Performance Evaluation of the Taiwanese Banking Industry before and after the COVID-19 Pandemic

Abstract

This study aimed to explore efficiency changes in Taiwan’s banking industry before and after the outbreak of coronavirus disease 2019 (COVID-19) by using the maximum slacks-based measure approach. The data, spanning from 2018 to 2021, categorized banks into three systems: state-owned, private, and foreign. Bank performance was measured from two perspectives: single-period evaluation (assessing bank performance in each year individually) and cross-period evaluation (assessing bank performance from 2018 to 2021 collectively). Inter-temporal changes in bank performance across the three banking systems were analyzed. The results indicated that only foreign banks rebounded rapidly after the COVID-19 outbreak, while the average performance of private banks remained stagnant, and state-owned banks performed worse than before the outbreak. Therefore, it is recommended that state-owned banks develop effective and rapid improvement policies to address major emergencies. Additionally, the study found that inefficiencies in banks were due to excessive input resources and/or failure to achieve the output targets. The input–output gap of inefficient banks was also analyzed, providing learning benchmarks and clear improvement targets that can help these banks formulate practical actions to improve their performance.

1. Introduction

The first outbreak of the coronavirus disease 2019 (COVID-19), caused by the SARS-CoV-2 virus in December 2019, triggered an unprecedented crisis in the 21st century. According to statistics from the World Health Organization, as of the end of December 2022, the disease had caused approximately 6.6 million deaths worldwide, with over 640 million confirmed cases. The Taiwanese government implemented contingency strategies such as social distancing, quarantine measures, and hybrid work schedules to curb the large-scale spread of COVID-19. In response to the COVID-19 outbreak in northern Taiwan, the central government raised the national epidemic alert to the third level. Consequently, over-the-counter transactions at banks were restricted, and bank employees adopted a hybrid work schedule. During this period, deposit and loan interest rates at banks fell to 0.45% and 1.68%, respectively. The interest rate spread shrank to 1.23%, the lowest since 2010. Despite emergency response measures such as deferring payments and waiving late fees, maintaining operational performance during the epidemic posed significant challenges for many banks.

To reduce the risk of infection from physical contact during over-the-counter bank transactions, the Taiwanese banking industry quickly adopted digital financial technologies such as online financial management, account opening, transfers, and mobile payments. The government encouraged banks to use digital solutions to minimize in-person visits for loan applications, while ensuring adherence to personal loan safety control standards and bailout loan regulations [1]. Stable digital platforms, user-friendly interfaces, competitive incentives, and responsive customer service have emerged as pivotal strategies for banks to maintain operational continuity and customer satisfaction. Prior to COVID-19, a critical metric in the banking industry was the number of branches. The pandemic has highlighted the importance of digital transformation in enhancing convenience and security for customers.

This study used data envelopment analysis (DEA) to evaluate bank performance [2,3]. DEA is a mathematical model based on linear programming. For a set of homogeneous decision-making units (DMUs), DEA objectively determines the efficiency frontier and calculates the relative efficiency value of each DMU by considering multiple input and output indicators. The relative efficiency value for each DMU ranges from 0 and 1, with higher values indicating better relative efficiency. For example, a value of 1 signifies that the DMU is relatively efficient, while a value less than 1 indicates relative inefficiency. As DEA is a non-parametric efficiency evaluation methodology, it does not require a preset production function or optimal parameters, making it fairer and more objective than other efficiency analysis methods. In addition, DEA can provide quantified targets for input and output improvement for inefficient DMUs. Therefore, it has recently been applied to address input resource allocation and output target setting problems [4].

Looking back at the development history of various DEA performance evaluation models, the Charnes–Cooper–Rhodes (CCR) model [5], the Banker–Charnes–Cooper (BCC) model [6] and the slacks-based measure (SBM) model [7] are among the most widely used. Among these, the CCR and BCC models are radial models, while the SBM model is a non-radial model. Radial models use the origin as the projection endpoint to calculate the input reduction and output expansion of an inefficient DMU as it moves to the efficiency frontier. In contrast, non-radial models use slack variables to calculate the input and output differences between the inefficient DMU and the efficiency frontier. Therefore, for an inefficient DMU, the non-radial SBM model can more accurately calculate the required adjustments of the input resources and output targets than the radial CCR and BCC models. It is worth emphasizing that the conventional SBM model is also called the SBM-Min model. It minimizes the efficiency value of a DMU while maximizing both the input and output differences to yield the furthest projection, representing the distance an inefficient DMU moves to the efficiency frontier. Therefore, the optimal solution produced by the SBM-Min model provides a stringent improvement suggestion, which may not always be feasible to implement in practice. To enhance the practicality of the analysis results of the SBM model, Tone adopted an approach that minimized both the input and output differences [8]. He proposed the novel SBM-Max model to calculate the efficiency values for DMUs, allowing inefficient DMUs to project toward the nearest efficiency frontier. This approach facilitates more practical performance improvement solutions.

