Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9, 1437-1453 2025 Publisher: Learning Gate DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate © 2025 by the authors; licensee Learning Gate History: Received: 14 August 2025; Revised: 4 September 2025; Accepted: 8 September 2025; Published: 22 September 2025 * Correspondence: vinhhx@vnu.edu.vn Efficiency, technological progress and productivity growth of Vietnamese commercial banks in the period 2008–2024: A Malmquist index approach Pham Tien Dung1, Dưong Nguyen Hong Anh2, Trinh Hoang Phuong3, Hoang Xuan Vinh4* 1VNU Tran Nhan Tong Institute, Hanoi, Vietnam; dungpt.vtnt@vnu.edu.vn (P.T.D.). 2AOF Academy of Financial,Vietnam. honganhdn170@gmail.com (D.N.H.A.). 3,4VNU University of Economics and Business, Hanoi, Vietnam; Trinhhoangphuong@vnu.edu.vn (T.H.P.) vinhhx@vnu.edu.vn (H.X.V.). Abstract: This study evaluates the efficiency and productivity growth of 22 Vietnamese commercial banks over the period 2008–2024 using a non-parametric approach. Applying the output-oriented Malmquist Productivity Index under constant returns to scale (CRS), we decompose total factor productivity (TFP) into efficiency change (EC) and technical change (TC). The results show that EC values remained close to unity for most banks, indicating relatively stable managerial performance. However, TC values varied significantly across institutions, suggesting that technological progress is the primary driver of TFP divergence. Among the 22 banks, only six achieved positive TFP growth, led by NVB, SEAB, and ABB—banks that demonstrated strong adaptability through technical improvements. In contrast, HDB, BIDV, and VPB recorded notable declines in productivity, largely due to lagging technological progress rather than inefficiency. These findings emphasize the critical role of digital transformation and innovation in sustaining long-term productivity. The study contributes updated empirical evidence on banking performance in Vietnam and offers strategic implications for bank executives and policymakers aiming to enhance competitiveness in a rapidly evolving financial environment. Keywords: DEA, Digital transformation, Efficiency, Malmquist index, Productivity, Technical change, Vietnamese banks. 1. Introduction In the process of economic transformation, the banking sector plays a vital role as a financial intermediary and stabilizing force within the national economy. In Vietnam, the banking system has undergone significant changes over the past two decades, both in terms of organizational structure and technological modernization. The last ten years have seen an active wave of mergers and acquisitions, leading to the consolidation of commercial banks and the reshaping of market dynamics. Simultaneously, both globally and domestically, the banking industry has experienced profound shifts driven by regulatory reforms and the advancement of technology. The integration of Industry 4.0 innovations, digital banking platforms, fintech solutions, and new financial instruments has radically transformed banking operations. These technological developments have reshaped the production technology of banks, raising important questions regarding their impact on banking efficiency and productivity. A key issue, therefore, is how such structural and technological changes have influenced the performance of banks. In a seminal review, Berger and Humphrey in Berger, et al. [1] provided a comprehensive overview of efficiency measurement techniques in the banking sector and emphasized the importance of both parametric and non-parametric approaches. Among these, Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) have become the most widely applied methods to estimate banking efficiency. 1438 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate This study aims to apply non-parametric methods, particularly the Malmquist Productivity Index under constant returns to scale (CRS), to assess the efficiency, technological progress, and total factor productivity (TFP) growth of Vietnamese commercial banks during the period 2008–2024. This timeframe captures an important phase of restructuring in the Vietnamese banking sector, marked by institutional consolidation and the rise of digital transformation. Studies on productivity in the banking sector have traditionally focused on comparisons of cost ratios. Several cost-based indicators have been developed, each addressing a specific dimension of banking operations. However, given that banks utilize multiple inputs to generate multiple outputs, researchers have questioned the appropriateness of simple aggregations and instead examined suitable forms of input-output modeling [2]. Although early efforts attempted to estimate average practice cost functions, such approaches often failed to reflect the productivity levels of the best-performing banks. These limitations of the "classical" productivity approach have led to alternative methods that incorporate multiple inputs and outputs, as well as the concept of relative efficiency. A major advancement in this domain is the frontier-based analysis, which classifies decision-making units