, and an overall increase is 3.2%. It can be seen from Figure 1 that the Cbiem of the sample banks decreased first and then increased from 2010 to 2020, but the value of Cbiem is less than 1 in 2020. It shows that the value of Cbiem is steadily rising after being impacted by internet finance. In 2020, their innovation efficiency is less than 1, which may be due to the impact of the COVID-19 epidemic.Figure 1
The change trend for efficiency of the 49 banks from 2010 to 2020.It can be seen from Table6 that the Effch increased by 2.2%, and the Techch increased by 1%. It indicates that the innovation management level and resource utilization efficiency play a major role in improving the Cbiem of the sample banks, followed by the driving role of technological progress. These banks need to further realize efficient innovation by improving their technical level.From 2011 to 2012, the Effch is 0.991 and the Techch is 1.071; from 2016 to 2017, the Effch is 0.990 and the Techch is 1.014; from 2017 to 2018, the Effch is 0.957 and Techch is 1.096; and from 2018 to 2019 the Effch is 1.011 and the Techch is 1.251. In these years, the Techch has made a major contribution to the improvement of innovation efficiency of the sample banks. In other periods, the Effch has a great impact on the improvement of innovation efficiency. From 2010 to 2020, the average of Sech is 1.013 and the average of Pech is 1.009, both of which are greater than 1. They both show an upward trend. The Sech in 2011-2012, 2014-2015, and 2016-2018 is less than 1, reflecting that scale efficiency inhibits the growth of their innovation efficiency.The calculation results of the Malmqusit index and its decomposition of innovation efficiency of the 49 banks are shown in Table7.Table 7
Malmquist index and decomposition index of innovation efficiency of the 49 banks.
BankEffchTechchPechSechCbiemBank of China0.9901.0150.9990.9911.005China Construction Bank0.9991.0321.0000.9991.031Industrial and Commercial Bank of China1.0001.0521.0001.0001.052Agricultural Bank of China1.0091.0341.0230.9861.043Bank of Communications1.0131.0220.9981.0151.034Industrial Bank0.9961.0431.0000.9961.039China Guangfa Bank1.0151.0351.0180.9971.050Shanghai Pudong Development Bank1.0321.0101.0001.0321.043Ping An Bank1.0311.1001.0241.0071.135China Minsheng Bank0.9851.1220.9851.0001.106China Merchants Bank1.0021.0341.0001.0021.036China CITIC Bank1.0071.0190.9951.0121.027China Everbright Bank1.0171.0520.9971.0201.070Huaxia Bank1.0640.9871.0321.0311.050Bank of Beijing1.0081.0091.0001.0081.017Bank of Shanghai1.0591.0091.0191.0391.068Bank of Nanjing1.0060.9960.9811.0261.002Bank of Guangzhou0.9811.0190.9830.9991.000Bank of Chengdu1.0480.9771.0131.0341.024Bank of Lanzhou1.0660.9470.9951.0711.009Bank of Ningbo1.0190.9931.0171.0021.012Bank of Jinhua0.9881.0121.0080.9801.000Qilu Bank1.0510.9771.0221.0281.027Bank of Kunlun1.0000.9301.0001.0000.930Bank of Jiaxing1.0501.1281.0520.9991.184Bank of Hangzhou1.0421.0261.0251.0171.069Hankou Bank1.0361.0651.0241.0111.104Bank of Guiyang1.0410.9801.0151.0251.020China Resources Bank of Zhuhai1.0751.0141.0001.0751.090Bank of Liuzhou1.0580.9961.0471.0101.053Xiamen Bank1.0710.9621.0551.0151.030Bank of Ningxia1.0070.9570.9891.0190.964Bank of Cangzhou1.0290.9781.0231.0061.006Bank of Jiangsu1.0570.9841.0221.0341.041Zhejiang Mintai Commercial Bank0.9930.9900.9771.0160.983Huarong Xiangjiang Bank1.0050.9600.9981.0070.964Bank of Huzhou1.0120.9771.0310.9810.989Bank of Changsha0.9991.0251.0080.9911.025Bank of Wenzhou1.0561.0101.0311.0241.067Leshan City Commercial Bank1.0561.0821.0001.0561.143Shanghai Rural Commercial Bank1.0461.0051.0031.0421.052Ningbo Yinzhou Rural Commercial Bank1.0010.9850.9881.0130.986Beijing Rural Commercial Bank1.0201.0431.0071.0131.064Jiangsu Suzhou Rural Commercial Bank1.0130.9791.0001.0130.992Guangdong Nanhai Rural Commercial Bank1.0540.9941.0301.0231.048Foshan Rural Commercial Bank0.9570.9450.9630.9940.904Jiangsu Jiangyin Rural Commercial Bank0.9960.9760.9851.0110.973Zhejiang Wenling Rural Commercial Bank1.0331.0111.0490.9851.043Yuhuan Rural Commercial Bank1.0131.0231.0001.0131.037State-owned commercial banks1.0021.0311.0040.9981.033Joint-stock commercial banks1.0171.0451.0061.0111.062City commercial banks1.0311.0001.0131.0181.032Rural commercial banks1.0150.9961.0031.0121.011Average1.0221.0101.0091.0131.032It can be seen from Table7 that from 2010 to 2020, there are 40 banks for which their Cbiem is greater than equal to 1, while 9 banks for which their Cbiem is less than 1. It shows that the Cbiem of most sample banks is constantly improving and presents a well development trend. Through the analysis of Cbiem, it can be seen that the Techch of Huaxia Bank, Bank of Nanjing, Bank of Chengdu, Bank of Lanzhou, Jiangsu Suzhou Rural Commercial Bank, and other commercial banks has decreased, and the improvement of their Cbiem mainly comes from the improvement of Effch. The Cbiem improvement of Bank of China, China Construction Bank, Industrial Bank, Bank of Guangzhou, Bank of Jinhua, and Bank of Changsha mainly benefits from Techch. The Effch and Techch of commercial banks such as Agricultural Bank of China, China Merchants Bank, Bank of Beijing, and Beijing Rural Commercial Bank synchronously change, that is, Effch and Techch play a synergistic role in promoting the improvement of Cbiem. The Effch and Techch of Zhejiang Mintai Commercial Bank, Foshan Rural Commercial Bank, and Jiangsu Jiangyin Rural Commercial Bank are less than 1. These banks should improve their innovation efficiency by improving their technical level and management level and adjusting the scale of innovation investment.From 2010 to 2020, the Cbiem average of large state-owned commercial banks, joint-stock banks, city commercial banks, and rural commercial banks is 1.033, 1.062, 1.032, and 1.011, i.e., they are in the order of joint-stock commercial banks > state-owned commercial banks > city commercial banks > rural commercial banks. Although the Cbiem of various commercial banks fluctuated up and down in different years, it showed an upward trend on the whole. The Cbiem of joint-stock commercial banks has rapidly increased, mainly due to the rapid Techch. The Sech of state-owned commercial banks shows a downward trend so that they should adjust the scale of innovation to improve their Sech. The Techch of city commercial banks is slowly growing, and this indicates that they should use new technologies and increase technological investment to improve their Techch. The Techch of rural commercial banks shows a downward trend, which shows that technological progress is the main restrictive factor for these banks to improve innovation efficiency, and they should improve their technical level.