To the best of our knowledge, this study is the first to use the SBM-Max model to examine efficiency changes in Taiwan’s banking industry before and after the outbreak of coronavirus disease 2019 (COVID-19). Regarding DEA application in bank performance evaluation (see Section 2 for details), efficiency decomposition and undesirable outputs are the most common research topics. For instance, Luo emphasized that bank efficiency should be decomposed into profitability efficiency and market efficiency [9], while Partovi and Matousek pointed out that non-performing loans are a common indicator of undesirable outputs in the banking sector [10]. To date, few scholars have explored efficiency changes and subsequent substantive improvements made by banks during serious infectious disease outbreaks or major emergencies. Additionally, different banking systems, namely state-owned banks, private banks, and foreign banks, have significant differences in their characteristics. Unlike state-owned banks, which benefit from government economic support, private banks lack such backing. Conversely, state-owned banks may not possess the same adaptive capabilities as private banks. Foreign banks tend to establish partnerships more easily with large listed foreign companies [11]. This study adopted a longitudinal research perspective and analyzed two research topics based on periods before (2018 to 2019) and after (2020 to 2021) the COVID-19 outbreak: (1) changes in bank operational performance under different banking systems, and (2) under different banking systems, the tangible actions, specifically input resource allocation and output target setting, that banks can take to improve their own performance.

2. Literature Review

2.1. Application of Quantitative Analysis Tools on Bank Performance

Assessing bank performance has been a popular research topic using various quantitative analysis tools. Commonly used tools include joint analysis, ordinary least squares regression analysis, and the stochastic frontier approach (SFA). This section reviews relevant literature from the past two decades.

Hasan and Marton applied SFA to evaluate the efficiency changes of 193 commercial banks in Hungary from 1993 to 1998, emphasizing the dynamic efficiency of banks rather than conventional indicators of return on assets and return on equity [12]. The study pointed out that when liberal policies are formulated for foreign banks to participate in domestic financial institutions, a more stable and efficient banking system can be established. In addition, banks with a higher proportion of foreign ownership exhibit relatively higher operating inefficiency. Barth et al. applied ordinary least squares regression analysis to evaluate the banking supervisory structure in 55 countries and compared the relationship between bank supervisory structure and bank profitability efficiency [13]. The results showed that bank supervisory structures had a minimal impact on bank profitability efficiency. Weill applied SFA to analyze the operating performance of foreign and domestic banks in the Czech Republic and Poland [14]. The research results showed that the degree of openness of foreign capital entering the financial market had a positive impact on the performance of the banking industry. Bonin et al. used SFA to evaluate the performance of 225 multinational banks in 11 developed countries and found that foreign banks had higher operating performance [15].

Beccalli measured the performance of 737 banks in Europe between 1995 and 2000 and explored the impact of bank investment in information technology on bank performance [16]. The analysis found that bank investment in information technology services from external suppliers had a positive impact on accounting profits and profitability performance. However, investment in hardware and software may reduce bank performance. Lin and Zhang used joint analysis to measure the performance of China’s state-owned, private, and foreign banks from 1997 to 2004 [17]. Among them, banks acquired by foreign capital and publicly listed banks performed better, while state-owned banks performed worse than other bank types. Assaf et al. applied the bootstrapped Malmquist index and the Bayesian distance frontier approach to evaluate the performance of Japanese credit associations and prefectures [18]. The study found that the efficiency and productivity of Japanese credit associations did not improve significantly between 2000 and 2006. Fahlenbrach and Stulz applied multiple regression to evaluate the performance of 95 banks, focusing specifically on the 2006 credit crisis period to explore the impact of bank CEO incentive mechanisms on bank performance [19]. Their results showed that if the incentive mechanism of bank CEOs aligned more with the interests of shareholders rather than the needs of the bank’s internal operations, the bank’s performance would be worse. Beltratti and Stulz applied the same method to identify key factors contributing to the poor performance of banks in various countries during the credit crisis from 2007 to 2008, which caused the Great Recession [20].

Liang et al. collected and analyzed data of 50 Chinese banks from 2003 to 2010, and found that the banks’ boards of directors played a crucial role in bank governance in China [21]. The size and political participation of bank boards were negatively associated with bank performance and loan quality. García-Meca et al. used Tobin’s Q ratio and data from 159 multinational banks to evaluate the impact of board diversity on bank performance [22]. The study found that gender diversity improved bank performance, while national diversity constrained it. Mamatzakis et al. modified a translog enhanced hyperbolic distance function of two undesirable outputs, namely problem loans and problem other earning assets, to explore the relationship between special loans and bank performance [23]. Then, they used a vector autoregression model to measure long-term changes in bank performance. The results indicated that non-performing loans had a greater impact on bank performance than problems with other earning assets. Moreover, the study found that investment in technological innovation initially increased the bank costs, but contributed to improved performance in the long-term. Sidhu et al. applied dynamic panel data regression to evaluate the performance of Indian commercial banks from 2010 to 2021, focusing on net stable funding ratio (NSFR), net interest margins (NIMs), and non-performing assets (NPAs) [24]. They found that NIMs decrease as the NSFR increases. Additionally, for banks with higher institutional holdings, the relationship between NPA level and NSFR is positive. Potapova et al. explored the correlation between the level of digitalization and key performance indicators among 100 Russian commercial banks, and found that digital maturity provided a competitive advantage [25].