into efficient and inefficient performers relative to a constructed frontier. The most widely adopted non-parametric method is Data Envelopment Analysis (DEA), introduced by Charnes, et al. [3]. DEA utilizes linear programming to form a piecewise linear frontier enveloping the efficient units and measures the relative efficiency of all others against it. In Vietnam, DEA-based research remains relatively limited. Early domestic contributions include who examined banking efficiency and super-efficiency. Expanding the empirical landscape, Minh, et al. [4] analyzed the performance of 32 commercial banks in Vietnam during the period 2001–2005 using a super-efficient DEA model under variable returns to scale (VRS). The study adopted the slack-based measure and performed a series of sensitivity tests by allowing simultaneous changes in input–output subsets. The authors further applied Spearman's rank correlation and Kendall's tau-b to compare rankings derived from Tone's method and the Andersen-Petersen approach. Their findings revealed strong consistency in banking, suggesting robustness in relative efficiency assessment regardless of DEA specification. 2. Methodology 2.1. Production Efficiency Measuring the level of absolute efficiency is generally not feasible due to the absence of a universally applicable production function that defines the maximum output for all banks within the same industry. To address this limitation, Farrell [5] proposed a method for evaluating relative efficiency, which compares a bank's performance with that of the best-performing banks sharing similar characteristics within the industry. This approach enables efficiency to be assessed even in the absence of a known production frontier. Farrell's framework further decomposes overall efficiency into two distinct components: technical efficiency and allocative efficiency. Technical efficiency reflects a bank's ability to produce the maximum feasible output given the available inputs and current technology. In contrast, allocative efficiency examines whether, once a bank is technically efficient, it also selects the optimal combination of inputs based on given input prices—thereby minimizing costs [6]. Figure 1 provides a simplified graphical illustration of these two dimensions of efficiency under the assumption of constant returns to scale in banking production. The figure visually distinguishes between technical inefficiency (due to input-output mismatch) and allocative inefficiency (due to suboptimal input mix given price constraints), highlighting the conceptual importance of both in measuring performance. 1439 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate Figure 1. Technical and allocative efficiency. (Source: Banker, et al. [6]). In Figure 1, the curve labeled IAI′ represents the isoquant of a bank, depicting all combinations of two inputs, x 1 and x 2 , that can produce a given level of output. The straight line SS′ represents the isocost line, which reflects combinations of inputs that yield equal total cost, given relative input prices. It is assumed, consistent with standard microeconomic production theory, that banks possess a concave production function with respect to these inputs. Under the behavioral assumption of cost minimization, a bank operating optimally will choose a point on the isoquant where the marginal rate of technical substitution (MRTS) equals the input price ratio. This optimal point is identified as point A, where the bank minimizes its input cost for the given level of output. Meanwhile, point B represents a technically efficient production point, where the bank uses the minimum input quantities necessary to achieve the same level of output on the isoquant IAI′. However, if the bank instead operates at point C, it uses more inputs than necessary to achieve the same output, and is thus technically inefficient. The extent of technical inefficiency is quantified by the ratio OC/OB, indicating the proportional excess of input use compared to the efficient benchmark at point B. Even if a bank achieves technical efficiency at point B, it may still incur allocative inefficiency if the combination of inputs does not minimize cost, given the input prices. Point A, which lies on both the isoquant and isocost line SS′, is the cost-minimizing point. The allocative efficiency is thus measured by the ratio OD/OB, where OD is the cost at point A and OB is the cost at point B. Consequently, the overall productive efficiency of a bank is the product of its technical efficiency and allocative efficiency, and can be expressed as: Product ive Efficiency OB OD OD OC OB OC æ ö æ ö÷ ÷ç ç÷ ÷= ´ =ç ç÷ ÷ç ç÷ ÷ç çè ø è ø This formulation captures the combined impact of input-saving efficiency and cost-minimizing behavior, and provides a comprehensive measure of banking performance. 