## 5. Conclusions

From the above empirical study on the innovation efficiency of 49 Chinese commercial banks from 2010 to 2020, we can drown conclusions as follows.From the static analysis of the DEA-BCC model, it can be seen that the comprehensive innovation efficiency of these 49 banks did not reach DEA efficiency in 2013 and 2020. The innovation efficiency of different Chinese commercial banks greatly varies. Most Chinese commercial banks have room to improve their pure technical efficiency and scale efficiency to varying degrees. Therefore, these banks should pay attention to improve the management and operation level of innovation, design a reasonable innovation management system and innovation incentive system, and adjust innovation investment to achieve the best scale.According to the dynamic analysis of the DEA-Malmquist index, the average innovation efficiency index of these 49 banks from 2010 to 2020 is 1.032. It shows that the overall innovation efficiency is rising. Moreover, the technological efficiency of innovation plays a major role in the improvement of comprehensive efficiency, followed by technological progress. Therefore, these banks need to increase their technology investment and improve their technology level to improve their innovation efficiency. From the perspective of individual banks, the innovation efficiency of different banks greatly varies and shows fluctuations at different times. From the growth of banks’ innovation efficiency, they are in the order of joint-stock commercial banks > state-owned commercial banks > city commercial banks > rural commercial banks. Therefore, we suggest that all Chinese commercial banks should overcome their own shortages in technological innovation capability to elevate their innovation efficiency.



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*Source: 3866516-2022-05-14.xml*