In summary, during global economic crises, such as the Great Recession or the credit crisis, quantitative analysis tools have been applied to evaluate bank performance and identify key influencing factors [19,20]. Banking systems can be broadly divided into state-owned, private, and foreign banks, each characterized by distinct organizational cultures and operational traits. However, there are limited studies exploring the performance of different banking systems during these crises. This article aims to address this research gap by utilizing DEA to assess efficiency changes among different banking systems before and after an emergency crisis. Additionally, for banks with lower efficiency, this study analyzed the adjustment of input resources and output targets required to improve performance.

2.2. DEA Application on Bank Performance

This section reviews studies from the past two decades that utilized DEA to evaluate bank performance. Jemric and Vujcic applied DEA to assess bank performance in Croatia between 1995 and 2000 [26]. The results showed that foreign banks outperformed other types of banks. Lo et al. [27] employed Tone’s [7] SBM and super-SBM to evaluate 30 banks in Taiwan. They used the two-stage DEA model proposed by Seiford and Zhu [28] and divided the performance of financial holding companies (FHCs) into profitability performance and marketability performance.

Fukuyama and Weber used a two-stage DEA model to evaluate the performance of Japanese banks from 2000 to 2006 [29]. In the first stage, the inputs were labor, physical capital, and equity capital, and the output was deposits. In the second stage, the deposits became the inputs, and the outputs were loans and securities investments. Lin and Chiu combined independent components analysis and the network slacks-based measure model to assess the overall performance of FHCs, focusing on production, service, and profitability efficiencies [30]. Fujii et al. adapted the weighted Russell directional distance model to evaluate the performance and non-performing loans of Indian banks from 2004 to 2011 [31]. To evaluate the impact of non-performing loans on bank performance, Fukuyama and Matousek applied the revenue inefficiency model and established a two-stage network DEA model to evaluate the performance of Japanese banks from 2001 to 2013 [32]. Li et al. used a two-stage network DEA model to evaluate the performance of 16 Internet banks in China, dividing their operations into the value operation stage and value creation stage [33]. The study revealed that China’s Internet banks performed significantly better in the value creation stage than the value operation stage. To examine productivity changes after the 2009 global financial crisis, Laporšek et al. applied DEA and the Malmquist Productivity Index to evaluate 1915 European banks from 2013 to 2018 [34]. Nearly 50% of the banks experienced significant productivity growth, especially those in a non-Euro area.

More recently, Shi et al. proposed an improved slacks-based measure (SBM) model with undesirable outputs using a by-production framework, treating the bank’s operating process as a parallel system [35]. This approach splits bank efficiency into two parallel stages, enabling decision makers to identify the source of overall inefficiency, and effectively capture the efficiency differences between the two types of costs. The feasibility of this approach was demonstrated using data from 36 commercial banks in China from 2016 to 2021. The empirical results showed that changes in overall bank efficiency were mainly due to the changes in the second stage. Boubaker et al. used conventional inverse DEA to evaluate the performance and efficiency of 49 Islamic banks across 10 countries during 2019–2020, and to assess how these banks could preserve their performance and resilience in the aftermath of the COVID-19 pandemic [36]. Their results indicate that due to reductions in outputs, 31 out of the 49 banks would need to reduce their inputs to maintain efficiency. Shabani et al. proposed a new mixed-integer DEA model to evaluate the performance of commercial bank branches in dynamic and competitive conditions, where banks seek a greater proportion of shared resources, as seen in real-world scenarios [37]. The model was applied to a case study of 38 branches of an Iranian commercial bank from 2016 to 2020.

The DEA applied in the aforementioned studies utilized conventional efficiency measurement methods and did not incorporate the shortest improvement distance advocated by SBM-Max. In other words, the mathematically optimal solutions for projecting inefficient banks onto the efficiency frontier suggested by DEA may not offer practical solutions. To ensure feasibility and ease of implementation, this study adopted the SBM-Max model to evaluate bank performance, and analyzed the optimal input resources and output targets tailored to different banking systems (state-owned, private, and foreign banks).

3. Methodology

3.1. SBM Model

Compared with the output-oriented and input-oriented CCR and BCC models, the SBM model is non-oriented and non-radial. It uses slack variables to guide the improvement projection of a DMU, aiming to simultaneously minimize the inputs and maximize the outputs. The SBM model has two characteristics: unit invariance and monotonicity, which ensure that the efficiency values are unaffected by the units of measurement, and excess inputs and insufficient outputs decrease in the same direction, respectively.

Assume there are n DMUs, each using m inputs and producing s outputs. The input vector and output vector for the j^th DMU are defined as x_ij = (x_1j, …, x_mj) and y_rj = (y_1j, …, y_sj), respectively. ρ_k represents the efficiency value of the k^th DMU being evaluated by the SBM model. λ_j is a vector of intensities. $s_i^{-}$ and $s_r^{+}$ denote the slack variables of the input and the output, respectively. $s_i^{-}$ is the slack variable of the i^th input, while $s_r^{+}$ is the slack variable of the r^th output. ρ_k ranges between 0 and 1; when $\rho$_k $=1$ and $s_i^{-}=s_r^{+}=0$, the DMU is relatively efficient. Conversely, when ${\rho }_k<1$, the DMU is relatively inefficient. The SBM model is shown in Equation (1).