1440 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate 2.2. Technical Efficiency and the Production Frontier Following the general discussion on productive efficiency, this section focuses specifically on technical efficiency, which measures a bank's ability to maximize output given a fixed set of inputs and current technology. A bank with a technical efficiency (TE) score of 1 is considered fully efficient— operating on the production frontier and achieving the highest output level feasible relative to its peers. Contrary, a TE score less than 1 indicates that the bank is operating below the frontier and has potential to improve its performance. Figure 2 provides a graphical illustration of technical efficiency using a simplified production function with one input and one output. Points A, B, C, D, E, and F represent banks with different input–output combinations. The production frontier is defined by the piecewise curve ACD, representing the most efficient combinations. Banks operating on the frontier (eg, points A, C, and D) are considered technically efficient, while those below the frontier (points B, E, and F) are inefficient. The ray from the origin illustrates constant returns to scale. A bank located on both the frontier and the ray—point C—achieves maximum technical efficiency, combining both pure technical efficiency and scale efficiency. In contrast, banks at points A and D are technically efficient but do not lie on the rays, indicating they are not operating at optimal scale. Meanwhile, banks at points B and F have input levels matching those of technically efficient banks (C and D, respectively) and therefore exhibit scale efficiency, but they do not reach the frontier, indicating inefficiencies in their operations. Finally, point E reflects a bank that is inefficient both in terms of scale and net technical efficiency, as it lies below the frontier and shares no input levels with any bank on the frontier. This graphical analysis illustrates how technical efficiency can be decomposed into pure technical efficiency and scale efficiency, providing insight into different banking sources of inefficiency within the sector. Figure 2. Technical efficiency. Subsequent studies on relative efficiency, building on Farrell's foundational framework, have mainly focused on the estimation of the production function—also referred to in some contexts as production technology—and the identification of its structural form. 1441 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate Parametric methods such as SFA assume a specific functional form and include a composed error term to separate inefficiency from statistical noise. In contrast, non-parametric methods like DEA construct the efficiency frontier directly from observed data without imposing any prior functional structure. Both approaches offer complementary insights, with parametric models better suited for hypothesis testing and statistical inference, and non-parametric models offering greater flexibility in modeling multi-input, multi-output production environments. This relevant DEA (linear programming) paradigm will be briefly explained. For each DMU, we suppose that each bank has K inputs and M outputs. The inputs and outputs for the ith DMU are represented by the vectors and, respectively. We seek to determine the ratio of all outputs to all inputs for each bank (DMU), like ik ik 1 im im 1 K k M m u y v x = = å å , where u i and v i are weight vectors. To choose the optimal weights, the following problem is proposed: ik ik 1 im im 1 K k M m u y v x = = å å with constraints ik ik 1 im im 1 1 , 0 1, 2, ik im K k M m u N x u v v i y = = £ ³ = ¼ å å There are infinitely many solutions with this model's representation, as is well known. You can prevent this by adding a constraint im im 1 1 M m v x = =å , and obtain the multiplier form of the linear programming problem: ik ik 1 min K k u y = ®å with constraints im im 1 1 M m v x = =å ik ik im im 1 1 , 0 0 1, 2, ik i k m K M m u N u v i y v x = = - £ ³ = ¼ å å Charnes, et al. [3] derive an equivalent envelope form from the dual property of this linear programming problem: , min iq l q with constraints 1442 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate 1 1 , 1, 2, ..., , 1, 2, ..., 0 1, 2, ..., N j kj ki j N j mj i mi j j y y k K x x m M i N l l q l = = ³ = £ = ³ = å å 2.3. The Malmquist Productivity Index Let x t and y t represent the input and output vectors for a bank at time t. The output distance function ( , )t t t t D x y measures the maximal proportional feasible expansion of output vector y t , given input vector x t and the production technology available at time t. Formally, the output distance function is defined as: ( , ) inf 0 : ( )t t t t t t t y D x y P xq q ì üæ öï ï÷ï ïçï ï÷ç= > Îí ý÷ç ÷ï ïç ÷è øï ïï ïî þ where: • θ is a scalar representing the proportion by which the output vector must be contracted to lie on the production possibility set P t (x t ) at time t, • P t (x t ) is the output set for input x t at time t, ie, the set of all output vectors produceable by x t at time t, • If ( , ) 1t t t t D x y = , the DMU lies on the frontier (technically efficient), • If ( , ) 1t t t t D x y < , the DMU is inefficient. This function allows for non-parametric estimation using DEA, where ( , )t t t t D x y is obtained as the solution to a linear programming problem under Constant Returns to Scale (CRS) or Variable Returns to Scale (VRS). In the computation