$$\begin{array}{c}Min={\rho }_k={\displaystyle \frac{1-(\frac{1}{m}){\sum }_{i=1}^m\frac{s_i^{-}}{x_{ik}}}{1+(\frac{1}{s}){\sum }_{r=1}^s\frac{s_r^{+}}{y_{rk}}}}\hfill \\ s.t. {\sum }_{j=1}^n{\lambda }_j{x}_{ij}+s_i^{-}=x_{ik},i=1,...,m\hfill \\ \hspace{1em}\hspace{1em}{\sum }_{j=1}^n{\lambda }_i{y}_{rj}-s_r^{+}=y_{rk},r=1,\dots ,s\hfill \\ \hspace{1em}\hspace{1em}{\lambda }_j,s_i^{-},s_r^{+}\ge 0,j=1,\dots ,n,i=1,...,m,r=1,...,s.\hfill \end{array}$$

(1)

3.2. SBM-Max Model

For an inefficient DMU, the SBM model calculates the minimum efficiency value, projecting the DMU to the efficiency frontier at the furthest distance. Consequently, the efficiency improvement suggestions may be challenging to implement. Addressing this concern, Tone proposed the SBM-Max model as an alternative [8]. Unlike the SBM model, the SBM-Max model calculates the shortest distance to project an inefficient DMU to the efficiency frontier, aiming to achieve the maximum efficiency value.

Before running the SBM-Max model, one should first use the SBM model (Equation (1)) to compute the efficiency score of DMU_k and obtain (x_k, y_k) (k = 1, …, n). The optimal solution of Equation (1) is (${\lambda }_j^{*},s_i^{-*},s_r^{+*}$). Let R^eff represent all efficient DMUs, $R$^eff$=\left\{j|{\rho }_j^{min}=1,\right.\left.j=1,...,n\right\}$. These efficient DMUs are defined as ($x_1^{eff},y_1^{eff}$), ($x_2^{eff},y_2^{eff}$), …, ($x_{Neff}^{eff},y_{Neff}^{eff}$), where Neff is the number of efficient DMUs. For an inefficient DMU (x_k, y_k), we defined the local reference set $R_k^{local}$ as the set of efficient DMUs for DMU (x_k, y_k). That is, $R_k^{local}=\left\{j|{\lambda }_j^{*}>0,j=1,\dots ,n\right\}$. For each inefficient DMU, where ${\rho }_j^{min}<1$, we solved the following program.

This method defines the efficiency value obtained through Equation (1) as $R^{eff}$, which satisfies $R^{eff}=\left\{j|{\rho }_j=1,\right.\left.j=1,...,n\right\}$. The local efficiency of the DMU is defined as $R_0^{local}$, which satisfies $R_0^{local}=\left\{j|{\lambda }_j^{*}>0,\right.\left.j=1,...,n\right\}$. The pseudo-max index is defined as ${\rho }_k^{Pseudomax}$. Next, Equations (2) and (3) are applied to obtain the relative efficiency of the DMU.

$$\begin{array}{c}Max {\displaystyle \frac{1-\frac{1}{m}{\sum }_{i=1}^m\frac{s_{ik}^{-}}{x_{ik}}}{1+\frac{1}{s}{\sum }_{r=1}^s\frac{s_{rk}^{+}}{y_{rk}}}}\hfill \\ s.t.x_{ik}={\sum }_{j\in R_o^{local}}{x}_j{\lambda }_j+s_i^{-}, i=1,\dots ,m\hfill \\ \hspace{1em}\hspace{1em}{y}_{rk}={\sum }_{j\in R_o^{local}}{y}_j{\lambda }_j-s_r^{+},r=1,\dots ,s\hfill \\ \hspace{1em}\hspace{1em}{\lambda }_j,s_i^{-},s_r^{+}\ge 0,j=1,\dots ,n,i=1,...,m,r=1,...,s.\hfill \end{array}$$

(2)

The optimal solution of Equation (2) is defined as ($s_i^{-*}$,$s_r^{+*}$), which is used to solve Equation (3).

$$\begin{array}{c}Min {\displaystyle \frac{1-\frac{1}{m}{\sum }_{i=1}^m\frac{s_{ik}^{-}}{x_{ik}-s_i^{-*}}}{1+\frac{1}{s}{\sum }_{r=1}^s\frac{s_{rk}^{+}}{y_{rk}+s_r^{+*}}}}\hfill \\ s.t.x_{ik}-s_i^{-*}={\sum }_{j\in R^{eff}}{x}_j^{eff}{\lambda }_j+s_i^{-}, i=1,\dots ,m\hfill \\ \hspace{1em}\hspace{1em}{y}_{rk}+s_r^{+*}={\sum }_{j\in R^{eff}}{y}_j^{eff}{\lambda }_j-s_r^{+},r=1,\dots ,s\hfill \\ \hspace{1em}\hspace{1em}{\lambda }_j,s_i^{-},s_r^{+}\ge 0,j=1,\dots ,n,i=1,...,m,r=1,...,s.\hfill \end{array}$$

(3)

The optimal solution of Equation (3) is defined as ($s_i^{-**}$,$s_r^{+**}$), which is applied in Equation (4) to calculate the Pseudo-Max score index.

$${\rho }_k^{Pseudo max}={\displaystyle \frac{1-\frac{1}{m}{\sum }_{i=1}^m\frac{s_{ik}^{-*}+s_{ik}^{-**}}{x_{ik}}}{1+\frac{1}{s}{\sum }_{r=1}^s\frac{s_{rk}^{+*}+s_{rk}^{+**}}{y_{rk}}}}$$

(4)

3.3. Numerical Analysis Example

This section presents a numerical case to demonstrate how the SBM-Max model uses the shortest distance to project an inefficient DMU to the efficiency frontier and calculate the maximum efficiency value. Assume that there are five DMUs, A, B, C, D, and E, each utilizing two inputs, x₁ and x₂, to produce an output y. The values of the inputs and output are detailed in columns 2 through 4 of

Table 1. Raw data and analytical results of the numerical example.

DMU	x1	x2	y	Efficiency Score
				BCC	SBM	SBM-Max
A	2	7	1	1	1	1
B	4.5	2	1	1	1	1
C	2.5	5	1	1	1	1
D	6	5	1	0.556	0.550	0.708
E	3	3	1	1	1	1

. Next, a radial DEA (BCC model) and two non-radial DEA (SBM and SBM-Max models) were applied to calculate the efficiency values of the DMUs, as presented in columns 5 through 7 of Table 1. For instance, under the BCC model, the efficiency values of DMUs A, B, C, D, and E were 1, 1, 1, 0.556, and 1, respectively.

From Table 1, DMU D was evaluated as inefficient by the BCC, SBM, and SBM-Max models. It is worth emphasizing that for the inefficient DMU D, the SBM-Max model produced the highest efficiency (0.708), followed by the BCC model (0.556) and the SBM model (0.550). The efficiency value calculated by the SBM-Max model was significantly higher than those of the BCC and SBM models. Figure 1 plots the improvement paths of the inefficient DMU D based on the three models. The three improvement paths for DMU D are as follows: (1) The SBM-Max model requires DMU D to reduce x₁ by 3.5 units to move to coordinate C; (2) the SBM model requires DMU D to reduce x₁ by 3 units and x₂ by 2 units to move to coordinate E; and (3) the BCC model requires DMU D to reduce x₁ by 2.67 units and x₂ by 2.22 units to move to coordinate D’. Clearly, the SBM-Max model identifies the efficiency frontier closest to DMU D as the projection point (improvement target). This makes the optimal solution easier to implement for improvement, aligning with the concept of continuous improvement (Kaizen) emphasized by Tone [8].

4. Empirical Case Analysis

4.1. Case Background

In Taiwan, there are 28 banks with total assets exceeding $300 billion. Due to data availability, this study selected 18 banks as research targets. These 18 banks were categorized into three different banking systems: state-owned, private, and foreign. Subsequently, the performance and adjustments of inputs and outputs across these three banking systems were compared. After conducting a comprehensive literature review (see Section 2), this study identified the inputs as operating expenses, employment expenses, lending, and interest expenses. The outputs were identified as net interest income, handling fees, and after-tax surplus. The definitions of the input and output variables are clearly stated in

Table A1. Definition of the input and output variables.

Variable	Definition
Operating expenses	An expenditure that a business incurs as a result of performing its normal business operations.
Employment expenses	All costs, expenses, debts, liabilities, and obligations related to or incurred in respect of employment including salaries, fees, wages, incentive pay, gratuities, bonuses, vacation pay, holiday pay, other paid leave, overtime, standby pay, sick pay, workers’ compensation legislation contributions, or costs.
Lending	The activity of lending money to people and organizations that they pay back with interest.
Interest expenses	Interest payable on any borrowings—bonds, loans, convertible debt, or lines of credit.
Net interest income	The difference between the revenue generated from interest-bearing assets and the expenses associated with paying on its interest-bearing liabilities.
Handling fees	What a customer is charged in order to cover expenses not related to the product or shipping.
After-tax surplus	The profit or earnings after all expenses have been deducted from revenue.

(see Appendix A). Figure 2 illustrates the input–output conversion process in evaluating bank performance. These data were sourced from the annual financial reports disclosed by the individual banks.

Table 2. Descriptive statistics of the input and output variables.

Year	Statistics	Operating Expenses	Employment Expenses	Lending	Interest Expenses	Net Interest Income	Handling Fees	After-Tax Surplus
2018	Average	14,653	8254	1,032,203	13,224	18,147	6417	29,009
	Minimum value	1277	373	16,139	2037	1	91	3333
	Maximum value	30,118	15,377	2,592,200	38,259	34,776	16,527	58,486
	Standard deviation	7866	4513	761,217	9365	10,145	4825	15,691
	Kurtosis	−0.569	−1.051	−0.688	1.403	−0.801	0.409	−0.808
	Skewness	0.134	−0.061	0.347	1.018	−0.200	1.039	0.062
2019	Average	15,381	8594	1,082,031	14,712	18,135	6708	30,336
	Minimum value	1285	424	3206	2560	1	291	1882
	Maximum value	31,940	15,855	2,676,141	39,355	34,900	18,725	60,114
	Standard deviation	8645	5126	771,205	9944	10,430	5480	16,903
	Kurtosis	−0.580	−1.220	−0.597	0.414	−0.857	0.303	−0.870
	Skewness	0.273	−0.174	0.387	0.752	−0.136	1.046	0.015
2020	Average	15,474	8696	1,162,400	9706	17,255	6566	28,791
	Minimum value	1172	387	12,453	795	628	168	2868
	Maximum value	32,494	15,795	2,869,204	26,565	33,740	19,831	58,669
	Standard deviation	8838	5838	821,171	6844	10,330	5396	16,515
	Kurtosis	−0.528	0.050	−0.625	0.500	−1.101	1.005	−0.781
	Skewness	0.321	0.370	0.333	0.705	−0.035	1.280	0.299
2021	Average	15,597	9134	1,144,183	5824	18,011	6849	29,466
	Minimum value	1249	379	22,443	279	885	192	2876
	Maximum value	31,926	16,718	2,455,870	13,001	35,731	21,324	61,210
	Standard deviation	8967	5428	864,482	4865	11,461	5763	17,256
	Kurtosis	−0.647	−1.108	−0.848	0.734	−1.301	1.127	−0.832
	Skewness	0.237	−0.189	0.236	0.816	−0.034	1.245	0.261