of the Malmquist Productivity Index, two additional distance functions play a crucial role in capturing the technological change component. These are referred to as cross-period distance functions: • 1 1 1 ( , )t t t t D x y+ + + : the distance of the period t+1 observation evaluated against the period t technology. • 1 ( , )t t t t D x y + : the distance of the period t observation evaluated against the period t+1 technology. Forward-looking cross-distance: 1 1 1 1 1 ( , ) inf 0 : ( )t t t t t t t y D x y P xq q + + + + + ì üæ öï ï÷ï ïçï ï÷ç= > Îí ý÷ç ÷ï ïç ÷çè øï ïï ïî þ This function measures how well the future observation (from t+1) would have performed under the technology available at time t. Backward-looking cross-distance: 1 1 ( , ) inf 0 : ( )t t t t t t t y D x y P xq q + + ì üæ öï ï÷ï ïçï ï÷ç= > Îí ý÷ç ÷ï ïç ÷è øï ïï ïî þ This function evaluates how well the past observation (from t) would perform under the updated technology at time t+1. Interpretation in Malmquist Index 1443 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate Together, these two cross-period distances reflect shifts in the production frontier: • If 1 1 1 ( , ) 1t t t t D x y+ + + < , it indicates that the future observation performs better under the future technology than it would under the past technology → technological progress. • If 1 ( , ) 1t t t t D x y + > , it implies that the past observation performs worse under the future technology → further evidence of frontier advancement. The technological change (TC) component of the Malmquist index is then computed as: 1/ 2 1 1 1 1 ( , ) ( , ) t t t t t t t t D x y T C D x y + + + + é ù ê ú= ê ú ê úë û This geometric mean formulation accounts for asymmetries in technology shifts and stabilizations cross-period comparisons. 2.4. Full Malmquist Index Using Output Distance Functions With the distance functions defined, the Malmquist Productivity Index (MPI) between time t and t+1 can be expressed as: 1/ 2 1 1 1 1 1 1 1 1 1 1 ( , )( , ) ( , , , ) ( , ) ( , ) tt t t tt t t t t t t t t t t t t t t D x yD x y M x y x y D x y D x y + + + + + + + + + + é ù é ù ê ú ê ú= ´ê ú ê ú ê ú ê úë û ë û Where: • The first term measures efficiency change (EC): how much closer or further the DMU is to the frontier from t to t+1, • The second term measures technological change (TC): the shift of the frontier itself between the two periods. This decomposition provides a complete view of whether productivity growth arises from internal improvements (catching up) or from external innovation (technological progress). 3. Specification of Inputs and Outputs for Banks Before analyzing bank-level productivity and efficiency indicators, it is necessary to clearly define the functional objectives of a commercial bank and, based on those, determine the appropriate inputs and outputs. There has long been debate in the literature regarding what constitutes valid outputs in banking. Banking outputs include "transaction services and portfolio management services provided to depositors while performing intermediation." This definition implies that the scope of bank outputs may be quite broad and depends heavily on the financial development of the economy. As such, both the breadth (diversity) and depth (complexity) of financial services vary across countries and over time, requiring context-specific input–output selection. In the literature, three main methodological approaches are commonly used to define banking production: 1. Asset Approach: This perspective considers banks primarily as financial intermediaries between depositors and borrowers. Under this approach, loans and other earning assets are treated as outputs, while deposits and other liabilities are considered inputs [7]. 2. User-Cost Approach: Inputs and outputs are classified based on the net financial contribution of each asset or liability item. If the return on an asset exceeds its opportunity cost (or if the cost of a liability is less than its opportunity cost), it is categorized as an output; otherwise, it is an input [8]. While theoretically elegant, this method is sensitive to interest rate fluctuations and suffers from practical challenges in measuring marginal revenue and cost. 3. Value-Added Approach: Both assets and liabilities may exhibit output characteristics, but only those that contribute clearly to value creation are classified as outputs. This approach actually 1444 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate uses operating cost shares rather than theoretical pricing models and has been widely used in empirical banking research [1, 9]. The value-added approach also allows for the differentiation of functional roles performed by banks. Taranova, et al. [10] identified five essential objectives in effective bank management: profit maximization, risk management, service provision, intermediation, and utility creation. For simplicity, these can be grouped into two broader functions: (1) profit maximization (including risk control), and (2) service delivery (including intermediation and utility) [11]. In reality, most banking operations involve both functions, and this duality is reflected