presents the descriptive statistics of the research data.

4.2. Bank Performance

The research data spanned from 2018 to 2021. This article applied two perspectives to measure bank performance: single-period evaluation (assessing the bank performance in each year individually) and cross-period evaluation (assessing the bank performance from 2018 to 2021 collectively). The first perspective assessed the annual operating performance of banks from 2018 to 2021 individually. The second perspective evaluated the annual operating performance of banks by integrating data from 2018 to 2021.

Based on the first perspective,

Table 3. Bank performance from 2018 to 2021.

Banking System	DMUs	2018 Efficiency (Rank)	2019 Efficiency (Rank)	2020 Efficiency (Rank)	2021 Efficiency (Rank)
State-owned banks	Bank of Taiwan	0.986 (13)	0.789 (18)	0.850 (18)	0.780 (18)
	Land Bank of Taiwan	1 (1)	1 (1)	1 (1)	1 (1)
	Changhua Commercial Bank	0.983 (14)	0.928 (15)	0.946 (16)	0.950 (15)
	Taiwan Cooperative Bank	1 (1)	1 (1)	1 (1)	1 (1)
	First Commercial Bank	1 (1)	1 (1)	0.965 (12)	1 (1)
	Taiwan Business Bank	0.962 (16)	0.945 (14)	0.949 (15)	0.965 (14)
	Overall average	0.989	0.944	0.952	0.949
Private banks	Cathay United Bank	1 (1)	1 (1)	1 (1)	1 (1)
	Shin Kong Commercial Bank	1 (1)	1 (1)	1 (1)	1 (1)
	E.Sun Commercial Bank	1 (1)	1 (1)	1 (1)	1 (1)
	Union Bank of Taiwan	0.977 (14)	0.996 (12)	0.960 (13)	0.973 (13)
	Taishin International Bank	0.863 (18)	0.879 (16)	0.915 (17)	0.931 (17)
	Yuanta Commercial Bank	0.961 (17)	0.991 (13)	0.951 (14)	0.938 (16)
	Overall average	0.967	0.978	0.971	0.974
Foreign banks	Standard Chartered Bank	1 (1)	0.805 (17)	1 (1)	1 (1)
	Citibank	1 (1)	1 (1)	1 (1)	1 (1)
	MUFG Bank	1 (1)	1 (1)	1 (1)	1 (1)
	The Shanghai Commercial and Savings Bank	1 (1)	1 (1)	1 (1)	1 (1)
	Fubon Bank	1 (1)	1 (1)	1 (1)	1 (1)
	UBS	1 (1)	1 (1)	1 (1)	1 (1)
	Overall average	1	0.968	1	1

shows the annual operating performance of banks from 2018 to 2021 individually. Among the state-owned banks, Land Bank of Taiwan and Taiwan Cooperative Bank performed the best, with an efficiency value of 100% every year. The First Commercial Bank also had an efficiency score of 100% every year, except in 2020. In contrast, Taiwan Business Bank, Changhua Commercial Bank, and Bank of Taiwan did not achieve 100% efficiency during these years. These state-owned banks should be prioritized for improvement.

For the private banks, Cathay United Bank, Shin Kong Commercial Bank, and E.Sun Commercial Bank achieved an efficiency value of 100% every year. However, Union Bank of Taiwan, Taishin International Bank, and Yuanta Commercial Bank did not reach an efficiency score of 100%, so these private banks should be improved. Among these banking systems, foreign banks performed the best. Citibank, MUFG Bank, The Shanghai Commercial and Savings Bank, Fubon Bank, and UBS consistently achieved 100% efficiency over the years. Standard Chartered Bank also achieved this, except in 2019.

Figure 3 illustrates the average performance of the three banking systems. In 2018, the year before the COVID-19 outbreak, the foreign banking system performed the best, followed by state-owned banks, and then private banks. However, the COVID-19 outbreak at the end of 2019 had a negative impact on the performance of both foreign and state-owned banks that year, while private banks showed the opposite trend. In 2020, following the COVID-19 outbreak, foreign banks rebounded to achieve 100% efficiency. They demonstrated the fastest organizational response to significant emergencies. State-owned banks also performed well, showing slight growth compared to 2019. In contrast, private banks performed poorly, with their average performance declining after the outbreak. Moving to 2021, foreign banks maintained their 100% efficiency. State-owned banks experienced a decline in performance, while private banks showed improvement.

Examining the efficiency changes in the banking industry before and after the COVID-19 outbreak revealed that foreign banks performed well overall. State-owned banks were significantly impacted negatively post-COVID-19, while private banks showed mediocre performance. Specifically, only foreign banks rebounded rapidly after the COVID-19 outbreak, while the average performance of private banks remained stagnant, and state-owned banks performed worse than before the outbreak. Therefore, state-owned banks should develop effective and rapid improvement plans to better respond to major crises.

Next, the banks were evaluated based on the second perspective. Multi-year data from 2018 to 2021 were aggregated to conduct a comprehensive evaluation of bank performance. In essence, this study used samples spanning four consecutive years, covering the period before and after the COVID-19 outbreak, for comparison. This multi-year comprehensive evaluation method was more stringent than the independent annual evaluations due to its extended timeframe.

Table 4. Banks with 100% efficiency performance (labeled as ☺), based on a comprehensive annual evaluation.

Banking System	Bank	2018	2019	2020	2021
State-owned banks	Bank of Taiwan
	Land Bank of Taiwan	☺	☺		☺
	Changhua Commercial Bank
	Taiwan Cooperative Bank	☺	☺	☺	☺
	First Commercial Bank	☺	☺		☺
	Taiwan Business Bank
Private banks	Cathay United Bank	☺	☺		☺
	Shin Kong Commercial Bank	☺
	E.Sun Commercial Bank	☺	☺		☺
	Union Bank of Taiwan
	Taishin International Bank
	Yuanta Commercial Bank
Foreign banks	Standard Chartered Bank		☺		☺
	Citibank	☺	☺	☺	☺
	MUFG Bank	☺	☺	☺	☺
	The Shanghai Commercial and Savings Bank	☺	☺		☺
	Fubon Bank		☺	☺	☺
	UBS	☺	☺		☺

summarizes the banks that achieved 100% efficiency across multiple years, spanning before and after the COVID-19 outbreak. Taiwan Cooperative Bank, Citibank, and MUFG Bank maintained 100% efficiency for four consecutive years. Land Bank of Taiwan, First Commercial Bank, Cathay United Bank, Shin Kong Commercial Bank, E.Sun Commercial Bank, Standard Chartered Bank, The Shanghai Commercial and Savings Bank, Fubon Bank, and UBS achieved 100% efficiency in three out of four years. These banks should consider slight revisions to their operating models to optimize resource consumption. On the other hand, Bank of Taiwan, Chang Hwa Commercial Bank, Taiwan Business Bank, Union Bank of Taiwan, Taishin International Bank, and Yuanta Commercial Bank did not achieve 100% efficiency over the four-year period. These banks need urgent adjustments in operating resources, for example, reducing their operating expenditures in the short-term. Notably, among the 18 banks evaluated, one state-owned bank and three foreign banks maintained efficiency in 2020, while none of the private banks did. This highlights the substantial impact of the COVID-19 outbreak on bank performance. In addition, all foreign banks returned to 100% efficiency in 2021, demonstrating superior organizational flexibility in major emergencies. This serves as a valuable benchmark for state-owned and private banks in formulating effective emergency response measures.

4.3. Analysis of the Input–Output Gap of Inefficient Banks

Generally, inefficiency results from either excessive input resources or failing to achieve output targets. Beyond objectively assessing bank performance, DEA can, more importantly, provide learning benchmarks and clear improvement targets for banks identified as inefficient. This section presents the input–output gap analysis of inefficient banks across three different banking systems.

Figure 4 shows the four-year average reduction rate of input resources from 2018 to 2021 for inefficient banks. These reductions highlight the input resources a DMU excessively utilized and needed adjustment to achieve efficiency. Detailed data are provided in

Table 5. The average input reductions from 2018 to 2021 for inefficient banks.

Year-Input Variable	State-Owned Banks	Private Banks	Foreign Banks
2018—Operating expenses	0%	27.38%	0%
2019—Operating expenses	4.88%	32.06%	29.47%
2020—Operating expenses	1.69%	35.00%	0%
2021—Operating expenses	2.96%	39.53%	0%
Overall average	2.38%	33.49%	7%
2018—Employment expenses	55.14%	29.97%	0%
2019—Employment expenses	20.46%	36.91%	44.48%
2020—Employment expenses	21.12%	21.87%	0%
2021—Employment expenses	12.12%	36.29%	0%
Overall average	27.21%	31.26%	11%
2018—Lending	40.67%	42.63%	0%
2019—Lending	43.57%	31.03%	0%
2020—Lending	41.49%	37.70%	0%
2021—Lending	43.98%	17.46%	0%
Overall average	42.43%	32.20%	0%
2018—Interest expenses	4.19%	0.02%	0%
2019—Interest expenses	31.09%	0%	0%
2020—Interest expenses	35.70%	5.43%	0%
2021—Interest expenses	40.95%	6.72%	0%
Overall average	27.98%	3.04%	0%

. In this table, state-owned banks should reduce operating expenses by an average of 2.38% over four years, employee expenses by 27.21%, lending by 42.43%, and interest expenses by 27.98%. Private banks should reduce operating expenses by an average of 33.49%, employee expenses by 31.26%, lending by 32.20%, and interest expenses by 3.04% over the same period. Foreign banks, meanwhile, should reduce their operating expenses by an average of 7% and employee expenses by 11%, with no changes needed for lending and interest expenses.