in model construction [12]. No explicit weights are assigned; rather, the influence of both functions is inherently incorporated. In some cases, separate output sets may be constructed to emphasize one function over the other. Building on the above conceptual insights, prior empirical work, and taking into account the structure and limitations of the available data, this study adopts the asset approach to specify inputs and outputs for both the DEA efficiency model and the Malmquist productivity analysis. Based on the financial intermediation role of banks, the model includes three key outputs and four input variables: • Outputs: ▪ Y1 : Total loans ▪ Y2 : Securities holdings ▪ Y3 : Operating income • Inputs: ▪ X1 : Fixed assets ▪ X2 : Total deposits ▪ X3 : Operating expenses ▪ X4 : Number of employees (labor) The inclusion of labor reflects the real-world production process in banking, where human capital plays a central role in both service quality and operational management. The dataset used in this study was constructed from manually collected financial information obtained from the annual reports of 22 Vietnamese commercial banks for the period 2008–2024 . The dataset includes a balanced set of 7 key indicators , covering both outputs and inputs relevant to bank operations. The full sample spans 17 years , enabling the assessment of long-term trends in efficiency and productivity under different economic and regulatory conditions. This consistent and rich dataset enables the application of both DEA (Data Envelopment Analysis) and the Malmquist Productivity Index , with input–output configurations that reflect real-world banking operations in Vietnam. The data coverage also captures critical transitions in the banking sector, including consolidation, digitalization, and post-restructuring adjustments after the global financial crisis and COVID-19 pandemic. Table 1 presents a list of 22 Vietnamese commercial banks used in the study, including the full English name of each bank (column “Name of bank”) and the corresponding abbreviation code (column “DMU” – Decision Making Unit). Each DMU code represents a decision-making unit in the efficiency and productivity growth analysis model, which is often used to mark on the horizontal axis of charts or tables of results. The use of abbreviations such as CTG, VPB, TCB, BIDV... facilitates data processing and comparison of results with specific banking entities. This is an important basis for analyzing operational efficiency, comparing productivity and assessing technological changes among banks during the research period from 2008 to 2024. 1445 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate Table 1. List of 22 Vietnamese commercial banks used in the study, including the full English name of each bank (column “Name of bank”) and the corresponding abbreviation code (column “DMU” – Decision Making Unit). Name of bank DMU Vietnam Joint Stock Commercial Bank for Industry and Trade CTG Vietnam Joint Stock Commercial Bank for Foreign Trade VPB Vietnam Technological and Commercial Joint Stock Bank TCB Bank for Investment and Development of Vietnam BIDV Military Commercial Joint Stock Bank MBB Vietnam Prosperity Joint Stock Commercial Bank VBP Saigon Thuong Tin Commercial Joint Stock Bank STB Asia Commercial Bank ACB Vietnam Export Import Commercial Joint Stock Bank EIB Saigon – Hanoi Commercial Joint Stock Bank SHB Maritime Commercial Joint Stock Bank MSB Ho Chi Minh City Development Joint Stock Commercial Bank HDB Tien Phong Commercial Joint Stock Bank TPB Vietnam International Commercial Joint Stock Bank VIB Southeast Asia Commercial Joint Stock Bank SEAB Orient Commercial Joint Stock Bank OCB An Binh Commercial Joint Stock Bank ABB Nam A Commercial Joint Stock Bank NAB Kien Long Commercial Joint Stock Bank KLB Saigon Bank for Industry and Trade SGB National Citizen Commercial Joint Stock Bank NVB Petrolimex Group Commercial Joint Stock Bank PGP 4. Results and Discussion We ran the model for 16 consecutive periods, namely from 2008 to 2024, corresponding to the periods: 2008–2009, 2009–2010, 2010–2011, …, 2023–2024. Each period consists of two consecutive years (t and t+1), which allows the calculation of the output gap functions and the Malmquist index according to the standard formula. In total, there are 16 calculations for each bank to determine: Efficiency Change (EC), Technical Change (TC) and Malmquist TFP Index, then, taking the geometric mean of these 16 periods to analyze the long-term performance of each bank. Below we analyze some typical periods. 1446 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate Table 2. Technical efficiency, technological progress and Malmquist index for the period 2008-2009. idDMU DMU Year_t year_(t+1) EC TC Malmquist 1 CTG 2008 2009 1 0.546 0.739 2 VPB 2008 2009 1 1.004 1.002 3 TCB 2008 2009 1.298 1.585 1.434 4 BIDV 2008 2009 1 0.888 0.942 5 MBB 2008 2009 1 0.522 0.723 6 VBP 2008 2009 1 1,021 1.01 7 STB 2008 2009 1.035 0.839 0.932 8 ACB 2008 2009 1.125 0.829 0.966 9 EIB 2008 2009 0.981 0.872 0.925 10 SHB 2008 2009 1,067 0.747 0.893 11 MSB 2008 2009 0.982 0.742 0.854 12 HDB 2008 2009 1.36 1,215 1,286 13 TPB 2008 2009 1 0.238 0.487 14 VIB 2008 2009 0.96 0.826 0.891 15 SEAB 2008 2009 1.183 2.707 1.79 16 OCB 2008 2009 0.983 1,053 1,017 17 ABB 2008 2009 1.454 1.183 1,312 18 NAB 2008 2009 0.986 0.713 0.838 19 KLB 2008 2009 0.624 0.47 0.542 20 SGB 2008 2009 1.047 1.211 1.126 21 NVB 2008 2009 0.856 0.811 0.833 22 PGP 2008 2009 1.211 0.789 0.977 The results of calculating the Malmquist index for 22 Vietnamese commercial banks in Table 2 during the period of 2008–2009 show a clear differentiation among banks in improving operational efficiency and technological innovation. In terms of the technical efficiency change index, most banks achieved a value of 1 or higher, demonstrating the ability to maintain or improve their relative position compared to the efficient frontier. Notably, some banks have very high EC levels such as ABB (1.454), HDB (1.36) or SEAB (1.183), showing significant improvements in the ability to use inputs effectively. However, there are still cases with low efficiency such as KLB (0.624), NVB (0.856) or EIB (0.981), reflecting inefficiency in operations, which may come from management factors or high operating costs compared to the output generated. In terms of technological change, the results show a large difference between banks. While SEAB achieved a very high TC (2.707), showing that this bank has made great strides in technological innovation, invested in processes or applied advanced management methods, on the contrary, many other banks are lagging behind in technology such as TPB (0.238), KLB (0.470) or MB (0.522). This reflects the uneven level of access and application of innovation among banks, especially in the context after the 2008 global financial crisis, when the requirement for technological modernization and risk management has become more urgent than ever. 1447 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate Table 3. Technical efficiency, technological progress and Malmquist index for the period 2009-2010. idDMU DMU year_t year_(t+1) EC TC Malmquist 1 CTG 2009 2010 1 0.949 0.974 2 VPB 2009 2010 1 0.877 0.937 3 TCB 2009 2010 0.913 0.794 0.852 4 BIDV 2009 2010 1 1,059 1,029 5 MBB 2009 2010 1.173 2.414 1.683 6 VBP 2009 2010 1 1.118 1,058 7 STB 2009 2010 0.787 1.052 0.91 8 ACB 2009 2010 0.955 0.714 0.826 9 EIB 2009 2010 0.871 0.857 0.864 10 SHB 2009 2010 0.775 0.898 0.834 11 MSB 2009 2010 1 0.63 0.794 12 HDB 2009 2010 0.747 0.755 0.751 13 TPB 2009 2010 1 0.843 0.918 14 VIB 2009 2010 1 0.431 0.657 15 SEAB 2009 2010 0.845 0.49 0.644 16 OCB 2009 2010 0.902 1.101 0.997 17 ABB 2009 2010 0.819 0.955 0.884 18 NAB 2009 2010 0.784 0.952 0.864 19 KLB 2009 2010 1 0.959 0.979 20 SGB 2009 2010 0.899 1.078 0.985 21 NVB 2009 2010 1 0.921 0.96 22 PGP 2009 2010 0.862 0.942 0.901 Combining both EC and TC factors in the Malmquist index shows that some banks have strong growth in total factor productivity such as SEAB (1.790), TCB (1.434), ABB (1.312) and HDB (1.286). These banks have not only improved the efficiency of resource use but also reached out to advanced technology, demonstrating a sustainable development strategy. In contrast, banks such as TPB (0.487), KLB (0.542), MB (0.723) and CTG (0.739) all showed a decline in total factor productivity, mainly due to weaknesses in improving operational efficiency and lack of technological innovation. Some special cases such as PGP (EC = 1.211, TC = 0.789) reflect the tendency that banks can improve their internal efficiency but without simultaneous technological improvements, overall productivity growth remains limited. During the 2009–2010 period, the Malmquist index analysis results in Table 3 continued to reflect the differentiation in productivity and efficiency among Vietnamese commercial banks. In terms of technical efficiency, most banks maintained an EC level equal to or close to 1, indicating relatively stable operating efficiency compared to the frontier. Some banks continued to improve strongly, such as MBB (1.173), reflecting internal efforts in optimizing resources and operating processes. Meanwhile, HDB (0.747), SHB (0.775) or SEAB (0.845) recorded low EC levels, indicating a decline in internal management and inefficient use of inputs. Regarding the technology progress index, many banks recorded positive growth, most notably MBB (2,414) - this is a sudden increase, possibly due to strong technological innovation or the application of a new core banking system. Banks such as BIDV (1.059), VBP (1.118) and SGB (1.078) also showed a positive shift in the technology frontier. However, many banks showed a clear lag in technology such as VIB (0.431), MSB (0.63) and SEAB (0.49) - this raises a warning about slow technological adaptation in a period when system modernization is becoming urgent. Combining the two factors EC and TC into the total factor productivity index, some banks have impressive growth rates such as MBB (1.683), BIDV (1.029) and VBP (1.058) - showing comprehensive growth in both operations and technology. On the contrary, many banks still maintain TFP < 1, showing declining productivity levels such as HDB (0.751), ACB (0.826), EIB (0.864) or TCB (0.852) - 1448 