State-owned banks had excessive loan quotas primarily due to their generally more favorable loan interest rates compared to private and foreign banks, making them preferred lenders. Private banks, on the other hand, needed to reduce their operating expenses, employment expenses, and lending by more than 30% each. This underscores the necessity for private banks to streamline operational and personnel expenses. Private banks tended to increase loan quotas under legal constraints to attract loan applications and boost interest income. In contrast, compared to both state-owned and private banks, foreign banks demonstrated greater efficiency in managing input resources.

Figure 5 shows the four-year average growth rates of outputs for inefficient banks from 2018 to 2021. These rates indicate that the outputs of the DMUs had not met targets and needed to increase for efficiency. Detailed data are available in

Table 6. The average output growth from 2018 to 2021 for inefficient banks.

Year-Input Variable	State-Owned Banks	Private Banks	Foreign Banks
2018—Operating expenses	0%	27.38%	0%
2019—Operating expenses	4.88%	32.06%	29.47%
2020—Operating expenses	1.69%	35.00%	0%
2021—Operating expenses	2.96%	39.53%	0%
Overall average	2.38%	33.49%	7%
2018—Employment expenses	55.14%	29.97%	0%
2019—Employment expenses	20.46%	36.91%	44.48%
2020—Employment expenses	21.12%	21.87%	0%
2021—Employment expenses	12.12%	36.29%	0%
Overall average	27.21%	31.26%	11%
2018—Lending	40.67%	42.63%	0%
2019—Lending	43.57%	31.03%	0%
2020—Lending	41.49%	37.70%	0%
2021—Lending	43.98%	17.46%	0%
Overall average	42.43%	32.20%	0%
2018-Interest expenses	4.19%	0.02%	0%
2019-Interest expenses	31.09%	0%	0%
2020—Interest expenses	35.70%	5.43%	0%
2021—Interest expenses	40.95%	6.72%	0%
Overall average	27.98%	3.04%	0%

. In this table, state-owned banks are advised to achieve an average growth of 9.74% in net interest income, 62.38% in handling fees, and 27.88% in after-tax earnings over four years. Private banks should grow their net income by an average of 20.84%, handling fees by 16.85%, and after-tax earnings by 62.30% over the same period. Foreign banks, meanwhile, should aim for an average growth rate of 41.66% in net interest income, 8.34% in handling fees, and no growth in after-tax earnings.

Regarding the expected growth rate of outputs, state-owned banks prioritize serving the public and emphasize social responsibility, reflected in their typically lower handling fees and loan interest rates compared to private and foreign banks. Therefore, the substantial room for growth in handling fees is evident from the average four-year growth rate of 62.38%. Private banks, on the other hand, should focus on the growth of after-tax earnings, with an average four-year growth rate target of 62.30%. This likely stems from challenges in controlling operating expenses and employee expenses. As indicated in Table 5, private banks should reduce operating expenses and personnel costs by an average of 33.49% and 31.26% over four years, respectively. Foreign banks should focus on the growth of net interest income, with an average four-year growth rate of 41.66%. As shown in Table 5, foreign banks exceled in managing interest expenses, maintaining a 0% reduction rate. This highlights their superior control over interest expenses compared to state-owned and private banks. Therefore, foreign banks should concentrate on interest income to enhance their net interest income growth.

5. Conclusions

To facilitate the formulation of emergency response measures for the banking industry in Taiwan, this study evaluated the performance of state-owned, private, and foreign banks following the COVID-19 outbreak. In the annual evaluation of bank performance, these banks were found to be relatively efficient: Land Bank of Taiwan, Taiwan Cooperative Bank, Cathay United Bank, Shin Kong Commercial Bank, E.Sun Commercial Bank, Citibank, MUFG Bank, The Shanghai Commercial and Savings Bank, Fubon Bank, and UBS. Notably, foreign banks were generally the most efficient, indicating that their response measures after the COVID-19 outbreak were more effective than those of state-owned and private banks. After the outbreak of COVID-19, the bank performance showed negative growth. This observation was more pronounced among state-owned banks than foreign and private banks. After the COVID-19 outbreak, state-owned and private banks adopted hybrid work schedules or adjusted branch operations, while foreign banks promptly shifted to remote home working. To improve performance, state-owned banks should prioritize formulating robust emergency response measures. Key strategies include reducing employment costs before a crisis, and after a crisis, focusing on reducing lending while increasing handling fees and after-tax surplus. For private banks, the strategy should involve reducing operating expenses and increasing after-tax surplus before a crisis. Foreign banks should focus on reducing lending before a crisis and cutting interest expenses afterward.

While the research results are robust, this study acknowledges several limitations. Notably, the DEA efficiency scores were sensitive to the selected input and output variables. Therefore, the results and discussion in Section 4 are relevant only to these selected variables. Additionally, this study did not account for individual bank policies and cultural factors, which could significantly impact bank performance. Furthermore, due to data availability, this study only examined the changes in the banking industry from 2018 to 2021. Future studies can extend this work by considering the Malmquist productivity index and dynamic network DEA models to explore efficiency changes over time. Additionally, qualitative analyses could provide a richer context regarding the impact of the COVID-19 pandemic on the Taiwanese banking industry.