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate reflecting that although operations have improved somewhat, the level of innovation is not strong enough to boost overall productivity. Table 4. Technical efficiency, technological progress and Malmquist index for the period 2022-2023. idDMU DMU year_t year_(t+1) EC TC Malmquist 1 CTG 2022 2023 0.976 0.856 0.914 2 VPB 2022 2023 0.988 0.894 0.94 3 TCB 2022 2023 1,002 1,078 1.04 4 BIDV 2022 2023 1 0.96 0.98 5 MBB 2022 2023 1.011 1.15 1,078 6 VBP 2022 2023 1 0.966 0.983 7 STB 2022 2023 1,041 1,024 1,033 8 ACB 2022 2023 0.961 0.93 0.945 9 EIB 2022 2023 1,012 1,067 1,039 10 SHB 2022 2023 1 0.821 0.906 11 MSB 2022 2023 1 0.715 0.845 12 HDB 2022 2023 1 1,013 1,007 13 TPB 2022 2023 1 1.16 1,077 14 VIB 2022 2023 1 0.744 0.862 15 SEAB 2022 2023 1 1,015 1,007 16 OCB 2022 2023 1 0.915 0.957 17 ABB 2022 2023 0.999 0.975 0.987 18 NAB 2022 2023 0.976 0.943 0.959 19 KLB 2022 2023 0.862 0.804 0.832 20 SGB 2022 2023 0.983 0.992 0.987 21 NVB 2022 2023 1,044 0.964 1,003 22 PGP 2022 2023 0.924 0.896 0.91 In the period 2022–2023, the results of the Malmquist index analysis (Table 4) continue to show a clear differentiation among Vietnamese commercial banks in maintaining and improving overall productivity. In terms of technical efficiency, banks with EC levels exceeding 1 such as MB (1.011) , STB (1.041) , EIB (1.012) and NVB (1.044) show that they not only maintain efficiency but also have clear improvements in operational management and resource optimization. However, there are also banks with EC levels lower than 1 such as KLB (0.862) , PGP (0.924) or NAB (0.976) - this is a sign that some units are still facing difficulties in controlling costs or organizing effective operations, especially in the context of many economic fluctuations after COVID-19 and increasing interest rate pressure. In terms of technological progress, the most outstanding results belong to MB (1.15) , TPB (1.16) and TCB (1.078) , showing that these banks continue to invest and adapt well to digital technologies, modernize core banking systems or upgrade operational capacity. On the contrary, some banks have low TC levels below 0.9 such as MSB (0.715) , SHB (0.821) or KLB (0.804) , showing delays in technological innovation or not keeping up with the development level of the industry. Overall, the total factor productivity index reflects comprehensive performance from both technical efficiency and technological progress. Banks with impressive productivity growth include MBB (1.078) , TPB (1.077) , TCB (1.04) and EIB (1.039) . In contrast, banks such as KLB (0.832) , MSB (0.845) or PGP (0.91) face many challenges in simultaneously improving operational efficiency and modernizing technology. 1449 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate Table 5. Technical efficiency, technological progress and Malmquist index for the period 2023-2024. idDMU DMU year_t year_(t+1) EC TC Malmquist 1 2023 2024 1 0.954 0.977 2 2023 2024 0.994 0.873 0.932 3 2023 2024 0.959 0.837 0.896 4 2023 2024 1 0.953 0.976 5 2023 2024 0.989 0.807 0.893 6 2023 2024 1 0.973 0.986 7 2023 2024 1.03 0.97 0.999 8 2023 2024 0.91 0.821 0.864 9 2023 2024 0.92 0.839 0.879 10 2023 2024 1 1.203 1.097 11 2023 2024 1 0.685 0.828 12 2023 2024 1 0.662 0.813 13 2023 2024 1.084 1.033 1.058 14 2023 2024 1 0.988 0.994 15 2023 2024 1.045 0.925 0.983 16 2023 2024 1 0.973 0.986 17 2023 2024 0.977 0.916 0.946 18 2023 2024 1.079 1.179 1,128 19 2023 2024 1.196 1.1 1.147 20 2023 2024 1.021 0.993 1,007 21 2023 2024 1.397 1.243 1.318 22 2023 2024 1.098 0.942 1.017 The period 2023–2024 (Table 5) – the end of the observation period in the study – continues to show significant changes in the efficiency and productivity of Vietnamese commercial banks. In terms of technical efficiency index, some prominent banks such as NVB (1.397), KLB (1.196) and NAB (1.079) show outstanding improvements in terms of operations. On the other hand, some banks still show relative weakness in technical efficiency such as ACB (0.91), EIB (0.92) and TCB (0.959). This may stem from internal problems such as high operating costs, ineffective resource allocation strategies or being affected by an unfavorable business environment in 2023. In terms of the technological change index – a proxy for the level of technological innovation and improvement – banks such as SHB (1.203), NAB (1.179), KLB (1.1) and especially NVB (1.243) show a strong shift in the technological frontier. This reflects strong investments in digital technology, e- banking, or business process improvement. On the contrary, some banks still have significantly low TC such as MSB (0.685) and HDB (0.662), raising questions about the system’s ability to innovate technology and adapt to digital transformation requirements. Combining the above two factors, the total factor productivity index comprehensively reflects the performance of the bank. Some banks achieved very high growth rates such as NVB (1.318), KLB (1.147), NAB (1.128) and SHB (1.097), while banks such as EIB (0.879), ACB (0.864), VPB (0.932) and VCB (0.932) recorded an overall productivity level below 1, indicating a slight decline in productivity in the context of market fluctuations. 1450 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate Table 6. Technical efficiency, technological progress and average Malmquist index for the period 2008-2024. idDMU DMU EC TC Malmquist 1 CTG 0.999966 0.923316 0.960865 2 VPB 1.004577 0.901526 0.951698 3 TCB 0.999727 0.929064 0.963902 4 BIDV 1 0.887193 0.941842 5 MBB 1.00002 0.968696 0.980744 6 VBP 1 0.94641 0.972807 7 STB 0.999418 1.018225 1.008818 8 ACB 1.002569 0.982712 0.992497 9 EIB 0.999912 1.047435 1.023366 10 SHB 0.984822 0.929663 0.956829 11 MSB 0.998847 0.990365 0.994767 12 HDB 0.999896 0.842789 0.91808 13 TPB 1.005074 0.919035 0.960857 14 VIB 0.997397 0.962156 0.979721 15 SEAB 1.002732 1.046631 1.024446 16 OCB 0.992556 1.021951 1.007159 17 ABB 1.007269 1.040725 1.023814 18 NAB 0.989456 0.940766 0.964749 19 KLB 0.994272 0.97893 0.986524 20 SGB 1.014278 1.031685 1.022789 21 NVB 1.016499 1.080606 1.047978 22 PGP 1.016915 0.974752 0.99569 After aggregating the results from 16 consecutive periods (Table 6), the average Malmquist index provides a more comprehensive view of the long-term trend in efficiency and productivity growth of commercial banks in Vietnam. In general, banks have an EC level fluctuating around the value of 1 , indicating relatively stable performance compared to the efficient frontier over time. Banks such as TPB (EC = 1.0051) , SGB (1.0143) , NVB (1.0165) and PGP (1.0169) have an average EC above 1 – this reflects good management capacity and continuous improvement in operating efficiency in the long term. However, the TC index – representing the ability to innovate technology and shift the production frontier – has a larger difference between banks. Some units such as NVB (TC = 1.0806) , SGB (1.0317) and SEAB (1.0466) show a clear level of investment in technology and digital transformation. Meanwhile, some large banks such as BIDV (0.8871) , HDB (0.8428) and VPB (0.9015) have a significantly lower average TC level, indicating that the speed of approaching technological innovation is still slow or ineffective. total factor productivity index – the product of EC and TC – reflects the combined results of both operational efficiency and technological progress. Banks with high average Malmquist scores include NVB (1.0480) , SEAB (1.0244) , EIB (1.0234) , SGB (1.0228) , and ABB (1.0238) . This is a group of banks with real productivity growth in the long term. In contrast, some large banks such as CTG (0.9609) , VPB (0.9517) , BIDV (0.9418) , and HDB (0.9181) have average productivity lower than 1 – reflecting a trend of declining productivity due to not keeping up with the growth rate of the industry or lacking strong reforms. 1451 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate Figure 3. Technical efficiency, technological progress index and average Malmquist index of 22 banks. Figure 3 shows that the technical efficiency of banks is relatively stable around level 1, reflecting the ability to maintain long-term operational efficiency. However, the technological progress index fluctuates more strongly among banks, indicating large differences in the level of investment in innovation and digital transformation. Some banks such as NVB , SEAB , SGB and ABB have Malmquist levels > 1 , showing increased productivity due to a good combination of effective management and technology. In contrast, banks such as BIDV or HDB have decreased productivity due to limited technological progress. Figure 4. Arrange banks in descending order of average Malmquist index. 1452 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 9: 1437-1453, 2025 DOI: 10.55214/2576-8484.v9i9.10141 © 2025 by the authors; licensee Learning Gate Figure 4, which ranks banks in descending order of average Malmquist index, shows a clear divergence in productivity growth. Banks such as NVB , SEAB , ABB and EIB are in the top group, with outstanding productivity growth due to a good combination of technical efficiency and technological innovation. In contrast, banks such as BIDV and HDB have the lowest Malmquist scores, mainly due to a sharp decline in TC index, indicating limited technological innovation. This result emphasizes the key role of technological innovation in improving bank productivity. 5. Conclude This study used the data envelopment analysis method and the Malmquist index to evaluate the technical efficiency, technological progress and productivity growth of 22 Vietnamese commercial banks during the period 2008–2024. Data collected from the financial statements and annual reports of banks showed significant productivity differentiation among banks. The results indicated that the technical efficiency of most banks remained around level 1, reflecting relatively stable management capabilities. However, large differences in technological progress were the main factor creating the gap in the total factor productivity index. Banks such as NVB, SEAB, ABB, EIB and SGB were prominent with strong productivity growth, while some large banks such as BIDV, HDB and VPB showed productivity decline due to technology not catching up. 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